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ABSTRACT
Title of dissertation: ESSAYS ON
MONETARY ECONOMICS AND
INTERNATIONAL FINANCE
Salih Fendoglu, Doctor of Philosophy, 2012
Dissertation directed by: Professor Boragan Aruoba
Department of Economics
This thesis consists of two chapters. In the ?rst chapter, I study optimal
monetary policy rules in a general equilibrium model with ?nancial market imper-
fections and uncertain business cycles. Earlier consensus view –using models with
?nancial ampli?cation with disturbances that have no direct e?ect on credit market
conditions– suggests that ?nancial variables should not be assigned an independent
role in policy making. Introducing uncertainty, time-variation in cross-sectional dis-
persion of ?rms’ productive performance, alters this policy prescription. The results
show that (i) optimal policy is to dampen the strength of ?nancial ampli?cation
by responding to uncertainty (at the expense of creating a mild degree of ?uctu-
ations in in?ation). (ii) a higher uncertainty makes the planner more willing to
relax ‘?nancial stress’ on the economy. (iii) Credit spreads are a good proxy for
uncertainty, and hence, within the class of simple monetary policy rules I consider,
a non-negligible interest rate response to credit spreads (32 basis points in response
to a 1% change in credit spreads) -together with a strong anti-in?ationary stance-
achieves the highest aggregate welfare possible.
In the second chapter, I study global, regional and idiosyncratic factors in
driving the sovereign credit risk premium (as measured by sovereign credit default
swaps) for a set of 25 emerging market economies during the last decade. The
results show that (i) On average, global and regional factors account for a substantial
portion of the movements in sovereign risk premium (of 63% and 21%, respectively).
(ii) there exists noticeable heterogeneity in the contribution of factors across the
emerging markets. (iii) The (extracted) global factor is best re?ected by the VIX
(investors’ risk sentiment) among the ?nancial market indicators considered. (iv)
There are regime changes in the relation between the global factor and the ?nancial
market indicators.
ESSAYS ON MONETARY ECONOMICS AND INTERNATIONAL
FINANCE
by
Salih Fendo? glu
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial ful?llment
of the requirements for the degree of
Doctor of Philosophy
2012
Advisory Committee:
Professor Boragan Aruoba, Chair
Professor Anton Korinek
Professor Pablo Derasmo
Professor Carlos Vegh
Professor Phillip L. Swagel (PUAF)
c Copyright by
Salih Fendoglu
2012
Dedication
To my family,
ii
Acknowledgments
I owe my gratitude to all the people who have made this thesis possible and
because of whom my graduate experience has been one that I will cherish forever.
Foremost, I would like to express my sincere gratitude to my advisor Prof.
Boragan Aruoba for his continuous support and guidance in the process of writing
my dissertation. His guidance helped me in all the time of research and writing of
this thesis.
I would like to thank Prof. Anton Korinek, Prof. Pablo Derasmo and Prof.
Carlos Vegh for sparing their invaluable time reviewing the manuscript, and for
agreeing to serve on my thesis committee. I also would like express my deepest
gratitude to Prof. Sanjay Chugh for all the support and guidance during most
stages of my dissertation.
I also would like to thank my fellow colleagues Yasin Mimir, Enes Sunel, Emre
Tiftik, Orhan Torul, Pablo Federico, and David Ruiz, for their comments throughout
the entire process, and for sharing their time to exchange ideas on various topics
beyond the dissertation and more. I also would like to express my deepest thanks
to Ali Fuad Selvi, Bedrettin Yazan, Bengu Caliskan Selvi, Elif Ture, Ferhan Ture,
Simal Ince and Tugrul Ince. I have been blessed with such a friendly and cheerful
group.
The help and support of sta? members at the Department of Economics was
invaluable. I would like to thank Vickie Fletcher, Elizabeth Martinez and Terry
Davis for accommodating my logistic needs and helping me out with technical issues
iii
regarding the doctorate program.
Last but not the least, I would like to thank my father Hasan Tahsin and my
mother Rabia who sincerely supported me in any moment of my life and always
kept their belief in me. I also would like to thank my brothers Bekir and Cem for
the support and cheering me up when I looked gloomy. And special thanks to my
beloved one Burcu Polat for standing by me through the good and bad times.
iv
Table of Contents
List of Tables vii
List of Figures viii
1 Optimal Monetary Policy Rules, Financial Ampli?cation,and Uncertain Business Cycles 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Entrepreneurs . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3 Retailers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.4 Monetary Authority and the Government . . . . . . . . . . . . 18
1.2.5 Equilibrium and Aggregation . . . . . . . . . . . . . . . . . . 19
1.3 Functional Forms and Calibration . . . . . . . . . . . . . . . . . . . . 21
1.4 Decentralized Equilibrium and Cross-Sectional Dispersion . . . . . . . 26
1.4.1 Long-run equilibrium and long-run cross sectional dispersion . 27
1.4.2 Dynamics of the model and cross-sectional dispersion . . . . . 29
1.4.2.1 Productivity and Government Spending Shocks . . . 29
1.4.2.2 Uncertainty Shocks . . . . . . . . . . . . . . . . . . . 31
1.5 Welfare Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.6 Optimal Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . 38
1.6.1 Sources of Ine?ciencies . . . . . . . . . . . . . . . . . . . . . . 38
1.6.2 Ramsey optimal policy problem . . . . . . . . . . . . . . . . . 41
1.6.2.1 Cyclical Volatilities . . . . . . . . . . . . . . . . . . . 42
1.6.2.2 Reducing the strength of ?nancial ampli?cation . . . 43
1.6.2.3 Reducing the contribution of uncertainty on business cycles 44
1.6.2.4 Impulse Responses . . . . . . . . . . . . . . . . . . . 45
1.7 Optimal Simple and Implementable Policy Rules . . . . . . . . . . . . 48
1.8 Further Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
1.10 Appendix - Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
1.11 Appendix - Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
1.12 Appendix - Competitive Equilibrium, Calibration and Further Discussions 74
2 Global and Regional Factors in Driving Emerging Markets’ Sovereign Risk Premium 96
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.2 Data and the Methodology . . . . . . . . . . . . . . . . . . . . . . . . 103
2.3 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.3.1 Evolution of Global and Regional Factors . . . . . . . . . . . . 109
2.3.2 Contribution of Factors . . . . . . . . . . . . . . . . . . . . . . 114
2.3.3 Idiosyncratic factor and four examples. . . . . . . . . . . . . . 115
2.4 Interpreting the Global Risk Factor . . . . . . . . . . . . . . . . . . . 118
2.5 Robustness (Including Advanced Economies & Using Higher Frequency)124
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
v
2.7 Appendix - Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . 127
2.8 Appendix - Tables and Figures . . . . . . . . . . . . . . . . . . . . . 129
vi
List of Tables
1.1 Timing of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3 Variance Decomposition (Decentralized Economy) . . . . . . . . . . . 35
1.4 Cyclical Volatilities (%-standard deviations) . . . . . . . . . . . . . . 43
1.5 Variance Decomposition (Decentralized Economy vs. Ramsey Planner’s) 45
1.6 Simple Rules versus Optimal Policy (Baseline Calibration) . . . . . . 61
1.7 Business Cycle Statistics -Decentralized Economy- . . . . . . . . . . . 64
1.8 Business Cycle Statistics -Planner’s Economy- . . . . . . . . . . . . . 65
1.9 Business Cycle Statistics (only ?nancial frictions) -Decentralized Economy- 66
1.10 Business Cycle Statistics (only ?nancial frictions) -Planner’s Economy- 67
1.11 Estimated AR(1) Processes . . . . . . . . . . . . . . . . . . . . . . . 94
2.1 Descriptive Statistics for Sovereign Credit Default Swap . . . . . . . . 130
2.2 Cross-correlations between Common External Factors . . . . . . . . . 130
2.3 Contribution of Factors to the Sovereign CDS . . . . . . . . . . . . . 131
2.4 Global Factor - Global Financial Market Indicators . . . . . . . . . . 132
vii
List of Figures
1.1 Long-run equilibria as a function of long-run cross-sectional dispersion 28
1.2 Impulse Responses to a 1 sd. increase in total factor productivity . . 30
1.3 Change in the cross-sectional dispersion . . . . . . . . . . . . . . . . . 32
1.4 Impulse Responses to a 1 sd. increase in uncertainty . . . . . . . . . 33
1.5 Strength of Financial Ampli?cation (Planner’s Economy) . . . . . . . 44
1.6 Ramsey Impulse Responses to a 1 sd. increase in total factor productivity 46
1.7 Ramsey Impulse Responses to a 1 sd. increase in uncertainty . . . . . 47
1.8 Responding to Asset Prices -productivity shocks- . . . . . . . . . . . 50
1.9 Responding to Asset Prices -uncertainty shocks- . . . . . . . . . . . . 51
1.10 Welfare Surfaces (Benchmark Uncertainty versus High Uncertainty) . 52
1.11 Welfare Surfaces (Responding to Uncertainty) . . . . . . . . . . . . . 53
1.12 Shadow Value of Relaxing the Financial Constraint . . . . . . . . . . 59
1.13 Long-run equilibria as a function of monopolistic competition . . . . . 62
1.14 Long-run equilibria as a function of long-run in?ation . . . . . . . . . 63
1.15 Impulse Responses to a 1 sd. increase in government spending . . . . 68
1.16 Strict In?ation Stabilization versus Ramsey Policy -productivity shocks- 69
1.17 Responding to Output Gap -productivity shocks- . . . . . . . . . . . 70
1.18 Responding to Output Gap -uncertainty shocks- . . . . . . . . . . . . 71
1.19 Welfare Surface -TFP and G Shocks- . . . . . . . . . . . . . . . . . . 71
1.20 Welfare Surface -Uncertainty Shock- . . . . . . . . . . . . . . . . . . 72
1.21 Welfare Surface -All Shocks- . . . . . . . . . . . . . . . . . . . . . . . 72
1.22 Welfare Surface -Uncertainty Shock- . . . . . . . . . . . . . . . . . . 73
1.23 Welfare Surface -All Shocks- . . . . . . . . . . . . . . . . . . . . . . . 73
1.24 TFP and Real Government Spending (G) . . . . . . . . . . . . . . . . 93
1.25 VXO or Cross-Sectional Dispersion . . . . . . . . . . . . . . . . . . . 93
1.26 TFP, Government Spending, and Uncertainty Shocks . . . . . . . . . 95
2.1 5-year Sovereign CDS Spreads . . . . . . . . . . . . . . . . . . . . . . 133
2.2 Global Factor and Major Events . . . . . . . . . . . . . . . . . . . . . 134
2.3 Sovereign CDS and Regions . . . . . . . . . . . . . . . . . . . . . . . 135
2.4 Common Factor versus the European Factor . . . . . . . . . . . . . . 136
2.5 Decomposing Sovereign CDS . . . . . . . . . . . . . . . . . . . . . . . 137
2.6 Chinn-Ito Index versus the Contribution of External Factors . . . . . 138
2.7 Financial Market Indicators . . . . . . . . . . . . . . . . . . . . . . . 138
2.8 Global Factor -Including Developed Economies- . . . . . . . . . . . . 139
2.9 European Regional Risk Factor -Including Developed Economies- . . 139
2.10 Smoothed States -Two-Factor DFM- . . . . . . . . . . . . . . . . . . 140
2.11 Smoothed States -Single-Factor DFM- . . . . . . . . . . . . . . . . . 141
2.12 Smoothed States (Developed Economies and Weekly Frequency) . . . 142
2.13 Con?dence Interval Construction for the Thresholds (using the VIX) 143
viii
Chapter 1
Optimal Monetary Policy Rules, Financial Ampli?cation,
and Uncertain Business Cycles
1.1 Introduction
Should ?nancial variables per se be important for monetary policy making? This
question has attracted considerable attention in both policy and academic circles
during the last decade. The conventional wisdom, as stated in many central banks’
statutory mandates, is that in?ation and output stability should be the central goal
of monetary policy: While ?nancial variables (e.g. credit spreads or asset prices)
are with no doubt important ingredients for policy making, they are argued to be
useful in so far they help predicting in?ation and real economic activity.
1
Intro-
ducing uncertainty, time-variation in cross-sectional dispersion of ?rms’ productive
performance, alters the conventional wisdom: Optimal policy prescribes a direct and
systematic response to credit spreads (above and beyond what in?ation and output
gap would imply).
2
Such a policy dampens distortionary e?ects of uncertainty, and
helps containing adverse feedback e?ects between ?nancial conditions and the real
1
For potential channels through which ?uctuations in ?nancial variables transmit into business
cycles, see Cecchetti et al. (2000), Gilchrist and Leahy (2002), and Gilchrist, Sim, and Zakrajsek
(2010). The former two focus on asset prices, and the latter on corporate bond credit spreads.
2
For recent studies on uncertainty, see among others Bloom (2009), Bloom, Floetotto, and
Jaimovich (2010), Gilchrist, Sim and Zakrajsek (2010), Arellano, Bai and Kehoe (2010), Christiano,
Motto and Rostagno (2010), Bachmann and Bayer (2011), Bekaert, Hoerova, and Duca (2011),
Chugh (2011), and Basu and Bundick (2011). These shocks have also been labeled as risk or
dispersion shocks in the literature.
1
economy.
I use a canonical New-Keynesian model with ?nancial market imperfections
to study optimality of responding to ?nancial variables.
3
Providing a tight link
between market imperfections and ?nancial variables, the ?nancial ampli?cation
model of Bernanke, Gertler, and Gilchrist (BGG, hereforth), a workhouse model
widely used in the New-Keynesian ?nancial frictions literature, o?ers a natural en-
vironment to study optimality of responding to ?nancial variables. Existence of
these imperfections, however, does not necessarily imply a direct response to ?nan-
cial variables as a way to mitigate the resulting distortions and improve aggregate
welfare. Using traditional ?rst-moment shocks that have no direct e?ect on credit
market conditions, earlier consensus view suggests that it is optimal not to assign
an independent role to ?nancial variables in policy making.
4
As an additional pulse driving the business cycles, I introduce uncertainty,
exogenous time-variation in cross-sectional dispersion of ?rms’ productive perfor-
mance. Among potential channels through which uncertainty may transmit into
business cycle ?uctuations, here I consider credit channel owing to ?nancial frictions
3
Such imperfections manifest themselves through existence of a spread, a wedge between bor-
rowing and lending rates, that would be absent under perfect capital markets. At the heart of the
mechanism lie credit spreads being linked to borrowers’ indebtedness (leverage) which in turn is
driven by movements in asset prices.
4
In the presence of any sort of asset price imbalances, a gap between observed and fundamen-
tal/potential level of asset prices, it might be optimal to respond to ?nancial variables (if the policy
maker could measure these imbalances at the ?rst place). See Bernanke and Gertler (2001), Dupor
(2005), and Gilchrist and Saito (2008), among others. Here I do not consider non-fundamental
movements in asset prices. Faia and Monacelli (2007), using traditional ?rst-moment shocks, show
that there might be a non-negligible marginal welfare gain of responding to (fundamental level
of) asset prices under a reasonably low degree of anti-in?ationary stance (roughly between one to
two, as typically studied in the literature). They conclude that the policy makers should pursue
a lean-with-the-wind policy reaction to movements in asset prices (e.g. decrease the policy rate in
response to an increase in asset prices). Interested readers may refer to Gilchrist and Saito (2008)
for a brief literature review on the pre-crisis consensus view.
2
in the model.
5
In particular, uncertainty has two direct e?ects on credit market con-
ditions. First, it a?ects the measure of borrowers that will go bankrupt. Second, it
a?ects net worth that will be retained by borrowers, and hence the quality of balance
sheet of borrowers. Accordingly, a higher dispersion, for instance, implies a higher
risk for banks’ overall loan portfolio, making banks less willing to extend credit. As
a result, the equilibrium level of credit spread rises and investment declines.
The main contribution of this paper is that, despite the emphasis on uncer-
tainty as a potential driver of business cycles in the literature, whether and how
monetary policy prescriptions would di?er from the conventional wisdom under un-
certain business cycles remains an open question. Moreover, in models with costly-
state-veri?cation type ?nancial market imperfections (e.g. BGG), uncertainty, as
discussed above, is primarily a ‘?nancial’ shock, directly a?ecting borrowers’ ability
to raise funds. In this regard, studying uncertainty also sheds light on normative
implications of introducing disturbances that are of ?nancial type on monetary pol-
icy.
6
The results suggest that optimal policy is to dampen the strength of ?nancial
5
Using models with ?nancial frictions, Gilchrist, Sim and Zakrajsek (2010), Arellano, Bai and
Kehoe (2010), Christiano, Motto and Rostagno (2010), and Chugh (2011) also consider a credit
channel. For other potential channels, see Bloom (2009), Bloom, Floetotto, and Jaimovich (2010),
Bachmann and Bayer (2011), and Basu and Bundick (2011).
6
See, among others, Nolan and Thoenissen (2009), Gilchrist, Ortiz and Zakrajsek (2009), Es-
pinoza et al. (2009), Christiano, Motto, and Rostagno (2010), Jermann and Quadrini (2011),
and Gilchrist and Zakrajsek (2011) on the contribution of ?nancial shocks (shocks that have a
direct e?ect on credit market conditions) on business cycle ?uctuations. This class of distur-
bances includes (but not limited to) shocks that lead to exogenous movements in borrowers’ net
worth -that a?ects e?ciency of contractual relations between borrowers and lenders- (Gilchrist and
Leahy, 2002; Nolan and Thoenissen, 2009; Gilchrist, Ortiz and Zakrajsek, 2010; Christiano, Motto,
and Rostagno, 2010), external ?nance premium -that a?ects e?ciency of ?nancial intermediation-
(Gilchrist, Ortiz and Zakrajsek, 2010), sensitivity of external ?nance premium to the leverage -
that a?ects the strength of ?nancial ampli?cation- (Dib, 2010), or borrowers’ ability to raise funds
(Jerman and Quadrini, 2011).
3
ampli?cation by responding to uncertainty.
7
The planner achieves so by reducing
the sensitivity of external ?nance premium to borrowers’ leverage, e?ectively in-
creasing the e?ciency of ?nancial intermediation that would otherwise occur in a
decentralized economy. This, however, comes at the expense of creating a mild
degree of ?uctuations in in?ation. The intuition lies on the fact that the tension
between price stickiness (which creates ?uctuations in the intratemporal wedge) and
?nancial frictions (which creates ?uctuations in the intertemporal wedge) tends to
be resolved in favor of the latter if uncertainty shocks come into play. Note also
that the planner is endowed with a single policy tool, the short-term nominal inter-
est rate. Introducing appropriate additional tools (e.g. macro-prudential policies)
would imply a lesser role for the short-term nominal interest rate in smoothing the
intertemporal wedge (or in neutralizing ?nancial market imperfections).
A key question then is whether simple policy rules, that include only a few
observable macroeconomic variables, can attain a welfare level close to the planner’s,
and the optimal magnitude of response to ?nancial variables (if not nil). As an
additional input to policy making (besides in?ation and output gap), I consider
credit spread, the key variable that is tightly linked to ?nancial distortions. In
practice, credit spreads are easily observable to policy makers, and accordingly can
be thought as a desirable input to the policy. For comparison purposes with the
earlier literature, I also study (fundamental level of) asset prices as an additional
7
The planner maximizes aggregate welfare subject to competitive equilibrium conditions, using
the short-term nominal interest rate as the policy tool. To have accurate welfare comparisons, I
conduct second-order approximation to the policy and welfare functions. Note also that uncer-
tainty, as a second-moment shock, has a ?rst-order e?ect on equilibrium dynamics.
4
input to the policy.
8
Con?rming the conventional wisdom, if the economy is driven only by tradi-
tional ?rst-moment disturbances, it is optimal not to respond to ?nancial variables,
and strict in?ation stabilization is the welfare maximizing policy. If the economy is
driven also by uncertainty shocks, the optimal rules suggest a non-negligible lean-
against-the-wind policy reaction to credit spreads. Such a response is mainly due
to spreads being driven mostly by uncertainty shocks.
9
The optimal magnitude of
response to credit spreads is generally less than one-to-one. Under the benchmark
scenario (when spreads ?uctuate moderately), the policy rate should be reduced by
32 basis points in response to a 1% increase in credit spreads.
10
This result holds
for su?ciently low level of anti-in?ationary reaction (less than 3). A stronger in?a-
tionary reaction would decrease the optimal magnitude of response to credit spreads
towards zero, as strict in?ation stabilization welfare dominates the optimized rule
(however small it is). Last but not least, the policy maker, if instead allowed to
react to uncertainty directly, would choose to do so to improve aggregate welfare.
To shed further light on the results, I study how strong the planner values
relaxing the ‘?nancial constraint’ from a historical perspective.
11
The results show
the higher the uncertainty, the stronger the planner values relaxing the ?nancial
8
I focus on the fundamental (as opposed to non-fundamental) movements in asset prices, since
modeling asset price imbalances is not the immediate goal of this paper.
9
If asset prices, which are driven mostly by productivity shocks in the model, is the ?nancial
variable included in the policy rule, then the corresponding policy response should be nil.
10
A 1% increase in credit spreads amounts to roughly a 2- to 3-standard-deviation increase in
credit spreads.
11
The key equation in the ?nancial ampli?cation mechanism links external ?nance premium to
aggregate leverage ratio. One can express this equation as a ?nancial constraint in that ?rms
can borrow a certain fraction of their net worth, the fraction depending on aggregate ?nancial
conditions.
5
constraint.
12
The planner’s willingness to relax the constraint exhibits a rapid de-
terioration starting in mid-2002, and hits record low by the end of 2006. During
recession periods, especially for the recent one, marginal bene?t of relaxing the
constraint rises substantially.
The main policy lesson, as hinted above, is that policy makers should closely
monitor time-variation in cross-sectional dispersion of ?rms performance. From a
practical point of view, however, the availability and the quality of information on
the dispersion may not be available in real time. Yet, since credit spreads could
serve as a good proxy for uncertainty, responding to the credit spreads can be used
as a general policy to have better aggregate outcomes.
Closely related to my work, Gilchrist and Zakrajsek (2011) use a similar model
with BGG-type ?nancial market imperfections. They show that a spread-augmented
policy rule dampens the e?ect of ?nancial ampli?cation and induces powerful stabi-
lizing e?ects on real and ?nancial variables. They, however, do not consider optimal
policy problem. Angeloni and Faia (2011) introduce a banking sector in an oth-
erwise standard New-Keynesian model, and show that containing ?uctuations in
asset prices (combined with mildly acyclical capital requirements) improves aggre-
gate welfare compared to simple policy rules. Curdia and Woodford (2010), using a
model with costly ?nancial intermediation, conclude that in response to disturbances
a?ecting e?ciency of ?nancial intermediation directly, it is optimal to respond to
credit spreads, with the optimal degree generally being less than one-to-one. Our
12
This result can also be interpreted along the lines of Gilchrist, Sim and Zakrajsek (2010). In
a richer model, they show that investment becomes more sensitive to borrowers’ net worth when
uncertainty is higher. Accordingly, the measure of ?rms which are ?nancially constrained is higher
and aggregate output declines in response to a higher uncertainty.
6
results suggest that it is not necessarily the credit supply channel per se that makes
containing ?uctuations in credit spreads optimal, but it is the underlying set of
disturbances that has a direct e?ect on credit market conditions that matters.
The chapter proceeds as follows: Section 1.2 presents the model economy,
Section 1.3 the functional forms and the calibration. Section 1.4 studies long-run
equilibria as a function of long-run cross-sectional dispersion, and the model dy-
namics in the decentralized equilibrium. Section 1.5 presents how to approximate
aggregate welfare, Section 1.6 the optimal monetary policy problem, and Section
1.7 the optimal simple policy rules. Section 1.8 provides the historical analysis, and
Section 1.9 concludes.
1.2 The Model
This section presents a brief description of the BGG. Readers may refer to Appendix
A for details. The di?erence is the existence of uncertainty shocks in the model
environment and recursively formulating some of the equilibrium conditions.
The economy is populated by a representative household, a monetary authority
and three types of producers: wholesale-good producers (entrepreneurs), capital-
good producers and retailers.
Entrepreneurs play the key role in the model. They produce wholesale goods
using physical capital constructed by capital producers, and labor supplied by both
households and entrepreneurs. To ?nance capital expenditures, entrepreneurs need
to rely on external ?nancing: In excess of their own net worth, entrepreneurs borrow
7
from a perfectly competitive ?nancial intermediary. The intermediary could only
observe the distribution of entrepreneurs’ idiosyncratic productivity at the time debt
contract is made. This asymmetric information leads to a costly state veri?cation
problem as in Townsend (1979). The need for external ?nancing induces a non-zero
probability of default, which, in equilibrium, induces a positive premium over the
riskless rate, the external ?nance premium. The premium depends positively on the
aggregate leverage ratio of the entrepreneurs, the key relation that the ampli?cation
model exhibits.
The retailers are introduced solely to motivate price stickiness. They buy
wholesale goods at perfectly competitive markets, and di?erentiate them costlessly.
The ?nal consumption goods are then demanded by households, capital producers,
and the government.
Readers may ?nd it helpful the timing of events presented in Table 1.1.
Table 1.1: Timing of Events
At the end of Period t-1:
1. Entrepreneurs accumulate net worth.
2. Uncertainty (of period t) is realized.
3. Entrepreneurs decide how much capital to borrow, and state-contingent debt contract is made.
Period t:
1. TFP shock and the idiosyncratic productivities are realized.
2. Wholesale production is done.
3. Threshold level of idiosyncratic productivity and contractual returns are determined.
4. Defaulting entrepreneurs’ projects are seized, and the wholesale goods are sold to the retailers.
5. Some of the entrepreneurs leave the market exogenously.
6. Entrepreneurs accumulate net worth.
7. Uncertainty (of period t + 1) is realized.
8. Entrepreneurs decide how much capital to borrow, and state-contingent debt contract is made.
8
1.2.1 Households
There is an in?nitely-lived representative household that derives utility from a com-
posite ?nal consumption good C
t
=
_
_
1
0
c
1?
1
it
di
_ 1
1?
1
and leisure, 1 ? H
t
, where c
it
denotes the level of consumption for each retail good i at period t, and is the
intratemporal elasticity of substitution across the retail goods.
Households supply labor H
t
to the entrepreneurs and receive W
t
as the real
wage per labor hour. They earn a total of ?
t
as dividends from the retailers,
pay lump-sum taxes T
t
to the ?scal authority, and receive the riskless real rate of
return R
t
on their deposits D
t
with the intermediary. Formally, the representative
household solves
max
{Ct,Ht,D
t+1
}
?
t=0
E
0
?
t=0
?
t
U (C
t
, H
t
) (1.1)
subject to the period budget constraints
C
t
+D
t+1
= W
t
H
t
+R
t
D
t
?T
t
+ ?
t
(1.2)
where ? ? (0, 1) is the subjective discount rate. E
t
is the expectation operator
conditional on the information set available at t, which includes current and past
values of endogenous state variables, and distributions of shocks to total factor pro-
ductivity, real government spending, and cross-sectional dispersion of entrepreneurs’
idiosyncratic productivity. Following Bloom (2009), I label shocks to cross-sectional
dispersion as uncertainty shocks.
9
The riskless real rate of return is de?ned as R
t
=
1+r
n
t
1+?
t+1
, where r
n
t
is the (net)
nominal interest rate and ?
t+1
is the (net) price in?ation of the ?nal good from t to
t + 1. The nominal interest rate is set by the monetary authority as an operating
target, and a?ects real allocations due to existence of price stickiness in the model
environment.
The household’s optimality conditions imply standard consumption-savings
and labor supply conditions:
?U(t)
?C
t
= ?R
t
E
t
_
?U(t + 1)
?C
t+1
_
W
t
= ?
?U(t)
?Ht
?U(t)
?Ct
(1.3)
where U(t) denotes the period-t utility function. One-period stochastic discount fac-
tor, which is taken as given by the sector(s) owned by the household, is then given by
?
t+1|t
= ?E
t
_
?U(t+1)
?C
t+1
/
?U(t)
?Ct
_
. A no-Ponzi condition on households, lim
T??
E
t
?
T
?
t+T|t
D
t+T
?
0 completes the household’s problem.
1.2.2 Entrepreneurs
The entrepreneur i starts each period t with physical capital K
it
that is purchased
from capital producers at the end of period t ?1 at a real price Q
t?1
. They produce
wholesale goods Y
it
with labor and capital. The labor used in the production, L
it
, is
composed of household labor H
it
and the entrepreneurial labor H
e
it
such that L
it
=
H
?
it
(H
e
it
)
(1??)
where ? is the share of households’ income in total labor income.
13
13
Entrepreneurs are allowed to supply labor not only for their own projects but also for other
entrepreneurial projects. This helps to aggregate the entrepreneurial sector. The share of labor
income accruing to the entrepreneur, 1 ? ?, is assumed to be very small (of an order of .01).
Hence, including entrepreneurial labor in the standard production function does not a?ect the
results signi?cantly.
10
The wholesale production of entrepreneur i is done via a constant returns to scale
(CRTS) technology given by Y
it
= ?
it
A
t
K
?
it
L
1??
it
where A
t
is total factor productivity
common across all entrepreneurs, and ?
it
is the idiosyncratic productivity level of
the entrepreneur i.
The idiosyncratic level of productivity, ?
it
, is assumed to be i.i.d across en-
trepreneurs and time, with a continuous at least once-di?erentiable cdf F(.), with
E[?] = 1 and variance ?
t
.
14
The cross-sectional dispersion of entrepreneurial id-
iosyncratic productivity at time t is given by ?
t
, and exogenous movements in ? are
due to uncertainty shocks. Note that shocks to ?
t
is a mean-preserving spread for
the distribution of idiosyncratic productivity ?
i
.
15
Given the level of capital acquired at the end of t ?1 (K
it
), the entrepreneur
chooses the demands for labor at the beginning of t to maximize real pro?ts. The
entrepreneur earns revenues from selling the wholesale goods to the retailers, and
from selling non-depreciated capital to the capital producers, ?
it
Q
t
(1 ? ?)K
it
.
16
Then, the entrepreneur determines how much capital to demand (or in other words,
how much to borrow).
17
Hence, the entrepreneur’s optimization problem can be
analyzed in two stages, ?rst labor demand is determined at the beginning of the
current period, and second capital demand is determined at the end of the period.
14
Assuming ?
it
to be i.i.d over entrepreneurs and time is to have an ex-post representative
entrepreneurial sector.
15
In particular, let F(.) be a log-normal distribution. Then, E[?] = 1 implies ln(?)?
N(
?1
2
?
2
, ?
2
) since E[?] = e
?1
2
?
2
+
1
2
?
2
. Now consider an exogenous change in ? to ¯ ? due to
uncertainty. Then, ln(?)? N(
?1
2
¯ ?
2
, ¯ ?
2
), and that implies E[?] = e
?1
2
¯?
2
+
1
2
¯?
2
= 1.
16
Hence, ?
it
is assumed to a?ect not only the level of entrepreneurial production, but also the
e?ective level of capital holdings. In this regard, ?
it
also a?ects the quality of capital held by the
entrepreneurs (see the discussions in Gertler et al., 2003; and Gilchrist and Saito, 2008).
17
The entrepreneurs are assumed to be more impatient than the ultimate lenders (households)
which ensures that external borrowing exists in the model.
11
The entrepreneur’s maximization problem at the beginning of t is:
max
H
it
,H
e
it
1
X
t
?
it
A
t
K
?
it
_
H
?
it
(H
e
it
)
(1??)
_
(1??)
?W
t
H
it
?W
e
t
H
e
it
(1.4)
where X
t
=
Pt
P
W
t
> 1 is the average mark-up of retail goods over wholesale goods
in gross terms. The solution to the above problem yields standard optimal labor
demand decisions for both types of labor: W
t
= (1 ? ?)?
Y
it
H
it
1
Xt
, and W
e
t
= (1 ?
?)(1 ? ?)
Y
it
H
e
it
1
Xt
. Each equation equates the marginal products with the respective
real wages paid to each labor input.
For the entrepreneur to be able to repay his debt, the revenue from the whole-
sale production (after labor is paid), ?
1
Xt
Y
it
+ ?
it
Q
t
(1 ? ?)K
it
, should exceed the
ex-post value of debt to the ?nancial intermediary. In particular, denote the total
external ?nancing need of the entrepreneur by B
it
= Q
t?1
K
it
?N
it
, where N
it
is the
entrepreneur’s (own) net worth. Then, the entrepreneur is able to repay his debt at
period t if
?
1
X
t
Y
it
+?
it
Q
t
(1 ??)K
it
? Z
it
(?
t
; ?
t
)B
it
(1.5)
where Z
it
(?
t
; ?
t
) is the (state-contingent) contractual rate which depends on the
aggregate macroeconomic state of the economy at t.
18
Second stage of the entrepreneur’s problem is to determine optimal capital
demand. The capital demand depends on (i) the expected marginal return to holding
18
This notation is to emphasize that debt contract is state-contingent. It should be understood
that all other endogenous variables are state-contingent as well, e.g. Y
it
? Y
it
(?
t
; ?
t
), X
t
?
X
t
(?
t
; ?
t
), Q
t
? Q
t
(?
t
; ?
t
), etc. I suppress this notation for brevity.
12
capital; and (ii) the expected marginal cost of ?nancing capital expenditures.
(i) The ex-post marginal (real) return to holding capital from t ? 1 to t,
R
k
t
(?
t
; ?
t
), depends on the marginal pro?t from wholesale production at t plus the
capital gain accrued from t ?1 to t. Hence, R
k
t
(?
t
; ?
t
) =
1
X
t
?Y
t
K
it
+Qt(1??)
Q
t?1
, where Y
t
is
the average wholesale output across the entrepreneurs.
19
Then equation (1.5) can
be equivalently represented as:
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
? Z
i
t
(?
t
; ?
t
)B
i
t
(1.6)
Hence, there exists a threshold level of productivity ?
it
, that satis?es ?
it
R
k
t
(?
t
; ?
t
)
Q
t?1
K
it
= Z
i
t
(?
t
; ?
t
)B
i
t
. Accordingly, an entrepreneur i with ?
it
> ?
it
repays
the loan and keeps the equity (?
it
? ?
it
)R
k
t
(?
t
; ?
t
)Q
t?1
K
it
. If, on the other hand,
?
it
< ?
it
, the entrepreneur declares bankruptcy, the intermediary monitors the en-
trepreneurial production and seizes (1 ? µ)?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
.
20
The defaulting
entrepreneur receives nothing.
(ii) The expected marginal cost of ?nancing is characterized by the debt con-
tract problem between the entrepreneur and the intermediary. The intermediaries
are assumed to operate in perfectly competitive markets, earning zero pro?ts in
equilibrium and perfectly diversifying any idiosyncratic risk. Hence, the debt con-
tract problem is characterized by maximizing expected return to capital to the
entrepreneur given that the intermediary earns his opportunity cost of funding (the
riskless rate) in expected terms. The solution to the problem determines how the
19
Details are provided in Appendix A1.
20
The debt contract problem is incentive compatible in that an entrepreneur has no gain from
misreporting the project outcome.
13
expected gross payo? from the contract, R
k
t
(?
t
; ?
t
)Q
t?1
K
it
, is split between the two
parties, pinning down the desired capital stock K
it
, and the state-contingent thresh-
old level ?
it
.
The entrepreneurial sector can be aggregated given two assumptions: (i) The
fraction of entrepreneurs that remains alive at the end of each period is constant.
(ii) The wholesale production technology exhibits CRTS. Given CRTS, the leverage
ratio does not depend on ?rm-speci?c factors (the idiosyncratic productivity). That
is, regardless of the idiosyncratic productivity level, each entrepreneur chooses the
same level of leverage,
Q
t?1
Kt
Nt
, hence face the same level of EFP. Similarly, aggre-
gate wholesale production can be represented by Y
t
= A
t
K
?
t
_
H
?
t
(H
e
t
)
(1??)
_
(1??)
,
where K
t
denotes the aggregate capital purchased in t ?1, H
t
is the aggregate labor
supplied by the households, and H
e
t
is the aggregate entrepreneurial labor. More-
over, the optimal labor demands can be read without ?rm-speci?c subscripts. Since
the bankruptcy costs are proportional to the wholesale output, the supply of capital
can be aggregated as well.
As shown in Appendix A2, the debt contract problem implies that the external
?nance premium (EFP), de?ned as the ratio of cost of external funds to that of
internal funds, is an increasing function of the aggregate leverage ratio (
QtK
t+1
N
t+1
?1),
EFP
t
?
R
k
t+1
R
t
=
_
1 ?
N
t+1
Q
t
K
t+1
__
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
)
_
?1
(1.7)
where the term in square brackets is the net contractual share going to the lender,
14
and decreasing in ? for Q
t
K
t
> N
t
.
21
Intuitively, as the external borrowing need
increases, it is more likely that the entrepreneur declares default. This, in turn,
induces an increase in expected monitoring costs, and hence a higher equilibrium
level of premium over the riskless rate. The ampli?cation mechanism is driven
mainly by this key equation, the EFP being positively related with the aggregate
leverage ratio.
The aggregate net worth of entrepreneurs at the end of period t consists of
the net worth of entrepreneurs who survived from t ? 1 to t and the period-t en-
trepreneurial wage. That is, the evolution of aggregate net worth satis?es
N
t+1
= ?[R
k
t
(?
t
; ?
t
)Q
t?1
K
t
?
_
R
t
+
µ ?
_
?
0
?F(?)R
k
t
(?
t
; ?
t
)Q
t?1
K
t
Q
t?1
K
t
?N
t
_
? (Q
t?1
K
t
?N
t
)] +W
e
t
H
e
t
(1.8)
The ?rst term in square brackets is the real gross return to holding K
t
amount
of capital from t ? 1 to t, and the second term is the total payment to the ?-
nancial intermediaries. Note that the ratio of default costs to quantity borrowed,
µ?
_
?(?
t
;?
t
)
0
?F(?)R
k
t
(?t;?t)Q
t?1
Kt
Q
t?1
Kt?Nt
, re?ects the EFP. The term inside the square brackets
is the net payo? from capital investment, part of which is lost due to exogenous
survival probability ? < 1. The last term, W
e
t
H
e
t
, is the total wage received by the
entrepreneurs.
Finally, the entrepreneurs who exogenously leave the market at the end of t
21
The debt contract problem is presented in Appendix A2.
15
consumes the residual net worth:
C
e
t
= (1??)
_
R
k
t
Q
t?1
K
t
?
_
R
t
+
µ
t
?
_
?
0
?F(?)R
k
t
(?
t
; ?
t
)Q
t?1
K
t
Q
t?1
K
t
?N
t
_
? (Q
t?1
K
t
?N
t
)
_
(1.9)
Capital Producers. They purchase ?nal goods I
t
and use existing capital stock
K
t
to produce new capital goods K
t+1
. The new capital good is then sold to the
entrepreneurs.
22
They face capital adjustment cost ?
_
It
Kt
_
, with ?(0) = 0, ?
(.) >
0, and ?
(.) < 0. Hence, the law of motion for aggregate capital stock is
K
t+1
= (1 ??)K
t
+K
t
?
_
I
t
K
t
_
(1.10)
Capital producers’ problem of choosing I
t
to maximize their pro?ts, Q
t
K
t+1
?Q
t
(1?
?)K
t
? I
t
, subject to the evolution of aggregate capital stock yields the standard
Q-relation for the price of capital:
Q
t
=
_
?
_
I
t
K
t
_
_
?1
(1.11)
1.2.3 Retailers
A measure-one continuum of retailers operate in monopolistically competitive mar-
kets and face implicit costs of adjusting prices. The price stickiness is of standard
Calvo (1983) and Yun (1996) type. Retailers purchase wholesale goods from the
22
The capital producers lease capital stock of entrepreneurs (K
t
) at period t before the produc-
tion of K
t+1
.
16
entrepreneurs at the marginal cost (P
W
t
), and di?erentiate them costlessly.
The retailers’ maximization of expected discounted real pro?ts given iso-elastic
demands for each retail good yields the standard optimality condition that a retailer
who is able to change its price at t sets the price such that the expected discounted
di?erence between the real marginal cost (
P
W
t
Pt
) and real marginal revenue (
P
?
t
Pt
) is
zero, given the environment that the ?rm is unable to change its price with proba-
bility ? in future periods. Formally,
E
t
?
s=t
?
t,t+s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
?
t
P
s
?
?1
P
w
s
P
s
_
= 0 (1.12)
where P
?
t
denote the price set by retailers who are allowed to change their price
at t, P
t
is the aggregate price level, and Y
f
t
=
_
_
1
0
y
t
(j)
1?
1
_ 1
1?
1
is the Dixit-Stiglitz
aggregate of retail goods y
t
(j).
23
The conventional approach in most New-Keynesian
literature is to log-linearize this equation around a non-in?ationary steady state, and
proceed to the standard New-Keynesian Phillips curve. However, since I employ
second-order approximation to the policy functions, I represent eq. (1.12) in a
recursive format.
First de?ne
x
1
t
= E
t
?
s=t
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
?
t
P
s
_
(1.13)
and
23
See Appendix A3 for details.
17
x
2
t
= E
t
?
s=t
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
w
s
P
s
_
(1.14)
As shown in Appendix A4, x
1
t
and x
2
t
can represented in a recursive format as
x
1
t
= ¯ p
t
1?
Y
f
t
+E
t
?
t,t+1
?(1 +?
t+1
)
?1
_
¯ p
t
¯ p
t+1
_
1?
x
1
t+1
(1.15)
where ¯ p
t
=
P
?
t
Pt
; and
x
2
t
= ¯ p
t
?
Y
f
t
1
X
t
+E
t
?
t,t+1
?(1 +?
t+1
)
_
¯ p
t
¯ p
t+1
_
?
x
2
t+1
(1.16)
I focus on the symmetric equilibrium such that optimizing retailers at a given
time choose the same price. Then, the evolution of aggregate price satis?es P
1?
t
=
?(P
t?1
)
1?
+ (1 ??)(P
?
t
)
1?
. Dividing this expression by P
1?
t
yields
1 = ?(1 +?
t
)
?1
+ (1 ??) ¯ p
t
1?
(1.17)
1.2.4 Monetary Authority and the Government
The monetary authority sets the short-term nominal interest rate via a simple mon-
etary policy rule.
24
The rule, in its most general version, prescribes potential reac-
tions to in?ation, and output (as in the standard Taylor rule), as well as ?nancial
variables (all in deviations from their respective long-run values). Formally,
24
A rule is simple if it includes only a few observable macroeconomic variables and ensures a
unique rational expectations equilibrium (and hence implementable). Second, a rule is optimal if
it minimizes the welfare distance between the decentralized economy and the planner’s economy.
For further discussion, see Schmitt-Grohe and Uribe (2006).
18
log
_
1 +r
n
t
1 +r
n
_
= ?
r
log
_
1 +r
n
t?1
1 +r
n
_
+(1??
r
)
_
?
?
log
_
1 +?
t
1 +?
_
+?
Y
log
_
Y
t
Y
_
+?
F
log
_
F
t
F
__
(1.18)
where F stands for Financial and denotes either asset price (Q) or external ?nance
premium (EFP), and overlined variables denote the corresponding deterministic
steady state values. The policy can also exhibit some inertia/smoothing (?
r
?
0). Note that the authority follows such a policy rule only under a decentralized
economy. In planner’s economy, the planner does not follow a rule, but instead uses
the short-run interest rate as the policy tool to maximize aggregate welfare.
The ?scal policy is assumed to be non-distortionary that the exogenous stream
of government expenditures G
t
is ?nanced by lump-sum taxes, G
t
= T
t
.
25
1.2.5 Equilibrium and Aggregation
Each retailer faces a downward-sloping demand from the households (c
jt
=
_
P
jt
Pt
_
?
C
t
),
the capital producers (i
jt
=
_
P
jt
Pt
_
?
I
t
), and the government (g
jt
=
_
P
jt
Pt
_
?
G
t
).
26
Moreover, entrepreneurial consumption (c
e
jt
) and monitoring costs (amc
jt
) soke up
some of the retail good supply j. Hence, supply should be equal to demand at the
?rm-level implies
y
t
(j) = c
jt
+i
jt
+g
jt
+c
e
jt
+amc
jt
(1.19)
25
Assuming away ?scal policy is to simplify the analysis and to focus on monetary policy pre-
scriptions.
26
See Appendix A5 for details.
19
for each j. Given the demand curves for each retail good, the above equation can
be expressed as
y
t
(j) = (C
t
+I
t
+G
t
)
_
P
jt
P
t
_
?
+c
e
jt
+amc
jt
(1.20)
for each j. Note that the retailers are not a productive unit in the economy, implying
that the aggregate amount of retail goods should be equal to the aggregate wholesale
production Y
f
? Y = F(K, H, H
e
). Hence, aggregating over all the retail goods
implies an aggregate market clearing for the ?nal goods market:
Y
t
= (C
t
+I
t
+G
t
)
_
1
0
_
P
jt
P
t
_
?
dj +C
e
t
+AMC
t
(1.21)
where C
e
t
=
_
1
0
c
e
jt
dj and AMC
t
=
_
1
0
amc
jt
dj.
To represent the goods-market clearing condition in a tractable way, I represent
S
t
?
_
1
0
_
P
jt
Pt
_
?
dj in a recursive format. As details are shown in Appendix A6,
S
t
?
_
1
0
_
P
it
P
t
_
?
di
= (1 ??)
_
P
?
t
P
t
_
?
+?
_
P
t?1
P
t
_
?
S
t?1
= (1 ??) ¯ p
t
?
+??
t
S
t?1
(1.22)
20
Hence, the aggregate resource constraint is represented by the following three
conditions:
Y
t
= C
t
+C
e
t
+I
t
+G
t
+AMC
t
(Aggregate Demand) (1.23)
Y
t
?C
e
t
?AMC
t
=
1
S
t
(F(K
t
, H
t
, H
e
t
) ?C
e
t
?AMC
t
) (Aggregate Supply) (1.24)
?
t
= (1 ??)¯ p
?
t
+??
t
S
t?1
(1.25)
I leave the de?nition of stationary competitive equilibrium of this economy to
Appendix B.
27
1.3 Functional Forms and Calibration
I calibrate the model to match the US economy for the period 1989Q1-2009Q1.
This sample choice is mainly for calibration purposes which will be clear below. For
some parameters, I use conventional estimates reported in the literature. Table 1.2
summarizes the parameter values.
I choose the period utility function of the form
27
The de?nition of equilibrium includes optimality conditions of the debt contract problem -not
shown for brevity in Section 2.2-. These optimality conditions are derived in Appendix A2.
21
U (C
t
, H
t
) = log(C
t
) ??
H
1+?
1 +?
(1.26)
which is typically studied in the New-Keynesian literature. I set ? at 0.55 which
implies a Frisch labor supply elasticity (
1
?
) of 1.80.
28
Then I set ? at 6.05 so that
the household spends
1
3
of her time working at the deterministic steady state.
The aggregate production of wholesale goods is governed by a CRTS technol-
ogy given by
Y
t
= A
t
K
?
t
_
H
?
t
(H
e
t
)
(1??)
_
(1??)
(1.27)
where ? = 0.35, ? =
0.64
0.65
, and H
e
= 1, following BGG. Setting ? = 0.35 ensures that
wages constitute 65% of the total production cost in the model, in accordance with
the US economy. ? =
0.64
0.65
implies that entrepreneurial labor earns approximately 1%
of the total income. Moreover, the entrepreneurial labor is assumed to be supplied
inelastically and normalized to unity.
The subjective discount factor, ?, is taken to be 0.9902, in line with the ob-
served 4% annual real rate of interest in the US economy. The quarterly depreciation
rate is assumed to be ?xed at 0.025. Following Klenow and Malin (2010), I set the
Calvo price stickiness parameter, ?, equal to 0.66. This value implies an average
frequency of price changes of approximately 3 quarters.
29
Moreover, is set at 11,
28
This level of elasticity is well in the range studied in the macro- business cycle literature.
For recent discussions on the labor supply elasticity, see Rogerson and Wallenius (2009), and
Christiano, Trabandt, and Walentin (2010) and references therein. I take the average of ?s studied
by Christiano, Trabandt, and Walentin (2010) as two extreme cases (?=1 and ?=0.1).
29
Klenow and Malin (2010) reports that the mean (non-sale) price duration of non-durable goods
is 8.3 months, and it is 9.6 months for services goods. Weighting these price durations by their
22
implying a 10% long-run price mark-up over the marginal cost (under zero long-run
in?ation).
The capital adjustment cost function takes the following quadratic form
?
_
I
t
K
t
_
=
I
t
K
t
?
?
k
2
_
I
t
K
t
??
_
2
(1.28)
I set ?
k
= 10 so that the elasticity of price of capital with respect to investment to
capital ratio is 0.25 at the deterministic steady state.
30
The monetary authority is assumed to have a perfect control over the short-
term nominal interest rate, and targets an (annual) in?ation rate of ?=2.66% (the
average CPI-based in?ation rate).
31
Following BGG, I assume that the monetary
authority reacts only to the in?ation.
32
The (long-run) in?ation feedback coe?cient,
?
?
, is set at 1.77, and the policy persistence parameter, ?
r
, is set at 0.84, following
Smets and Wouters (2007).
The remaining three parameters, the bankruptcy cost (µ), the long-run cross-
sectional dispersion of idiosyncratic productivity (?), and the entrepreneur’s survival
shares in the CPI gives out 2.93 quarters. This level of duration in turn implies ? = 0.66. This
value is well in the range calibrated/estimated in the New-Keynesian DSGE literature (for a list
of studies, see Schmitt-Grohe and Uribe, 2010).
30
BGG argues that a reasonable calibration for ?
k
should imply an elasticity in the range of
0 to 0.50. I simply follow BGG, taking the average of these values. Recent estimates imply an
elasticity up to 0.60 (see for instance Christensen and Dib, 2008). A larger elasticity would imply
a stronger reaction of asset prices to disturbances, leading to larger movements in entrepreneurs’
net worth and in turn a stronger ?nancial ampli?cation. I, however, take a conservative stand,
and set the parameter as in BGG.
31
Following Rudebusch (2006), I calculate ?
t
using the price index for consumption expenditures
excluding food and energy. Denoting the index by P
t
, ?
t
=400log(P
t
/P
t?1
).
32
In Section 7 where I study optimal simple policy rules, I consider the most general case in
which the monetary authority is allowed to react to in?ation, output gap, and ?nancial variables.
The reason of not including the latter two under the benchmark economy is mainly for comparison
purposes with the BGG and to elicit in Section 6 the planner’s motive to mitigate the degree of
?nancial ampli?cation that would prevail under the benchmark economy.
23
Table 1.2: Parameters
Description Parameter Value Target/Source
Households
The quarterly subjective discount rate ? 0.9902 4% Real rate
Preference Parameter ? 6.05 1/3 working time
(Inverse) Frisch labor supply elasticity ? 0.55 CTW (2010)
Firms
Share of capital in production ? 0.35 RBC
Share of HH’s labor income ? 0.64/0.65 BGG
Depreciation rate of capital ? 0.025 RBC
Calvo price stickiness parameter ? 0.66 Klenow & Malin (2010)
Intra-temporal elasticity of substitution 11 BGG
Capital adjustment cost parameter ?
k
10 BGG
Financial Variables
Bankruptcy Rate µ 0.13 Bankruptcy rate (3%)
Survival Rate 1 ?? 0.982 Leverage ratio (1.05)
(a)
L-R Cross-sectional Dispersion ? 0.261 EFP (227 BP)
(b)
Exogenous Processes
Persistence Parameter, log(TFP) ?
A
0.95 RBC
Persistence Parameter, log(G) ?
G
0.87 SGU (2007)
Persistence Parameter, log(?) ?
?
0.83 Chugh (2010)
Stdev. of innovations to log(TFP) ?
?
A 0.0082 Cyclical volatility of GDP
Stdev. of innovations to log(G) ?
?
G 0.0076 Cyclical volatility of G
Stdev. of innovations to log(?) ?
U
0.0151 Cyclical volatility of EFP
(c)
Monetary Policy Rule
Policy rate persistence ?
r
0.84 Smets & Wouters (2007)
In?ation feedback coe?cient ?
?
1.77 Smets & Wouters (2007)
(a) Chugh (2011).
(b) Long-run average of (i) prime-lending rate and 6-month constant maturity treasury bill, (ii) prime-
lending rate and 3-month constant maturity treasury bill, (iii) Moody’s BAA-rated and AAA-rated cor-
porate bonds, (iv) Moody’s BAA-rated corporate bond and 10-year constant maturity treasury bill.
(c) Average cyclical volatility of these credit spreads. Sensitivity analysis is performed as well.
rate (?) are jointly calibrated to match three long-run ?nancial targets: An annual
bankruptcy rate of 3% (following BGG), the aggregate leverage ratio of non-?nancial
?rms of 1.05 (following Chugh, 2011), and the long-run level of external ?nance
24
premium of 227 basis points.
3334
The ?rst-moment shocks that I consider are those typically studied in the
literature, the innovations to aggregate TFP and real government expenditures.
35
They both follow a ?rst-order autoregressive (AR(1)) process in logs:
log(A
t
) = ?
A
? log(A
t?1
) +?
A
t
(1.29)
log(G
t
) = (1 ??
G
)log(G) +?
G
log(G
t?1
) +?
G
t
(1.30)
where ?
A
, ?
G
are the respective persistence parameters, G is the long-run level
of real government expenditures, and ?
A
t
and ?
G
t
are the respective i.i.d Gaussian
innovations. I set ?
A
= 0.95 following the real business cycle literature, and ?
G
=
0.87 following Schmitt-Grohe and Uribe (2006). I set G equal to 19.56% of the real
33
To obtain the long-run average of external ?nance premium, I use the average of credit spreads
that are generally used as an aggregate measure for the spread: two paper-bill spreads, and two
corporate bond spreads, i.e. (i) prime-lending rate and 6-month constant maturity treasury bill,
(ii) prime-lending rate and 3-month constant maturity treasury bill, (iii) Moody’s BAA-rated
and AAA-rated corporate bonds, (iv) Moody’s BAA-rated corporate bond and 10-year constant
maturity treasury bill; all taken from the Fed St. Louis Database. The long-run average of these
premia, which I take as the calibration target, is 227 basis points. An annual bankruptcy rate
of 3% is within the range of recent estimates for the bankruptcy rates of US non-?nancial ?rms
(see Gilchrist, Yankov and Zakrajsek, 2010). Chugh (2011) establishes business cycle statistics
of aggregate ?nancial variables of the US non-?nancial ?rms, and use the sample period 1989Q1-
2009Q1.
34
Note that these ?nancial targets are aggregate measures, and their empirical counterparts are
not clear. The level of premium, for instance, depends on the maturity structure of underlying
instruments, borrowing ?rms’ characteristics like age, equity, loan size etc., and hence is ?rm-
speci?c. Use of heterogeneity in these ?nancial targets in a general equilibrium model, however,
requires a heterogenous-agent framework, and the BGG, as most agency-cost general equilibrium
models, assumes no heterogeneity in this dimension mainly for computational ease. For empirical
studies based on micro-level data on EFP and default frequencies, see Levin, Natalucci, and
Zakrajsek (2004), and Gilchrist, Yankov and Zakrajsek (2010).
35
By minimizing the set of ?rst-moment shocks (one for supply and one for demand), I keep the
analysis simple. Moreover, the studies that closely resemble this paper, Schmitt-Grohe and Uribe
(2006) and Faia and Monacelli (2007), use these disturbances to drive ?uctuations in the economy.
25
GDP in the long run, inline with the US economy for the sample period.
The uncertainty shock, U
t
, is de?ned as disturbances to cross-sectional disper-
sion of entrepreneur’s idiosyncratic productivity. In particular, the cross-sectional
dispersion follows an AR(1) process in logs:
log(?
t
) = (1 ??
?
)log(?) +?
?
log(?
t?1
) +U
t
(1.31)
where ?
?
is the persistence parameter, and U
t
is an i.i.d. Gaussian innovation. I set
?
?
equal to 0.83, the estimate reported by Chugh (2010) using ?rm-level data.
Given the structural parameters set so far, I jointly calibrate standard de-
viations of innovations ?
A
t
, ?
G
t
, and U
t
to match the observed cyclical volatilities
of real GDP, real government expenditures, and the credit spread in the data.
36
The resulting parameter values are ?
?
A = 0.0082, ?
?
G = 0.0074, and ?
U
= 0.0151
respectively.
1.4 Decentralized Equilibrium and Cross-Sectional Dispersion
I ?rst study the long-run deterministic equilibrium as a function of long-run cross
sectional dispersion, ?. This analysis provides a step-en-route to discuss how credit
frictions a?ect model dynamics and interlinked with the monopolistic competition
and the long-run in?ation. Second, I present model dynamics in response to produc-
tivity, government spending and uncertainty shocks, and the relative importance of
36
The cyclical volatility of the aforementioned credit spreads are, in respective order, .2805,
.2195, .2497, and .4812. The average, which I take as the calibration target, is 0.308. In Section 7,
I consider sensitivity of the normative results with respect to using a di?erent credit spread. For
data de?nitions, see Appendix C.
26
uncertainty shocks in driving the business cycles.
1.4.1 Long-run equilibrium and long-run cross sectional dispersion
Figure 1.1 plots the long-run equilibria as a function of long-run cross-sectional
dispersion.
37
As the dispersion reduces to zero, the idiosyncratic entrepreneurial
project outcomes become a common knowledge. In other words, the asymmetric
information between the lender and the entrepreneurs dissipates. As a result, exter-
nal ?nance premium, bankruptcies as well as aggregate monitoring costs shrink to
zero.
38
Moreover, long-run capital accumulation rises as the dispersion fades away.
39
Similarly, aggregate investment, consumption and output rise as the dispersion dis-
sipates. Moreover, households’ welfare is monotonically decreasing in cross-sectional
dispersion (not shown for brevity).
Nevertheless, investment and output displays a non-monotonic behavior, that
they begin to rise for values of dispersion above a certain level. This is not due to
any sort of non-monotonicity in contractual terms (as suggested by the monotonic
path of ?nancial variables). This is rather due to entrepreneurs’ relying much less
on external borrowing: total debt and leverage shrink to zero as the dispersion
rises. Hence, e?ectively, the strength of ?nancial frictions starts to decrease in the
deterministic long-run equilibrium as the dispersion rises substantially.
37
All other parameters are held ?xed at those presented in Table 1.2.
38
When the dispersion is exactly equal to zero, the entrepreneurial sector becomes managed
by the intermediary. Hence, neither leverage nor the loan amount can be identi?ed when the
dispersion is exactly zero.
39
Note that aggregate investment at the deterministic steady state is equal to stock of depreciated
capital. Hence, an equivalent diagram for total capital stock would be just a scaled-up version of
the diagram for investment.
27
Figure 1.1: Long-run equilibria as a function of long-run cross-sectional dispersion
0 0.1 0.2 0.3 0.4 0.5
1
1.05
1.1
1.15
?
O
u
t
p
u
t
0 0.1 0.2 0.3 0.4 0.5
0.52
0.54
0.56
0.58
0.6
?
C
o
n
s
u
m
p
t
io
n
0 0.1 0.2 0.3 0.4 0.5
0.19
0.2
0.21
0.22
0.23
0.24
0.25
?
I
n
v
e
s
t
m
e
n
t
0 0.1 0.2 0.3 0.4 0.5
2
4
6
8
10
?
T
o
t
a
l
D
e
b
t
0 0.1 0.2 0.3 0.4 0.5
1
2
3
4
5
6
?
N
e
t
W
o
r
t
h
0 0.1 0.2 0.3 0.4 0.5
0
2
4
6
8
?
L
e
v
e
r
a
g
e
0 0.1 0.2 0.3 0.4 0.5
0
1
2
3
4
5
?
B
a
n
k
r
u
p
t
c
y
R
a
t
e
(
p
p
t
s
)
0 0.1 0.2 0.3 0.4 0.5
0
50
100
150
200
250
300
?
P
r
e
m
iu
m
(
b
p
t
s
)
0 0.1 0.2 0.3 0.4 0.5
0
1
2
3
4
5
6
x 10
?4
?
A
g
g
r
e
g
a
t
e
M
o
n
it
o
r
in
g
C
o
s
t
s
Notes. All other parameters are held ?xed at those presented in Table 1.2.
These comparative statics bear the question of whether the responses are
driven solely by the agency-cost framework, or a?ected by speci?ed degrees of long-
run in?ation (? > 0) and monopolistic competition (captured by ). Since ?nancial
variables in the absence of aggregate shocks are determined within partial equilib-
rium, ?nancial frictions are (almost) independent from the degree of monopolistic
competition and the level of long-run in?ation at the deterministic steady state.
Nevertheless, as we elaborate below, ?nancial frictions are interlinked with the other
two features in the model dynamics.
28
1.4.2 Dynamics of the model and cross-sectional dispersion
I simulate the model economy around the deterministic steady-state using second-
order approximation to the policy functions. All statistics are based on HP-?ltered
cyclical components (with a smoothing parameter 1600). Impulse responses refer to
how endogenous variables react to an unexpected one-time one-standard-deviation
increase in the underlying exogenous state. All responses are in percentage devia-
tions from respective deterministic steady state values unless otherwise noted.
1.4.2.1 Productivity and Government Spending Shocks
For comparison purposes with the literature, I present the equilibrium responses of
real and ?nancial variables in response to a favorable productivity shock (Figure
1.2). Dashed lines show the dynamics under no ?nancial ampli?cation. To shut
o? the ampli?cation, I set the external ?nance premium ?xed at its deterministic
long-run value (227 basis points).
40
An exogenous increase in total factor productivity leads to an unexpected rise
in ex-post marginal real return to capital, which, due to capital adjustment costs,
raises the price of capital, Q
t
. For a given level of net worth, a rise in Q
t
induces an
increase in borrowing needs. However, the rise in Q
t
drives the net worth up more
than proportionately, leading to a decrease in the leverage.
41
EFP then falls on
40
I should make the following distinction between shutting ?nancial ampli?cation o? and shutting
?nancial frictions o?. The former refers to ?xing the EFP at its deterministic long-run value
(so that the ampli?cation is turned o?), whereas the latter refers to no ?nancial frictions in the
economy, EFP being zero at all times. For presentation purposes, I choose to shut the ampli?cation
o?, since the former and the benchmark model then share the same deterministic equilibrium.
41
One can algebraically show that how sensitive the net worth is to unexpected changes in ex-
post return to capital depends on the leverage ratio: Net worth rises more than proportionately
to the extent entrepreneurs are leveraged (see BGG, p. 1359).
29
impact, generating an ampli?ed response of asset prices and aggregate investment.
An exogenous increase in aggregate supply of wholesale goods drives the nom-
inal marginal costs down that the retailers face. Hence, the retailers that are able to
set prices chooses a price lower than the average price level in the economy. Average
price level, P
t
, then decreases, but, due to sticky prices, not as much as the decrease
in P
W
t
. As a result, average mark-up in the economy,
Pt
P
W
t
, rises and in?ation goes
below its long-run value.
42
Figure 1.2: Impulse Responses to a 1 sd. increase in total factor productivity
0 20 40
0
0.5
1
Output
0 20 40
0
0.5
1
Consumption
0 20 40
?1
0
1
Labor
0 20 40
?2
0
2
Investment
0 20 40
?0.5
0
0.5
Asset Price
0 20 40
?2
0
2
Net Worth
0 20 40
?1
0
1
Debt
0 20 40
?1
0
1
Leverage Ratio
0 20 40
?10
0
10
Premium (bpts)
0 20 40
?0.2
0
0.2
Bankruptcy Rate (ppts)
0 20 40
?0.5
0
0.5
Threshold Prod. (?)
0 20 40
0
0.5
Mark-up
0 20 40
?1
?0.5
0
In?ation Rate (ppts)
0 20 40
?0.4
?0.2
0
Policy Rate (ppts)
0 20 40
?0.2
0
0.2
Real Rate (ppts)
Notes. Solid line: Financial ampli?cation, Dashed line: No ?nancial ampli?cation
(EFP is ?xed). Unless otherwise noted, the responses are in terms of percentage
deviation from the respective deterministic steady states.
Note that existence of ?nancial ampli?cation dampens the response of in?a-
42
These responses are by and large in line with the literature. See BGG, Faia and Monacelli
(2005), and Christiano, Motto and Rostagno (2010).
30
tion to a rise in productivity. For an economy without ampli?cation (the dashed
lines), the rise in aggregate supply of wholesale goods is lower, which dampens the
decrease in nominal marginal costs. Average mark-up in the economy then rises less
than what would be without ?nancial ampli?cation. As a result, in?ation decreases
much less on impact. Hence, there exists a relative de?ationary e?ect of ?nancial
ampli?cation in response to productivity shocks.
43
An unexpected expansionary government spending serves as a typical favorable
demand shock. A rise in demand for wholesale goods leads to a rise in output and en-
trepreneurial net worth, and eventually a decrease in premium and the bankruptcy.
A higher demand for wholesale goods pushes wholesale prices (nominal marginal
costs) up. Retailers that are able to set their prices set a higher price, which leads
to an increase in in?ation. The average price, P
t
, though, does not increase as much
as the increase in P
W
t
, and hence, average mark-up in the economy,
Pt
P
W
t
falls.
44
1.4.2.2 Uncertainty Shocks
Before presenting the corresponding model dynamics, it might be useful to discuss
brie?y how an exogenous increase in the cross-sectional dispersion a?ect ?nancial
variables in partial equilibrium. Figure 1.3, in particular, shows the e?ect of a two-
standard deviation increase on the cross-sectional dispersion, based on the bench-
mark values of ? and ?
U
. If the threshold level of productivity, ?, were to remain
unchanged in response to an increase in the dispersion, the measure of entrepreneurs
43
See Faia and Monacelli (2005) for a similar result.
44
See Figure 1.15 in the Appendix for impulse responses of real and ?nancial variables in response
to the government spending shock.
31
whose productivity is below the threshold level (?
i
< ?) rises. Since the distribution
of ? is known at the time the debt contract is made, lenders now understand that
there will be fewer ?rms who will be able pay their debts. Since the lenders should
be compensated for the increase in the associated expected monitoring costs, this in
turn induces a higher equilibrium level of EFP. The threshold level of productivity
is endogenous though, and the general equilibrium e?ect of an exogenous increase
in ?
t
is quantitative in nature.
Figure 1.3: An increase in the cross-sectional dispersion of entrepreneurs’
idiosyncratic productivity
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Firm Idiosyncratic Productivity
?
(
.
)
An increase in cross?sectional dispersion of firms’ idiosyncratic productivity
Figure 1.4 provides the impulse responses of real and ?nancial variables to an
unfavorable uncertainty shock (an unexpected rise in the cross-sectional dispersion).
It is evident that it serves as a prototypical aggregate demand shock. An increase
in the dispersion implies a higher risk for the overall loan portfolio of the lenders.
Hence, expected monitoring costs rise for which lenders should be compensated.
Moreover, due to decrease in expected return to capital, aggregate net worth of the
entrepreneurs goes down. These eventually lead to an equilibrium increase in the
32
leverage and in the premium. The rise in the premium tightens the ?nancing terms,
which lowers aggregate investment and in turn aggregate demand.
Figure 1.4: Impulse Responses to a 1 sd. increase in uncertainty
0 20 40
?0.2
?0.1
0
Output
0 20 40
?0.1
0
0.1
Consumption
0 20 40
?0.4
?0.2
0
Labor
0 20 40
?1
?0.5
0
Investment
0 20 40
?0.5
0
0.5
Asset Price
0 20 40
?1
?0.5
0
Net Worth
0 20 40
0
0.5
1
Debt
0 20 40
0
0.5
1
Leverage Ratio
0 20 40
0
10
20
30
Premium (bpts)
0 20 40
0
0.5
1
Bankruptcy Rate (ppts)
0 20 40
0
0.1
0.2
Threshold Prod. (?)
0 20 40
?0.1
0
0.1
0.2
Mark-up
0 20 40
?0.2
0
0.2
In?ation (ppts)
0 20 40
?0.1
0
0.1
Policy Rate (ppts)
0 20 40
?0.1
0
0.1
Real Rate (ppts)
Notes. Unless otherwise noted, the responses are in terms of percentage deviation
from the respective deterministic steady states.
A reduction in aggregate demand for the retail goods leads to a lower demand
for wholesale goods, pushing wholesale prices (nominal marginal costs) down. Re-
tailers that are able to set their prices set a lower price, which leads to a decrease in
in?ation. The average price, P
t
, though, does not decrease as much as the decrease
in P
W
t
, and hence, average mark-up in the economy,
Pt
P
W
t
rises.
Although the model is rather simplistic, equilibrium responses are by and
large inline with the data. Gilchrist, Sim and Zakrajsek (2010) show in a VAR
33
framework that the real GDP declines by .2% after 2 quarters and exhibits a hump-
shaped response due to an unexpected one-standard-deviation (an approximately
8%) increase in the uncertainty.
45
We are able to generate this magnitude of decline,
but not the hump-shape response. Similarly for aggregate investment, the model
is able to generate the documented magnitude of decline yet misses the hump-
shape response. Moreover, although the impact e?ect on the premium seems to be
somewhat larger than that documented, it is hard to draw a conclusive picture in
this dimension, since the empirical counterpart of the model-based premium is not
clear.
46
The contribution of uncertainty shocks in driving aggregate ?uctuations is
presented in Table 1.3. The uncertainty shock accounts for around 85% of the
variations in EFP and the bankruptcy, and more than 15% of the volatility in
other ?nancial variables for both short- and long horizons. Since ?uctuations in
?nancial variables ?rst transmit into aggregate investment, investment turns out
to be the real variable that is driven by the uncertainty shock most (18% for one
period ahead). The remaining real variables are mostly driven by the ?rst-moment
shocks.
47
45
They estimate time-?xed e?ects in a panel-AR(1) regression of ?rms’ equity volatility to mea-
sure aggregate uncertainty. The uncertainty is de?ned as the innovation to idiosyncratic equity
volatility that are common to all ?rms at t. This de?nition is conformable with the uncertainty
de?ned in our model, time-variation in the cross-sectional dispersion of idiosyncratic productivity
that a?ects all the entrepreneurs.
46
Note also that the model implies a pro-cyclical debt which is at odds with the data. Note
however that I do not consider policy reaction to volume of debt in the policy rules in the normative
policy analysis. So, pro-cyclicality in debt should not pose a ?rst-order problem for our normative
results.
47
Christiano, Motto and Rostagno (2010) ?nds a more pronounced contribution of uncertainty
shock on the volatility of real and ?nancial variables. They report that almost all the ?uctuations in
the EFP, and nearly half of the ?uctuations in aggregate investment are driven by the risk shock.
In their analysis, most of the contribution comes from the anticipated portion of the uncertainty
34
Moreover, while a substantial portion of ?uctuations in EFP is driven by
uncertainty, only 18% of the ?uctuations in leverage is uncertainty-driven. This
suggests that uncertainty governs most of the ?uctuations in the sensitivity of EFP
to the leverage, or as labeled before, the strength of ?nancial ampli?cation.
Table 1.3: Variance Decomposition (Decentralized Economy)
Variable TFP+G Shocks Uncertainty Shocks
t = 1 t = 4 t = 8 t = ? t = 1 t = 4 t = 8 t = ?
Y 96.08 97.89 98.42 98.4 3.92 2.11 1.58 1.6
Real Variables C 98.73 98.86 99.28 99.3 1.27 1.14 0.72 0.7
I 81.67 88.19 90.85 93.16 18.33 11.81 9.15 6.84
Q 81.67 88.12 90.61 92.47 18.33 11.88 9.39 7.53
EFP 12.31 14.66 16.93 19.54 87.69 85.34 83.07 80.46
Net Worth 81.66 85.47 87.37 89.51 18.34 14.53 12.63 10.49
Financial Variables Debt 82.27 98.77 99.66 98.66 17.73 1.23 0.34 1.34
Leverage 81.66 81.62 81.18 75.01 18.34 18.38 18.82 24.99
Bankruptcy Rate 11.39 13.6 15.76 18.29 88.61 86.4 84.24 81.71
Monetary Variables Policy Rate 61.78 71.01 79.53 94.13 38.22 28.99 20.47 5.87
In?ation 61.78 67.49 70.86 81.14 38.22 32.51 29.14 18.86
Before presenting the normative results, note that when the economy is driven
only by the ?rst-moment shocks, the model cannot generate observed cyclical volatil-
ity of the external ?nance premium, the key variable in the ampli?cation mecha-
nism. Namely, for properly calibrated magnitudes of TFP and government spending
shocks, the simulation-based cyclical volatility of the premium is almost one third
than that observed in the data. If one is to match the volatility of premium by using
?rst-moment shocks only, the standard deviation of innovations to TFP should be
set at an implausibly high value, which, on the other hand, would yield an unre-
alistically high volatility in real GDP. Hence, the key role that uncertainty shocks,
or ?nancial shocks in general, play in a BGG-type ?nancial ampli?cation model is
to match the observed volatility in the premium. This role is especially important
for normative analysis, since credit frictions manifest itself through existence of an
shock.
35
EFP.
1.5 Welfare Evaluation
Aggregate welfare is given by
V
0
? E
0
t=?
t=0
?
t
U(C
t
, H
t
) (1.32)
Note that although the model exhibits heterogeneity of consumers (households
and entrepreneurs), the fraction of entrepreneurial consumption in aggregate con-
sumption can be reasonably assumed to be negligible, as emphasized in BGG, and
Faia and Monacelli (2005, 2008).
48
I conduct second-order approximation to the policy functions as well as to V
0
to
have accurate normative results. Note that, under ?rst-order approximation to the
policy functions, the expected value of endogenous variables would be equal to their
deterministic steady state values. Hence, welfare levels would be the same under
alternative policy rules. Moreover, since the economy exhibits distortions even at the
steady state, ?rst-order approximation to the policy rules induces incorrect welfare
rankings even under a second-order approximation to the welfare.
49
Accordingly, I
48
Note that since entrepreneurs are risk-neutral, they care only the mean level of entrepreneurial
consumption. Also, alternative policy rules imply not only the same deterministic equilibrium for
all the variables, but also the same stochastic mean for the entrepreneurial consumption. Hence,
in comparing alternative policy rules, entrepreneurial consumption, however small it is, can be
neglected. See also Faia and Monacelli (2005) and references therein.
49
In particular, at the deterministic steady state, I do not assume any ad-hoc subsidy scheme
to undo distortions due to monopolistic competition, nor I assume a zero long-run in?ation that
undoes price dispersion. Moreover, credit distortions are e?ective in the deterministic long-run
as well. Such a subsidy scheme facilitates log-linearization around a zero-in?ation steady state.
Without that scheme, one need to rely on higher order approximation to the policy functions as
well as to the welfare. For further discussion, see Schmitt-Grohe and Uribe (2006).
36
?rst de?ne welfare in recursive form:
V
0,t
? U(C
t
, H
t
) +?E
t
V
0,t+1
(1.33)
and conduct second-order approximation to V
0,t
(as well as to the policy functions).
SGU (2006) show that an equivalent representation is
V
0,t
= V
0
+
1
2
?(V
0
) (1.34)
where V
0
is the welfare evaluated at the deterministic steady state, and ? is the
constant correction term capturing the second-order derivative of the policy function
for V
0,t
with respect to the variance of shocks. Hence, equation (1.34) provides
an approximation to the aggregate welfare at t = 0 taking into account the lack
of certainty at the stochastic steady state. Aggregate welfares for decentralized
economies are conditional on the deterministic steady state of the Ramsey planner’s
economy.
50
I will discuss Ramsey planner’s problem in detail in the next section.
For each policy alternative, I perform standard consumption-based welfare
comparisons. In particular, let the aggregate welfare associated with a policy regime
a be given by
V
a
0,t
? E
0
t=?
t=0
?
t
U(C
a
t
, H
a
t
) (1.35)
and the welfare attained by the Ramsey planner be given by
50
Decentralized economy starts from the Ramsey deterministic long-run equilibrium. As will be
evident below, this corresponds to setting deterministic long-run in?ation rate equal to zero.
37
V
r
0,t
? E
0
t=?
t=0
?
t
U(C
r
t
, H
r
t
) (1.36)
Let ? denote the percentage of consumption in Ramsey planner’s economy r
that the household is willing to give up to be as well of under regime a. ? then is
implicitly given by
V
a
0,t
= E
0
t=?
t=0
?
t
U((1 ??)C
r
t
, H
r
t
) (1.37)
A positive ?, for instance, implies that Ramsey economy dominates the decen-
tralized economy in welfare terms. To ?nd optimal policy rules, I search over policy
feedback coe?cients that minimize ?.
1.6 Optimal Monetary Policy
1.6.1 Sources of Ine?ciencies
The model economy has three features that lead to ine?cient outcomes compared
to a ?rst-best ?exible-price economy: the ?rst two are monopolistic competition
and price stickiness, standard distortions in New-Keynesian models. For a detailed
textbook discussion on these distortions, interested readers may refer to Gali (2008).
The third distortion is due to ?nancial frictions.
Monopolistic Competition. Since the retailers are assumed to have imperfectly
elastic demand for their di?erentiated products, they are endowed with some market
power and set prices above marginal cost. Under ?exible prices and no ?nancial
38
frictions, ?
?U(t)
?Ht
/
?U(t)
?Ct
= W
t
= MPL
t
1
X
, where X =
?1
> 1 is the desired gross
mark-up, and MPL is the marginal product of labor under no ?nancial frictions.
Note that under the ?rst-best economy, marginal rate of substitution should be
equal to marginal product of labor, MPL
t
. Since, in equilibrium, marginal rate of
substitution is increasing in hours and marginal product of labor is decreasing in
hours, the presence of monopolistic competition, X > 1, leads to an ine?ciently low
level of employment and output since MPL
t
1
X
< MPL
t
.
Price Stickiness. To study this distortion in isolation, assume that distortions
due to monopolistic competition is undone by an optimal wage subsidy, ? =
1
,
which is ?nanced by lump-sum taxes.
51
Note that economy’s average mark-up is
de?ned by P
t
/P
W
t
(up to a ?rst-order). Then, existence of price stickiness together
with the optimal subsidy scheme implies ?
?U(t)
?Ht
/
?U(t)
?Ct
= W
t
= MPL
t
X
Xt
which
violates the e?ciency condition under the ?rst-best economy that ?
?U(t)
?Ht
/
?U(t)
?Ct
=
MPL
t
, unless X
t
is equal to X at all times. Moreover, due to constant (and equal)
elasticity of substitution across the intermediate goods, consumers would be willing
consume equal amount of each intermediate good. However, if there exists price
dispersion across the goods, then consumer would optimally choose di?erent levels
of intermediate goods, which induces a welfare loss.
Compared to a second-best economy that features monopolistic competition
and ?nancial frictions, the distortion due to price stickiness is due to ? = 0 implying
that ¯ p
t
= 1 and hence S
t
is greater than one. S
t
> 1 leads to an ine?cient output
loss (see equation 1.24).
51
A wage subsidy of ? =
1
implies ?
?U(t)
?Ht
/
?U(t)
?Ct
= W
t
= MPL
t
1
X(1??)
= MPL
t
.
39
Financial Frictions. Note that in an economy with no ine?ciencies (?rst-best
economy),
?U(t)
?Ct
= ?E
t
R
k
t+1
_
?U(t+1)
?C
t+1
_
. Introducing ?nancial frictions creates a wedge
between expected return to capital and the risk-free rate, distorting households’
intertemporal decision. De?ning the wedge as R
t+1
= (1 ? ?
k
t+1
)R
k
t+1
, I next show
that the wedge depends on aggregate ?nancial conditions.
As shown in Appendix A1, the intermediaries’ zero-pro?t condition for the
next period is,
[1?F(?
t+1
)]Z
t+1
(?
t+1
; ?
t+1
)B
t+1
+(1?µ)
_
?
t+1
0
?
t+1
R
k
t+1
(?
t+1
; ?
t+1
)Q
t
K
t+1
dF(?
t+1
) = R
t+1
B
t+1
(1.38)
Substituting in ?
t+1
R
k
t+1
(?
t+1
; ?
t+1
)Q
t
K
t+1
= Z
t+1
(?
t+1
; ?
t+1
)B
t+1
, and
dividing by R
k
t+1
(?
t+1
; ?
t+1
)(Q
t+1
K
t+1
) yields
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
) =
R
t+1
R
k
t+1
(?
t+1
; ?
t+1
)
B
t+1
Q
t
K
t+1
(1.39)
The wedge is then given by
1 ??
k
t+1
=
_
Q
t
K
t+1
B
t+1
__
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
)
_
(1.40)
It is evident that ?uctuations in the wedge are due to movements in aggregate
40
?nancial conditions. The (inverse) of the ?rst term is an increasing function of the
leverage (
QtK
t+1
N
t+1
), and the second term is the net contractual share going to the
lenders.
1.6.2 Ramsey optimal policy problem
I assume that there is a benevolent planner at t = 0 that has been operating for an
in?nite number of periods. The planner is assumed commit to her decisions made
at some indeterminate point in the past. In this sense, I consider an optimal policy
problem from a timeless perspective (Woodford, 2003).
In Ramsey planner’s economy, there is no exogenous monetary policy rule. The
planner chooses the allocations, prices, and the policy rate to maximize aggregate
welfare, respecting the competitive equilibrium conditions. The planner has only
one policy tool, the short-run nominal interest rate.
Ramsey planner using a single policy tool to smooth the two wedges implies
that the Ramsey problem is incomplete (in the sense of Chari and Kehoe, 1999). As
evident from Section 1.6.1, a tax on return to capital would complete the system.
Moreover, equation (1.40) suggests that the proposed tax should smooth ?uctuations
in the leverage and net contractual share going to the lenders. In this regard,
interest-rate policy would be less e?ective if such a ?scal policy tool is introduced.
Further analysis is left to future work.
Formally, the Ramsey planner chooses state-contingent processes {C
t
, H
t
, H
e
t
, K
t
, I
t
,
N
t
, R
t
, AMC
t
, R
k
t
, ?
t
; ?
t
, x
1
t
, x
2
t
,W
t
, W
e
t
, R
k
t
, X
t
, ¯ p
t
, Q
t
, ?
t
, ?(?
t
, ?
t
), G(?
t
, ?
t
), ?
(?
t
, ?
t
),
41
G
(?
t
, ?
t
), ?(?
t
, ?
t
), k(?
t
, ?
t
), s(?
t
, ?
t
), r
n
t
, R
t
, ?
t
}
t=?
t=0
to maximize (1.32), subject to
the competitive equilibrium conditions (as presented in Appendix B, excluding the
monetary policy rule), R
t
? 1, for t > ??; given values of endogenous variables
(including the Lagrange multipliers associated with the competitive equilibrium con-
ditions) for t < 0, and exogenous stochastic processes {?
A
t
, ?
G
t
, and U
t
}
?
t=0
.
52
At the deterministic long-run equilibrium, the Ramsey planner can not achieve
?rst-best level of welfare. The planner has no policy tool (such as factor subsidies)
to undo distortions due to monopolistic competition. Moreover, since the policy rate
cannot a?ect the level of premium in the deterministic long-run, ?nancial frictions
can not be eliminated as well.
53
In the stochastic steady state, however, the policy
tool can be used to balance the ‘tension’ between the three distortions. As will be
suggested by the impulse responses, the optimal in?ation rate is not zero at all times
as would be in standard cashless New-Keynesian models with the aforementioned
factor subsidies.
1.6.2.1 Cyclical Volatilities
A standard result in Ramsey optimal policy literature is that the planner would
like to smooth wedges (which distorts intra- and/or inter-temporal decisions) to
maximize aggregate welfare.
54
Note from Section 1.6.1 that the wedges in the model
economy ?uctuate due to movements in the EFP and aggregate gross mark-up
52
The endogenous objects, ?(?
t
, ?
t
), G(?
t
, ?
t
), ?
(?
t
, ?
t
), G
(?
t
, ?
t
) are related to the debt-
contract problem. See Appendix A2 for details.
53
The premium, in the absence of aggregate shocks, is determined purely within the partial
equilibrium debt-contract framework.
54
Among many others, see Chari and Kehoe (1999), and Chugh and Arseneau (2010).
42
(respectively for each wedge). As shown in Table 1.4 below, the results suggest that
the cyclical volatility of EFP is reduced by 17%, and that of in?ation (which is
intrinsically linked to mark-up) by 28% compared to the decentralized economy.
In addition, EFP being smoother while leverage being rather equally volatile
in the planner’s economy suggests that the planner smooths the sensitivity of pre-
mium to the leverage. I analyze this point more in detail in the next subsection.
Table 1.4: Cyclical Volatilities (%-standard deviations)
Variable Decentralized Economy Planner’s Economy
Y 1.14 1.16
Real Variables C 0.95 0.96
I 2.90 2.86
Q 0.73 0.72
EFP 0.31 0.25
Net Worth 1.48 1.44
Financial Variables Debt 0.28 0.35
Leverage 1.36 1.33
Bankruptcy Rate 0.53 0.44
Monetary Variables Policy Rate 0.16 0.91
In?ation 0.30 0.22
1.6.2.2 Reducing the strength of ?nancial ampli?cation
In the dynamics, the Ramsey planner smoothes ?uctuations in EFP, lowering its
volatility by approximately 17% compared to the decentralized economy.
55
The
way the planner reacts to EFP can be understood by decomposing it into two
parts: sensitivity of EFP to the leverage, h(?
t+1
), and the leverage,
_
1 ?
Nt
QtK
t+1
_
.
56
Simulation-based h(.) for the decentralized economy gets stronger as the leverage
rises for the decentralized economy (see Figure 1.5). For the planner’s economy,
55
A complete stabilization, however, is not optimal since that would imply higher level of ?uc-
tuations in in?ation and hence higher distortions due to price dispersion.
56
See equation (1.7).
43
on the other hand, sensitivity is rather smooth.
57
Accordingly, the spread reacts
smoother in the Ramsey economy as leverage changes. In other words, the planner
achieves a lower strength of ?nancial ampli?cation.
Figure 1.5: Strength of Financial Ampli?cation (Planner’s Economy)
.14
.16
.18
.20
.22
.24
.26
The Elasticity under the Competitive Equilibrium
The Elasticity under the Ramsey Equilibrium
1.02 1.07 1.12
Leverage Ratio
T
h
e
E
l
a
s
t
i
c
i
t
y
o
f
E
F
P
1.6.2.3 Reducing the contribution of uncertainty on business cycles
There are striking di?erences in the contribution of uncertainty shocks on the volatil-
ity of real and ?nancial variables under the benchmark against the Ramsey planner’s
economy (Table 1.5). The relative contribution of uncertainty on the volatility of
most real and ?nancial variables is much lower under the Ramsey economy. On the
other hand, ?uctuations in policy rate, mark-up, price dispersion and in?ation are
driven substantially by uncertainty. In sum, the planner uses the policy rate almost
57
In particular, I ?rst obtain simulated series for the EFP and the leverage for the two economies
(where each economy is simulated for 3000 periods, and the ?rst 500 periods are omitted). Then I
sort the sample according to the leverage, and run an ordinary least squares log-log regression of
EFP on leverage for the ?rst 1000 observations. Then I roll the sample by one observation -with
a ?xed window size-, and obtain the estimate for the elasticity for this sample. Rolling the sample
further and obtaining the slope estimates give out the elasticity series in Figure 1.5.
44
solely due to uncertainty to lessen the contribution of uncertainty on business cycle
?uctuations.
Table 1.5: Variance Decomposition (Decentralized Economy vs. Ramsey Planner’s)
Variable Decentralized Economy Planner’s Economy
TFP+G Shocks Uncertainty Shocks TFP+G Shocks Uncertainty Shocks
Y 96.08 3.92 97.7 2.3
Real Variables C 98.73 1.27 96.05 3.95
I 81.67 18.33 96.54 3.46
Q 81.67 18.33 96.52 3.48
EFP 12.31 87.69 23.05 76.96
Net Worth 81.66 18.34 99.12 0.88
Financial Variables Debt 82.27 17.73 59.4 40.59
Leverage 81.66 18.34 96.96 3.04
Bankruptcy Rate 11.39 88.61 21.07 78.93
Monetary Variables Policy Rate 61.78 38.22 3.34 96.66
In?ation 61.78 38.22 8.8 91.21
Further Insights Mark-up 48.41 51.59 5.19 94.8
Price Dispersion 61.78 38.22 8.8 91.21
1.6.2.4 Impulse Responses
Figure 1.6 provides the impulse responses to a one-standard deviation increase in
productivity for the Ramsey economy (dashed line) against the benchmark decen-
tralized equilibrium (solid line). First, recall from Figure 1.2 that existence of ?nan-
cial ampli?cation dampens the response of in?ation to productivity shocks. Hence,
there is no inherent trade-o? for the planner in neutralizing the distortions due to
?nancial frictions and price dispersion. The planner, endowed with a single tool,
partially neutralizes price stickiness distortion, exerting negligible e?ect on the dy-
namics of ?nancial variables.
58
When the economy is driven by the uncertainty shock, however, there is a no-
ticeable di?erence between the dynamics of decentralized economy and the planner’s
economy (Figure 1.7). The planner would like to smooth ?uctuations in ?nancial
58
See Faia and Monacelli (2005) for a similar result.
45
Figure 1.6: Ramsey Impulse Responses to a 1 sd. increase in total factor
productivity
0 10 20 30 40
0
0.5
1
Output
0 10 20 30 40
0
0.5
1
Consumption
0 10 20 30 40
?0.1
0
0.1
Labor
0 10 20 30 40
0
1
2
3
Investment
0 10 20 30 40
?0.5
0
0.5
1
Asset Price
0 10 20 30 40
0
0.5
1
1.5
Net Worth
0 10 20 30 40
?1.5
?1
?0.5
0
Debt
0 10 20 30 40
?2
?1
0
1
Leverage Ratio
0 10 20 30 40
?10
?5
0
5
Premium (bpts)
0 10 20 30 40
?0.2
0
0.2
Bankruptcy Rate (ppts)
0 10 20 30 40
?0.5
0
0.5
Threshold Prod. (?)
0 10 20 30 40
?0.2
0
0.2
Mark-up
0 10 20 30 40
?0.5
0
0.5
In?ation Rate (ppts)
0 10 20 30 40
?0.2
0
0.2
Policy Rate (ppts)
0 10 20 30 40
?0.1
0
0.1
Real Rate (ppts)
Notes. Solid line: Decentralized economy. Dashed line: Ramsey Planner’s economy.
variables, yet at an expense of higher volatility in in?ation. The intuition lies on
the fact that the planner faces a trade-o? in eliminating ?nancial frictions and price
dispersion. For instance, in response to an unfavorable uncertainty shock, the plan-
ner would like to reduce the real rate to contain movements in the premium. On
the other hand, planner would like to increase the real rate to reduce ?uctuations
in in?ation. In equilibrium, ?nancial frictions, which are more pronounced under
uncertainty shocks, overwhelms price dispersion, and the planner at the margin
chooses to reduce the real rate.
Before studying optimal policy rules, note that it is the existence of price stick-
46
Figure 1.7: Ramsey Impulse Responses to a 1 sd. increase in uncertainty
0 10 20 30 40
?0.2
0
0.2
Output
0 10 20 30 40
?0.2
0
0.2
Consumption
0 10 20 30 40
?0.5
0
0.5
Labor
0 10 20 30 40
?1
?0.5
0
0.5
Investment
0 10 20 30 40
?0.5
0
0.5
Asset Price
0 10 20 30 40
?0.5
0
0.5
Net Worth
0 10 20 30 40
?0.5
0
0.5
Debt
0 10 20 30 40
?0.5
0
0.5
Leverage Ratio
0 10 20 30 40
?20
0
20
40
Premium (bpts)
0 10 20 30 40
?0.5
0
0.5
Bankruptcy Rate (ppts)
0 10 20 30 40
?0.2
0
0.2
Threshold Prod. (?)
0 10 20 30 40
?0.5
0
0.5
Mark-up
0 10 20 30 40
?0.2
0
0.2
In?ation (ppts)
0 10 20 30 40
?1
?0.5
0
0.5
Policy Rate (ppts)
0 10 20 30 40
?1
?0.5
0
0.5
Real Rate (ppts)
Notes. Solid line: Decentralized economy. Dashed line: Ramsey Planner’s economy.
iness that enables the planner to reduce strength of ?nancial ampli?cation (or reduce
the contribution of uncertainty on the business cycles). Without price stickiness,
the policy tool, short-term nominal interest rate, cannot a?ect the real interest rate
and hence real allocations in the economy. In turn, the policy would be ine?ective
in neutralizing the distortions.
59
59
To formally analyze this, I consider the model with only ?nancial market imperfections (hence
no monopolistic competition or price stickiness). The cyclical volatilities and cross-correlations are
provided in Tables 1.9 and 1.10 in the Appendix. Without price stickiness and given symmetric
retailers, there will be no price dispersion (hence no resulting ine?ciencies). In this regard, the
planner has no incentive to smooth ?uctuations in in?ation. Accordingly, in?ation ?uctuates
substantially in the planner’s economy (and leading to frequent violation of zero lower bound for
the interest rate, which I ignore for the sake of this experiment). On the other hand, the planner
would be willing to smooth ?uctuations in the inter-temporal wedge to improve aggregate welfare,
though, unable to do so since the policy rate cannot a?ect real allocations.
47
1.7 Optimal Simple and Implementable Policy Rules
The planner’s problem yields equilibrium behavior of the policy rate as a function
of the state of the economy. Implementing the planner’s policy, hence, requires
the policy maker to observe the equilibrium values of all endogenous state variables
(including lagrange multipliers associated with the equilibrium conditions). Even if
the policy maker could observe the state of the economy, the equilibrium may not
render a unique competitive equilibrium. Hence, it is of particular interest whether a
simple and implementable monetary policy rule that includes only a few observable
macroeconomic variables and that ensures a (locally) unique equilibrium can achieve
an aggregate welfare level virtually identical to that under the planner’s economy.
The monetary policy rule is assumed to have the following form:
log
_
1 +r
n
t
1 +r
n
_
= ?
r
log
_
1 +r
n
t?1
1 +r
n
_
+(1??
r
)
_
?
?
log
_
1 +?
t
1 +?
_
+?
Y
log
_
Y
t
Y
_
+?
F
log
_
F
t
F
__
(1.41)
where F stands for Financial, and denotes either asset price (Q) or external ?nance
premium (EFP). In search for optimal values of ?
r
, ?
?
, ?
Y
, and ?
F
, I restrict
(long-run) in?ation feedback coe?cient to be within [1,3], persistence parameter to
be within [0,1] and other policy rule coe?cients to be within [-3,3]. The lower bound
for ?
?
is to ensure equilibrium determinacy. The upper bound for ?
?
, and the range
of [-3,3] for ?
Y
and ?
F
are set from a practical policy making view.
60
60
To obtain policy rule coe?cients, I search over 50000 alternative policy rules and calculate
conditional welfare for each rule using equation (1.34). Then given the results suggested by the
grid search, I use simulated annealing algorithm to pinpoint the policy rule that maximizes welfare.
48
As suggested by Schmitt-Grohe and Uribe (2006), a stronger policy reaction
than what these bounds suggest might be di?cult to implement in an actual econ-
omy. Moreover, I discuss potential implications of a binding upper bound for in-
?ation feedback coe?cient on the optimal magnitude of responses based on welfare
loss results.
Responding to ?nancial variables.
Con?rming the conventional ?nding in the literature, if the economy is driven
by traditional ?rst-moment shocks, it is optimal not to respond to ?nancial variables
(column 5 in Table 1.6). Consider, for instance, a monetary authority reacting to
asset prices in response to productivity shocks. In particular, ?
r
, ?
?
, and ?
Y
are
set at their optimal values (?
r
= 0.540, ?
?
= 3, ?
Y
= 0), while ?
Q
is set at 0.25 (a
lean-against-the wind policy reaction).
61
Figure 1.8 suggests that such a reaction
to asset prices leads to higher ?uctuations in in?ation, which in turn creates higher
distortions due to relative price dispersion.
If the economy is driven by uncertainty shocks, optimal policy prescribes a
reaction to ?nancial variables. In particular, consider the impulse responses un-
der two alternative policy rules (the optimal policy rule and a Taylor rule (?
r
=
0.85, ?
?
= 1.5, ?
Y
= 0.5/4, ?
EFP
= 0)), versus the Ramsey economy.
62
Figure 1.9
shows that the optimal rules yield dynamics closer to the Ramsey economy.
63
Note
61
One can use a lean-on-the-wind policy reaction to asset prices (?
Q
< 0) as well. This would
just exacerbate the di?erence between optimal and the non-optimal rule.
62
I report the dynamics under the optimal rule with a reaction to premium (?
r
= 0, ?
?
=
2.94, ?
Y
= 0, and ?
EFP
= ?0.681). The optimal rule with a reaction to asset prices yields
virtually the same dynamics.
63
Similarly, one can show that such a response to ?nancial variables would decrease the sensitivity
of EFP to ?uctuations in leverage.
49
Figure 1.8: Responding to Asset Prices -productivity shocks-
0 20 40
0
0.5
1
Output
0 20 40
0
0.5
1
Consumption
0 20 40
0
1
2
3
Investment
0 20 40
?0.5
0
0.5
1
Asset Price
0 20 40
0
0.5
1
1.5
Net Worth
0 20 40
?1.5
?1
?0.5
0
Debt
0 20 40
?1.5
?1
?0.5
0
Leverage Ratio
0 20 40
?10
?5
0
Premium (bpts)
0 20 40
?0.2
?0.1
0
Bankruptcy Rate (ppts)
0 20 40
?1
?0.5
0
Threshold Prod. (?)
0 20 40
?0.1
0
0.1
0.2
Mark-up
0 20 40
?0.5
0
0.5
In?ation Rate (ppts)
0 20 40
?0.4
?0.2
0
Policy Rate (ppts)
0 20 40
?0.05
0
0.05
Real Rate (ppts)
Notes. Solid line: Policy rule with ?
Q
= 0.25 (other policy parameters are as in the optimal rule). Dashed
Line: Optimal Rule.
that although mark-up ?uctuates less under the optimal rule (compared to Ramsey
dynamics), it yields a lower aggregate welfare. The reason lies on the fact that the
premium ?uctuates less under Ramsey economy, implying milder ?uctuations in the
intertemporal wedge. Such a di?erence seems to o?set the welfare loss originated
from higher price dispersion under the Ramsey economy.
If the economy is driven by ?rst-moment as well as uncertainty shocks, then
it is optimal to respond to credit spreads but not to asset prices (Table 1.6). This
50
Figure 1.9: Responding to Asset Prices -uncertainty shocks-
0 5 10
?0.2
0
0.2
Output
0 5 10
?0.2
0
0.2
Consumption
0 5 10
?1
?0.5
0
0.5
Investment
0 5 10
?0.2
0
0.2
Asset Price
0 5 10
?0.5
0
0.5
Net Worth
0 5 10
?0.5
0
0.5
Debt
0 5 10
?0.5
0
0.5
Leverage Ratio
0 5 10
0
10
20
30
Premium (bpts)
0 5 10
0
0.2
0.4
Bankruptcy Rate (ppts)
0 5 10
?0.2
0
0.2
Threshold Prod. (?)
0 5 10
?0.5
0
0.5
Mark-up
0 5 10
?0.2
0
0.2
In?ation (ppts)
0 5 10
?1
?0.5
0
0.5
Policy Rate (ppts)
0 5 10
?1
?0.5
0
0.5
Real Rate (ppts)
Notes. Solid line: Optimal rule. Dashed line: Taylor rule (?
r
=0.85, ?
?
=1.5, and ?
Y
= 0.5/4). Dotted
Line: Ramsey economy.
is mainly due to credit spreads being driven mostly by uncertainty shocks, whereas
asset prices being driven mostly by productivity shocks (see Table 1.3). This is
inline with planner’s motive to mitigate ?uctuations in uncertainty as discussed in
the previous section. The optimal degree of response suggests that in response to a
1% increase in credit spreads, the policy rate should be reduced by 32 basis points.
The optimized rule with a reaction to credit spreads achieves a welfare elvel slightly
less than the strict in?ation stabilization.
Note also that the upper bound for in?ation is hit in this case (when all shocks
51
are present).
64
Since strict in?ation stabilization dominates the optimized rule in
welfare terms (though by a small margin), setting a higher upper bound for in?ation
would imply a higher optimal reaction to in?ation and a decrease in the optimal
magnitude of response to credit spreads. Eventually as one increases the upper
bound, the optimal magnitude of response to credit spreads would be driven down
to zero.
Figure 1.10: Welfare Surfaces (Benchmark Uncertainty versus High Uncertainty)
?3
?2.7
?2.4
?2.1
?1.8
?1.5
?1.2
?0.9
?0.6
?0.3
0
0.3
0.6
0.9
1.9
2.2
2.5
2.8
?132.8
?132.78
?132.76
?132.74
?132.72
?132.7
?132.68
?132.66
Response to Premium
Response to Inflation
C
o
n
d
i
t
i
o
n
a
l
W
e
l
f
a
r
e
Higher
Uncertainty
Benchmark
Uncertainty
For sensitivity analysis, I consider an alternative calibration for uncertainty
shocks (an increase in ?
U
to 0.25).
65
For brevity in the discussion that follows, I will
64
As argued above, the upper bound is set at 3 from a practical policy making view (Schmitt-
Grohe and Uribe, 2006).
65
In particular, I calibrate ?
U
to match the cyclical volatility of the spread between BAA-rated
corporate bond yield and 10-year constant maturity treasury bill, the most volatile spread among
the ones I consider. Joint calibration of ?
?
A, ?
?
G, and ?
U
now implies 0.00808, 0.00764, and
0.02506, respectively.
52
call this case as higher uncertainty. Under higher uncertainty, optimal policy pre-
scription suggests a stronger reaction to premium. In particular, the optimized rule
suggests ?
r
= 0, ?
?
= 3, ?
Y
= 0 and ?
EFP
= ?0.60 (Figure 1.10). Moreover, the
welfare surface under higher uncertainty not only shifts down and induces a stronger
reaction to the premium, but also shows more concavity around the optimal rule.
A zero policy response to the premium under higher uncertainty would then imply
a much higher welfare loss compared to an economy under benchmark uncertainty.
Figure 1.11: Welfare Surfaces (Responding to Uncertainty)
?3
?2.7
?2.4
?2.1
?1.8
?1.5
?1.2
?0.9
?0.6
?0.3
0
0.3
0.6
0.9
1.9
2.2
2.5
2.8
?134.4
?134.2
?134
?133.8
?133.6
?133.4
?133.2
?133
?132.8
?132.6
?132.4
Response to Uncertainty
Response to Inflation
C
o
n
d
i
t
i
o
n
a
l
W
e
l
f
a
r
e
?
Y
=0.1
?
Y
=0.2
?
Y
=0
To provide a further understanding on whether time-variation in cross-sectional
dispersion is welfare detrimental, I next consider normative implications of react-
ing to the uncertainty itself in the policy rule.
66
This point is especially relevant,
66
Note that the deterministic steady state value of the uncertainty shock is equal to zero. Hence,
the relevant part of the policy rule cannot be modi?ed as log deviation of U from its deterministic
value. I accordingly modify the relevant part as ...+?
F
(U).
53
since including asset prices or credit spreads in the policy rule counterfactually as-
sumes that the central bank cannot observe uncertainty. In contrast, the central
bank is able observe uncertainty, and importantly, would like to react directly to
uncertainty, since the Ramsey optimal policy results suggest that the planner would
like reduce the contribution of uncertainty on the business cycles. Welfare surfaces
suggests that policy maker is willing to react to the uncertainty directly in a simple
policy rule (Figure 1.11).
67
Moreover, the welfare surface remains concave for higher degrees of in?ationary
reaction. Essentially, the optimal policy rule that includes uncertainty fares even
better than the strict in?ation stabilization (although slightly), and yields a welfare
gain of 0.0026% in consumption terms.
68
In sum, I conclude that the time variation
in cross-sectional dispersion induce ine?ciencies in the economy. This is why it is
the credit spreads, ?uctuations in which are mostly driven by uncertainty shocks,
call for a negative response, whereas asset prices, ?uctuations in which are driven
mostly by ?rst-moment shocks, call for a zero response in the optimal policy rule.
Responding to in?ation.
Under ?rst-moment shocks, strict in?ation stabilization that completely elimi-
nates distortions due to relative price dispersion turns out to be the welfare-maximizing
67
With optimal policy rule coe?cients ?
r
= 0, ?
?
= 3, ?
Y
= 0 and ?
U
= ?0.20.
68
Interestingly, under this counterfactual scenario in which the policy maker could directly react
to an exogenous state variable, the economy under the optimal policy rule welfare dominates the
Ramsey economy slightly by 0.0022% in consumption terms. This is mainly due to approximating
welfare at t=0 (taking into account lack of certainty at the stochastic steady state). Since the rule
includes one of the exogenous state itself, the resulting correction term becomes closer to zero,
increasing the welfare signi?cantly, leading to this result. This result that the Ramsey planner
might be dominated (even slightly) by an optimal rule is a result also noted in Schmitt-Grohe and
Uribe (2006).
54
policy (Table 1.6). Comparing the impulse responses under strict in?ation stabiliza-
tion and that under Ramsey policy shows that the dynamics of real and ?nancial
variables are almost the same.
69
In a model with ?nancial frictions, the reason
why such an emphasis is given to price stickiness distortion manifests itself in the
simulated volatility of external ?nance premium. In particular, in response to ?rst-
moment shocks, ?uctuations in the premium is unrealistically low, suggesting an
unrealistic low degree of ?nancial ampli?cation. Hence, less emphasis is given to
mitigating ?nancial ampli?cation.
If the economy is driven by uncertainty shocks, the optimal policy allows for
mild ?uctuations in in?ation, inline with Ramsey policy ?ndings. Optimal rules
achieve a welfare higher than the strict in?ation stabilization.
If the economy is driven by all shocks, the price dispersion distortion becomes
more relevant (mainly due to ?rst-moment shocks), and the welfare attained under
the optimal rule is slightly less than that under strict in?ation stabilization (Table
1.6).
Responding to output gap.
If the economy is driven by ?rst-moment shocks, a positive response to out-
put gap exacerbates ?uctuations in average mark-up in the economy, leading to
much higher distortions due to price dispersion.
70
Consider, for instance, in Fig-
69
Shown in the Appendix Figure 1.1g in the Appendix. Curiously though, conditional on the
initial state being the deterministic Ramsey steady state, strict in?ation stabilization welfare dom-
inates the Ramsey economy though by only a negligible amount. A consumer in the Ramsey
economy would prefer a consumption subsidy of 3 ? 10
?7
% to be as well o? as under the strict
in?ation stabilization regime. See Schmitt-Grohe and Uribe (2006) for a similar result.
70
For a detailed discussion, see Schmitt-Grohe and Uribe (2006).
55
ure 1.17 in the Appendix, the model dynamics under the benchmark policy rule
(?
r
= 0.85, ?
?
= 2.309, ?
Y
= 0) and those under the calibrated rule (?
r
= 0.85, ?
?
=
2.309, ?
Y
= 0.593/4). It is evident that an output response reduces ?uctuations
in the premium, yet leads to much higher ?uctuations in average mark-up in the
economy. Welfare losses presented in Table 1.6 suggest that the distortion due to
increase in relative price dispersion outweighs the potential welfare gain from having
a smoother premium. Similarly, a comparison of Taylor rules (with no persistence)
shows that an output reaction of ?
Y
= 0.5 leads to a welfare loss equal to 0.4% in
consumption terms.
71
In response to uncertainty shocks, as evident from welfare surfaces (Figures
1.19 to 1.22 in the Appendix), responding to output gap becomes much less welfare
reducing. For a mild policy reaction to in?ation (such as ?
?
=1.5), a positive policy
response to output might even be welfare improving.
Gradualism in the policy.
The optimality of gradual policy reaction to (?rst-moment) disturbances has
also been recognized in the literature.
72
Such a result implies that monetary policy
should be backward looking. Nevertheless, welfare losses from acting proactively
is negligible. Comparing the optimized rules shows that decreasing the persistence
parameter ?
r
by approximately 0.1 induce a welfare loss less than one-thousandth
of a percentage in consumption terms. Moreover, for ?
?
= 1.5 as in the Taylor
71
In 2005$s, this welfare loss amounts to 24 billions dollars. To get this number, I ?rst calculate
the average real consumption expenditures on non-durables and services for 1989Q1-2009Q1, which
is approximately 6 trillion (in 2005$s). Calculating the fraction of 0.4% then yields the desired
number.
72
See for instance Schmitt-Grohe and Uribe (2006).
56
rule, an increase in the persistence to .85 from nil costs 0.003% of consumption.
Under uncertainty shocks, policy making should be pro-active (no gradual policy
reaction). Yet, welfare losses due to a milder persistence seems negligible. Consider
for instance an increase in the persistence from ?
r
= 0 to ?
r
= 0.85 in standard
Taylor rules reported in Table 1.6. The resulting welfare loss is around 0.003%.
Under a stronger anti-in?ationary stance, the loss would even be lower.
1.8 Further Discussion
The analysis so far shows that policy makers should contain business cycle ?uc-
tuations due to uncertainty, by either directly responding to uncertainty, or more
practically, by responding to credit spreads (which, themselves, are a good proxy
for uncertainty). In this section, with the caveat in mind that the model is rather
simplistic, I provide further insights on this result from a historical perspective.
First, note that the key equation in the ?nancial ampli?cation mechanism -
that relates the external ?nance premium (EFP) to the aggregate leverage ratio
(
QtK
t+1
N
t+1
)- can be expressed as a ‘collateral’ constraint. In particular,
EFP
t
?
R
k
t+1
R
t
=
_
1 ?
N
t+1
Q
t
K
t+1
__
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
)
_
?1
which implies that
AmountBorrowed
¸ .. ¸
Q
t
K
t+1
?N
t+1
=
_
_
1
1 ?EFP
t
_
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
)
_
?1
_
_
NetWorth
¸ .. ¸
N
t+1
57
Hence, ?rms can borrow a certain fraction of their net worth, the fraction
depending on aggregate ?nancial conditions in the economy.
How strong does the planner value marginally relaxing this constraint over the
actual business cycles? Technically, how does the Lagrange multiplier associated
with this constraint evolve over time?
To address this question, I use the stochastic processes for innovations to
TFP, government spending, and cross-sectional dispersion derived from actual US
data for the sample period 1989Q1 to 2009Q1. For uncertainty, I use three di?erent
measures, a macro-level measure, the implied stock market volatility (the VXO), and
two micro-level measures, cross-sectional dispersion of industrial TFP growth, and of
?rm-level stock returns’ growth.
73
For deriving each series of innovations, I estimate
an AR(1) process for cyclical TFP, government spending, and the dispersion series
(or the VXO). Actual series as well as details on the estimation are provided in
Appendix D.
Figure 1.12 suggests that planner’s willingness to relax the ?nancial constraint
shows a rapid deterioration starting in mid-2002 and eventually hits record low
levels by the end of 2006. When industry-level dispersion is used as a measure
of uncertainty, such rapid deterioration starts in 2001 and ceases by 2005. These
all indicate that the planner -who respects the competitive equilibrium conditions-
values relaxing the ?nancial constraint at a historically low level in the run up to
the recent crisis.
73
For the latter two, I use the data set provided by Bloom et al. (2010). You may refer to
http://www.stanford.edu/
~
nbloom/RUBC_data.zip
58
Figure 1.12: Shadow Value of Relaxing the Financial Constraint
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
90 92 94 96 98 00 02 04 06 08
Shadow Value (Uncertainty: Industry-Level)
Shadow Value (Uncertainty: Firm-Level)
Shadow Value (Uncertainty: VXO)
Moreover, marginal bene?t of relaxing the ?nancial constraint follows the dis-
persion (or the VXO) at a great extent.
74
In this regard, uncertainty captures well
how strong the planner values relaxing the constraint. The reason lies on the fact
that uncertainty drives most of the ?uctuations in credit spread, the ease at which
borrowers are able to fund their projects.
1.9 Conclusion
This paper studies normative implications of uncertainty, or as also called in the
literature risk or dispersion shocks, on monetary policy. Uncertainty shocks, having
a direct e?ect on aggregate ?nancial conditions, prescribes that ?nancial variables
per se should matter for monetary policy making.
The results suggests that optimal policy is to contain business cycle ?uctua-
74
See Figure 1.25 in the Appendix for the dispersion or the VXO series.
59
tions due to uncertainty. Moreover, a higher uncertainty makes the planner more
willing to relax the ?nancial constraints. From a practical point of view, however,
the availability and the quality of information on the dispersion may not be available
in real time. Yet, since credit spreads can serve as a good proxy for uncertainty,
responding to credit spreads can be used as a general policy to have better aggre-
gate outcomes. The optimal degree of response is generally less than one-to-one
under various scenarios. A strict in?ation stabilization, compared to the optimal
rule, yields negligible welfare gains. Under ‘higher uncertainty’, the precise degree
to which the policy maker should respond to the spread rises.
Note however that there are many credit spreads in an actual economy, busi-
ness cycle properties of which, although mostly follow a common trend, might dif-
fer during abnormal times. Moreover, potential interaction between ?rst-moment
shocks and uncertainty can also be explored. To the extent ?rst-moment shocks (e.g.
productivity) lead to ?uctuations in cross-sectional dispersion, and accordingly, in-
duce more pronounced distortions in capital supply decisions, optimal policy would
still prescribe a response to credit spreads. The optimal magnitude of response,
though, requires a quantitative exercise. Besides, facing not a single but many mea-
sures of ?nancial stability, monetary authorities, in a real economy, is to conjecture
an optimal response to various types of disturbances (of real and ?nancial types) de-
pending on the quantity and the quality of the information available. These points
are left to future work.
60
Table 1.6: Simple Rules versus Optimal Policy (Baseline Calibration)
First-Moment Shocks ?
r
?
?
?
Y
?
F
?
r
?
?
?
Y
?
EFP
CEV (%)
Taylor Rules
0 1.5 0 0 0.190 0.126 1.180 0.131 0.0092
0 1.5 0.5/4 0 1.197 1.167 1.135 0.123 0.4015
0.85 1.5 0 0 0.169 0.375 1.088 0.101 0.0121
0.85 1.5 0.5/4 0 0.748 1.815 0.794 0.023 0.3050
Benchmark Rule
0.84 1.770 0 - 0.132 0.235 1.124 0.113 0.0022
0.84 1.770 0.640/4 - 0.710 1.482 0.863 0.027 0.2325
Strict In?ation Stabilization - - - - 0.067 0 1.177 0.131 0.000
Ramsey Policy - - - - 0.166 0.064 1.149 0.120 0
Optimized Rules
with Asset Price 0.540 3 0 0 0.092 0.043 1.174 0.129 0.0006
with Premium 0.445 3 0 0 0.093 0.039 1.175 0.130 0.0006
Uncertainty Shocks ?
r
?
?
?
Y
?
F
?
r
?
?
?
Y
?
EFP
CEV (%)
Taylor Rules
0 1.5 0 0 0.252 0.166 0.119 0.270 0.0063
0 1.5 0.5/4 0 0.170 0.078 0.111 0.268 0.0052
0.85 1.5 0 0 0.092 0.229 0.192 0.289 0.0100
0.85 1.5 0.5/4 0 0.042 0.078 0.132 0.275 0.0069
Benchmark Rule
0.84 1.770 0 - 0.094 0.189 0.175 0.285 0.0086
0.84 1.770 0.640/4 - 0.048 0.071 0.129 0.274 0.0062
Strict In?ation Stabilization - - - - 0.116 0 0.094 0.265 0.0033
Ramsey Policy - - - - 0.891 0.206 0.176 0.219 0
Optimized Rules
with Asset Price 0 2.947 0 0.281 0.082 0.042 0.087 0.264 0.0032
with Premium 0 2.921 0 -0.684 0.090 0.031 0.090 0.264 0.0032
First-Moment & Uncertainty Shocks ?
r
?
?
?
Y
?
F
?
r
?
?
?
Y
?
EFP
CEV (%)
Taylor Rules
0 1.5 0 0 0.316 0.208 1.186 0.300 0.0126
0 1.5 0.5/4 0 1.209 1.169 1.141 0.295 0.4037
0.85 1.5 0 0 0.192 0.440 1.105 0.306 0.0191
0.85 1.5 0.5/4 0 0.749 1.187 0.805 0.276 0.3090
Benchmark Rule
0.84 1.770 0 - 0.162 0.301 1.138 0.307 0.0107
0.84 1.770 0.640/4 - 0.712 1.484 0.873 0.275 0.2385
Strict In?ation Stabilization - - - - 0.133 0 1.181 0.296 0.0004
Ramsey Policy - - - - 0.907 0.216 1.162 0.250 0
Optimized Rules
with Asset Price 0 3 0 0 0.186 0.062 1.183 0.297 0.0016
with Premium 0 3 0 -0.325 0.169 0.050 1.181 0.296 0.0014
61
1.10 Appendix - Tables
1.11 Appendix - Figures
Figure 1.13: Long-run equilibria as a function of monopolistic competition
5 10 15 20
0.8
0.9
1
1.1
1.2
1.3
Output
5 10 15 20
0.45
0.5
0.55
0.6
0.65
Consumption
5 10 15 20
0.16
0.18
0.2
0.22
0.24
0.26
0.28
Investment
5 10 15 20
2
4
6
8
10
Total Debt
5 10 15 20
0
1
2
3
4
5
Net Worth
5 10 15 20
1
2
3
4
5
6
7
8
Leverage
5 10 15 20
0
0.5
1
1.5
2
2.5
3
3.5
Bankruptcy Rate (ppts)
5 10 15 20
0
50
100
150
200
250
Premium (bpts)
5 10 15 20
0
1
2
3
4
5
6
x 10
?4
Agg. Monitoring Costs
Notes. Dashed line: No ?nancial frictions (? 0), Solid line: Financial frictions (? = 0.263).
62
Figure 1.14: Long-run equilibria as a function of long-run in?ation
0 0.01 0.02 0.03
0.7
0.8
0.9
1
1.1
Output
0 0.01 0.02 0.03
0.35
0.4
0.45
0.5
0.55
0.6
Consumption
0 0.01 0.02 0.03
0.1
0.15
0.2
0.25
Investment
0 0.01 0.02 0.03
2
4
6
8
10
Total Debt
0 0.01 0.02 0.03
0
1
2
3
4
Net Worth
0 0.01 0.02 0.03
0
2
4
6
8
Leverage
0 0.01 0.02 0.03
0
1
2
3
4
Bankruptcy Rate (ppts)
0 0.01 0.02 0.03
?50
0
50
100
150
200
250
Premium (bpts)
0 0.01 0.02 0.03
?2
0
2
4
6
x 10
?4
Agg. Monitoring Costs
Notes. Dashed line: No ?nancial frictions (? 0), Solid line: Financial frictions (? = 0.263).
63
Table 1.7: Business Cycle Statistics -Decentralized Economy-
Real Variables Financial Variables Monetary Variables
Y C I Q EFP Net Worth Debt Leverage Bankruptcy Rate Policy Rate In?ation
Std. Dev (%) 1.14 0.95 2.90 0.73 0.31 1.48 0.28 1.36 0.53 0.16 0.30
Auto. corr. 0.73 0.75 0.72 0.72 0.66 0.72 0.93 0.70 0.66 0.85 0.32
Real Variables
Y 1 0.93 0.97 0.96 -0.50 0.96 0.53 -0.94 -0.48 -0.58 -0.44
C 1 0.86 0.85 -0.23 0.85 0.60 -0.81 -0.21 -0.81 -0.62
I 1 1.00 -0.68 0.99 0.47 -0.99 -0.67 -0.44 -0.34
Financial Variables
Q 1 -0.68 0.98 0.40 -0.99 -0.67 -0.42 -0.35
Premium 1 -0.69 -0.19 0.71 1.00 -0.28 -0.23
Net Worth 1 0.52 -0.98 -0.68 -0.42 -0.34
Debt 1 -0.36 -0.19 -0.62 -0.02
Leverage 1 0.70 0.33 0.37
Bankruptcy Rate 1 -0.29 -0.24
Monetary Variables
Policy Rate 1 0.54
In?ation 1
6
4
Table 1.8: Business Cycle Statistics -Planner’s Economy-
Real Variables Financial Variables Monetary Variables
Y C I Q EFP Net Worth Debt Leverage Bankruptcy Rate Policy Rate In?ation
Std. Dev (%) 1.16 0.96 2.86 0.72 0.25 1.44 0.35 1.33 0.44 0.91 0.22
Auto. corr. 0.71 0.71 0.71 0.71 0.66 0.72 0.83 0.71 0.66 -0.15 -0.37
Real Variables
Y 1 0.97 0.98 0.97 -0.44 0.98 0.46 -0.95 -0.42 -0.13 0.05
C 1 0.96 0.95 -0.34 0.98 0.47 -0.95 -0.32 -0.21 0.07
I 1 1.00 -0.54 0.99 0.46 -0.95 -0.52 -0.08 0.05
Financial Variables
Q 1 -0.55 0.98 0.40 -0.95 -0.53 -0.07 0.04
Premium 1 -0.46 -0.51 0.36 1.00 -0.52 0.20
Net Worth 1 0.44 -0.97 -0.44 -0.07 -0.01
Debt 1 -0.21 -0.51 -0.15 0.36
Leverage 1 0.34 0.04 0.11
Bankruptcy Rate 1 -0.53 0.20
Monetary Variables
Policy Rate 1 -0.85
In?ation 1
6
5
Table 1.9: Business Cycle Statistics (only ?nancial frictions) -Decentralized Economy-
Real Variables Financial Variables Monetary Variables
Y C I Q EFP Net Worth Debt Leverage Bankruptcy Rate Policy Rate In?ation
Std. Dev (%) 1.20 0.92 3.00 0.76 0.30 1.57 0.25 1.46 0.51 0.17 0.44
Auto. corr. 0.72 0.72 0.71 0.71 0.66 0.71 0.93 0.71 0.66 0.69 -0.05
Real Variables
Y 1 0.95 0.98 0.97 -0.51 0.98 0.46 -0.98 -0.49 -0.55 -0.33
C 1 0.90 0.89 -0.28 0.92 0.50 -0.90 -0.26 -0.78 -0.45
I 1 1.00 -0.65 0.99 0.42 -1.00 -0.63 -0.46 -0.29
Financial Variables
Q 1 -0.65 0.98 0.34 -1.00 -0.63 -0.44 -0.29
Premium 1 -0.63 -0.29 0.63 1.00 -0.34 -0.20
Net Worth 1 0.50 -0.99 -0.62 -0.48 -0.29
Debt 1 -0.37 -0.29 -0.33 0.02
Leverage 1 0.61 0.46 0.31
Bankruptcy Rate 1 -0.35 -0.21
Monetary Variables
Policy Rate 1 0.57
In?ation 1
6
6
Table 1.10: Business Cycle Statistics (only ?nancial frictions) -Planner’s Economy-
Real Variables Financial Variables Monetary Variables
Y C I Q EFP Net Worth Debt Leverage Bankruptcy Rate Policy Rate In?ation
Std. Dev (%) 1.20 0.92 3.01 0.76 0.30 1.57 0.25 1.47 0.51 3682330310.15 3646188341.77
Auto. corr. 0.72 0.72 0.71 0.71 0.66 0.71 0.93 0.71 0.66 0.43 0.43
Real Variables
Y 1 0.95 0.98 0.97 -0.51 0.98 0.45 -0.98 -0.49 0.15 0.10
C 1 0.90 0.89 -0.28 0.92 0.50 -0.90 -0.27 0.43 0.29
I 1 1.00 -0.65 0.99 0.42 -1.00 -0.63 0.05 0.02
Financial Variables
Q 1 -0.65 0.98 0.34 -1.00 -0.63 0.04 0.01
Premium 1 -0.63 -0.29 0.63 1.00 0.66 0.45
Net Worth 1 0.50 -0.99 -0.62 0.07 0.03
Debt 1 -0.37 -0.29 0.05 0.10
Leverage 1 0.62 -0.06 -0.02
Bankruptcy Rate 1 0.67 0.46
Monetary Variables
Policy Rate 1 0.43
In?ation 1
6
7
Figure 1.15: Impulse Responses to a 1 sd. increase in government spending
0 20 40
0
0.1
0.2
Output
0 20 40
?0.2
0
0.2
Consumption
0 20 40
?0.1
0
0.1
0.2
Labor
0 20 40
?0.5
0
0.5
Investment
0 20 40
?0.1
0
0.1
Asset Price
0 20 40
?0.1
0
0.1
Net Worth
0 20 40
?0.1
0
0.1
Debt
0 20 40
?0.1
0
0.1
Leverage Ratio
0 20 40
?1
?0.5
0
0.5
Premium (bpts)
0 20 40
?0.02
?0.01
0
0.01
Bankruptcy Rate (ppts)
0 20 40
?0.04
?0.02
0
Threshold Prod. (?)
0 20 40
?0.1
0
0.1
Mark-up
0 20 40
?0.1
0
0.1
In?ation Rate (ppts)
0 20 40
?0.1
0
0.1
Policy Rate (ppts)
0 20 40
?0.05
0
0.05
Real Rate (ppts)
Notes. Solid line: Financial ampli?cation, Dashed line: No ?nancial ampli?cation (EFP is
?xed). Unless otherwise noted, the responses are in terms of percentage deviation from the
respective deterministic steady states.
68
Figure 1.16: Strict In?ation Stabilization versus Ramsey Policy -productivity
shocks-
0 20 40
0
0.5
1
Output
0 20 40
0
0.5
1
Consumption
0 20 40
0
1
2
3
Investment
0 20 40
?0.5
0
0.5
1
Asset Price
0 20 40
0
0.5
1
1.5
Net Worth
0 20 40
?1.5
?1
?0.5
0
Debt
0 20 40
?2
?1
0
1
Leverage Ratio
0 20 40
?10
?5
0
5
Premium (bpts)
0 20 40
?0.2
0
0.2
Bankruptcy Rate (ppts)
0 20 40
?1
?0.5
0
0.5
Threshold Prod. (?)
0 20 40
?0.1
0
0.1
Mark-up
0 20 40
?0.1
0
0.1
In?ation Rate (ppts)
0 20 40
?0.1
0
0.1
Policy Rate (ppts)
0 20 40
?0.1
0
0.1
Real Rate (ppts)
Notes. Solid line: Strict in?ation stabilization. Dashed Line: Ramsey economy.
69
Figure 1.17: Responding to Output Gap -productivity shocks-
0 20 40
0
0.5
1
Output
0 20 40
0
0.5
1
Consumption
0 20 40
?1
?0.5
0
0.5
Labor
0 20 40
0
1
2
Investment
0 20 40
?0.5
0
0.5
Asset Price
0 20 40
0
0.5
1
1.5
Net Worth
0 20 40
?1
?0.5
0
Debt
0 20 40
?1
?0.5
0
0.5
Leverage Ratio
0 20 40
?10
?5
0
5
Premium (bpts)
0 20 40
?0.2
0
0.2
Bankruptcy Rate (ppts)
0 20 40
?0.5
0
0.5
Threshold Prod. (?)
0 20 40
0
0.5
1
Mark-up
0 20 40
?2
?1
0
In?ation Rate (ppts)
0 20 40
?1
?0.5
0
Policy Rate (ppts)
0 20 40
?0.5
0
0.5
1
Real Rate (ppts)
Notes. Solid line: Benchmark policy rule with a response to output gap (?
r
=0.84, ?
?
=1.770,
?
Y
= 0.640/4). Dashed Line: Benchmark policy rule (?
r
=0.84, ?
?
=1.770).
70
Figure 1.18: Responding to Output Gap -uncertainty shocks-
0 10 20 30 40
?0.2
0
0.2
Output
0 10 20 30 40
?0.2
0
0.2
Consumption
0 10 20 30 40
?1
?0.5
0
0.5
Investment
0 10 20 30 40
?0.5
0
0.5
Asset Price
0 10 20 30 40
?1
?0.5
0
0.5
Net Worth
0 10 20 30 40
?0.5
0
0.5
1
Debt
0 10 20 30 40
?0.5
0
0.5
Leverage Ratio
0 10 20 30 40
?20
0
20
40
Premium (bpts)
0 10 20 30 40
?0.5
0
0.5
Bankruptcy Rate (ppts)
0 10 20 30 40
?0.2
0
0.2
Threshold Prod. (?)
0 10 20 30 40
?0.5
0
0.5
Mark-up
0 10 20 30 40
?0.5
0
0.5
In?ation (ppts)
0 10 20 30 40
?1
?0.5
0
0.5
Policy Rate (ppts)
0 10 20 30 40
?1
?0.5
0
0.5
Real Rate (ppts)
Notes. Solid line: Taylor rule with policy intertia (?
r
=0.85, ?
?
=1.5, and ?
Y
= 0). Dashed
Line: Taylor rule with policy inertia and response to output gap (?
r
=0.85, ?
?
=1.5, and ?
Y
=
0.5/4). Dotted Line: Ramsey economy.
Figure 1.19: Welfare Surface -TFP and G Shocks-
?0.5
?0.2
0.1
0.4
0.7
1
1.3
1.6
1.9
1.6
1.9
2.2
2.5
2.8
?136.5
?136
?135.5
?135
?134.5
?134
?133.5
?133
?132.5
Response to Asset Price
Response to Inflation
C
o
n
d
it
io
n
a
l
W
e
lf
a
r
e
?
Y
=0.2
?
Y
=0.4
?
Y
=0
Notes. ?
r
is set at its optimal value.
71
Figure 1.20: Welfare Surface -Uncertainty Shock-
?0.5
?0.2
0.1
0.4
0.7
1
1.3
1.6
1.9
1.9
2.2
2.5
2.8
?132.705
?132.7
?132.695
?132.69
?132.685
?132.68
?132.675
?132.67
Response to Asset Price
Response to Inflation
C
o
n
d
it
io
n
a
l
W
e
lf
a
r
e
?
Y
=0.2
?
Y
=0
?
Y
=0.4
Notes. ?
r
is set at its optimal value.
Figure 1.21: Welfare Surface -All Shocks-
?0.5
?0.2
0.1
0.4
0.7
1
1.3
1.6
1.9
1.9
2.2
2.5
2.8
?136
?135.5
?135
?134.5
?134
?133.5
?133
?132.5
Response to Asset Price
Response to Inflation
C
o
n
d
i
t
i
o
n
a
l
W
e
l
f
a
r
e
?
Y
=0.2
?
Y
=0.4
?
Y
=0
Notes. ?
r
is set at its optimal value.
72
Figure 1.22: Welfare Surface -Uncertainty Shock-
?3
?2.7
?2.4
?2.1
?1.8
?1.5
?1.2
?0.9
?0.6
?0.3
0
0.3
0.6
0.9
1.9
2.2
2.5
2.8
?132.69
?132.685
?132.68
?132.675
?132.67
?132.665
Response to Premium
Response to Inflation
C
o
n
d
it
io
n
a
l
W
e
lf
a
r
e
?
Y
=0
?
Y
=0.2
?
Y
=0.4
Notes. ?
r
is set at its optimal value.
Figure 1.23: Welfare Surface -All Shocks-
?3
?2.7
?2.4
?2.1
?1.8
?1.5
?1.2
?0.9
?0.6
?0.3
0
0.3
0.6
0.9
1.9
2.2
2.5
2.8
?132.72
?132.71
?132.7
?132.69
?132.68
?132.67
?132.66
Response to Premium
Response to Inflation
C
o
n
d
it
io
n
a
l
W
e
lf
a
r
e
Notes. ?
r
and ?
Y
are set at their optimal values. The welfare surfaces under ?
Y
= 0.2 or
?
Y
= 0.4 are not presented for presentation purposes. They are much lower than the one
presented.
73
1.12 Appendix - Competitive Equilibrium, Calibration and Further
Discussions
Appendix A1. Derivation of ex-post marginal real return to capital
The ex-post real marginal return to holding capital from t?1 to t for an entrepreneur
i is given by
R
i,k
t
=
?
1
Xt
Y
it
+?
it
Q
t
(1 ??)K
it
Q
t?1
K
it
(1.42)
= ?
it
1
Xt
?Yt
K
it
+Q
t
(1 ??)
Q
t?1
(1.43)
where Y
t
is the average wholesale production across the entrepreneurs (Y
it
=
?
it
Y
t
). Hence, the expected average return to capital across the entrepreneurs,
E
t?1
R
i,k
t
, is
E
t?1
_
R
i,k
t
_
= E
t?1
1
Xt
?Yt
K
it
+Q
t
(1 ??)
Q
t?1
(1.44)
under the assumption that E
t?1
?
it
= 1 and CRTS production technology. The
ex-post return to capital, R
k
t
(?
t
; ?
t
), therefore, is the right hand side of the above
equation without the expectation operator.
74
Appendix A2 - Debt Contract Problem
The intermediaries are assumed to operate in perfectly competitive markets, earning
zero pro?ts in equilibrium and perfectly diversifying any idiosyncratic risk. Hence,
the opportunity cost of funds that the intermediaries face is the economy-wide real
return of holding riskless government bonds from t ?1 to t, R
t
. The debt contract
problem should then satisfy that the intermediary earns his opportunity costs in
expected terms, i.e.
E
t?1
_
[1 ?F(?
it
)]Z
i
t
(?
t
; ?
t
)B
i
t
+ (1 ?µ)
_
?
it
0
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
dF(?
it
)
_
= R
t
B
i
t
(1.45)
The ?rst term inside the square brackets amounts to the total receipts that
the intermediary earns from the non-defaulting entrepreneurs. The second term is
the receipts from the defaulting entrepreneurs which amounts to the net wholesale
revenue (after proportional monitoring costs are incurred).
On the ?ip side, the expected return to holding capital for the entrepreneur is
given by
E
t?1
__
?
?
it
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
dF(?
it
) ?[1 ?F(?
it
)]?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
(1.46)
The ?rst term inside the square brackets is the expected total return to capital
(taking into account the probability that the entrepreneur i’s idiosyncratic produc-
75
tivity ?
it
is above the threshold level ?
it
). The second term is the amount that
the non-defaulting entrepreneur pays to the intermediary. Note that in the case of
no-default, the entrepreneur keeps the equity (?
it
??
it
)R
k
t
(?
t
; ?
t
)Q
t?1
K
it
.
Hence, the entrepreneur’s maximization problem is
max
K
it
,?
it
E
t?1
__
?
?
it
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
dF(?
it
) ?[1 ?F(?
it
)]?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
(1.47)
subject to
E
t?1
_
[1 ?F(?
it
)]Z
i
t
(?
t
; ?
t
)B
i
t
+ (1 ?µ)
_
?
it
0
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
dF(?
it
)
_
= R
t
B
i
t
(1.48)
The entrepreneur takes net worth and asset prices as given in the maximization
problem. Before deriving the ?rst-order necessary conditions, I will manipulate the
objective function and the constraint to make the problem more tractable.
After algebraic manipulation, the entrepreneur’s expected return to holding
capital can be expressed as
E
t?1
__
1 ?
_
?
it
_
?
?
it
dF(?
it
) +
_
?
it
0
?
it
dF(?
it
)
__
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
(1.49)
and the zero-pro?t condition as
76
E
t?1
___
?
it
_
?
?
it
dF(?
it
) +
_
?
it
0
?
it
dF(?
it
)
_
?µ
_
?
it
0
?
it
dF(?
it
)
_
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
= R
t
B
i
t
(1.50)
Now let
?(?
it
) = ?
it
_
?
?
it
dF(?
it
) +
_
?
it
0
?
it
dF(?
it
(1.51)
and
G(?
it
) =
_
?
it
0
?
it
dF(?
it
) (1.52)
Then, the maximization problem can be expressed shortly as
max
Kt,?
it
E
t?1
_
1 ?(?(?
it
)) R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
(1.53)
subject to
E
t?1
_
(?(?
it
) ?µG(?
it
)) R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
= R
t
_
Q
t?1
K
i
t
?N
it
_
(1.54)
where 1 ? ?(?
it
) denotes the net share of contractual return going to the en-
trepreneur, and ?(?
it
) ? µG(?
it
) is the net contractual share of the lender. As
optimality conditions are presented in Appendix A3 of BGG (p.1385), then one can
show that ex-ante external ?nance premium is an increasing function of leverage.
77
Moreover, in simulating the model, unexpected changes in return to capital due
to aggregate shocks can be accommodated using partial-equilibrium debt contract
problem optimality conditions together with ex-post marginal real return to capital
(as de?ned in Appendix A1).
75
I now present the equilibrium debt contract optimality conditions where R
k
t+1
is assumed to known in advance and ?
i
is assumed to be log-normal. Let ?(?) =
_
?
0
?f(?)d? + ?
_
?
?
f(?)d? denote the expected payo? share of the lender. Note
that 1 ??
(?) = F(?) denotes the bankruptcy rate of entrepreneurs. Let µG(?) ?
µ
_
?
0
?f(?)d? denote the expected monitoring costs. Hence, the expected net payo?
share to the lender is ?(?) ?µG(?), and the normalized payo? to the entrepreneur
is 1 ??(?). Accordingly, the optimal contract problem is
max
K
t+1
,(?)
(1 ??(?))R
k
t+1
Q
t
K
t+1
subject to
(?(?) ?µG(?)) R
k
t+1
Q
t
K
t+1
= R
t
(Q
t
K
t+1
?N
t+1
)
The problem is easier to solve using k =
QtK
t+1
N
t+1
the capital-to-wealth ratio
(which is equal to one plus the leverage ratio -the ratio of external debt to the net
worth-) as the choice variable. Let s =
R
k
t+1
Rt
denote the external ?nance premium
75
Indeed, simulation results show that the ex-ante premium is an increasing function of leverage
(regardless of aggregate shocks), whereas the ex-post premium may or may not be an increasing
function of leverage, depending on various factors, one of which is the policy rule. A very aggressive
policy response to output gap, for instance, might induce a pro-cyclical ex-post premium.
78
over the riskless rate. Then, the problem becomes
max
k,(?)
(1 ??(?))sk
subject to
(?(?) ?µG(?)) sk = k ?1
Assuming an interior solution, the ?rst-order optimality conditions imply
?
(?) ??(?)(?(?) ?µG
(?)) = 0
?(?)s ??(?) = 0
(?(?) ?µG(?))sk ?(k ?1) = 0
where ? ? 1 ??(?) +?(?)(?(?) ?µG(?)).
76
Rearranging gives
s(?) =
?(?)
?(?)
76
A su?cient condition for an interior solution is
s <
1
?(?
?
) ?µG(?
?
)
? s
?
79
k(?) =
?(?)
1 ??(?)
and
?(?) =
?
(?)
?
(?) ?µG
(?)
.
BGG shows that s
(?) > 0 for s > 1 su?ciently low. Then,
k(?) = ?(s(?))
where ?
> 0. Using the expressions for the return to capital, the evolution of net
worth, and the parameters, one can deduce ?. The equation above implies that the
external ?nance premium depends inversely on the capital-to-net-worth ratio.
The algebraic expressions for ?(?) and ?(?) ? µG(?) can be derived by as-
suming that ? is log-normally distributed. In particular, let ln(?) ? N(?
1
2
?
2
?
, ?
2
?
).
Then using the central limit theorem, z ? (ln(?) +0.5?
2
)/? is distributed standard
normal. Hence, the set of equations characterizing the debt contract problem is
z = (log(?) + 0.5?
2
t
)/?
t
?(?) = ?(z ??
t
) +?(1 ??(z))
80
?(?) ?µG(?) = (1 ?µ)?(z ??
t
) +?(1 ??(z))
?
(?) = ?(z ??
t
) + (1 ?(?(z)) ?
?(z)
?
t
?
(?) ?µG
(?) = ?
(?) ?µ
?(z ??
t
)
??
t
?(?) =
?
(?)
?
(?) ?µG
(?)
k(?) = 1 + (?(?) ? (?(?) ?µG(?))/(1 ??(?))
s(?) = ?(?)/((1 ??(?)) ? k(?))
where k(?) is the equilibrium capital to wealth ratio (
QtK
t+1
N
t+1
), and s(?) is the ex-
ternal ?nance premium over the riskless rate.
81
Appendix A3. Retailers’ Problem
Let y
t
(j) be the output of retailer j, and Y
f
t
the ?nal good. We assume that the
?nal goods are produced via the following Dixit-Stiglitz aggregator with elasticity
of substitution :
Y
f
t
=
__
1
0
y
t
(j)
1?
1
_
1
1?
1
(1.55)
and sold at a price of P
t
which satis?es
P
t
=
__
1
0
P
t
(j)
1?
dj
_
1
1?
(1.56)
where P
t
(j) is the price of the retail good j. The demand for each retail good
satis?es the following iso-elastic demand curve:
y
t
(j) =
_
P
t
(j)
P
t
_
?
Y
f
t
(1.57)
The retailers, those who are allowed to change their prices, maximize their
pro?ts given this demand curve and given the price of wholesale goods. In particular,
let P
?
t
denote the price set by retailers who are allowed to change their price at t,
y
?
(j) be the demand given this price, and P
t
the aggregate price level for the ?nal
goods. Then, the retailers’ maximization problem is
max
P
?
t
E
t
?
s=t
?
t,s
?
s?t
P
?
t
?P
W
s
P
s
y
?
s
(j) (1.58)
82
subject to
y
?
s
(j) =
_
P
?
t
P
s
_
?
Y
f
s
?s ? t (1.59)
where ?
t,s
is the shareholders’ (households’) intertemporal elasticity of substitution
which is taken as given by the retailers.
Appendix A4. Deriving the New-Keynesian Phillips Curve in recursive
format
Let
x
1
t
= E
t
?
s=t
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
?
t
P
s
_
(1.60)
=
_
P
?
t
P
t
_
1?
Y
f
t
+E
t
?
s=t+1
?
t,s
?
s?t
_
P
?
t
P
s
_
1?
Y
f
s
=
_
P
?
t
P
t
_
1?
Y
f
t
+E
t
?
t,t+1
?
_
P
?
t
P
?
t+1
_
1?
E
t+1
?
s=t+1
?
t+1,s
?
s?t?1
_
P
?
t+1
P
s
_
1?
Y
f
s
=
_
P
?
t
P
t
_
1?
Y
f
t
+E
t
?
t,t+1
?
_
P
?
t
P
?
t+1
_
1?
x
1
t+1
De?ning ¯ p
t
=
P
?
t
Pt
, we have
83
= ¯ p
t
1?
Y
f
t
+E
t
?
t,t+1
?(1 +?
t+1
)
?1
_
¯ p
t
¯ p
t+1
_
1?
x
1
t+1
Similarly,
x
2
t
= E
t
?
s=t
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
w
s
P
s
_
(1.61)
=
_
P
?
t
P
t
_
?
Y
f
t
_
P
w
t
P
t
_
+E
t
?
s=t+1
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
w
s
P
s
_
=
_
P
?
t
P
t
_
?
Y
f
t
_
P
w
t
P
t
_
+E
t
?
t,t+1
?
_
P
?
t
P
?
t+1
_
?
E
t+1
?
s=t+1
?
t+1,s
?
s?t?1
_
P
?
t+1
P
s
_
?
Y
f
s
_
P
w
s
P
s
_
=
_
P
?
t
P
t
_
?
Y
f
t
_
P
w
t
P
t
_
+E
t
?
t,t+1
?
_
P
?
t
P
?
t+1
_
?
x
2
t+1
= ¯ p
t
?
Y
f
t
1
X
t
+E
t
?
t,t+1
?(1 +?
t+1
)
_
¯ p
t
¯ p
t+1
_
?
x
2
t+1
84
Appendix A5. Deriving the Demand for the Final Goods
For any given level of demand for the composite consumption good C
t
, the demand
for each c
it
solves the problem of minimizing total expenditures,
_
1
0
P
it
c
it
di subject
to the aggregation constraint C
t
=
_
_
1
0
c
1?
1
it
di
_ 1
1?
1
, where P
it
is the nominal price
of variety c
it
. The solution to this problem yields the optimal demand for c
it
which
satis?es
c
it
=
_
P
it
P
t
_
?
C
t
(1.62)
where the aggregate price P
t
is
P
t
=
__
1
0
P
1?
it
di
_
1
1?
(1.63)
Similarly, the investment good I
t
is assumed to be a composite good made with
varieties i
it
, satisfying I
t
=
_
_
1
0
i
1?
1
it
di
_ 1
1?
1
. Then, capital producers minimize the
total expenditure of buying investment goods,
_
1
0
P
it
i
it
di, which implies a demand
for i
it
satisfying i
it
=
_
P
it
Pt
_
?
I
t
.
For a given level of G
t
, the government minimizes the total cost of absorbing
G
t
. Hence, the public demand for each retail good j is given by g
jt
=
_
P
jt
Pt
_
?
G
t
.
Appendix A6. Deriving S
t
in recursive format
Let 1?? measure of retailers choose a price level P
?
t
at the (symmetric) equilibrium,
and the remaining measure of retailers does not change their prices. Those who have
85
not changed their prices in the current period, however, might have been allowed to
change their prices (with probability 1 ??) and choose P
?
t?1
in the previous period.
Similarly going backwards, one can get a recursive representation for S
t
. Namely,
S
t
?
_
1
0
_
P
it
P
t
_
?
di
= (1 ??)
_
P
?
t
P
t
_
?
+?
_
_
(1 ??)
_
P
?
t?1
P
t
_
?
+ (1 ??)?
_
P
?
t?2
P
t
_
?
+...
_
_
= (1 ??)
_
P
?
t
P
t
_
?
+?
_
P
t?1
P
t
_
?
_
_
(1 ??)
_
P
?
t?1
P
t?1
_
?
+ (1 ??)?
_
P
?
t?2
P
t?1
_
?
+...
_
_
= (1 ??)
_
P
?
t
P
t
_
?
+?
_
P
t?1
P
t
_
?
S
t?1
= (1 ??) ¯ p
t
?
+??
S
t?1
(1.64)
Appendix B - Competitive Equilibrium
The competitive equilibrium for this economy is a set of endogenous objects {C
t
, H
t
, H
e
t
, K
t
, I
t
,
N
t
, R
t
, AMC
t
, R
k
t
, ?
t
; ?
t
, x
1
t
, x
2
t
,W
t
, W
e
t
, R
k
t
, X
t
, ¯ p
t
, Q
t
, ?
t
, ?(?
t
), G(?
t
), ?
(?
t
), G
(?
t
), ?(?
t
),
k(?
t
), s(?
t
)}
t=?
t=0
, given exogenous stochastic processes A
t
, G
t
, ?
t
, the long-run in?a-
86
tion ?, the parameters and the functional forms, such that the following block of
equations are satis?ed:
• The Households:
?U(t)
?C
t
= ?R
t
E
t
_
?U(t + 1)
?C
t+1
_
W
t
= ?
?U(t)
?Ht
?U(t)
?Ct
• The Evolution of Relative Price and the New-Keynesian Phillips Curve:
1 = ?(1 +?)
?1+
+ (1 ??) ¯ p
t
1?
x
1
t
= ¯ p
t
1?
Y
f
t
+E
t
?
t,t+1
?(1 +?
t+1
)
?1
_
¯ p
t
¯ p
t+1
_
1?
x
1
t+1
x
2
t
= ¯ p
t
?
Y
f
t
1
X
t
+E
t
?
t,t+1
?(1 +?
t+1
)
_
¯ p
t
¯ p
t+1
_
?
x
2
t+1
x
1
t
=
?1
x
2
t
• Aggregate Resource Constraint
87
Y
t
= C
t
+C
e
t
+I
t
+G
t
+AMC
t
Y
t
?C
e
t
?AMC
t
=
1
?
t
; ?
t
(F(K
t
, H
t
, H
e
t
) ?C
e
t
?AMC
t
)
?
t
; ?
t
= (1 ??)¯ p
?
t
+??
t
S
t?1
where
AMC
t
= µ ?
_
?
0
?F(?)R
k
t
Q
t?1
K
t
• The Optimal Contract Problem
z = (log(?) + 0.5?
2
t
)/?
t
?(?) = ?(z ??
t
) +?(1 ??(z))
?(?) ?µG(?) = (1 ?µ)?(z ??
t
) +?(1 ??(z))
88
?
(?) = ?(z ??
t
) + (1 ?(?(z)) ?
?(z)
?
t
?
(?) ?µG
(?) = ?
(?) ?µ
?(z ??
t
)
??
t
?(?) =
?
(?)
?
(?) ?µG
(?)
k(?) = 1 + (?(?) ? (?(?) ?µG(?))/(1 ??(?))
s(?) = ?(?)/((1 ??(?)) ? k(?))
where k(?) is the equilibrium capital to wealth ratio (
QtK
t+1
N
t+1
), and s(?) is the ex-
ternal ?nance premium over the riskless rate.
• Capital Accumulation and Investment Demand
E
t
R
k
t+1
= E
t
_
_
1
X
t+1
?Y
t+1
K
t+1
+ (1 ??)Q
t+1
Q
t
_
_
89
E
t
R
k
t+1
= R
t
s(?)
Q
t
=
_
?
_
I
t
K
t
_
_
?1
K
t+1
= (1 ??)K
t
+K
t
?
_
I
t
K
t
_
where ?
_
It
Kt
_
=
It
Kt
?
?
k
2
_
It
Kt
??
_
2
• Labor Demands
W
t
= (1 ??)?
Y
t
H
t
1
X
t
W
e
t
= (1 ??)(1 ??)
Y
t
H
e
t
1
X
t
H
e
t
= 1
• Evolution of Net Worth and Entrepreneurial Consumption
90
N
t+1
= ?
t
_
R
k
t
Q
t?1
K
t
?
_
R
t
+
AMC
t
Q
t?1
K
t
?N
t
_
? (Q
t?1
K
t
?N
t
)
_
+W
e
t
?
e
t
= (1 ??
t
)
_
R
k
t
Q
t?1
K
t
?E
t?1
R
k
t
B
t
_
• Exogenous Processes
log(A
t
) = ?
A
? log(A
t?1
) +?
A
t
log(G
t
) = (1 ??
G
)log(G) +?
G
log(G
t?1
) +?
G
t
log(?
t
) = (1 ??
?
)log(?) +?
?
log(?
t?1
) +U
t
• Monetary Policy Rule and the Fiscal Policy
log
_
1 +r
n
t
1 +r
n
_
= ?
r
log
_
1 +r
n
t?1
1 +r
n
_
+(1??
r
)
_
?
?
log
_
1 +?
t
1 +?
_
+?
Y
log
_
Y
t
Y
_
+?
F
log
_
F
t
F
__
where r
n
t
? 0, R
t
=
1+r
n
t
1+?
t+1
, 1 +? = ?(1 +r
n
), ? = 0 or = 1.0266
1/4
.
G
t
= T
t
91
Appendix C- Data De?nitions
The data is over the period 1989:Q1-2009:Q1, and is taken from Federal Reserve
St.Louis FRED. All the statistics are based on cyclical components of the variables
(based on HP ?lter with a smoothing parameter 1600). The cyclical volatility is
de?ned as the log-deviation of a variable from its HP-trend.
Consumption (C) de?ned as the sum of real personal consumption expendi-
tures of non-durable goods and services.
Investment (I) is the sum of real personal consumption expenditures on durables
and real gross domestic private investment.
Government Expenditures (G)- is de?ned as the real government consumption
expenditures and gross investment.
Real GDP (Y ) is the sum of C, I, and G as de?ned above.
Labor hours (H)- is the the average private labor hours times the total number
of workers.
External Finance Premium (EFP)- is the average of the (annualized) yield
spreads between (i) prime-lending rate and 6-month constant maturity treasury bill,
(ii) prime-lending rate and 3-month constant maturity treasury bill, (iii) Moody’s
BAA-rated and AAA-rated corporate bonds, (iv) Moody’s BAA-rated corporate
bond and 10-year constant maturity treasury bill.
92
Appendix D - Further Discussion
The actual processes for TFP, government spending, and uncertainty (measured
either at a macro- or micro-level) are given in Figures 1.24 and 1.25.
Figure 1.24: TFP and Real Government Spending (G)
.00048
.00052
.00056
.00060
.00064
.00068
90 92 94 96 98 00 02 04 06 08
TFP
1,700
1,800
1,900
2,000
2,100
2,200
2,300
2,400
2,500
2,600
90 92 94 96 98 00 02 04 06 08
Government Spending
Notes. G is de?ned as the real government consumption expenditures and gross investment.
Figure 1.25: VXO or Cross-Sectional Dispersion
10
20
30
40
50
60
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
VXO
.08
.10
.12
.14
.16
.18
.20
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Cross-sectional Dispersion (Firm-Level)
.010
.015
.020
.025
.030
.035
.040
.045
.050
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Cross-section Dispersion (Industry-Level)
Source: Bloom et al. (2010) and own calculations. At the ?rm-level, cross-sectional dispersion
in ?rms’ sales growth is reported. At the industry-level, cross-sectional dispersion of industrial
TFP growth is reported. The implied volatility is the Chicago Board of Options Exchange
VXO index of percentage implied volatility. I use the VXO, rather than the VIX, since the
VIX starts only after 1990. The correlation between the two series is above 0.99.
I use the log-linearly de-trended series in estimating the following AR(1) pro-
93
cesses for the period 1989Q1-2009Q1.
log(A
t
) = ?
A
? log(A
t?1
) +?
A
t
(1.65)
log(G
t
) = (1 ??
G
)log(G) +?
G
log(G
t?1
) +?
G
t
(1.66)
log(?
t
) = (1 ??
?
)log(?) +?
?
log(?
t?1
) +U
t
(1.67)
where ?
A
, ?
G
, ?
?
are the respective persistence parameters, G is the long-run
level of real government expenditures, ? is the long-run cross-sectional dispersion,
and ?
A
t
, ?
G
t
, and U
t
are the respective i.i.d Gaussian innovations. The estimated
parameters are given in Table 1.11.
Table 1.11: Estimated AR(1) Processes
Dependent Variable ? (Persistence) ?
?
(Std. of innovations) R
2
TFP 0.976 0.0066 0.848
G 0.955 0.0074 0.928
?
f
0.815 0.1145 0.615
?
i
0.823 0.1451 0.582
VXO 0.879 0.1859 0.728
Notes. A superscript f denotes cross-sectional dispersion of ?rm-level sales growth, i denotes cross-sectional
dispersion of industry-level TFP growth. See Bloom et al. (2010) for details on the data set.
The estimated shock processes are given in Figure 1.26.
94
Figure 1.26: TFP, Government Spending, and Uncertainty Shocks
-.03
-.02
-.01
.00
.01
.02
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Innovations to TFP
-.020
-.016
-.012
-.008
-.004
.000
.004
.008
.012
.016
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Innovations to Government Spending
-.4
-.2
.0
.2
.4
.6
.8
-.4
-.2
.0
.2
.4
.6
.8
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Uncertainty (Industry-Level)
Uncertainty (Firm-Level)
Uncertainty (VXO)
Uncertainty
95
Chapter 2
Global and Regional Factors in Driving Emerging Markets’
Sovereign Risk Premium
2.1 Introduction
Sovereign credit risk is an important driver of emerging markets’ business cycles, as
studied by many papers including Blanchard (2004), Favero and Giavazzi (2004),
Neumeyer and Perri (2005), and Izquierdo et al. (2007). Large ?uctuations in credit
risk are often associated with swings in capital ?ows, creating challenges for policy
makers such as ensuring a stable exchange rate, maintaining in?ation or ?nancial
stability.
1
Given its relevance for business cycles as well as the challenges it poses,
understanding the nature of sovereign credit risk is of crucial importance for policy
makers in emerging markets.
In this paper, I study the nature of sovereign risk premia in emerging markets
by decomposing the premia into global, regional, and idiosyncratic factors using
dynamic factor modeling (DFM). Moreover, I assess how global ?nancial market
indicators often used in the literature to gauge global risk fare in explaining the
extracted latent global factor, accounting for potential regime changes. I also assess
estimated evolution of idiosyncratic factors by using easily identi?able idiosyncratic
1
See Blanchard (2004), Reinhart and Reinhart (2008), and Cardarelli et al. (2010) for policy
challenges for emerging markets due to ?uctuations in capital ?ows.
96
events, such as major political events or rating downgrades. Last, the contribution
of each factor to sovereign risk premium and potential policy implications are noted.
To measure sovereign credit risk, I use credit default swap (CDS) premia on
the external sovereign debt. A CDS is simply an asset that facilitates transfer of
default risk of one or more entities from one party to another. The premium re?ects
market expectation of a sovereign credit event, e.g. failure to pay, restructuring or
repudiation of the external debt, or even a drop in the borrower’s credit rating. I
use the CDS premia rather than another popular measure, the bond yield spreads,
since CDS markets are typically more liquid, and CDS premia provide a more direct
market-based measure of likelihood of a credit event, as argued by Pan and Singleton
(2008), Stultz (2010), and Ang and Longsta? (2011).
The data set includes a large set of emerging market economies with di?erent
geopolitical properties and credit risk, providing a good base to study common and
idiosyncratic risk factors. In selecting the countries, I require that countries have
su?ciently developed external debt markets, hence the information content is not
driven by idiosyncratic pricing of sovereign risk. For convenience, I choose those
included in the J.P. Morgan’s Emerging Market Bond Index (EMBI+ or EMBI
Global) for at least a year during the last decade.
2
The selection criteria is satis?ed
for 25 economies.
3
The sample includes 8 Latin American, 10 European, and 7
2
Instruments in the EMBI are required to have a minimum face value of $500 million and meet
certain liquidity criteria. EMBI+ has a more strict liquidity criteria than the EMBI Global.
3
The economies included are Argentina, Brazil, Bulgaria, Chile, China, Colombia, Croatia,
Greece, Hungary, Indonesia, Korea, Lithuania, Malaysia, Mexico, Panama, Peru, Philippines,
Poland, Romania, Russia, Thailand, Turkey, Ukraine, Venezuela, and Vietnam. I exclude African
economies, Egypt, Nigeria and South Africa, since having only 3 countries (especially for a re-
gion that exhibits weaker ?nancial and trade linkages compared to other regions) would not be
reasonable to use to extract the regional factor.
97
Asian countries. The list includes economies with a recent default/restructuring
(e.g. Argentina), restructuring (e.g. Greece), high in?ation (e.g. Venezuela), high
volume of commodity exports (e.g. Chile, Venezuela), high political instability
(e.g. Philippines), to name a few. The list in other words re?ects a wide range of
geopolitical features and risk patterns, hence suitable for studying common external
and idiosyncratic factors.
I use dynamic factor modeling (DFM) as it is well suited to study comove-
ment of macroeconomic series.
4
DFM is widely used in the literature on a variety
of topics, including constructing coincident macroeconomic indicators (Stock and
Watson, 1989), forecasting (Stock and Watson, 2002a, 2002b; Forni et al., 2005),
monetary policy analysis (Bernanke, Boivin and Eliasz, 2005; Stock and Watson,
2005; Forni and Gambetti, 2010), and international business cycles (Kose et al.,
2003, 2008; Del Negro and Otrok, 2008; Aruoba et al., 2011; Crucini et al., 2011).
This paper mainly follows the last strand. DFM can capture potential dynamics
of common driver(s), handles missing observations (through Kalman ?ltering), and
is immune to measurement errors. Last but not the least, and importantly for the
focus of this paper, it does not rely on restrictive assumptions about the choice of
variables that potentially re?ect global, regional or idiosyncratic factors.
The results suggest the following: First, emerging markets’ sovereign risk pre-
4
A pure bivariate correlation analysis, while providing a priori evidence, does not disentangle
the common versus the idiosyncratic factors, and misses potential persistence in common ?uctua-
tions. A simple principal component analysis (PCA) can extract the common factors, but cannot
handle missing observations. For instance, using PCA for our data set would imply using only one
third of the data set. Nor does it capture the persistence of common factors. Interested readers
may refer to Diebold and Rudebusch (1996), Breitung and Meier (2005), Bai and Ng (2008), and
Stock and Watson (2010) for literature surveys on DFM.
98
mium is mostly due to common external factors. On average, about 63% of the
movements in the sovereign risk premium is due to the global factor, and about
21% due to regional factors. There is, however, substantial heterogeneity among
the emerging markets. The contribution of external factors are substantially low
for economies that have experienced major idiosyncratic events, e.g. Greece, Philip-
pines. Moreover, there are a few economies that seem to decouple from regional
risk factors, e.g. Chile, Venezuela and Turkey, as the contribution of regional factor
is rather low for these economies. In addition, sovereign risk of largest economies
in the regions (e.g. Brazil and China) appears to move strongly with the regional
factor, potentially suggesting that these economies are by-and-large the driver of
regional comovement of sovereign risk premium.
Second, the extracted latent global risk factor can be explained fairly well by
global ?nancial variables considered. It appears that the global risk factor is best
re?ected by the CBOE’s VIX, a re?ection of investors’ risk sentiment, regardless
of the regimes. VIX explains around 87% of the global factor during ‘high stress’
times, and around 55% on average. As a re?ection of credit and liquidity risks in
global ?nancial markets, the TED spread (spread between London Interbank O?er
Rate (LIBOR) and 3-month US Treasury Bill) captures the global factor at a lesser
extent (20% on average). During high stress times, though, the TED spread explain
nearly half of the movements in the global factor. The yield spread between long-
term US Treasury notes has a lower power in explaining the global factor (of about
7% to 25%). Global ?nancial variables becoming much more powerful in explaining
the global risk factor during high-stress times indicates that volatility, credit and
99
liquidity risks are heightened substantially during the global crisis starting in late
2008. Furthermore, the results also suggest that in times of high stress, investors
seek for safe US assets, which contributes to a rise in emerging markets’ sovereign
risk.
Third, idiosyncratic factor matters, e.g. political instability, major idiosyn-
cratic economic events (isolated banking, currency, or debt crises, or rating down-
grades) matter for sovereign risk premium. For instance, nearly 60% of the move-
ments in Philippines’ sovereign risk premium is due to idiosyncratic factor which
can mostly be attributed to political instability. For Greece, political instability and
?scal solvency issues seem to contribute nearly 80% of the variations in her sovereign
risk premium.
Moreover, increasing concerns about the future of the Eurozone appear to
be a global risk factor in the recent era. In particular, I ?rst estimate a DFM
with a single factor and compare the estimated evolution of common factor with the
regional European factor estimated from the baseline two-factor DFM. The common
factor follows the European risk factor surprisingly well starting in June 2010. This
result suggest that the European debt crisis has gone beyond its boundaries and
become a global factor in driving sovereign risk premium.
The results so far are based on emerging markets. A natural question then is
how “global” is the estimated global factor? To address this question, I use a set of
35 developed and emerging market economies. Given recent ?scal solvency problems
in developed economies (e.g. Portugal, Spain, Italy, etc.), it may also be of interest
of its own studying sovereign risk of debt-crippled developed economies. Moreover,
100
I use higher frequency (weekly) to see whether using monthly frequency misses rel-
evant information. The results show that the evolution of common external factors
are by and large robust to including developed economies and using higher frequency.
This result suggests that emerging markets’ sovereign risk premium during the last
decade is not decoupled from how developed economies perform.
The contribution of this paper is two-fold: First, I study which ?nancial market
indicators best re?ect the global factor, and whether there are statistically signi?cant
regime changes in the relation. The relevance of global factors in driving emerging
markets’ sovereign risk is recognized in the literature. Numerous studies show that
global ?nancial market variables a?ect emerging markets’ sovereign risk signi?cantly.
For example, using global and local ?nancial market variables, Longsta? et al. (2011)
show that US ?nancial market variables are more signi?cant than the country-
speci?c variables in explaining changes in sovereign CDS. Ebner (2009) studies 11
central and eastern European economies’ bond spreads, using a large set of country-
speci?c variables, and proxies for external common factors. Common external factor,
as captured by market volatility, appears to a?ect the bond spreads signi?cantly.
Country-speci?c variables also matter, though less signi?cantly, for sovereign risk.
Yet, such analyses rely on restrictive assumptions about which variable captures the
global risk. Here I instead extract the global risk factor using DFM, and report the
contribution of global factor for each economy. Moreover, I assess how commonly
used global ?nancial market indicators fare in explaining the global risk factor.
5
5
To test whether there are regime changes in the relation, I employ Hansen’s (2000) threshold
estimation.
101
Second, I explicitly study regional risk factor. The analysis sheds light on
heterogeneity among the regions, and which economies (if any) are decoupled from
regional factors. Moreover, incorporating the regional risk factor provides a better
picture on the ‘true’ global risk factor. Recent experience has shown compelling
evidence that there exists noticeable heterogeneity in the sovereign risk among the
regions. For instance, European debt crisis unfolding in mid 2010 led to a surge in
European economies’ sovereign CDS, while having a less strong e?ect on Latin Amer-
ican economies. Moreover, economies with relatively sound fundamentals might be
decoupled from regional risk factors. These points are relatively unexplored in the
literature.
6
Closely related to my work, Longsta? et al. (2011) have pointed out that there
is a single common component explaining an average of 64% of the movements in
sovereign CDS (for a set of 26 economies).
7
They document that about two thirds of
the spread is due to default component, and on average, it is the default component
that is strongly linked to global ?nancial variables. Ciarlone et al. (2009) extracts a
single common factor driving bond spreads of 14 emerging markets. Using principal
factoring, they conclude that 85% of the variation in bond spreads is explained
by a single common factor. They report that the VIX is strongly signi?cant in
explaining the common factor, and it performs better than other ?nancial market
indicators considered. They also note country-speci?c fundamentals having a non-
6
Longsta? et al. (2011) report second and third principal components of sovereign risk as
potentially re?ecting regional factors, though do not study in detail. Existing literature focusing
on both the global and the regional factors are mostly related to business cycles, see for instance
Kose et al. (2003, 2008), Aruoba et al. (2011).
7
Of these, there are 23 emerging markets and 3 developed economies.
102
negligible e?ect on the spreads. This paper di?ers from these studies in several
respects. First, DFM provides a better picture of the relative contribution of each
factor on sovereign risk. The DFM is widely used in the literature ranging from
coincident macroeconomic indicators to international business cycles, though, to
my best knowledge, have not been employed using sovereign CDS spread data.
Second, I address whether global ?nancial market variables fare well in explaining
the global risk, and whether that depends on regime changes. Third, I explicitly
study the regional factor. Last, I use longer time span and more countries (and
further include developed economies for robustness).
The chapter proceeds as follows. Section 2.2 presents the the data and the
methodology. Section 2.3 presents the empirical results, Section 2.4 the relationship
between the global factor and ?nancial market indicators. Section 2.5 presents
robustness analysis, and Section 2.6 concludes.
2.2 Data and the Methodology
Credit default swaps enable transfer of credit risk from one party to another. Credit
event may be triggered due to failure to pay beyond any grace period allowed on
the obligation indenture; restructuring of the debt, altering the principal amount,
coupon, currency or maturity; repudiation/moratorium of the debt; or even a drop
if borrower’s credit rating.
8
A seller of a CDS contract (protection seller) receives
annual payments, but incurs the cost of a credit event. The buyer (protection buyer),
8
Note that bankruptcy/default is not taken as a credit event (as there is no international court
to force a sovereign to honor its premises), as typically around 40-50% of the debt is recovered (see
Reinhart and Rogo?, 2008). For a detailed de?nition of credit event, see Barclays (2010).
103
pays the premium and receives a payment equivalent to the loss in case of the credit
event. The CDS ‘spread’ is the annual amount that the protection buyer must pay
the protection seller till the maturity of the contract, expressed in percentage of the
notional amount. For instance, consider a protection buyer paying a spread of 500
basis points to insure $100 of debt. She would pay $5 per annum till the maturity of
the CDS contract to insure herself against a credit event of the reference entity (the
sovereign in our case).
9
Moreover, magnitude of the spread is intrinsically linked to
the likelihood of the sovereign default. Assuming that the loss associated with the
default is 60% and the maturity is ?ve years, the risk-neutral likelihood of default
is 12.5% for each year over the next 5 years.
10
I choose the CDS pricing data rather than another popular measure, bond
spreads, since the CDS markets are typically more liquid than the bond markets,
and CDS spreads provide a more direct measure of sovereign risk. Bond spreads, for
instance, are driven not only by sovereign risk, but also by ?uctuations in interest
rate and by illiquidity e?ects on sovereign debt prices.
11
Moreover, I choose the
sovereign CDS with 5-year maturity since it is generally the most liquid one among
other maturities.
12
9
Most CDS contracts are cash settled where an auction determines the market price of the dis-
tressed bond and thus the recovery value. In physical settlements, the CDS issuer receives the bond
in exchange for money. However, most contracts are cash settled, since physical delivery would
make the protection seller worse o? in case the corresponding bond market becomes illiquid. In
certain cases, the protection buyer could sell the bond at its par value, though if the corresponding
market had become illiquid, could sell any list of bonds or loans with equivalent seniority rights
depending on the contractual terms.
10
See Hull et al. (2005) for details on the derivation of default probability using CDS premium.
11
See Ang and Longsta? (2011), and Longsta? et al. (2011) for a similar discussion on why CDS
markets may be preferred over bonds market to measure sovereign credit risk.
12
See Pan and Singleton (2008) and Longsta? et al. (2011) for bid-ask spreads on a selective
number of emerging market sovereign CDSs.
104
The data set consists of a large set of emerging market economies with su?-
ciently developed external debt markets. For convenience, I choose those included
in the J.P. Morgan’s Emerging Market Bond Index (EMBI+ or EMBI Global) for
at least a year during the last decade. The selection criteria pick 25 economies:
Argentina, Brazil, Bulgaria, Chile, China, Colombia, Croatia, Greece, Hungary, In-
donesia, Korea, Lithuania, Malaysia, Mexico, Panama, Peru, Philippines, Poland,
Romania, Russia, Thailand, Turkey, Ukraine, Venezuela, and Vietnam.
13
The sam-
ple includes 8 Latin American, 10 European, and 7 Asian economies. The frequency
is monthly (monthly average), and the sample period covers October 2000 to Febru-
ary 2012. The starting period is due to data limitations, since the sovereign CDS
markets have been developed after 2000.
Table 2.1 presents the descriptive statistics of the data. The values are reported
in basis points. As evident from the starting dates of sovereign CDS trading, the
data become available for most of the countries by 2003 (20 economies).
14
The
data range widely across the countries. Average sovereign CDS ranges from 59
basis points (China) to 909 basis points (Argentina, which experienced an external
default along with banking and currency crises during 2001-2005), with standard
deviation ranging from 47 to 934 basis points. The CDS spread reaches as high as
4280 basis points for Ukraine (in late 2009), for which a default was imminent had
external funding not extended, while it is a mere 230 basis points for China. To
accompany Table 2.1, Figure 2.1 displays the evolution of sovereign CDSs during the
13
I exclude African economies, Egypt, Nigeria and South Africa.
14
Note that two economies with the same start date might have di?erent number of observations
(e.g. Colombia and Peru) due to missing observations.
105
sample period. The ?gure by itself suggests some degree of comovement in sovereign
risk: There is a noticeable jump in late 2008 and a re-surge in mid 2011 for most
economies.
Next, I present the DFM to extract the global, regional and idiosyncratic
components of sovereign risk. I assume that sovereign CDS pricing data, y
it
, have
the following factor structure:
y
it
= µ
i
+ ?
G
i
G
t
+ ?
R
i
R
t
+?
it
for i = 1, 2, ..., n (2.1)
where G
t
is the global factor a?ecting all the countries, and R
t
? (R
1
t
, R
2
t
, ..., R
k
t
)
are
the k regional factors. ?
G
i
and ?
R
i
? (?
1
i
, ?
2
i
, ..., ?
k
i
) are the factor loadings for global
and regional factors for country i. To separately identify the two common factors,
I assume that each regional factor a?ects only the countries in the corresponding
region. For a European country i, for example, the above equation simpli?es to
y
it
= µ
i
+ ?
G
i
G
t
+ ?
Europe
i
R
Europe
t
+?
it
(2.2)
?
i
captures all the variation in y
i
that is not captured by the common factors, re?ect-
ing idiosyncratic factors, and potentially, measurement errors. µ
i
is unconditional
mean of sovereign CDS for country i.
I assume that the factors follow a stationary autoregressive process of order
one, and are independent from each other:
G
t
= ?
G
1
G
t?1
+u
G
t
u
G
t
? i.i.d.N(0, 1) (2.3)
106
R
j
t
= ?
R
j
1
R
j
t?1
+u
R
j
t
u
R
j
t
? i.i.d.N(0, 1) j = 1, 2, ...k (2.4)
?
it
= ?
1
?
it?1
+?
it
?
it
? i.i.d.N(0, ?
2
i
) (2.5)
where E[?
it
?
js
] = 0 for i = j, and where G
0
and R
0
are uncorrelated with v
t
and u
t
for all t. The model above is a backbone DFM for a variety of DFMs used in the
literature. It is a simple version of DFM studied in, for instance, Kose et al. (2003)
(on international business cycles), Del Negro and Otrok (2008) (on the European
business cycles), and Stock and Watson (2008) (on the US housing market).
Identi?cation.
The identi?cation assumptions are as follows. First, the relative scale of the
model is indeterminate. Consider multiplying the common factor by ?,
F
t
= ?F
t
.
Also divide the factor loading by ?,
¯
? = ?/?. The scale of the model ?F
t
is
observationally equivalent to
¯
?
F
t
. To normalize the scale, I set global and regional
factor shock variances equal to one (Stock and Watson, 1993).
15
Second, the sign of the factor loadings and factors cannot be separately iden-
ti?ed. Consider setting ? above equal to -1. Similarly as above, ?F
t
is again
observationally equivalent to
¯
?
F
t
. As a remedy, I initialize factor loadings (for all
the factors) to be positive. Such a restriction identi?es the sign of the factors. Note
that scale and sign normalization has no e?ect on economic inferences such as the
15
Note that the scaling does not a?ect economic inferences such as the estimated evolution of
factors or variance decomposition. There might be applications for which the exact identi?cation
of F
t
is not sought, e.g. forecasting, yet, since I study the evolution of factors, such a scaling
assumption is necessary.
107
estimated evolution of factors and their contribution to the observable variables.
Third, common factors (global and regional factors) cannot be identi?ed sep-
arately. I make a natural assumption that, for a country i in region s, the factor
loadings on other regions are zero. That is, ?
j
i
is set equal to zero if i ? R
j
for all
j = 1, 2, . . . , k and for all i = 1, 2, . . . , n.
Number of Factors.
A modeling assumption made above is that the data generating process admits
two common factors, global and regional. Potentially, however, there can be many
common factors, e.g. one might include sub-regions as well. Although a conventional
way to see how many (independent) factors are needed to capture covariation in the
data su?ciently well is to obtain proportion of variance that is explained by each
common factor (through principle component analysis), it is not comparable to the
dynamic model above since there is only a single common factor, i.e. the global
factor, and the regional factors are common only those within the region. Hence, I
rather verify the relevance of global and regional factors by documenting whether
they account for a large portion of movements in sovereign risk premium for each
country.
Contribution of Factors.
The estimated fraction of volatility in y
i
that is explained by global and re-
gional factors can be calculated by simply applying the variance operator to each
signal equation. Using the fact that the factors are orthogonal to each other, the
fraction of movements in y
i
that is explained by the global factor is given by
108
(?
G
i
)
2
var(G)
var(y
i
)
(2.6)
and, similarly, the fraction of movements in y
i
that is explained by the regional
factor is given by
(?
R
i
)
2
var(R)
var(y
i
)
(2.7)
2.3 Empirical Results
The CDS series are ?rst standardized to have mean zero and standard deviation one
to ensure that an individual economy does not have a direct impact on the evolution
of factors. The model is then estimated by Gaussian maximum likelihood, where
the likelihood function is evaluated using the Kalman ?lter. The estimated state
variables are presented in the Appendix Figure 2.10.
The stationarity of the system is veri?ed through analyzing the estimated
model. The estimated autoregressive coe?cients for all the factors are below 1 (rang-
ing in between 0.08 to 0.99, with an average of 0.88). The estimates for smoothed
state disturbances and one-period-ahead signal disturbances are stationary (with
p-values 0.00) based on standard univariate or group unit root tests.
2.3.1 Evolution of Global and Regional Factors
Global Factor.
Figure 2.2 presents the evolution of global factor. The global factor captures
109
the common driver of sovereign CDS for all the emerging markets in the data set.
In reporting the factors, hereforth, I use October 2001 onwards to have the results
robust to initial state values and since the data become available for most of the
countries by this time. The estimated evolution of the global factor seems to follow
major economic events during the sample period. To shed light on the magnitude
of the global factor, note that the estimated standard deviation is roughly equal to
three.
The global factor hits unusually high levels during late 2002 and in late 2008,
consistent with the currency and banking crisis in Latin America and Turkey in
2001 and 2002, and with the US ?nancial turmoil started in late 2007. The sharp
increase in the global factor in October 2008 suggests that the recent US recession
have become a global risk factor after the Lehman Brothers’ collapse. Compared
to its pre-crisis levels, the factor rises by about four standard deviation. The ?gure
also suggests that proactive policy responses in advanced economies, –e.g. TARP,
CPFF, and in an international scale, extending swap lines among central banks,
IMF’s provision of short-term liquidity with looser terms for economies battered by
the ?nancial crises, e.g. Iceland, Ukraine, Hungary, Belarus, Romania, Mexico, to
name a few,– seem to avoid further increases in the global risk factor.
16
By late 2009, the global risk factor gets stabilized, though, around a level
higher than its pre-crisis level (about one standard deviation higher). It is only
16
To name a few, Ukraine signed a stand-by agreement with the IMF on Oct. 2008 to condi-
tionally receive $16.5 billion, Hungary on Nov. 2008 to receive $15 billion, Belarus on Jan. 2009
to receive $2.5 billion, and Romania on March 2009 to receive $27 billion (together with the EU,
WB, and EBRD). Through Flexible Credit Line, Mexico on March 2009 have secured $47 billion
line of (unconditional) credit from IMF.
110
after increased concerns about Italy and Spain rolling over its debt (hence concerns
about the Eurozone’s future) that the global factor starts to rise again (August
2011).
17
In the next section, I provide a further analysis on this recent episode.
Regional Factors.
Figure 2.3 presents the European, Latin American, and Asian regional risk
factors. The regional factor captures the comovement of the sovereign risk for the
economies within the region, and shows the pricing of sovereign risk independent
from global or idiosyncratic factors.
18
The estimated evolution of regional factors seems to follow major regional
economic events during the sample period. To shed light on the magnitude of
regional factors, note that the standard deviation is roughly 4 for the Latin American
and the Asian, and 4.5 for the European factor.
The European risk factor starts at a relatively high level in late 2001, mostly
due to Russian and Turkish ?nancial crisis. Then, as subsequent years and more
economies chime in the estimation, the regional factor becomes stable till the Lehman
Brother’s collapse in October 2008. Following October 2008, the European regional
factor surges. This surge implies that, the European factor feeds further risk to the
European economies (on top of the global factor). Moreover, European emerging
markets (on average) are hit more during this time compared to emerging markets
in other regions. This result might suggest that Europe has stronger ?nancial and
17
Note that Italy holds around 25% and Spain around 15%, in percent of total euro area gov-
ernment debt (on average for the last three years).
18
While this orthogonality assumption hinders potential spillover from other factors to the re-
gional factor, studying the spillover mechanism requires restrictive identi?cation assumptions, and
is not the focus of this paper. Note also that the orthogonality assumption is standard in the DFM
literature that studies global and regional factors (see, for instance, Kose et al. 2003; 2008).
111
trade linkages with the US (compared to other regions), though further investigation
is needed.
For the European regional risk factor, there are two distinctive episodes after
2009. The regional factor rises from mid-2009 to 2010 corresponding to the ?rst-
phase of European debt crisis, which is mostly limited to Greece and Ireland. The
second phase starts in mid-2011, exhibiting a surge in the regional risk. This period
corresponds to increased concerns about the future of Eurozone, as ?scal solvency
problems arouse for two large indebted economies in Euro area, Spain and Italy,
and further concerns about Greece.
Note that the second phase also coincides with the increase in the global factor,
potentially suggesting that the second phase in Europe goes beyond the boundaries,
and a?ects the sovereign risk of all the emerging markets. To shed further light on
this, I estimate a DFM with a single common factor (the single-factor DFM), and
plot the estimated common factor with the regional European factor (Figure 2.4).
19
The evolution of two series coincide surprisingly well for the recent era, suggesting
that concerns about the Eurozone become a global risk factor thereafter (after June
2010).
The Latin American factor, on the other hand, shows a di?erent risk pattern
than the European, noticeably for early 2000s and 2008 onwards. The factor is at
historically high levels during mid 2002, due to political instability in Brazil at the
time, contagious e?ects on the region of Argentina’s debt, currency, and banking
crises starting in 2001. The region enjoys a slowly decreasing risk, as the economies
19
For all the estimated factors in the single-factor DFM, see Appendix A2.
112
implement sound policies (and some follow IMF supported programs, e.g. Brazil
in 2002, and Colombia in 2003 and 2005). At the time global factor hits record
high levels in late 2008, the Latin American factor falls noticeably, suggesting that
the markets were pricing the Latin American economies’ sovereign risk lower than
the rest of the emerging markets. By 2010, the regional factor returns back to its
pre-crisis levels.
The Asian factor has an increasing pattern from 2003 till early 2008, poten-
tially due to Asian economies experiencing stable CDSs despite the decrease in the
global risk factor during this period. The nearly-discrete change in the regional
factor in 2008 happens to be earlier for Asian economies, coinciding with the start
of the US recession. The factor goes back to its pre-crisis levels by mid to late 2009,
and then keeps rising for the last three years.
Note that the regional factors are constructed to be orthogonal to each other
as well as to the global factor. However, estimation results suggest some degree of
correlation (Table 2.2). Two results emerge: First, regional factors are only slightly
correlated with the global factor, with the correlation ranging from -0.09 to 0.19,
inline with how the DFM is constructed. On the other hand, regional factors appear
to be correlated with each other, with the correlation ranging from -0.53 to 0.80.
The second result suggests that there are within-month spillovers across the regions.
This point is left to future work.
113
2.3.2 Contribution of Factors
Table 2.3 presents the contribution of global, regional and idiosyncratic factors to
the emerging economies’ sovereign CDSs.
A substantial portion of emerging markets’ sovereign risk is driven by external
factors (84%). On average, the global factor accounts for 63%, and the regional
factor 21% of the variations in sovereign risk. The contribution of external factors
di?ers widely across the economies. The global factor, for instance, accounts for as
low as 1% for Greece, and as high as 93% for Chile.
20
The wide range for the contribution of external factors can be due to di?erent
degrees of capital market openness across the economies. Moreover, one might
expect a higher contribution of external factors for more open economies. In Figure
2.6, I plot the Chinn-Ito capital account openness index (averaging over 2001-2010)
against the total contribution of external factors for all the countries.
21
For countries
with more open capital accounts, the contribution of external factors is higher.
The regional factor, on average, accounts for 21% of the ?uctuations in emerg-
ing markets’ sovereign risk. The contribution of which is highest for Brazil (82%)
20
Comparison of contributions across the economies should be handled with care, though. Con-
sider, for instance, two countries for which the contribution of global factor on her sovereign risk
premium is close (e.g. Ukraine versus Chile), while the former having a higher level of ?uctuations
in sovereign risk. A surge in global risk might push the former into a near default stage while
exerting comparatively negligible e?ect on the latter. In this sense, comparison should be made
along with country-speci?c macroeconomic conditions.
21
Chinn-Ito (2008) index is based on extracting the common factor for variables (i) indicating
presence of multiple exchange rates, (ii) indicating restrictions on current and capital account
transactions, and (iii) indicating the requirement of the surrender of export proceeds. The graph
shows the Chinn-Ito index against the contribution of external factor for all the economies with
the exceptions Greece and Argentina. I exclude Greece –which is a fairly open economy– whose
CDS is driven substantially by the idiosyncratic factor. Moreover, Argentina has defaulted for
nearly half of the sample period, and since the default was idiosyncratic, I set the contribution of
idiosyncratic factor at 50%.
114
in Latin America, Croatia (52%) in Europe, and China (20%) in Asia. It is no co-
incidence that Brazil’s and Chinese sovereign risk, of the largest economies in their
regions, move strongly with the regional factors. It is reasonable to think that these
economies are the main driver of regional risk, leading to a strong comovement with
the regional factor. For other economies with a high level of contribution of regional
risk factors, e.g. Colombia (67%), Peru (57%), Croatia (52%), they might possibly
be driven by (rather than drive) the regional factor. In these regards, the estimated
contribution of regional factors seems economically plausible.
The idiosyncratic factor, on average, accounts for 8% of the variations in
sovereign risk. The wide range applies to the idiosyncratic factor as well: it is
as high as 78% for Greece, 57% for Philippines, and nearly nil for Colombia and
Thailand.
To shed further light on the validity of evolution and contribution of factors,
next I study decomposition of sovereign CDS for four economies with di?erent credit
risk patterns: Chile, Greece, Philippines and Turkey (see Figure 2.5).
2.3.3 Idiosyncratic factor and four examples.
I choose four economies with ‘di?erent’ sovereign risk patterns: Chile, Greece,
Philippines and Turkey, di?erent in the sense that the contribution of each fac-
tor di?ers noticeably across these economies. The contribution of global factor is
highest for Chile (93%), that of the idiosyncratic factor is highest for Philippines in
Asia (57%), and for Greece in Europe (78%). The global and idiosyncratic factors
115
each share nearly half of the movements for Turkey. Moreover, Greece, Philippines
and Turkey have experienced idiosyncratic events that can be conveniently identi-
?ed (debt, in?ation, banking or political crisis) during the last decade, hence the
estimated evolution of idiosyncratic factors can be conveniently judged against.
It is also worth noting that the idiosyncratic factor should not be thought
as a sole re?ection of country-speci?c fundamentals commonly used in the related
literature (such as international reserves to imports, total external debt to real
GDP, imports to export ratios, to name a few). The idiosyncratic factor is orthog-
onal to global and regional factors, whereas country-speci?c variables (particularly
those pertaining to external balances) are most likely to be a?ected by global or
regional economic stance. Idiosyncratic factor, instead, can be interpreted as the
idiosyncratic nature of a sovereign’s credit risk, such as rule of law or institutional
quality, transparency in economic policy decisions and objectives, central bank in-
dependence, strength of business environment, e?ectiveness/e?ciency of the public
sector (in raising taxes, cutting spending, selling assets), default history, or robust-
ness/e?ectiveness of ?nancial sector.
22
Chile is one of the most stable and prosperous economies in the Latin American
region. Moreover, as a commodity-exporter, Chile has one of most sound sovereign
wealth fund in the world. The country enjoys one of the lowest public debt to GDP
ratio and in?ation rate in the region, e.g. of around 6% and 4-5% respectively as of
2011.
23
In line with these, the decomposition results suggest that Chilean sovereign
22
For variables which are potentially idiosyncratic, see for instance IMF (2010, p. 101).
23
To give a sense of these numbers, the largest economy in the region, Brazil, has a public debt
to GDP ratio of 60% and an in?ation rate of 9%.
116
risk is driven only negligibly by the Latin American-speci?c risk factors. Moreover,
due to its rather stable economy, the contribution of idiosyncratic factor is small
(7%). It is therefore mostly the global factor that drives the sovereign risk (however
comparatively small the movements are).
Greek credit risk, on the other hand, is driven only negligibly by the global
factor. After a long stable period, the Greek CDS rises after the Lehman Brother’s
collapse (as for all the emerging markets). Markets at the time seem to be pricing
the Greek sovereign risk lower than its global and regional counterparts, as re?ected
in the decline in the idiosyncratic factor. After 2009, there are three distinctive
surges in the Greek CDS, where each one is re?ected in the idiosyncratic factor.
The ?rst occurs in December 2009, coinciding with the announcement of debt to
GDP (of nearly 13%, which is to be revised later), and the downgrade of Greek
credit rating. It is only after the IMF and EU’s bailout package (of about $145bn)
that it slows down the increase in the sovereign risk. The second occurs in February
2011, in which the Greek authorities slammed EU and IMF o?cials’ overseeing
e?orts to reform its debt-crippled economy. The third occurs in July 2011, in which
Greek credit rating were downgraded by all the main three rating agencies to a
level associated with a substantial risk of default. These Greek-speci?c events are
captured by the evolution of its idiosyncratic factor.
Philippines’ sovereign risk is driven mostly by the idiosyncratic factor (57%),
where the idiosyncratic factor seems to capture phases of political instability in the
economy, e.g. a surge in the CDS due to increasing political tension till March
2003, the Oakwood mutiny in July 2003, and a relatively long-lived decline in the
117
CDS during a relatively calm political environment after July 2005. In other words,
political instability seems to contribute more than half of the Philippines’ sovereign
risk.
Turkish sovereign risk is driven mainly by global and idiosyncratic factors.
Despite strong trade and ?nancial linkages with Europe, the contribution of regional
European factor to Turkish sovereign risk is weak (of about 7%). Before 2005, the
idiosyncratic factor seems to capture political instability, e.g. resignation of eight
cabinet members in July 2002, elections in November 2002, political upheaval in
late 2003, all captured by a jump in the idiosyncratic factor. After a ?ve-year stable
period, the idiosyncratic factor declines in early 2008 till early 2009, suggesting that
Turkish sovereign risk is perceived to be lower than European emerging markets.
The idiosyncratic factor resumes back to its pre-crisis level by the end of 2010 (where
it had been for nearly 5 years). 2011 is characterized by a noticeable surge in
the idiosyncratic factor. Potential explanations might be increasing concerns about
current account de?cit to real GDP reaching record high levels through the year and
a jump in exchange rate volatility towards the end of the year. The idiosyncratic
factor starts to decline in 2012, suggesting that investors start to perceive Turkish
idiosyncratic risk at a lower level.
2.4 Interpreting the Global Risk Factor
The analysis so far sheds light on the evolution of global factor by associating it
with major ?nancial events. This section takes a formal stand. It provides an
118
understanding on the nature of global factor by linking it to global ?nancial market
indicators, taking into account potential regime changes in the relation.
I consider three ?nancial market indicators often quoted in the literature as
a way to gauge the stance of global ?nancial markets: the TED spread, the yield
spread between long-term Treasury notes (10- and 20-year Treasury notes), and
Chicago Board of Exchange’s Implied Volatility Index (VIX).
24
As discussed brie?y
below, these variables capture the strength of credit or liquidity risks, as well as
risk averseness in the US ?nancial markets. The evolution of these indicators are
provided in Figure 2.7.
The TED spread is the di?erence between the interest rate at which the US
government is able to borrow on a 3-month period (3-month U.S. Treasury bill), and
the rate at which banks are willing to lend to each other in a 3-month period (mea-
sured by 3-month USD LIBOR). The spread measures estimated risks that banks
pose on each other (compared to the likelihood of default of the US Treasury, which
is practically nil). The higher the perceived risk due to one or several banks having
liquidity or solvency problems, the higher the lending rate in interbank markets. In
this regard, the TED spread captures credit and liquidity risk in interbank markets.
Moreover, for periods of high risk averseness during which investors seek for ‘safe
havens’, the yield on risk-free rate would be pushed downward, resulting in a rise
in the spread. In this regard, in times of high credit/liquidity risks, a portion of
movements in the spread would be due to ‘?ight to quality’.
24
See Gonzales-Hermosillo (2008), and Gonzales-Hermosillo and Hesse (2009) for a thorough
analysis on ?nancial market indicators that are potentially global.
119
The yield spread between long-term US Treasury notes (e.g. 10- to 20-year
Treasury notes) re?ects how strong markets value the liquidity.
25
Since the two
bonds have essentially the same default risk, the yield spread re?ects expected aver-
age future yields (from 10 to 20 years) and a liquidity premium. To the extent the
former is stable, changes in the spread capture changes in liquidity premium. I use
the percentage change in the yield spread compared to the previous year.
The VIX, CBOE’s Volatility Index, re?ects the expected future volatility in
S&P500 (over the next 30 days) implied by the current index option prices. It
indicates how strong investors value insuring their portfolios (in a sense, capturing
investors’ fear gauge).
To explore potential regime changes in the relation between the global factor
and the ?nancial market indicators, I employ Hansen (2000)’s threshold regression
model.
26
I use the following threshold regression speci?cation:
?G
t
= ?
1
?x
t
+e
t
?G
t
? ? (2.8)
?G
t
= ?
2
?x
t
+e
t
?G
t
> ? (2.9)
where x
t
is one of the ?nancial market indicators mentioned above, ?x
t
= x
t
?x
t?1
,
?G
t
is the threshold variable used to split the samples into two groups or “regimes”,
and ? is the (endogenous) threshold parameter. The method is a sequential OLS
25
See Gonzales-Hermosillo (2008) for other potential variables to capture market liquidity risk.
Here I follow Gonzales-Hermosillo (2008), and use the yield spread between long-term US Treasury
notes.
26
I would like to thank Bruce Hansen for very helpful discussions on the methodology.
120
estimation, searching over all permissible ?s such that sum of squared errors of the
above system is minimized.
27
While the method determines the regimes endogenously, it may be the case
that the true data generating process admits a linear regression model, that is
H
0
: ?
1
= ?
2
cannot be rejected (hence no threshold e?ect). Testing H
0
, however,
is not straightforward since ? is not identi?ed under the null hypothesis. Hansen
(2000) introduces a heteroskedasticity-consistent bootstrap F-test procedure to test
the null of linearity. The procedure provides asymptotically correct p-values.
To further explore whether there are multiple regimes, I follow Hansen (2000)
and ?rst test whether there is a threshold in the whole sample. Then, given the
estimated threshold, I explore whether there are further thresholds within each
regime (sub-sample).
Table 2.4 presents the regression results, based on the whole sample as well
for each estimated regime.
Using the whole sample, VIX turns out to be the most powerful indicator in
27
In particular, ?rst write the equations above in a single equation form (by de?ning an indicator
variable). In particular, let I{q
i
? ?} be an indicator function that takes a value 1 if {.} is satis?ed
and 0 otherwise. And let x
i
(?) ? x
i
I{q
i
? ?}. Then the above model can be written as
y
i
= ?x
i
+?
n
x
i
(?) +e
i
(2.10)
where ? = ?
2
, and ?
n
= ?
2
??
1
. The least-squares estimators
´
?,
´
?, and ´?, jointly minimize
S
n
(?, ?, ?) =
i
(y
i
??x
i
+?
n
x
i
(?))
2
(2.11)
Conditional on ?, equation (10) is linear in ? and ?
n
. Conditional LS estimates
´
?(?) and
´
?(?)
can be obtained by regression y
i
on x
i
and x
i
(?). The conditional sum of squares is S
n
(?) ?
S
n
(
´
?(?),
´
?(?), ?). As shown in Hansen (2000), ´? can be de?ned uniquely as
´ ? = argmin
???n
S
n
(?) (2.12)
where ?
n
= ? ? {q
1
, ..., q
n
}.
121
explaining movements in the global factor (of about 58%). A rise in the VIX (a
decrease in investors’ risk appetite) leads to a statistically signi?cant increase in the
global factor. Similarly, a rise in the TED spread (an increase in credit/liquidity
risk) also induce a rise in the global factor. The TED spread can explain about 22%
of the movements in the global factor. The yield spread (the liquidity premium) has
the lowest explanatory power (of about 2%). Note that these results are based on
whole sample, and further investigation is needed as there are indeed regime changes
in the relation.
There are three regimes in the relation between the global factor and the ?nan-
cial market indicators: The high stress period (corresponding to large increases in
G
t
), the low-to-moderate stress period (corresponding to moderate changes in G
t
),
and the recovery period (corresponding to large declines in G
t
). These regimes are
determined based on estimated threshold values for ?G: ?
high
and ?
low
.
28
The two
thresholds are ‘statistically signi?cant’: the null of linearity is rejected at a 0.000
signi?cance level.
29
The estimated durations of these regimes are as follows: The
high stress period in sovereign risk markets seems to prevail for 6 to 11 months (de-
28
In particular, I ?rst test the signi?cance of the threshold in the whole sample, which splits the
sample into two regimes. The null of linearity is rejected with a p-value of 0.000. The threshold
value splits the sample into a small one (including 11 observations using the TED spread as the
independent variable, 6 observations using the yield spread, and 7 observations using the VIX),
and large one (including 113, 118 and 117 observations, respectively). I label the threshold that
splits the whole sample as ?
high
. I have not pursued splitting the small one into subsamples, as
that would imply excessively low degrees of freedom. I then test signi?cance of a threshold in
splitting the large sample, and the null of linearity is rejected at a p-value of 0.000. I label the
threshold splitting the large subsample as ?
low
.
29
For the likelihood ratio sequence used to construct the con?dence bands for the thresholds,
see Figure 2.13 in the Appendix. The likelihood ratio (LR) statistic gives out the change in sum of
squared errors under ? = ?
1
as compared to ? = ?
0
. The threshold estimate is where the sequence
reaches its minimum. The con?dence band limits are where the critical value intersects with the
LR sequence. The local minima in the ?rst graph sort of implies a second threshold, as further
validated by formal testing.
122
pending on which ?nancial market indicator is used). The low-to-moderate period
prevails for around 9 years. The estimated duration of this period seems to be rather
long, as this period captures a range of tranquil to moderately stressed periods in
the ?nancial markets. The recovery period, fast declines in the global risk, appears
to be for about 5 to 11 months.
The explanatory power of ?nancial market indicators is the highest under the
high-stress regime: The TED spread explains 49%, the yield spread 24%, and the
VIX 86% of the variations in the global factor. An increase in the TED spread,
which is potentially due to increased credit/liquidity risks in the interbank market
and ?ight to safe US assets, leads to a rise in the global factor. An increase in the
liquidity premium, which is captured by an increase in the yield spread, also implies
an increase in the global factor (though the e?ect is statistically insigni?cant). An
increase in the investors’ risk sentiment also leads to a rise in the global factor.
During the low-to-moderate stress period, all the three indicators explain the global
factor signi?cantly, though the explanatory power declines to 12%, 11%, and 35%,
respectively. Still, the investors’ risk sentiment (the VIX) stands out as the most
powerful indicator to explain the global factor. For the recovery period, ?nancial
market indicators are statistically insigni?cant in explaining the global risk (though
the point estimates with the expected sign). Fluctuations in the VIX explain 33% of
the movements in the global risk factor, the TED spread 19%, and the yield spread
7%.
The lessons I derive from the analysis are the following: First, investors’ risk
sentiment (or uncertainty about the US economy) is the single and most powerful
123
indicator of global risk factor a?ecting the emerging markets. Second, power of
?nancial market indicators in explaining the global factor depends on the state of
the global ?nancial markets. It is the high-stress period during which ?nancial
market variables have the highest explanatory power. Third, existence of ?ight
to safe US assets appears to be a relevant ingredient for the increase in emerging
markets’ sovereign risk premium in the recent era.
2.5 Robustness (Including Advanced Economies & Using Higher Fre-
quency)
How ‘global’ is the common driver of emerging markets’ sovereign risk? Given many
developed economies in Europe, how ‘European’ is the estimated European regional
risk factor? Does using monthly frequency (rather than a higher frequency) miss
important information? This section studies robustness of the results using a larger
sample (including advanced economies) and higher frequency (using weekly data).
I include all the economies for which the CDS trading exists for at least one
third of the sample period (October 2000 to February 2012). Additional countries
included are Belgium, France, Germany, Italy, Latvia, Netherlands, Portugal, Slo-
vakia, Spain and Sweden. Moreover, I use weekly (rather than monthly) average of
daily 5-year sovereign CDS data.
The estimated evolution of global factor is very similar to the one estimated
using the emerging markets alone (Figure 2.8).
30
As developed economies chimes
30
See Figure 2.12 in the Appendix for the estimated evolution of states. Note that estimated
idiosyncratic factors are inline with major economic events in these economies. Regarding the
124
in the estimation mostly after 2005, it is more fair to compare the evolutions after
2005. The global factor hits record high levels in late 2008, gets stabilized after
almost a year, and exhibits a further surge in mid 2011. While Latin American
and Asian regional factors follow similar patterns with the ones estimated before,
European regional risk factor is now noticeably higher due to including developed
economies (Figure 2.9).
2.6 Conclusion
This paper studies global, regional and idiosyncratic components of emerging mar-
kets’ sovereign credit risk premium, using a newly-developed data set, sovereign
credit default swaps. I use dynamic factor modeling to extract these components
rather than relying on restrictive assumptions on which variable would capture these
components. Moreover, I explore the performance of global ?nancial variables often
used in the literature to proxy global risk in explaining the extracted global risk
factor.
The results suggest that a large portion of emerging markets’ sovereign risk
premium is due to common external factors. On average, about 63% of the variations
in the sovereign risk is due to the global factor, and about 21% due to regional
factors. There is, however, substantial heterogeneity among the emerging markets.
Second, the global factor seems to be best re?ected by the CBOE’s VIX, a
idiosyncratic factor for the additional economies, for instance, the surge of the Italian CDS in mid
2011, of Portuguese and Spanish CDSs in 2010 are inline the unraveled ?scal solvency problems
in these economies at the time. Swedish idiosyncratic factor keeps declining during the last few
years, inline with the Swedish ?scal performance (maintaining very low levels of public debt to
GDP).
125
re?ection of investors’ risk sentiment, regardless of the regimes considered (high-
stress, low-to-moderate stress, or recovery regimes). VIX explains around 87% of
the global factor during high stress times, and of around 55% on average, while the
TED spread 50% during high stress times, and 20% on average. Furthermore, the
results also suggest that in times of high stress, investors seek for safe US assets,
which contributes to a rise in emerging markets’ sovereign risk. The yield spread
between long-term US Treasury notes which by-and-large re?ects liquidity premium
has a lower power in explaining the global factor (of about 7% to 25%).
Third, concerns about the future of Eurozone appear to go beyond the regional
boundaries, and become a global risk factor after June 2010. Estimating a DFM
with a single common driver, the results show that the common driver follows the
European risk factor surprisingly well starting in June 2010.
The evolution of common factors are by and large robust to including de-
veloped economies and using higher frequency. This result suggests that emerging
markets’ sovereign risks are not decoupled from how the developed economies per-
form.
For future research, linking the regional factors to ?nancial market variables
in central economies would shed further light on the nature of regional factors.
Moreover, to provide a further understanding on the contribution of regional factors,
one can partition economies within the regions using clustering methods. These
points are left to future research.
126
2.7 Appendix - Kalman Filter
Let y
t
denote an (nx1) vector of variables that are observable at t, and be driven
by a (kx1) vector of latent (unobserved) variables, s
t
. The dynamics of y
t
can
be represented by a state-space representation given by the following system of
equations:
y
t
= As
t
+u
t
[Signal equation] (2.13)
s
t+1
= Bs
t
+v
t+1
[State equation] (2.14)
where u
t
? N(0, R) and v
t
? N(0, Q), with E[u
t
u
?
] = R and E[v
t
v
?
] = Q if t = ?,
and 0 if t = ?. The matrices A, B, R, and Q have the dimensions nxk, kxk, nxn,
and kxk, respectively. Moreover, the disturbances u
t
and v
t
are assumed to be
uncorrelated at all lags, E[v
t
u
?
] = 0 ? t and ?. Also, the initial value of s
t
, s
1
, is
assumed to be uncorrelated with v
t
and u
t
?t.
The Kalman ?lter is an iterative algorithm whereby an initial estimate of the
latent factors is obtained from the state equation. This estimate is then used to
compute an estimate of the observable variables, y
t
. Using the observed and the
estimated values of y
t
, s
t
is updated through the Kalman gain.
In particular, denote conditional means of y
t
and s
t
by
y
t|t?1
= E
t?1
[y
t
] = As
t|t?1
(2.15)
127
s
t|t?1
= E
t?1
[s
t
] = Bs
t?1|t?1
(2.16)
and the conditional variables by
V
t|t?1
= E
t?1
[(y
t
?y
t|t?1
)(y
t
?y
t|t?1
)
] = AP
t|t?1
A
+R (2.17)
P
t|t?1
= E
t?1
[(s
t
?s
t|t?1
)(s
t
?s
t|t?1
)
] = BP
t?1|t?1
B
+Q (2.18)
Given s
1|0
and P
1|0
, one can deduce the adjustment to the factor estimate using the
observables. That is,
s
t|t
?s
t|t?1
= P
t|t?1
A
V
?1
t|t?1
(y
t
?y
t|t?1
) (2.19)
P
t|t
?P
t|t?1
= P
t|t?1
A
V
?1
t|t?1
AP
t|t?1
(2.20)
where G
t
= P
t|t?1
A
V
?1
t|t?1
is the Kalman gain, the adjustment to the latent factor
given the di?erence between the actual and estimated values of observables.
Initial values s
1|0
and P
1|0
are given by
s
1|0
= 0 (2.21)
vec(P
1|0
) = (I
kxk
?(B ?B))
?1
vec(Q) (2.22)
128
2.8 Appendix - Tables and Figures
129
Table 2.1: Descriptive Statistics for Sovereign Credit Default Swap (10/2000 -
4/2012)
Mean Std. Dev. Minimum Median Maximum Start N
Argentina 909.24 933.95 193.55 616.56 4271.17 6/2005 81
Brazil 476.22 659.90 65.68 177.12 3549.73 10/2001 125
Bulgaria 220.68 169.98 13.86 207.65 641.30 10/2000 137
Chile 70.20 55.03 12.98 61.43 259.14 1/2003 110
China 59.35 47.77 10.65 40.70 230.22 1/2003 110
Colombia 250.75 165.22 76.07 164.61 825.31 1/2003 110
Croatia 183.01 142.75 15.77 128.00 536.20 10/2000 137
Greece 285.91 603.89 5.46 13.93 3515.85 3/2003 104
Hungary 147.41 166.78 12.71 42.41 635.71 3/2002 120
Indonesia 230.84 141.00 100.90 193.63 805.69 10/2004 86
Korea 88.44 79.51 15.15 69.65 414.03 2/2002 121
Lithuania 313.15 174.72 6.00 285.65 765.38 12/2006 47
Malaysia 87.15 62.50 13.84 78.06 276.18 10/2001 125
Mexico 144.29 88.05 30.28 117.09 411.81 10/2001 125
Panama 171.28 84.07 65.20 143.37 435.00 10/2001 100
Peru 188.38 100.77 65.30 151.92 555.91 10/2003 101
Philippines 289.35 143.54 101.39 231.83 620.28 4/2002 119
Poland 77.86 76.38 8.34 46.87 360.63 10/2000 137
Romania 210.44 162.88 17.68 192.69 711.58 10/2002 113
Russia 283.35 252.89 39.42 189.68 1015.50 10/2000 137
Thailand 91.04 61.82 27.03 83.30 302.43 4/2002 118
Turkey 404.22 289.85 134.40 268.34 1212.50 10/2000 137
Ukraine 659.07 798.73 131.80 353.50 4280.02 8/2004 91
Venezuela 811.84 592.91 132.69 694.44 2824.82 1/2003 110
Vietnam 240.23 130.21 58.66 249.03 501.09 5/2006 67
Notes. The values are based on monthly average of daily 5-year sovereign CDS spreads. The
spreads are in basis points.
Table 2.2: Cross-correlations between Common External Factors
Global Europe Latin America Asia
Global 1
Europe 0.10 1
Latin America 0.19 -0.53 1
Asia -0.09 0.80 -0.61 1
130
Table 2.3: Contribution of Factors to the Sovereign CDS
Global Regional Idiosyncratic
Argentina
a
0.92 0.05 0.04
Brazil 0.11 0.82 0.07
Bulgaria 0.79 0.17 0.04
Chile 0.93 0.00 0.07
China 0.77 0.20 0.03
Colombia 0.33 0.67 0.00
Croatia 0.47 0.52 0.02
Greece 0.01 0.21 0.78
Hungary 0.44 0.18 0.38
Indonesia 0.85 0.00 0.14
Korea 0.78 0.05 0.17
Lithuania 0.82 0.08 0.10
Malaysia 0.81 0.16 0.03
Mexico 0.85 0.08 0.07
Panama 0.60 0.39 0.01
Peru 0.41 0.56 0.03
Philippines 0.41 0.02 0.57
Poland 0.36 0.33 0.30
Romania 0.53 0.29 0.18
Russia 0.85 0.01 0.14
Thailand 0.73 0.27 0.00
Turkey 0.51 0.07 0.43
Ukraine 0.91 0.01 0.08
Venezuela 0.69 0.01 0.30
Vietnam 0.74 0.06 0.19
Average 0.63 0.21 0.17
Median 0.73 0.16 0.08
Notes. Values in bold correspond to those above the median.
a
The values for Argentina are based on a rather recent period (Argen-
tinean CDS trading starts in 2005 after a 4-year default period). As there
is no data for the default period, Argentinean CDS seems to be driven only
negligibly by the idiosyncratic factor, though the default itself is mostly
idiosyncratic.
131
Table 2.4: Global Factor - Global Financial Market Indicators
?TED Spread ?T-Bill Spread (20y-10y) ?VIX
? 1.811
??
0.002
??
0.160
??
Whole [1.210,2.411] [0.000,0.004] [0.158,0.162]
Sample R
2
0.225 0.021 0.585
N 124 124 124
Regime 1 ? 2.556
??
0.0261 0.213
??
(High Stress) [0.301,5.991] [-0.031,0.080] [0.125,0.295]
(?G > ?
high
) R
2
0.493 0.244 0.858
N 11 6 7
?
high
0.675
††
1.036
††
0.947
††
[0.613,1.111] [1.036,1.116] [0.947,1.111]
Regime 2 ? 0.535
??
0.002
??
0.067
??
(Low-to-moderate Stress) [0.219,0.851] [0.000,0.003] [0.042,0.089]
(?
low
? ?G ? ?
high
) R
2
0.116 0.115 0.351
N 106 107 112
?
low
?1.096
††
?0.772
††
?1.338
††
[-1.139,-1.096] [-1.353,-0.638] [-1.353,-0.354]
Regime 3 ? 3.707 0.004 0.237
(Recovery) [-0.124,7.539] [-0.006,0.014] [-0.10,0.49]
(?G < ?
low
) R
2
0.192 0.073 0.331
N 7 11 5
Notes.
??
indicates signi?cance level at 1%. †† indicates the null of linearity is rejected at a 1% level. The TED spread
is the di?erence between the 3-month U.S. Treasury bill and 3-month USD LIBOR. The VIX is the Chicago Board of
Options Exchange index of percentage implied volatility.
1
3
2
Figure 2.1: 5-year Sovereign CDS Spreads
0
500
1,000
1,500
2,000
2,500
3,000
00 01 02 03 04 05 06 07 08 09 10 11
ARGENTINA BRAZIL BULGARIA
CHILE CHINA COLOMBIA
CROATIA GREECE HUNGARY
INDONESIA KOREA LITHUANIA
MALAYSIA MEXICO PANAMA
PERU PHILIPPINES POLAND
ROMANIA RUSSIA THAILAND
TURKEY UKRAINE VENEZUELA
VIETNAM
Brazil: 3550 bp
Argentina: 4271 bp
Ukraine: 4280 bp
Greece: 3516 bp
133
Figure 2.2: Global Factor and Major Events
-4
-2
0
2
4
6
8
10
12
01 02 03 04 05 06 07 08 09 10 11
Lehman Brothers
files for bankruptcy
(9/2008)
TARP; CPFF; TALF;
extending PDCF, AMLF, TSLF;
swap lines among major CBs;
IMF’s liquidity facility
(10/11/12 2008)
Fed’s extension of
liquidity facilities
(AMLF, CPFF,
PDCF, TSLF)
(6/2009)
Freddie Mac
announces
not buying
most risky MBSs
(2/2007)
1st bailout package
of 110bn to Greece
(5/2010)
Increased concerns
about Italy and Spain
(8/11)
3rd Greek
bailout (10/11)
Latin American Crisis
(Brazil: Debt Crisis, Elections, 6/2002)
(Argentina*: Default, Inflation
and Banking Crises, 2001-)
(Uruguay*: Banking Crisis, 7/2002-)
(contagious effects on the region)
____________________
IMF Programs-
(Brazil: 2001-2002)
(Argentina: 2001-2005)
(Colombia: 2003, 2005)
Abbreviations. AMLF: Asset-Backed Commercial Paper Money Market Mutual Fund Liquidity
Facility. CPFF: Commercial Paper Funding Facility. PDCF: Primary Dealer Credit Facility.
MBS: Mortgage-backed security. TARP: Troubled Asset Relief Program. TALF: Term Asset-
Backed Securities Loan Facility. TSLF: Term Securities Lending Facility.
134
Figure 2.3: Sovereign CDS and Regions
-2
-1
0
1
2
3
4
5
6
-12
-8
-4
0
4
8
12
16
20
01 02 03 04 05 06 07 08 09 10 11
BULGARIA CROATIA
GREECE HUNGARY
LITHUANIA POLAND
ROMANIA RUSSIA
TURKEY UKRAINE
European Factor (RHS) Global Factor (RHS)
-2
-1
0
1
2
3
4
5
-10
-5
0
5
10
15
20
25
01 02 03 04 05 06 07 08 09 10 11
ARGENTINA BRAZIL
CHILE COLOMBIA
MEXICO PANAMA
PERU VENEZUELA
Latin American Factor (RHS) Global Factor (RHS)
-2
-1
0
1
2
3
4
5
-12
-8
-4
0
4
8
12
16
01 02 03 04 05 06 07 08 09 10 11
CHINA INDONESIA
KOREA MALAYSIA
PHILIPPINES THAILAND
VIETNAM Asian Factor (RHS)
Global Factor (RHS)
135
Figure 2.4: Common Factor versus the European Factor
-15
-10
-5
0
5
10
15
20
25
01 02 03 04 05 06 07 08 09 10 11
Common Factor (Single-Factor DFM)
European Factor (Two-Factor DFM)
6/2010
10/2008
136
Figure 2.5: Decomposing Sovereign CDS
-2
-1
0
1
2
3
4
-10
-5
0
5
10
15
20
01 02 03 04 05 06 07 08 09 10 11
Chilean CDS, Standardized (LHS)
Global Factor (RHS)
Regional Factor, Latin America (RHS)
Idiosyncratic Factor (LHS)
Contribution of Factors:
Global: 93%
Regional: 0%
Idiosyncratic: 7%
-1
0
1
2
3
4
5
6
-8
-4
0
4
8
12
16
20
01 02 03 04 05 06 07 08 09 10 11
Greek CDS, Standardized (LHS)
Global Factor (RHS)
Regional Factor, Europe (RHS)
Idiosyncratic Factor (LHS)
Contribution of Factors:
Global: 1%
Regional: 21%
Idiosyncratic: 78%
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-12
-8
-4
0
4
8
12
16
20
01 02 03 04 05 06 07 08 09 10 11
Philippines’ CDS, Standardized (LHS)
Global Factor (RHS)
Regional Factor, Asia (RHS)
Idiosyncratic Factor (LHS)
Contribution of Factors:
Global: 41%
Regional: 2%
Idiosyncratic: 57%
-2
-1
0
1
2
3
4
-8
-4
0
4
8
12
16
01 02 03 04 05 06 07 08 09 10 11
Turkey’s CDS - Standardized (LHS)
Global Factor (RHS)
Regional Factor, Europe (RHS)
Idiosyncratic Factor (LHS)
Contribution of Factors:
Global: 51%
Regional: 7%
Idiosyncratic: 43%
1
3
7
Figure 2.6: Chinn-Ito Index versus the Contribution of External Factors
Figure 2.7: Financial Market Indicators
-1
0
1
2
3
4
5
10
20
30
40
50
60
70
01 02 03 04 05 06 07 08 09 10 11
TED Spread (LHS)
Yield Spread (annual %-change) (LHS)
VIX (RHS)
138
Figure 2.8: Global Factor -Including Developed Economies-
-10
-5
0
5
10
15
20
25
30
-4
-2
0
2
4
6
8
10
12
01 02 03 04 05 06 07 08 09 10 11
Global Factor (including developed economies) (LHS)
Global Factor (emerging markets) (RHS)
Figure 2.9: European Regional Risk Factor -Including Developed Economies-
-10
0
10
20
30
40
01 02 03 04 05 06 07 08 09 10 11
European Regional Risk Factor (emerging markets)
European Regional Risk Factor (including developed economies)
139
Figure 2.10: Smoothed States -Two-Factor DFM-
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Argentina Idiosyncratic Factor
-1.2
-0.8
-0.4
0.0
0.4
0.8
01 02 03 04 05 06 07 08 09 10 11
Brazil Idiosyncratic Factor
-.8
-.4
.0
.4
.8
01 02 03 04 05 06 07 08 09 10 11
Bulgaria Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Chile Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
01 02 03 04 05 06 07 08 09 10 11
China Idiosyncratic Factor
-.4
-.2
.0
.2
.4
01 02 03 04 05 06 07 08 09 10 11
Colombia Idiosyncratic Factor
-.8
-.4
.0
.4
.8
01 02 03 04 05 06 07 08 09 10 11
Croatia Idiosyncratic Factor
-4
-2
0
2
4
6
01 02 03 04 05 06 07 08 09 10 11
Greece Idiosyncratic Factor
-2
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Hungary Idiosyncratic Factor
-2
-1
0
1
2
3
01 02 03 04 05 06 07 08 09 10 11
Indonesia Idiosyncratic Factor
-3
-2
-1
0
1
01 02 03 04 05 06 07 08 09 10 11
Korea Idiosyncratic Factor
-2
-1
0
1
01 02 03 04 05 06 07 08 09 10 11
Lithuania Idiosyncratic Factor
-.8
-.4
.0
.4
.8
01 02 03 04 05 06 07 08 09 10 11
Malaysia Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
01 02 03 04 05 06 07 08 09 10 11
Mexico Idiosyncratic Factor
-0.8
-0.4
0.0
0.4
0.8
1.2
01 02 03 04 05 06 07 08 09 10 11
Panama Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Peru Idiosyncratic Factor
-2
-1
0
1
2
3
01 02 03 04 05 06 07 08 09 10 11
Philippines Idiosyncratic Factor
-3
-2
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Poland Idiosyncratic Factor
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Romania Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Russia Idiosyncratic Factor
-.4
-.2
.0
.2
.4
01 02 03 04 05 06 07 08 09 10 11
Thailand Idiosyncratic Factor
-3
-2
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Turkey Idiosyncratic Factor
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Ukraine Idiosyncratic Factor
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Venezuela Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Vietnam Idiosyncratic Factor
-5
0
5
10
15
01 02 03 04 05 06 07 08 09 10 11
Global Factor
-10
0
10
20
30
01 02 03 04 05 06 07 08 09 10 11
Latin America Factor
-10
0
10
20
01 02 03 04 05 06 07 08 09 10 11
Europe Factor
-12
-8
-4
0
4
8
12
01 02 03 04 05 06 07 08 09 10 11
Asia Factor
1
4
0
Figure 2.11: Smoothed States -Single-Factor DFM-
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Argentina Idiosyncratic Factor
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Brazil Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
03 04 05 06 07 08 09 10 11
Bulgaria Idiosyncratic Factor
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Chile Idiosyncratic Factor
-0.5
0.0
0.5
1.0
1.5
2.0
03 04 05 06 07 08 09 10 11
China Idiosyncratic Factor
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Colombia Idiosyncratic Factor
-2
-1
0
1
2
03 04 05 06 07 08 09 10 11
Croatia Idiosyncratic Factor
-2
0
2
4
6
03 04 05 06 07 08 09 10 11
Greece Idiosyncratic Factor
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Hungary Idiosyncratic Factor
-2
0
2
4
6
03 04 05 06 07 08 09 10 11
Indonesia Idiosyncratic Factor
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Korea Idiosyncratic Factor
-300
-200
-100
0
100
03 04 05 06 07 08 09 10 11
Lithuania Idiosyncratic Factor
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
03 04 05 06 07 08 09 10 11
Malaysia Idiosyncratic Factor
-3
-2
-1
0
1
2
03 04 05 06 07 08 09 10 11
Mexico Idiosyncratic Factor
-4
-2
0
2
4
6
03 04 05 06 07 08 09 10 11
Panama Idiosyncratic Factor
-4
-2
0
2
4
6
03 04 05 06 07 08 09 10 11
Peru Idiosyncratic Factor
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Philippines Idiosyncratic Factor
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Poland Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
03 04 05 06 07 08 09 10 11
Romania Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
03 04 05 06 07 08 09 10 11
Russia Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
03 04 05 06 07 08 09 10 11
Thailand Idiosyncratic Factor
-6
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Turkey Idiosyncratic Factor
-1
0
1
2
3
4
03 04 05 06 07 08 09 10 11
Ukraine Idiosyncratic Factor
-2
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Venezuela Idiosyncratic Factor
-50
0
50
100
03 04 05 06 07 08 09 10 11
Vietnam Idiosyncratic Factor
-20
-10
0
10
20
30
03 04 05 06 07 08 09 10 11
Global Factor
1
4
1
Figure 2.12: Smoothed States -Two-Factor DFM- (Including Developed Economies and Weekly Frequency)
-2
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Argentina Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Belgium Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Brazil Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
2000 2002 2004 2006 2008 2010
Bulgaria Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
2000 2002 2004 2006 2008 2010
Chile Idiosyncratic Factor
-0.8
-0.4
0.0
0.4
0.8
1.2
2000 2002 2004 2006 2008 2010
China Idiosyncratic Factor
-.8
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Colombia Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Croatia Idiosyncratic Factor
-.4
-.2
.0
.2
.4
2000 2002 2004 2006 2008 2010
France Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Germany Idiosyncratic Factor
-4
-2
0
2
4
6
2000 2002 2004 2006 2008 2010
Greece Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Hungary Idiosyncratic Factor
-2
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Indonesia Idiosyncratic Factor
-.8
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Italy Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Latvia Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Lithuania Idiosyncratic Factor
-.8
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Malaysia Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Mexico Idiosyncratic Factor
-3
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Netherlands Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
2000 2002 2004 2006 2008 2010
Panama Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
2000 2002 2004 2006 2008 2010
Peru Idiosyncratic Factor
-2
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Philippines Idiosyncratic Factor
-3
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Poland Idiosyncratic Factor
-2
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Portugal Idiosyncratic Factor
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Romania Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Russia Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
South Korea Idiosyncratic Factor
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Slovakia Idiosyncratic Factor
-.8
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Spain Idiosyncratic Factor
-2
0
2
4
2000 2002 2004 2006 2008 2010
Sweden Idiosyncratic Factor
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Thailand Idiosyncratic Factor
-2
0
2
4
2000 2002 2004 2006 2008 2010
Turkey Idiosyncratic Factor
-2
0
2
4
2000 2002 2004 2006 2008 2010
Ukraine Idiosyncratic Factor
-1
0
1
2
3
4
2000 2002 2004 2006 2008 2010
Venezuela Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Vietnam Idiosyncratic Factor
-10
0
10
20
30
2000 2002 2004 2006 2008 2010
Global Factor
-20
0
20
40
60
2000 2002 2004 2006 2008 2010
Latin American Factor
-20
0
20
40
60
2000 2002 2004 2006 2008 2010
European Factor
-20
-10
0
10
20
2000 2002 2004 2006 2008 2010
Asian Factor
1
4
2
Figure 2.13: Con?dence Interval Construction for the Thresholds (using the VIX)
?4 ?2 0 2 4 6 8
0
10
20
30
40
50
60
Threshold Variable:? G
L
ik
e
lih
o
o
d
R
a
t
io
S
e
q
u
e
n
c
e
in
?
LRN(?)
95% Critical
?4 ?3.5 ?3 ?2.5 ?2 ?1.5 ?1 ?0.5 0 0.5 1
0
5
10
15
20
25
30
35
40
45
50
Threshold Variable:? G
L
ik
e
lih
o
o
d
R
a
t
io
S
e
q
u
e
n
c
e
in
?
LRN(?)
95% Critical
143
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doc_983271529.pdf
The International Finance Corporation (IFC) is an international financial institution which offers investment, advisory, and asset management services to encourage private sector development in developing countries.
ABSTRACT
Title of dissertation: ESSAYS ON
MONETARY ECONOMICS AND
INTERNATIONAL FINANCE
Salih Fendoglu, Doctor of Philosophy, 2012
Dissertation directed by: Professor Boragan Aruoba
Department of Economics
This thesis consists of two chapters. In the ?rst chapter, I study optimal
monetary policy rules in a general equilibrium model with ?nancial market imper-
fections and uncertain business cycles. Earlier consensus view –using models with
?nancial ampli?cation with disturbances that have no direct e?ect on credit market
conditions– suggests that ?nancial variables should not be assigned an independent
role in policy making. Introducing uncertainty, time-variation in cross-sectional dis-
persion of ?rms’ productive performance, alters this policy prescription. The results
show that (i) optimal policy is to dampen the strength of ?nancial ampli?cation
by responding to uncertainty (at the expense of creating a mild degree of ?uctu-
ations in in?ation). (ii) a higher uncertainty makes the planner more willing to
relax ‘?nancial stress’ on the economy. (iii) Credit spreads are a good proxy for
uncertainty, and hence, within the class of simple monetary policy rules I consider,
a non-negligible interest rate response to credit spreads (32 basis points in response
to a 1% change in credit spreads) -together with a strong anti-in?ationary stance-
achieves the highest aggregate welfare possible.
In the second chapter, I study global, regional and idiosyncratic factors in
driving the sovereign credit risk premium (as measured by sovereign credit default
swaps) for a set of 25 emerging market economies during the last decade. The
results show that (i) On average, global and regional factors account for a substantial
portion of the movements in sovereign risk premium (of 63% and 21%, respectively).
(ii) there exists noticeable heterogeneity in the contribution of factors across the
emerging markets. (iii) The (extracted) global factor is best re?ected by the VIX
(investors’ risk sentiment) among the ?nancial market indicators considered. (iv)
There are regime changes in the relation between the global factor and the ?nancial
market indicators.
ESSAYS ON MONETARY ECONOMICS AND INTERNATIONAL
FINANCE
by
Salih Fendo? glu
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial ful?llment
of the requirements for the degree of
Doctor of Philosophy
2012
Advisory Committee:
Professor Boragan Aruoba, Chair
Professor Anton Korinek
Professor Pablo Derasmo
Professor Carlos Vegh
Professor Phillip L. Swagel (PUAF)
c Copyright by
Salih Fendoglu
2012
Dedication
To my family,
ii
Acknowledgments
I owe my gratitude to all the people who have made this thesis possible and
because of whom my graduate experience has been one that I will cherish forever.
Foremost, I would like to express my sincere gratitude to my advisor Prof.
Boragan Aruoba for his continuous support and guidance in the process of writing
my dissertation. His guidance helped me in all the time of research and writing of
this thesis.
I would like to thank Prof. Anton Korinek, Prof. Pablo Derasmo and Prof.
Carlos Vegh for sparing their invaluable time reviewing the manuscript, and for
agreeing to serve on my thesis committee. I also would like express my deepest
gratitude to Prof. Sanjay Chugh for all the support and guidance during most
stages of my dissertation.
I also would like to thank my fellow colleagues Yasin Mimir, Enes Sunel, Emre
Tiftik, Orhan Torul, Pablo Federico, and David Ruiz, for their comments throughout
the entire process, and for sharing their time to exchange ideas on various topics
beyond the dissertation and more. I also would like to express my deepest thanks
to Ali Fuad Selvi, Bedrettin Yazan, Bengu Caliskan Selvi, Elif Ture, Ferhan Ture,
Simal Ince and Tugrul Ince. I have been blessed with such a friendly and cheerful
group.
The help and support of sta? members at the Department of Economics was
invaluable. I would like to thank Vickie Fletcher, Elizabeth Martinez and Terry
Davis for accommodating my logistic needs and helping me out with technical issues
iii
regarding the doctorate program.
Last but not the least, I would like to thank my father Hasan Tahsin and my
mother Rabia who sincerely supported me in any moment of my life and always
kept their belief in me. I also would like to thank my brothers Bekir and Cem for
the support and cheering me up when I looked gloomy. And special thanks to my
beloved one Burcu Polat for standing by me through the good and bad times.
iv
Table of Contents
List of Tables vii
List of Figures viii
1 Optimal Monetary Policy Rules, Financial Ampli?cation,and Uncertain Business Cycles 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.2.2 Entrepreneurs . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2.3 Retailers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2.4 Monetary Authority and the Government . . . . . . . . . . . . 18
1.2.5 Equilibrium and Aggregation . . . . . . . . . . . . . . . . . . 19
1.3 Functional Forms and Calibration . . . . . . . . . . . . . . . . . . . . 21
1.4 Decentralized Equilibrium and Cross-Sectional Dispersion . . . . . . . 26
1.4.1 Long-run equilibrium and long-run cross sectional dispersion . 27
1.4.2 Dynamics of the model and cross-sectional dispersion . . . . . 29
1.4.2.1 Productivity and Government Spending Shocks . . . 29
1.4.2.2 Uncertainty Shocks . . . . . . . . . . . . . . . . . . . 31
1.5 Welfare Evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.6 Optimal Monetary Policy . . . . . . . . . . . . . . . . . . . . . . . . 38
1.6.1 Sources of Ine?ciencies . . . . . . . . . . . . . . . . . . . . . . 38
1.6.2 Ramsey optimal policy problem . . . . . . . . . . . . . . . . . 41
1.6.2.1 Cyclical Volatilities . . . . . . . . . . . . . . . . . . . 42
1.6.2.2 Reducing the strength of ?nancial ampli?cation . . . 43
1.6.2.3 Reducing the contribution of uncertainty on business cycles 44
1.6.2.4 Impulse Responses . . . . . . . . . . . . . . . . . . . 45
1.7 Optimal Simple and Implementable Policy Rules . . . . . . . . . . . . 48
1.8 Further Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
1.9 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
1.10 Appendix - Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
1.11 Appendix - Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
1.12 Appendix - Competitive Equilibrium, Calibration and Further Discussions 74
2 Global and Regional Factors in Driving Emerging Markets’ Sovereign Risk Premium 96
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
2.2 Data and the Methodology . . . . . . . . . . . . . . . . . . . . . . . . 103
2.3 Empirical Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.3.1 Evolution of Global and Regional Factors . . . . . . . . . . . . 109
2.3.2 Contribution of Factors . . . . . . . . . . . . . . . . . . . . . . 114
2.3.3 Idiosyncratic factor and four examples. . . . . . . . . . . . . . 115
2.4 Interpreting the Global Risk Factor . . . . . . . . . . . . . . . . . . . 118
2.5 Robustness (Including Advanced Economies & Using Higher Frequency)124
2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125
v
2.7 Appendix - Kalman Filter . . . . . . . . . . . . . . . . . . . . . . . . 127
2.8 Appendix - Tables and Figures . . . . . . . . . . . . . . . . . . . . . 129
vi
List of Tables
1.1 Timing of Events . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.2 Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3 Variance Decomposition (Decentralized Economy) . . . . . . . . . . . 35
1.4 Cyclical Volatilities (%-standard deviations) . . . . . . . . . . . . . . 43
1.5 Variance Decomposition (Decentralized Economy vs. Ramsey Planner’s) 45
1.6 Simple Rules versus Optimal Policy (Baseline Calibration) . . . . . . 61
1.7 Business Cycle Statistics -Decentralized Economy- . . . . . . . . . . . 64
1.8 Business Cycle Statistics -Planner’s Economy- . . . . . . . . . . . . . 65
1.9 Business Cycle Statistics (only ?nancial frictions) -Decentralized Economy- 66
1.10 Business Cycle Statistics (only ?nancial frictions) -Planner’s Economy- 67
1.11 Estimated AR(1) Processes . . . . . . . . . . . . . . . . . . . . . . . 94
2.1 Descriptive Statistics for Sovereign Credit Default Swap . . . . . . . . 130
2.2 Cross-correlations between Common External Factors . . . . . . . . . 130
2.3 Contribution of Factors to the Sovereign CDS . . . . . . . . . . . . . 131
2.4 Global Factor - Global Financial Market Indicators . . . . . . . . . . 132
vii
List of Figures
1.1 Long-run equilibria as a function of long-run cross-sectional dispersion 28
1.2 Impulse Responses to a 1 sd. increase in total factor productivity . . 30
1.3 Change in the cross-sectional dispersion . . . . . . . . . . . . . . . . . 32
1.4 Impulse Responses to a 1 sd. increase in uncertainty . . . . . . . . . 33
1.5 Strength of Financial Ampli?cation (Planner’s Economy) . . . . . . . 44
1.6 Ramsey Impulse Responses to a 1 sd. increase in total factor productivity 46
1.7 Ramsey Impulse Responses to a 1 sd. increase in uncertainty . . . . . 47
1.8 Responding to Asset Prices -productivity shocks- . . . . . . . . . . . 50
1.9 Responding to Asset Prices -uncertainty shocks- . . . . . . . . . . . . 51
1.10 Welfare Surfaces (Benchmark Uncertainty versus High Uncertainty) . 52
1.11 Welfare Surfaces (Responding to Uncertainty) . . . . . . . . . . . . . 53
1.12 Shadow Value of Relaxing the Financial Constraint . . . . . . . . . . 59
1.13 Long-run equilibria as a function of monopolistic competition . . . . . 62
1.14 Long-run equilibria as a function of long-run in?ation . . . . . . . . . 63
1.15 Impulse Responses to a 1 sd. increase in government spending . . . . 68
1.16 Strict In?ation Stabilization versus Ramsey Policy -productivity shocks- 69
1.17 Responding to Output Gap -productivity shocks- . . . . . . . . . . . 70
1.18 Responding to Output Gap -uncertainty shocks- . . . . . . . . . . . . 71
1.19 Welfare Surface -TFP and G Shocks- . . . . . . . . . . . . . . . . . . 71
1.20 Welfare Surface -Uncertainty Shock- . . . . . . . . . . . . . . . . . . 72
1.21 Welfare Surface -All Shocks- . . . . . . . . . . . . . . . . . . . . . . . 72
1.22 Welfare Surface -Uncertainty Shock- . . . . . . . . . . . . . . . . . . 73
1.23 Welfare Surface -All Shocks- . . . . . . . . . . . . . . . . . . . . . . . 73
1.24 TFP and Real Government Spending (G) . . . . . . . . . . . . . . . . 93
1.25 VXO or Cross-Sectional Dispersion . . . . . . . . . . . . . . . . . . . 93
1.26 TFP, Government Spending, and Uncertainty Shocks . . . . . . . . . 95
2.1 5-year Sovereign CDS Spreads . . . . . . . . . . . . . . . . . . . . . . 133
2.2 Global Factor and Major Events . . . . . . . . . . . . . . . . . . . . . 134
2.3 Sovereign CDS and Regions . . . . . . . . . . . . . . . . . . . . . . . 135
2.4 Common Factor versus the European Factor . . . . . . . . . . . . . . 136
2.5 Decomposing Sovereign CDS . . . . . . . . . . . . . . . . . . . . . . . 137
2.6 Chinn-Ito Index versus the Contribution of External Factors . . . . . 138
2.7 Financial Market Indicators . . . . . . . . . . . . . . . . . . . . . . . 138
2.8 Global Factor -Including Developed Economies- . . . . . . . . . . . . 139
2.9 European Regional Risk Factor -Including Developed Economies- . . 139
2.10 Smoothed States -Two-Factor DFM- . . . . . . . . . . . . . . . . . . 140
2.11 Smoothed States -Single-Factor DFM- . . . . . . . . . . . . . . . . . 141
2.12 Smoothed States (Developed Economies and Weekly Frequency) . . . 142
2.13 Con?dence Interval Construction for the Thresholds (using the VIX) 143
viii
Chapter 1
Optimal Monetary Policy Rules, Financial Ampli?cation,
and Uncertain Business Cycles
1.1 Introduction
Should ?nancial variables per se be important for monetary policy making? This
question has attracted considerable attention in both policy and academic circles
during the last decade. The conventional wisdom, as stated in many central banks’
statutory mandates, is that in?ation and output stability should be the central goal
of monetary policy: While ?nancial variables (e.g. credit spreads or asset prices)
are with no doubt important ingredients for policy making, they are argued to be
useful in so far they help predicting in?ation and real economic activity.
1
Intro-
ducing uncertainty, time-variation in cross-sectional dispersion of ?rms’ productive
performance, alters the conventional wisdom: Optimal policy prescribes a direct and
systematic response to credit spreads (above and beyond what in?ation and output
gap would imply).
2
Such a policy dampens distortionary e?ects of uncertainty, and
helps containing adverse feedback e?ects between ?nancial conditions and the real
1
For potential channels through which ?uctuations in ?nancial variables transmit into business
cycles, see Cecchetti et al. (2000), Gilchrist and Leahy (2002), and Gilchrist, Sim, and Zakrajsek
(2010). The former two focus on asset prices, and the latter on corporate bond credit spreads.
2
For recent studies on uncertainty, see among others Bloom (2009), Bloom, Floetotto, and
Jaimovich (2010), Gilchrist, Sim and Zakrajsek (2010), Arellano, Bai and Kehoe (2010), Christiano,
Motto and Rostagno (2010), Bachmann and Bayer (2011), Bekaert, Hoerova, and Duca (2011),
Chugh (2011), and Basu and Bundick (2011). These shocks have also been labeled as risk or
dispersion shocks in the literature.
1
economy.
I use a canonical New-Keynesian model with ?nancial market imperfections
to study optimality of responding to ?nancial variables.
3
Providing a tight link
between market imperfections and ?nancial variables, the ?nancial ampli?cation
model of Bernanke, Gertler, and Gilchrist (BGG, hereforth), a workhouse model
widely used in the New-Keynesian ?nancial frictions literature, o?ers a natural en-
vironment to study optimality of responding to ?nancial variables. Existence of
these imperfections, however, does not necessarily imply a direct response to ?nan-
cial variables as a way to mitigate the resulting distortions and improve aggregate
welfare. Using traditional ?rst-moment shocks that have no direct e?ect on credit
market conditions, earlier consensus view suggests that it is optimal not to assign
an independent role to ?nancial variables in policy making.
4
As an additional pulse driving the business cycles, I introduce uncertainty,
exogenous time-variation in cross-sectional dispersion of ?rms’ productive perfor-
mance. Among potential channels through which uncertainty may transmit into
business cycle ?uctuations, here I consider credit channel owing to ?nancial frictions
3
Such imperfections manifest themselves through existence of a spread, a wedge between bor-
rowing and lending rates, that would be absent under perfect capital markets. At the heart of the
mechanism lie credit spreads being linked to borrowers’ indebtedness (leverage) which in turn is
driven by movements in asset prices.
4
In the presence of any sort of asset price imbalances, a gap between observed and fundamen-
tal/potential level of asset prices, it might be optimal to respond to ?nancial variables (if the policy
maker could measure these imbalances at the ?rst place). See Bernanke and Gertler (2001), Dupor
(2005), and Gilchrist and Saito (2008), among others. Here I do not consider non-fundamental
movements in asset prices. Faia and Monacelli (2007), using traditional ?rst-moment shocks, show
that there might be a non-negligible marginal welfare gain of responding to (fundamental level
of) asset prices under a reasonably low degree of anti-in?ationary stance (roughly between one to
two, as typically studied in the literature). They conclude that the policy makers should pursue
a lean-with-the-wind policy reaction to movements in asset prices (e.g. decrease the policy rate in
response to an increase in asset prices). Interested readers may refer to Gilchrist and Saito (2008)
for a brief literature review on the pre-crisis consensus view.
2
in the model.
5
In particular, uncertainty has two direct e?ects on credit market con-
ditions. First, it a?ects the measure of borrowers that will go bankrupt. Second, it
a?ects net worth that will be retained by borrowers, and hence the quality of balance
sheet of borrowers. Accordingly, a higher dispersion, for instance, implies a higher
risk for banks’ overall loan portfolio, making banks less willing to extend credit. As
a result, the equilibrium level of credit spread rises and investment declines.
The main contribution of this paper is that, despite the emphasis on uncer-
tainty as a potential driver of business cycles in the literature, whether and how
monetary policy prescriptions would di?er from the conventional wisdom under un-
certain business cycles remains an open question. Moreover, in models with costly-
state-veri?cation type ?nancial market imperfections (e.g. BGG), uncertainty, as
discussed above, is primarily a ‘?nancial’ shock, directly a?ecting borrowers’ ability
to raise funds. In this regard, studying uncertainty also sheds light on normative
implications of introducing disturbances that are of ?nancial type on monetary pol-
icy.
6
The results suggest that optimal policy is to dampen the strength of ?nancial
5
Using models with ?nancial frictions, Gilchrist, Sim and Zakrajsek (2010), Arellano, Bai and
Kehoe (2010), Christiano, Motto and Rostagno (2010), and Chugh (2011) also consider a credit
channel. For other potential channels, see Bloom (2009), Bloom, Floetotto, and Jaimovich (2010),
Bachmann and Bayer (2011), and Basu and Bundick (2011).
6
See, among others, Nolan and Thoenissen (2009), Gilchrist, Ortiz and Zakrajsek (2009), Es-
pinoza et al. (2009), Christiano, Motto, and Rostagno (2010), Jermann and Quadrini (2011),
and Gilchrist and Zakrajsek (2011) on the contribution of ?nancial shocks (shocks that have a
direct e?ect on credit market conditions) on business cycle ?uctuations. This class of distur-
bances includes (but not limited to) shocks that lead to exogenous movements in borrowers’ net
worth -that a?ects e?ciency of contractual relations between borrowers and lenders- (Gilchrist and
Leahy, 2002; Nolan and Thoenissen, 2009; Gilchrist, Ortiz and Zakrajsek, 2010; Christiano, Motto,
and Rostagno, 2010), external ?nance premium -that a?ects e?ciency of ?nancial intermediation-
(Gilchrist, Ortiz and Zakrajsek, 2010), sensitivity of external ?nance premium to the leverage -
that a?ects the strength of ?nancial ampli?cation- (Dib, 2010), or borrowers’ ability to raise funds
(Jerman and Quadrini, 2011).
3
ampli?cation by responding to uncertainty.
7
The planner achieves so by reducing
the sensitivity of external ?nance premium to borrowers’ leverage, e?ectively in-
creasing the e?ciency of ?nancial intermediation that would otherwise occur in a
decentralized economy. This, however, comes at the expense of creating a mild
degree of ?uctuations in in?ation. The intuition lies on the fact that the tension
between price stickiness (which creates ?uctuations in the intratemporal wedge) and
?nancial frictions (which creates ?uctuations in the intertemporal wedge) tends to
be resolved in favor of the latter if uncertainty shocks come into play. Note also
that the planner is endowed with a single policy tool, the short-term nominal inter-
est rate. Introducing appropriate additional tools (e.g. macro-prudential policies)
would imply a lesser role for the short-term nominal interest rate in smoothing the
intertemporal wedge (or in neutralizing ?nancial market imperfections).
A key question then is whether simple policy rules, that include only a few
observable macroeconomic variables, can attain a welfare level close to the planner’s,
and the optimal magnitude of response to ?nancial variables (if not nil). As an
additional input to policy making (besides in?ation and output gap), I consider
credit spread, the key variable that is tightly linked to ?nancial distortions. In
practice, credit spreads are easily observable to policy makers, and accordingly can
be thought as a desirable input to the policy. For comparison purposes with the
earlier literature, I also study (fundamental level of) asset prices as an additional
7
The planner maximizes aggregate welfare subject to competitive equilibrium conditions, using
the short-term nominal interest rate as the policy tool. To have accurate welfare comparisons, I
conduct second-order approximation to the policy and welfare functions. Note also that uncer-
tainty, as a second-moment shock, has a ?rst-order e?ect on equilibrium dynamics.
4
input to the policy.
8
Con?rming the conventional wisdom, if the economy is driven only by tradi-
tional ?rst-moment disturbances, it is optimal not to respond to ?nancial variables,
and strict in?ation stabilization is the welfare maximizing policy. If the economy is
driven also by uncertainty shocks, the optimal rules suggest a non-negligible lean-
against-the-wind policy reaction to credit spreads. Such a response is mainly due
to spreads being driven mostly by uncertainty shocks.
9
The optimal magnitude of
response to credit spreads is generally less than one-to-one. Under the benchmark
scenario (when spreads ?uctuate moderately), the policy rate should be reduced by
32 basis points in response to a 1% increase in credit spreads.
10
This result holds
for su?ciently low level of anti-in?ationary reaction (less than 3). A stronger in?a-
tionary reaction would decrease the optimal magnitude of response to credit spreads
towards zero, as strict in?ation stabilization welfare dominates the optimized rule
(however small it is). Last but not least, the policy maker, if instead allowed to
react to uncertainty directly, would choose to do so to improve aggregate welfare.
To shed further light on the results, I study how strong the planner values
relaxing the ‘?nancial constraint’ from a historical perspective.
11
The results show
the higher the uncertainty, the stronger the planner values relaxing the ?nancial
8
I focus on the fundamental (as opposed to non-fundamental) movements in asset prices, since
modeling asset price imbalances is not the immediate goal of this paper.
9
If asset prices, which are driven mostly by productivity shocks in the model, is the ?nancial
variable included in the policy rule, then the corresponding policy response should be nil.
10
A 1% increase in credit spreads amounts to roughly a 2- to 3-standard-deviation increase in
credit spreads.
11
The key equation in the ?nancial ampli?cation mechanism links external ?nance premium to
aggregate leverage ratio. One can express this equation as a ?nancial constraint in that ?rms
can borrow a certain fraction of their net worth, the fraction depending on aggregate ?nancial
conditions.
5
constraint.
12
The planner’s willingness to relax the constraint exhibits a rapid de-
terioration starting in mid-2002, and hits record low by the end of 2006. During
recession periods, especially for the recent one, marginal bene?t of relaxing the
constraint rises substantially.
The main policy lesson, as hinted above, is that policy makers should closely
monitor time-variation in cross-sectional dispersion of ?rms performance. From a
practical point of view, however, the availability and the quality of information on
the dispersion may not be available in real time. Yet, since credit spreads could
serve as a good proxy for uncertainty, responding to the credit spreads can be used
as a general policy to have better aggregate outcomes.
Closely related to my work, Gilchrist and Zakrajsek (2011) use a similar model
with BGG-type ?nancial market imperfections. They show that a spread-augmented
policy rule dampens the e?ect of ?nancial ampli?cation and induces powerful stabi-
lizing e?ects on real and ?nancial variables. They, however, do not consider optimal
policy problem. Angeloni and Faia (2011) introduce a banking sector in an oth-
erwise standard New-Keynesian model, and show that containing ?uctuations in
asset prices (combined with mildly acyclical capital requirements) improves aggre-
gate welfare compared to simple policy rules. Curdia and Woodford (2010), using a
model with costly ?nancial intermediation, conclude that in response to disturbances
a?ecting e?ciency of ?nancial intermediation directly, it is optimal to respond to
credit spreads, with the optimal degree generally being less than one-to-one. Our
12
This result can also be interpreted along the lines of Gilchrist, Sim and Zakrajsek (2010). In
a richer model, they show that investment becomes more sensitive to borrowers’ net worth when
uncertainty is higher. Accordingly, the measure of ?rms which are ?nancially constrained is higher
and aggregate output declines in response to a higher uncertainty.
6
results suggest that it is not necessarily the credit supply channel per se that makes
containing ?uctuations in credit spreads optimal, but it is the underlying set of
disturbances that has a direct e?ect on credit market conditions that matters.
The chapter proceeds as follows: Section 1.2 presents the model economy,
Section 1.3 the functional forms and the calibration. Section 1.4 studies long-run
equilibria as a function of long-run cross-sectional dispersion, and the model dy-
namics in the decentralized equilibrium. Section 1.5 presents how to approximate
aggregate welfare, Section 1.6 the optimal monetary policy problem, and Section
1.7 the optimal simple policy rules. Section 1.8 provides the historical analysis, and
Section 1.9 concludes.
1.2 The Model
This section presents a brief description of the BGG. Readers may refer to Appendix
A for details. The di?erence is the existence of uncertainty shocks in the model
environment and recursively formulating some of the equilibrium conditions.
The economy is populated by a representative household, a monetary authority
and three types of producers: wholesale-good producers (entrepreneurs), capital-
good producers and retailers.
Entrepreneurs play the key role in the model. They produce wholesale goods
using physical capital constructed by capital producers, and labor supplied by both
households and entrepreneurs. To ?nance capital expenditures, entrepreneurs need
to rely on external ?nancing: In excess of their own net worth, entrepreneurs borrow
7
from a perfectly competitive ?nancial intermediary. The intermediary could only
observe the distribution of entrepreneurs’ idiosyncratic productivity at the time debt
contract is made. This asymmetric information leads to a costly state veri?cation
problem as in Townsend (1979). The need for external ?nancing induces a non-zero
probability of default, which, in equilibrium, induces a positive premium over the
riskless rate, the external ?nance premium. The premium depends positively on the
aggregate leverage ratio of the entrepreneurs, the key relation that the ampli?cation
model exhibits.
The retailers are introduced solely to motivate price stickiness. They buy
wholesale goods at perfectly competitive markets, and di?erentiate them costlessly.
The ?nal consumption goods are then demanded by households, capital producers,
and the government.
Readers may ?nd it helpful the timing of events presented in Table 1.1.
Table 1.1: Timing of Events
At the end of Period t-1:
1. Entrepreneurs accumulate net worth.
2. Uncertainty (of period t) is realized.
3. Entrepreneurs decide how much capital to borrow, and state-contingent debt contract is made.
Period t:
1. TFP shock and the idiosyncratic productivities are realized.
2. Wholesale production is done.
3. Threshold level of idiosyncratic productivity and contractual returns are determined.
4. Defaulting entrepreneurs’ projects are seized, and the wholesale goods are sold to the retailers.
5. Some of the entrepreneurs leave the market exogenously.
6. Entrepreneurs accumulate net worth.
7. Uncertainty (of period t + 1) is realized.
8. Entrepreneurs decide how much capital to borrow, and state-contingent debt contract is made.
8
1.2.1 Households
There is an in?nitely-lived representative household that derives utility from a com-
posite ?nal consumption good C
t
=
_
_
1
0
c
1?
1
it
di
_ 1
1?
1
and leisure, 1 ? H
t
, where c
it
denotes the level of consumption for each retail good i at period t, and is the
intratemporal elasticity of substitution across the retail goods.
Households supply labor H
t
to the entrepreneurs and receive W
t
as the real
wage per labor hour. They earn a total of ?
t
as dividends from the retailers,
pay lump-sum taxes T
t
to the ?scal authority, and receive the riskless real rate of
return R
t
on their deposits D
t
with the intermediary. Formally, the representative
household solves
max
{Ct,Ht,D
t+1
}
?
t=0
E
0
?
t=0
?
t
U (C
t
, H
t
) (1.1)
subject to the period budget constraints
C
t
+D
t+1
= W
t
H
t
+R
t
D
t
?T
t
+ ?
t
(1.2)
where ? ? (0, 1) is the subjective discount rate. E
t
is the expectation operator
conditional on the information set available at t, which includes current and past
values of endogenous state variables, and distributions of shocks to total factor pro-
ductivity, real government spending, and cross-sectional dispersion of entrepreneurs’
idiosyncratic productivity. Following Bloom (2009), I label shocks to cross-sectional
dispersion as uncertainty shocks.
9
The riskless real rate of return is de?ned as R
t
=
1+r
n
t
1+?
t+1
, where r
n
t
is the (net)
nominal interest rate and ?
t+1
is the (net) price in?ation of the ?nal good from t to
t + 1. The nominal interest rate is set by the monetary authority as an operating
target, and a?ects real allocations due to existence of price stickiness in the model
environment.
The household’s optimality conditions imply standard consumption-savings
and labor supply conditions:
?U(t)
?C
t
= ?R
t
E
t
_
?U(t + 1)
?C
t+1
_
W
t
= ?
?U(t)
?Ht
?U(t)
?Ct
(1.3)
where U(t) denotes the period-t utility function. One-period stochastic discount fac-
tor, which is taken as given by the sector(s) owned by the household, is then given by
?
t+1|t
= ?E
t
_
?U(t+1)
?C
t+1
/
?U(t)
?Ct
_
. A no-Ponzi condition on households, lim
T??
E
t
?
T
?
t+T|t
D
t+T
?
0 completes the household’s problem.
1.2.2 Entrepreneurs
The entrepreneur i starts each period t with physical capital K
it
that is purchased
from capital producers at the end of period t ?1 at a real price Q
t?1
. They produce
wholesale goods Y
it
with labor and capital. The labor used in the production, L
it
, is
composed of household labor H
it
and the entrepreneurial labor H
e
it
such that L
it
=
H
?
it
(H
e
it
)
(1??)
where ? is the share of households’ income in total labor income.
13
13
Entrepreneurs are allowed to supply labor not only for their own projects but also for other
entrepreneurial projects. This helps to aggregate the entrepreneurial sector. The share of labor
income accruing to the entrepreneur, 1 ? ?, is assumed to be very small (of an order of .01).
Hence, including entrepreneurial labor in the standard production function does not a?ect the
results signi?cantly.
10
The wholesale production of entrepreneur i is done via a constant returns to scale
(CRTS) technology given by Y
it
= ?
it
A
t
K
?
it
L
1??
it
where A
t
is total factor productivity
common across all entrepreneurs, and ?
it
is the idiosyncratic productivity level of
the entrepreneur i.
The idiosyncratic level of productivity, ?
it
, is assumed to be i.i.d across en-
trepreneurs and time, with a continuous at least once-di?erentiable cdf F(.), with
E[?] = 1 and variance ?
t
.
14
The cross-sectional dispersion of entrepreneurial id-
iosyncratic productivity at time t is given by ?
t
, and exogenous movements in ? are
due to uncertainty shocks. Note that shocks to ?
t
is a mean-preserving spread for
the distribution of idiosyncratic productivity ?
i
.
15
Given the level of capital acquired at the end of t ?1 (K
it
), the entrepreneur
chooses the demands for labor at the beginning of t to maximize real pro?ts. The
entrepreneur earns revenues from selling the wholesale goods to the retailers, and
from selling non-depreciated capital to the capital producers, ?
it
Q
t
(1 ? ?)K
it
.
16
Then, the entrepreneur determines how much capital to demand (or in other words,
how much to borrow).
17
Hence, the entrepreneur’s optimization problem can be
analyzed in two stages, ?rst labor demand is determined at the beginning of the
current period, and second capital demand is determined at the end of the period.
14
Assuming ?
it
to be i.i.d over entrepreneurs and time is to have an ex-post representative
entrepreneurial sector.
15
In particular, let F(.) be a log-normal distribution. Then, E[?] = 1 implies ln(?)?
N(
?1
2
?
2
, ?
2
) since E[?] = e
?1
2
?
2
+
1
2
?
2
. Now consider an exogenous change in ? to ¯ ? due to
uncertainty. Then, ln(?)? N(
?1
2
¯ ?
2
, ¯ ?
2
), and that implies E[?] = e
?1
2
¯?
2
+
1
2
¯?
2
= 1.
16
Hence, ?
it
is assumed to a?ect not only the level of entrepreneurial production, but also the
e?ective level of capital holdings. In this regard, ?
it
also a?ects the quality of capital held by the
entrepreneurs (see the discussions in Gertler et al., 2003; and Gilchrist and Saito, 2008).
17
The entrepreneurs are assumed to be more impatient than the ultimate lenders (households)
which ensures that external borrowing exists in the model.
11
The entrepreneur’s maximization problem at the beginning of t is:
max
H
it
,H
e
it
1
X
t
?
it
A
t
K
?
it
_
H
?
it
(H
e
it
)
(1??)
_
(1??)
?W
t
H
it
?W
e
t
H
e
it
(1.4)
where X
t
=
Pt
P
W
t
> 1 is the average mark-up of retail goods over wholesale goods
in gross terms. The solution to the above problem yields standard optimal labor
demand decisions for both types of labor: W
t
= (1 ? ?)?
Y
it
H
it
1
Xt
, and W
e
t
= (1 ?
?)(1 ? ?)
Y
it
H
e
it
1
Xt
. Each equation equates the marginal products with the respective
real wages paid to each labor input.
For the entrepreneur to be able to repay his debt, the revenue from the whole-
sale production (after labor is paid), ?
1
Xt
Y
it
+ ?
it
Q
t
(1 ? ?)K
it
, should exceed the
ex-post value of debt to the ?nancial intermediary. In particular, denote the total
external ?nancing need of the entrepreneur by B
it
= Q
t?1
K
it
?N
it
, where N
it
is the
entrepreneur’s (own) net worth. Then, the entrepreneur is able to repay his debt at
period t if
?
1
X
t
Y
it
+?
it
Q
t
(1 ??)K
it
? Z
it
(?
t
; ?
t
)B
it
(1.5)
where Z
it
(?
t
; ?
t
) is the (state-contingent) contractual rate which depends on the
aggregate macroeconomic state of the economy at t.
18
Second stage of the entrepreneur’s problem is to determine optimal capital
demand. The capital demand depends on (i) the expected marginal return to holding
18
This notation is to emphasize that debt contract is state-contingent. It should be understood
that all other endogenous variables are state-contingent as well, e.g. Y
it
? Y
it
(?
t
; ?
t
), X
t
?
X
t
(?
t
; ?
t
), Q
t
? Q
t
(?
t
; ?
t
), etc. I suppress this notation for brevity.
12
capital; and (ii) the expected marginal cost of ?nancing capital expenditures.
(i) The ex-post marginal (real) return to holding capital from t ? 1 to t,
R
k
t
(?
t
; ?
t
), depends on the marginal pro?t from wholesale production at t plus the
capital gain accrued from t ?1 to t. Hence, R
k
t
(?
t
; ?
t
) =
1
X
t
?Y
t
K
it
+Qt(1??)
Q
t?1
, where Y
t
is
the average wholesale output across the entrepreneurs.
19
Then equation (1.5) can
be equivalently represented as:
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
? Z
i
t
(?
t
; ?
t
)B
i
t
(1.6)
Hence, there exists a threshold level of productivity ?
it
, that satis?es ?
it
R
k
t
(?
t
; ?
t
)
Q
t?1
K
it
= Z
i
t
(?
t
; ?
t
)B
i
t
. Accordingly, an entrepreneur i with ?
it
> ?
it
repays
the loan and keeps the equity (?
it
? ?
it
)R
k
t
(?
t
; ?
t
)Q
t?1
K
it
. If, on the other hand,
?
it
< ?
it
, the entrepreneur declares bankruptcy, the intermediary monitors the en-
trepreneurial production and seizes (1 ? µ)?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
.
20
The defaulting
entrepreneur receives nothing.
(ii) The expected marginal cost of ?nancing is characterized by the debt con-
tract problem between the entrepreneur and the intermediary. The intermediaries
are assumed to operate in perfectly competitive markets, earning zero pro?ts in
equilibrium and perfectly diversifying any idiosyncratic risk. Hence, the debt con-
tract problem is characterized by maximizing expected return to capital to the
entrepreneur given that the intermediary earns his opportunity cost of funding (the
riskless rate) in expected terms. The solution to the problem determines how the
19
Details are provided in Appendix A1.
20
The debt contract problem is incentive compatible in that an entrepreneur has no gain from
misreporting the project outcome.
13
expected gross payo? from the contract, R
k
t
(?
t
; ?
t
)Q
t?1
K
it
, is split between the two
parties, pinning down the desired capital stock K
it
, and the state-contingent thresh-
old level ?
it
.
The entrepreneurial sector can be aggregated given two assumptions: (i) The
fraction of entrepreneurs that remains alive at the end of each period is constant.
(ii) The wholesale production technology exhibits CRTS. Given CRTS, the leverage
ratio does not depend on ?rm-speci?c factors (the idiosyncratic productivity). That
is, regardless of the idiosyncratic productivity level, each entrepreneur chooses the
same level of leverage,
Q
t?1
Kt
Nt
, hence face the same level of EFP. Similarly, aggre-
gate wholesale production can be represented by Y
t
= A
t
K
?
t
_
H
?
t
(H
e
t
)
(1??)
_
(1??)
,
where K
t
denotes the aggregate capital purchased in t ?1, H
t
is the aggregate labor
supplied by the households, and H
e
t
is the aggregate entrepreneurial labor. More-
over, the optimal labor demands can be read without ?rm-speci?c subscripts. Since
the bankruptcy costs are proportional to the wholesale output, the supply of capital
can be aggregated as well.
As shown in Appendix A2, the debt contract problem implies that the external
?nance premium (EFP), de?ned as the ratio of cost of external funds to that of
internal funds, is an increasing function of the aggregate leverage ratio (
QtK
t+1
N
t+1
?1),
EFP
t
?
R
k
t+1
R
t
=
_
1 ?
N
t+1
Q
t
K
t+1
__
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
)
_
?1
(1.7)
where the term in square brackets is the net contractual share going to the lender,
14
and decreasing in ? for Q
t
K
t
> N
t
.
21
Intuitively, as the external borrowing need
increases, it is more likely that the entrepreneur declares default. This, in turn,
induces an increase in expected monitoring costs, and hence a higher equilibrium
level of premium over the riskless rate. The ampli?cation mechanism is driven
mainly by this key equation, the EFP being positively related with the aggregate
leverage ratio.
The aggregate net worth of entrepreneurs at the end of period t consists of
the net worth of entrepreneurs who survived from t ? 1 to t and the period-t en-
trepreneurial wage. That is, the evolution of aggregate net worth satis?es
N
t+1
= ?[R
k
t
(?
t
; ?
t
)Q
t?1
K
t
?
_
R
t
+
µ ?
_
?
0
?F(?)R
k
t
(?
t
; ?
t
)Q
t?1
K
t
Q
t?1
K
t
?N
t
_
? (Q
t?1
K
t
?N
t
)] +W
e
t
H
e
t
(1.8)
The ?rst term in square brackets is the real gross return to holding K
t
amount
of capital from t ? 1 to t, and the second term is the total payment to the ?-
nancial intermediaries. Note that the ratio of default costs to quantity borrowed,
µ?
_
?(?
t
;?
t
)
0
?F(?)R
k
t
(?t;?t)Q
t?1
Kt
Q
t?1
Kt?Nt
, re?ects the EFP. The term inside the square brackets
is the net payo? from capital investment, part of which is lost due to exogenous
survival probability ? < 1. The last term, W
e
t
H
e
t
, is the total wage received by the
entrepreneurs.
Finally, the entrepreneurs who exogenously leave the market at the end of t
21
The debt contract problem is presented in Appendix A2.
15
consumes the residual net worth:
C
e
t
= (1??)
_
R
k
t
Q
t?1
K
t
?
_
R
t
+
µ
t
?
_
?
0
?F(?)R
k
t
(?
t
; ?
t
)Q
t?1
K
t
Q
t?1
K
t
?N
t
_
? (Q
t?1
K
t
?N
t
)
_
(1.9)
Capital Producers. They purchase ?nal goods I
t
and use existing capital stock
K
t
to produce new capital goods K
t+1
. The new capital good is then sold to the
entrepreneurs.
22
They face capital adjustment cost ?
_
It
Kt
_
, with ?(0) = 0, ?
(.) >
0, and ?
(.) < 0. Hence, the law of motion for aggregate capital stock is
K
t+1
= (1 ??)K
t
+K
t
?
_
I
t
K
t
_
(1.10)
Capital producers’ problem of choosing I
t
to maximize their pro?ts, Q
t
K
t+1
?Q
t
(1?
?)K
t
? I
t
, subject to the evolution of aggregate capital stock yields the standard
Q-relation for the price of capital:
Q
t
=
_
?
_
I
t
K
t
_
_
?1
(1.11)
1.2.3 Retailers
A measure-one continuum of retailers operate in monopolistically competitive mar-
kets and face implicit costs of adjusting prices. The price stickiness is of standard
Calvo (1983) and Yun (1996) type. Retailers purchase wholesale goods from the
22
The capital producers lease capital stock of entrepreneurs (K
t
) at period t before the produc-
tion of K
t+1
.
16
entrepreneurs at the marginal cost (P
W
t
), and di?erentiate them costlessly.
The retailers’ maximization of expected discounted real pro?ts given iso-elastic
demands for each retail good yields the standard optimality condition that a retailer
who is able to change its price at t sets the price such that the expected discounted
di?erence between the real marginal cost (
P
W
t
Pt
) and real marginal revenue (
P
?
t
Pt
) is
zero, given the environment that the ?rm is unable to change its price with proba-
bility ? in future periods. Formally,
E
t
?
s=t
?
t,t+s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
?
t
P
s
?
?1
P
w
s
P
s
_
= 0 (1.12)
where P
?
t
denote the price set by retailers who are allowed to change their price
at t, P
t
is the aggregate price level, and Y
f
t
=
_
_
1
0
y
t
(j)
1?
1
_ 1
1?
1
is the Dixit-Stiglitz
aggregate of retail goods y
t
(j).
23
The conventional approach in most New-Keynesian
literature is to log-linearize this equation around a non-in?ationary steady state, and
proceed to the standard New-Keynesian Phillips curve. However, since I employ
second-order approximation to the policy functions, I represent eq. (1.12) in a
recursive format.
First de?ne
x
1
t
= E
t
?
s=t
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
?
t
P
s
_
(1.13)
and
23
See Appendix A3 for details.
17
x
2
t
= E
t
?
s=t
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
w
s
P
s
_
(1.14)
As shown in Appendix A4, x
1
t
and x
2
t
can represented in a recursive format as
x
1
t
= ¯ p
t
1?
Y
f
t
+E
t
?
t,t+1
?(1 +?
t+1
)
?1
_
¯ p
t
¯ p
t+1
_
1?
x
1
t+1
(1.15)
where ¯ p
t
=
P
?
t
Pt
; and
x
2
t
= ¯ p
t
?
Y
f
t
1
X
t
+E
t
?
t,t+1
?(1 +?
t+1
)
_
¯ p
t
¯ p
t+1
_
?
x
2
t+1
(1.16)
I focus on the symmetric equilibrium such that optimizing retailers at a given
time choose the same price. Then, the evolution of aggregate price satis?es P
1?
t
=
?(P
t?1
)
1?
+ (1 ??)(P
?
t
)
1?
. Dividing this expression by P
1?
t
yields
1 = ?(1 +?
t
)
?1
+ (1 ??) ¯ p
t
1?
(1.17)
1.2.4 Monetary Authority and the Government
The monetary authority sets the short-term nominal interest rate via a simple mon-
etary policy rule.
24
The rule, in its most general version, prescribes potential reac-
tions to in?ation, and output (as in the standard Taylor rule), as well as ?nancial
variables (all in deviations from their respective long-run values). Formally,
24
A rule is simple if it includes only a few observable macroeconomic variables and ensures a
unique rational expectations equilibrium (and hence implementable). Second, a rule is optimal if
it minimizes the welfare distance between the decentralized economy and the planner’s economy.
For further discussion, see Schmitt-Grohe and Uribe (2006).
18
log
_
1 +r
n
t
1 +r
n
_
= ?
r
log
_
1 +r
n
t?1
1 +r
n
_
+(1??
r
)
_
?
?
log
_
1 +?
t
1 +?
_
+?
Y
log
_
Y
t
Y
_
+?
F
log
_
F
t
F
__
(1.18)
where F stands for Financial and denotes either asset price (Q) or external ?nance
premium (EFP), and overlined variables denote the corresponding deterministic
steady state values. The policy can also exhibit some inertia/smoothing (?
r
?
0). Note that the authority follows such a policy rule only under a decentralized
economy. In planner’s economy, the planner does not follow a rule, but instead uses
the short-run interest rate as the policy tool to maximize aggregate welfare.
The ?scal policy is assumed to be non-distortionary that the exogenous stream
of government expenditures G
t
is ?nanced by lump-sum taxes, G
t
= T
t
.
25
1.2.5 Equilibrium and Aggregation
Each retailer faces a downward-sloping demand from the households (c
jt
=
_
P
jt
Pt
_
?
C
t
),
the capital producers (i
jt
=
_
P
jt
Pt
_
?
I
t
), and the government (g
jt
=
_
P
jt
Pt
_
?
G
t
).
26
Moreover, entrepreneurial consumption (c
e
jt
) and monitoring costs (amc
jt
) soke up
some of the retail good supply j. Hence, supply should be equal to demand at the
?rm-level implies
y
t
(j) = c
jt
+i
jt
+g
jt
+c
e
jt
+amc
jt
(1.19)
25
Assuming away ?scal policy is to simplify the analysis and to focus on monetary policy pre-
scriptions.
26
See Appendix A5 for details.
19
for each j. Given the demand curves for each retail good, the above equation can
be expressed as
y
t
(j) = (C
t
+I
t
+G
t
)
_
P
jt
P
t
_
?
+c
e
jt
+amc
jt
(1.20)
for each j. Note that the retailers are not a productive unit in the economy, implying
that the aggregate amount of retail goods should be equal to the aggregate wholesale
production Y
f
? Y = F(K, H, H
e
). Hence, aggregating over all the retail goods
implies an aggregate market clearing for the ?nal goods market:
Y
t
= (C
t
+I
t
+G
t
)
_
1
0
_
P
jt
P
t
_
?
dj +C
e
t
+AMC
t
(1.21)
where C
e
t
=
_
1
0
c
e
jt
dj and AMC
t
=
_
1
0
amc
jt
dj.
To represent the goods-market clearing condition in a tractable way, I represent
S
t
?
_
1
0
_
P
jt
Pt
_
?
dj in a recursive format. As details are shown in Appendix A6,
S
t
?
_
1
0
_
P
it
P
t
_
?
di
= (1 ??)
_
P
?
t
P
t
_
?
+?
_
P
t?1
P
t
_
?
S
t?1
= (1 ??) ¯ p
t
?
+??
t
S
t?1
(1.22)
20
Hence, the aggregate resource constraint is represented by the following three
conditions:
Y
t
= C
t
+C
e
t
+I
t
+G
t
+AMC
t
(Aggregate Demand) (1.23)
Y
t
?C
e
t
?AMC
t
=
1
S
t
(F(K
t
, H
t
, H
e
t
) ?C
e
t
?AMC
t
) (Aggregate Supply) (1.24)
?
t
= (1 ??)¯ p
?
t
+??
t
S
t?1
(1.25)
I leave the de?nition of stationary competitive equilibrium of this economy to
Appendix B.
27
1.3 Functional Forms and Calibration
I calibrate the model to match the US economy for the period 1989Q1-2009Q1.
This sample choice is mainly for calibration purposes which will be clear below. For
some parameters, I use conventional estimates reported in the literature. Table 1.2
summarizes the parameter values.
I choose the period utility function of the form
27
The de?nition of equilibrium includes optimality conditions of the debt contract problem -not
shown for brevity in Section 2.2-. These optimality conditions are derived in Appendix A2.
21
U (C
t
, H
t
) = log(C
t
) ??
H
1+?
1 +?
(1.26)
which is typically studied in the New-Keynesian literature. I set ? at 0.55 which
implies a Frisch labor supply elasticity (
1
?
) of 1.80.
28
Then I set ? at 6.05 so that
the household spends
1
3
of her time working at the deterministic steady state.
The aggregate production of wholesale goods is governed by a CRTS technol-
ogy given by
Y
t
= A
t
K
?
t
_
H
?
t
(H
e
t
)
(1??)
_
(1??)
(1.27)
where ? = 0.35, ? =
0.64
0.65
, and H
e
= 1, following BGG. Setting ? = 0.35 ensures that
wages constitute 65% of the total production cost in the model, in accordance with
the US economy. ? =
0.64
0.65
implies that entrepreneurial labor earns approximately 1%
of the total income. Moreover, the entrepreneurial labor is assumed to be supplied
inelastically and normalized to unity.
The subjective discount factor, ?, is taken to be 0.9902, in line with the ob-
served 4% annual real rate of interest in the US economy. The quarterly depreciation
rate is assumed to be ?xed at 0.025. Following Klenow and Malin (2010), I set the
Calvo price stickiness parameter, ?, equal to 0.66. This value implies an average
frequency of price changes of approximately 3 quarters.
29
Moreover, is set at 11,
28
This level of elasticity is well in the range studied in the macro- business cycle literature.
For recent discussions on the labor supply elasticity, see Rogerson and Wallenius (2009), and
Christiano, Trabandt, and Walentin (2010) and references therein. I take the average of ?s studied
by Christiano, Trabandt, and Walentin (2010) as two extreme cases (?=1 and ?=0.1).
29
Klenow and Malin (2010) reports that the mean (non-sale) price duration of non-durable goods
is 8.3 months, and it is 9.6 months for services goods. Weighting these price durations by their
22
implying a 10% long-run price mark-up over the marginal cost (under zero long-run
in?ation).
The capital adjustment cost function takes the following quadratic form
?
_
I
t
K
t
_
=
I
t
K
t
?
?
k
2
_
I
t
K
t
??
_
2
(1.28)
I set ?
k
= 10 so that the elasticity of price of capital with respect to investment to
capital ratio is 0.25 at the deterministic steady state.
30
The monetary authority is assumed to have a perfect control over the short-
term nominal interest rate, and targets an (annual) in?ation rate of ?=2.66% (the
average CPI-based in?ation rate).
31
Following BGG, I assume that the monetary
authority reacts only to the in?ation.
32
The (long-run) in?ation feedback coe?cient,
?
?
, is set at 1.77, and the policy persistence parameter, ?
r
, is set at 0.84, following
Smets and Wouters (2007).
The remaining three parameters, the bankruptcy cost (µ), the long-run cross-
sectional dispersion of idiosyncratic productivity (?), and the entrepreneur’s survival
shares in the CPI gives out 2.93 quarters. This level of duration in turn implies ? = 0.66. This
value is well in the range calibrated/estimated in the New-Keynesian DSGE literature (for a list
of studies, see Schmitt-Grohe and Uribe, 2010).
30
BGG argues that a reasonable calibration for ?
k
should imply an elasticity in the range of
0 to 0.50. I simply follow BGG, taking the average of these values. Recent estimates imply an
elasticity up to 0.60 (see for instance Christensen and Dib, 2008). A larger elasticity would imply
a stronger reaction of asset prices to disturbances, leading to larger movements in entrepreneurs’
net worth and in turn a stronger ?nancial ampli?cation. I, however, take a conservative stand,
and set the parameter as in BGG.
31
Following Rudebusch (2006), I calculate ?
t
using the price index for consumption expenditures
excluding food and energy. Denoting the index by P
t
, ?
t
=400log(P
t
/P
t?1
).
32
In Section 7 where I study optimal simple policy rules, I consider the most general case in
which the monetary authority is allowed to react to in?ation, output gap, and ?nancial variables.
The reason of not including the latter two under the benchmark economy is mainly for comparison
purposes with the BGG and to elicit in Section 6 the planner’s motive to mitigate the degree of
?nancial ampli?cation that would prevail under the benchmark economy.
23
Table 1.2: Parameters
Description Parameter Value Target/Source
Households
The quarterly subjective discount rate ? 0.9902 4% Real rate
Preference Parameter ? 6.05 1/3 working time
(Inverse) Frisch labor supply elasticity ? 0.55 CTW (2010)
Firms
Share of capital in production ? 0.35 RBC
Share of HH’s labor income ? 0.64/0.65 BGG
Depreciation rate of capital ? 0.025 RBC
Calvo price stickiness parameter ? 0.66 Klenow & Malin (2010)
Intra-temporal elasticity of substitution 11 BGG
Capital adjustment cost parameter ?
k
10 BGG
Financial Variables
Bankruptcy Rate µ 0.13 Bankruptcy rate (3%)
Survival Rate 1 ?? 0.982 Leverage ratio (1.05)
(a)
L-R Cross-sectional Dispersion ? 0.261 EFP (227 BP)
(b)
Exogenous Processes
Persistence Parameter, log(TFP) ?
A
0.95 RBC
Persistence Parameter, log(G) ?
G
0.87 SGU (2007)
Persistence Parameter, log(?) ?
?
0.83 Chugh (2010)
Stdev. of innovations to log(TFP) ?
?
A 0.0082 Cyclical volatility of GDP
Stdev. of innovations to log(G) ?
?
G 0.0076 Cyclical volatility of G
Stdev. of innovations to log(?) ?
U
0.0151 Cyclical volatility of EFP
(c)
Monetary Policy Rule
Policy rate persistence ?
r
0.84 Smets & Wouters (2007)
In?ation feedback coe?cient ?
?
1.77 Smets & Wouters (2007)
(a) Chugh (2011).
(b) Long-run average of (i) prime-lending rate and 6-month constant maturity treasury bill, (ii) prime-
lending rate and 3-month constant maturity treasury bill, (iii) Moody’s BAA-rated and AAA-rated cor-
porate bonds, (iv) Moody’s BAA-rated corporate bond and 10-year constant maturity treasury bill.
(c) Average cyclical volatility of these credit spreads. Sensitivity analysis is performed as well.
rate (?) are jointly calibrated to match three long-run ?nancial targets: An annual
bankruptcy rate of 3% (following BGG), the aggregate leverage ratio of non-?nancial
?rms of 1.05 (following Chugh, 2011), and the long-run level of external ?nance
24
premium of 227 basis points.
3334
The ?rst-moment shocks that I consider are those typically studied in the
literature, the innovations to aggregate TFP and real government expenditures.
35
They both follow a ?rst-order autoregressive (AR(1)) process in logs:
log(A
t
) = ?
A
? log(A
t?1
) +?
A
t
(1.29)
log(G
t
) = (1 ??
G
)log(G) +?
G
log(G
t?1
) +?
G
t
(1.30)
where ?
A
, ?
G
are the respective persistence parameters, G is the long-run level
of real government expenditures, and ?
A
t
and ?
G
t
are the respective i.i.d Gaussian
innovations. I set ?
A
= 0.95 following the real business cycle literature, and ?
G
=
0.87 following Schmitt-Grohe and Uribe (2006). I set G equal to 19.56% of the real
33
To obtain the long-run average of external ?nance premium, I use the average of credit spreads
that are generally used as an aggregate measure for the spread: two paper-bill spreads, and two
corporate bond spreads, i.e. (i) prime-lending rate and 6-month constant maturity treasury bill,
(ii) prime-lending rate and 3-month constant maturity treasury bill, (iii) Moody’s BAA-rated
and AAA-rated corporate bonds, (iv) Moody’s BAA-rated corporate bond and 10-year constant
maturity treasury bill; all taken from the Fed St. Louis Database. The long-run average of these
premia, which I take as the calibration target, is 227 basis points. An annual bankruptcy rate
of 3% is within the range of recent estimates for the bankruptcy rates of US non-?nancial ?rms
(see Gilchrist, Yankov and Zakrajsek, 2010). Chugh (2011) establishes business cycle statistics
of aggregate ?nancial variables of the US non-?nancial ?rms, and use the sample period 1989Q1-
2009Q1.
34
Note that these ?nancial targets are aggregate measures, and their empirical counterparts are
not clear. The level of premium, for instance, depends on the maturity structure of underlying
instruments, borrowing ?rms’ characteristics like age, equity, loan size etc., and hence is ?rm-
speci?c. Use of heterogeneity in these ?nancial targets in a general equilibrium model, however,
requires a heterogenous-agent framework, and the BGG, as most agency-cost general equilibrium
models, assumes no heterogeneity in this dimension mainly for computational ease. For empirical
studies based on micro-level data on EFP and default frequencies, see Levin, Natalucci, and
Zakrajsek (2004), and Gilchrist, Yankov and Zakrajsek (2010).
35
By minimizing the set of ?rst-moment shocks (one for supply and one for demand), I keep the
analysis simple. Moreover, the studies that closely resemble this paper, Schmitt-Grohe and Uribe
(2006) and Faia and Monacelli (2007), use these disturbances to drive ?uctuations in the economy.
25
GDP in the long run, inline with the US economy for the sample period.
The uncertainty shock, U
t
, is de?ned as disturbances to cross-sectional disper-
sion of entrepreneur’s idiosyncratic productivity. In particular, the cross-sectional
dispersion follows an AR(1) process in logs:
log(?
t
) = (1 ??
?
)log(?) +?
?
log(?
t?1
) +U
t
(1.31)
where ?
?
is the persistence parameter, and U
t
is an i.i.d. Gaussian innovation. I set
?
?
equal to 0.83, the estimate reported by Chugh (2010) using ?rm-level data.
Given the structural parameters set so far, I jointly calibrate standard de-
viations of innovations ?
A
t
, ?
G
t
, and U
t
to match the observed cyclical volatilities
of real GDP, real government expenditures, and the credit spread in the data.
36
The resulting parameter values are ?
?
A = 0.0082, ?
?
G = 0.0074, and ?
U
= 0.0151
respectively.
1.4 Decentralized Equilibrium and Cross-Sectional Dispersion
I ?rst study the long-run deterministic equilibrium as a function of long-run cross
sectional dispersion, ?. This analysis provides a step-en-route to discuss how credit
frictions a?ect model dynamics and interlinked with the monopolistic competition
and the long-run in?ation. Second, I present model dynamics in response to produc-
tivity, government spending and uncertainty shocks, and the relative importance of
36
The cyclical volatility of the aforementioned credit spreads are, in respective order, .2805,
.2195, .2497, and .4812. The average, which I take as the calibration target, is 0.308. In Section 7,
I consider sensitivity of the normative results with respect to using a di?erent credit spread. For
data de?nitions, see Appendix C.
26
uncertainty shocks in driving the business cycles.
1.4.1 Long-run equilibrium and long-run cross sectional dispersion
Figure 1.1 plots the long-run equilibria as a function of long-run cross-sectional
dispersion.
37
As the dispersion reduces to zero, the idiosyncratic entrepreneurial
project outcomes become a common knowledge. In other words, the asymmetric
information between the lender and the entrepreneurs dissipates. As a result, exter-
nal ?nance premium, bankruptcies as well as aggregate monitoring costs shrink to
zero.
38
Moreover, long-run capital accumulation rises as the dispersion fades away.
39
Similarly, aggregate investment, consumption and output rise as the dispersion dis-
sipates. Moreover, households’ welfare is monotonically decreasing in cross-sectional
dispersion (not shown for brevity).
Nevertheless, investment and output displays a non-monotonic behavior, that
they begin to rise for values of dispersion above a certain level. This is not due to
any sort of non-monotonicity in contractual terms (as suggested by the monotonic
path of ?nancial variables). This is rather due to entrepreneurs’ relying much less
on external borrowing: total debt and leverage shrink to zero as the dispersion
rises. Hence, e?ectively, the strength of ?nancial frictions starts to decrease in the
deterministic long-run equilibrium as the dispersion rises substantially.
37
All other parameters are held ?xed at those presented in Table 1.2.
38
When the dispersion is exactly equal to zero, the entrepreneurial sector becomes managed
by the intermediary. Hence, neither leverage nor the loan amount can be identi?ed when the
dispersion is exactly zero.
39
Note that aggregate investment at the deterministic steady state is equal to stock of depreciated
capital. Hence, an equivalent diagram for total capital stock would be just a scaled-up version of
the diagram for investment.
27
Figure 1.1: Long-run equilibria as a function of long-run cross-sectional dispersion
0 0.1 0.2 0.3 0.4 0.5
1
1.05
1.1
1.15
?
O
u
t
p
u
t
0 0.1 0.2 0.3 0.4 0.5
0.52
0.54
0.56
0.58
0.6
?
C
o
n
s
u
m
p
t
io
n
0 0.1 0.2 0.3 0.4 0.5
0.19
0.2
0.21
0.22
0.23
0.24
0.25
?
I
n
v
e
s
t
m
e
n
t
0 0.1 0.2 0.3 0.4 0.5
2
4
6
8
10
?
T
o
t
a
l
D
e
b
t
0 0.1 0.2 0.3 0.4 0.5
1
2
3
4
5
6
?
N
e
t
W
o
r
t
h
0 0.1 0.2 0.3 0.4 0.5
0
2
4
6
8
?
L
e
v
e
r
a
g
e
0 0.1 0.2 0.3 0.4 0.5
0
1
2
3
4
5
?
B
a
n
k
r
u
p
t
c
y
R
a
t
e
(
p
p
t
s
)
0 0.1 0.2 0.3 0.4 0.5
0
50
100
150
200
250
300
?
P
r
e
m
iu
m
(
b
p
t
s
)
0 0.1 0.2 0.3 0.4 0.5
0
1
2
3
4
5
6
x 10
?4
?
A
g
g
r
e
g
a
t
e
M
o
n
it
o
r
in
g
C
o
s
t
s
Notes. All other parameters are held ?xed at those presented in Table 1.2.
These comparative statics bear the question of whether the responses are
driven solely by the agency-cost framework, or a?ected by speci?ed degrees of long-
run in?ation (? > 0) and monopolistic competition (captured by ). Since ?nancial
variables in the absence of aggregate shocks are determined within partial equilib-
rium, ?nancial frictions are (almost) independent from the degree of monopolistic
competition and the level of long-run in?ation at the deterministic steady state.
Nevertheless, as we elaborate below, ?nancial frictions are interlinked with the other
two features in the model dynamics.
28
1.4.2 Dynamics of the model and cross-sectional dispersion
I simulate the model economy around the deterministic steady-state using second-
order approximation to the policy functions. All statistics are based on HP-?ltered
cyclical components (with a smoothing parameter 1600). Impulse responses refer to
how endogenous variables react to an unexpected one-time one-standard-deviation
increase in the underlying exogenous state. All responses are in percentage devia-
tions from respective deterministic steady state values unless otherwise noted.
1.4.2.1 Productivity and Government Spending Shocks
For comparison purposes with the literature, I present the equilibrium responses of
real and ?nancial variables in response to a favorable productivity shock (Figure
1.2). Dashed lines show the dynamics under no ?nancial ampli?cation. To shut
o? the ampli?cation, I set the external ?nance premium ?xed at its deterministic
long-run value (227 basis points).
40
An exogenous increase in total factor productivity leads to an unexpected rise
in ex-post marginal real return to capital, which, due to capital adjustment costs,
raises the price of capital, Q
t
. For a given level of net worth, a rise in Q
t
induces an
increase in borrowing needs. However, the rise in Q
t
drives the net worth up more
than proportionately, leading to a decrease in the leverage.
41
EFP then falls on
40
I should make the following distinction between shutting ?nancial ampli?cation o? and shutting
?nancial frictions o?. The former refers to ?xing the EFP at its deterministic long-run value
(so that the ampli?cation is turned o?), whereas the latter refers to no ?nancial frictions in the
economy, EFP being zero at all times. For presentation purposes, I choose to shut the ampli?cation
o?, since the former and the benchmark model then share the same deterministic equilibrium.
41
One can algebraically show that how sensitive the net worth is to unexpected changes in ex-
post return to capital depends on the leverage ratio: Net worth rises more than proportionately
to the extent entrepreneurs are leveraged (see BGG, p. 1359).
29
impact, generating an ampli?ed response of asset prices and aggregate investment.
An exogenous increase in aggregate supply of wholesale goods drives the nom-
inal marginal costs down that the retailers face. Hence, the retailers that are able to
set prices chooses a price lower than the average price level in the economy. Average
price level, P
t
, then decreases, but, due to sticky prices, not as much as the decrease
in P
W
t
. As a result, average mark-up in the economy,
Pt
P
W
t
, rises and in?ation goes
below its long-run value.
42
Figure 1.2: Impulse Responses to a 1 sd. increase in total factor productivity
0 20 40
0
0.5
1
Output
0 20 40
0
0.5
1
Consumption
0 20 40
?1
0
1
Labor
0 20 40
?2
0
2
Investment
0 20 40
?0.5
0
0.5
Asset Price
0 20 40
?2
0
2
Net Worth
0 20 40
?1
0
1
Debt
0 20 40
?1
0
1
Leverage Ratio
0 20 40
?10
0
10
Premium (bpts)
0 20 40
?0.2
0
0.2
Bankruptcy Rate (ppts)
0 20 40
?0.5
0
0.5
Threshold Prod. (?)
0 20 40
0
0.5
Mark-up
0 20 40
?1
?0.5
0
In?ation Rate (ppts)
0 20 40
?0.4
?0.2
0
Policy Rate (ppts)
0 20 40
?0.2
0
0.2
Real Rate (ppts)
Notes. Solid line: Financial ampli?cation, Dashed line: No ?nancial ampli?cation
(EFP is ?xed). Unless otherwise noted, the responses are in terms of percentage
deviation from the respective deterministic steady states.
Note that existence of ?nancial ampli?cation dampens the response of in?a-
42
These responses are by and large in line with the literature. See BGG, Faia and Monacelli
(2005), and Christiano, Motto and Rostagno (2010).
30
tion to a rise in productivity. For an economy without ampli?cation (the dashed
lines), the rise in aggregate supply of wholesale goods is lower, which dampens the
decrease in nominal marginal costs. Average mark-up in the economy then rises less
than what would be without ?nancial ampli?cation. As a result, in?ation decreases
much less on impact. Hence, there exists a relative de?ationary e?ect of ?nancial
ampli?cation in response to productivity shocks.
43
An unexpected expansionary government spending serves as a typical favorable
demand shock. A rise in demand for wholesale goods leads to a rise in output and en-
trepreneurial net worth, and eventually a decrease in premium and the bankruptcy.
A higher demand for wholesale goods pushes wholesale prices (nominal marginal
costs) up. Retailers that are able to set their prices set a higher price, which leads
to an increase in in?ation. The average price, P
t
, though, does not increase as much
as the increase in P
W
t
, and hence, average mark-up in the economy,
Pt
P
W
t
falls.
44
1.4.2.2 Uncertainty Shocks
Before presenting the corresponding model dynamics, it might be useful to discuss
brie?y how an exogenous increase in the cross-sectional dispersion a?ect ?nancial
variables in partial equilibrium. Figure 1.3, in particular, shows the e?ect of a two-
standard deviation increase on the cross-sectional dispersion, based on the bench-
mark values of ? and ?
U
. If the threshold level of productivity, ?, were to remain
unchanged in response to an increase in the dispersion, the measure of entrepreneurs
43
See Faia and Monacelli (2005) for a similar result.
44
See Figure 1.15 in the Appendix for impulse responses of real and ?nancial variables in response
to the government spending shock.
31
whose productivity is below the threshold level (?
i
< ?) rises. Since the distribution
of ? is known at the time the debt contract is made, lenders now understand that
there will be fewer ?rms who will be able pay their debts. Since the lenders should
be compensated for the increase in the associated expected monitoring costs, this in
turn induces a higher equilibrium level of EFP. The threshold level of productivity
is endogenous though, and the general equilibrium e?ect of an exogenous increase
in ?
t
is quantitative in nature.
Figure 1.3: An increase in the cross-sectional dispersion of entrepreneurs’
idiosyncratic productivity
0 0.5 1 1.5 2 2.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Firm Idiosyncratic Productivity
?
(
.
)
An increase in cross?sectional dispersion of firms’ idiosyncratic productivity
Figure 1.4 provides the impulse responses of real and ?nancial variables to an
unfavorable uncertainty shock (an unexpected rise in the cross-sectional dispersion).
It is evident that it serves as a prototypical aggregate demand shock. An increase
in the dispersion implies a higher risk for the overall loan portfolio of the lenders.
Hence, expected monitoring costs rise for which lenders should be compensated.
Moreover, due to decrease in expected return to capital, aggregate net worth of the
entrepreneurs goes down. These eventually lead to an equilibrium increase in the
32
leverage and in the premium. The rise in the premium tightens the ?nancing terms,
which lowers aggregate investment and in turn aggregate demand.
Figure 1.4: Impulse Responses to a 1 sd. increase in uncertainty
0 20 40
?0.2
?0.1
0
Output
0 20 40
?0.1
0
0.1
Consumption
0 20 40
?0.4
?0.2
0
Labor
0 20 40
?1
?0.5
0
Investment
0 20 40
?0.5
0
0.5
Asset Price
0 20 40
?1
?0.5
0
Net Worth
0 20 40
0
0.5
1
Debt
0 20 40
0
0.5
1
Leverage Ratio
0 20 40
0
10
20
30
Premium (bpts)
0 20 40
0
0.5
1
Bankruptcy Rate (ppts)
0 20 40
0
0.1
0.2
Threshold Prod. (?)
0 20 40
?0.1
0
0.1
0.2
Mark-up
0 20 40
?0.2
0
0.2
In?ation (ppts)
0 20 40
?0.1
0
0.1
Policy Rate (ppts)
0 20 40
?0.1
0
0.1
Real Rate (ppts)
Notes. Unless otherwise noted, the responses are in terms of percentage deviation
from the respective deterministic steady states.
A reduction in aggregate demand for the retail goods leads to a lower demand
for wholesale goods, pushing wholesale prices (nominal marginal costs) down. Re-
tailers that are able to set their prices set a lower price, which leads to a decrease in
in?ation. The average price, P
t
, though, does not decrease as much as the decrease
in P
W
t
, and hence, average mark-up in the economy,
Pt
P
W
t
rises.
Although the model is rather simplistic, equilibrium responses are by and
large inline with the data. Gilchrist, Sim and Zakrajsek (2010) show in a VAR
33
framework that the real GDP declines by .2% after 2 quarters and exhibits a hump-
shaped response due to an unexpected one-standard-deviation (an approximately
8%) increase in the uncertainty.
45
We are able to generate this magnitude of decline,
but not the hump-shape response. Similarly for aggregate investment, the model
is able to generate the documented magnitude of decline yet misses the hump-
shape response. Moreover, although the impact e?ect on the premium seems to be
somewhat larger than that documented, it is hard to draw a conclusive picture in
this dimension, since the empirical counterpart of the model-based premium is not
clear.
46
The contribution of uncertainty shocks in driving aggregate ?uctuations is
presented in Table 1.3. The uncertainty shock accounts for around 85% of the
variations in EFP and the bankruptcy, and more than 15% of the volatility in
other ?nancial variables for both short- and long horizons. Since ?uctuations in
?nancial variables ?rst transmit into aggregate investment, investment turns out
to be the real variable that is driven by the uncertainty shock most (18% for one
period ahead). The remaining real variables are mostly driven by the ?rst-moment
shocks.
47
45
They estimate time-?xed e?ects in a panel-AR(1) regression of ?rms’ equity volatility to mea-
sure aggregate uncertainty. The uncertainty is de?ned as the innovation to idiosyncratic equity
volatility that are common to all ?rms at t. This de?nition is conformable with the uncertainty
de?ned in our model, time-variation in the cross-sectional dispersion of idiosyncratic productivity
that a?ects all the entrepreneurs.
46
Note also that the model implies a pro-cyclical debt which is at odds with the data. Note
however that I do not consider policy reaction to volume of debt in the policy rules in the normative
policy analysis. So, pro-cyclicality in debt should not pose a ?rst-order problem for our normative
results.
47
Christiano, Motto and Rostagno (2010) ?nds a more pronounced contribution of uncertainty
shock on the volatility of real and ?nancial variables. They report that almost all the ?uctuations in
the EFP, and nearly half of the ?uctuations in aggregate investment are driven by the risk shock.
In their analysis, most of the contribution comes from the anticipated portion of the uncertainty
34
Moreover, while a substantial portion of ?uctuations in EFP is driven by
uncertainty, only 18% of the ?uctuations in leverage is uncertainty-driven. This
suggests that uncertainty governs most of the ?uctuations in the sensitivity of EFP
to the leverage, or as labeled before, the strength of ?nancial ampli?cation.
Table 1.3: Variance Decomposition (Decentralized Economy)
Variable TFP+G Shocks Uncertainty Shocks
t = 1 t = 4 t = 8 t = ? t = 1 t = 4 t = 8 t = ?
Y 96.08 97.89 98.42 98.4 3.92 2.11 1.58 1.6
Real Variables C 98.73 98.86 99.28 99.3 1.27 1.14 0.72 0.7
I 81.67 88.19 90.85 93.16 18.33 11.81 9.15 6.84
Q 81.67 88.12 90.61 92.47 18.33 11.88 9.39 7.53
EFP 12.31 14.66 16.93 19.54 87.69 85.34 83.07 80.46
Net Worth 81.66 85.47 87.37 89.51 18.34 14.53 12.63 10.49
Financial Variables Debt 82.27 98.77 99.66 98.66 17.73 1.23 0.34 1.34
Leverage 81.66 81.62 81.18 75.01 18.34 18.38 18.82 24.99
Bankruptcy Rate 11.39 13.6 15.76 18.29 88.61 86.4 84.24 81.71
Monetary Variables Policy Rate 61.78 71.01 79.53 94.13 38.22 28.99 20.47 5.87
In?ation 61.78 67.49 70.86 81.14 38.22 32.51 29.14 18.86
Before presenting the normative results, note that when the economy is driven
only by the ?rst-moment shocks, the model cannot generate observed cyclical volatil-
ity of the external ?nance premium, the key variable in the ampli?cation mecha-
nism. Namely, for properly calibrated magnitudes of TFP and government spending
shocks, the simulation-based cyclical volatility of the premium is almost one third
than that observed in the data. If one is to match the volatility of premium by using
?rst-moment shocks only, the standard deviation of innovations to TFP should be
set at an implausibly high value, which, on the other hand, would yield an unre-
alistically high volatility in real GDP. Hence, the key role that uncertainty shocks,
or ?nancial shocks in general, play in a BGG-type ?nancial ampli?cation model is
to match the observed volatility in the premium. This role is especially important
for normative analysis, since credit frictions manifest itself through existence of an
shock.
35
EFP.
1.5 Welfare Evaluation
Aggregate welfare is given by
V
0
? E
0
t=?
t=0
?
t
U(C
t
, H
t
) (1.32)
Note that although the model exhibits heterogeneity of consumers (households
and entrepreneurs), the fraction of entrepreneurial consumption in aggregate con-
sumption can be reasonably assumed to be negligible, as emphasized in BGG, and
Faia and Monacelli (2005, 2008).
48
I conduct second-order approximation to the policy functions as well as to V
0
to
have accurate normative results. Note that, under ?rst-order approximation to the
policy functions, the expected value of endogenous variables would be equal to their
deterministic steady state values. Hence, welfare levels would be the same under
alternative policy rules. Moreover, since the economy exhibits distortions even at the
steady state, ?rst-order approximation to the policy rules induces incorrect welfare
rankings even under a second-order approximation to the welfare.
49
Accordingly, I
48
Note that since entrepreneurs are risk-neutral, they care only the mean level of entrepreneurial
consumption. Also, alternative policy rules imply not only the same deterministic equilibrium for
all the variables, but also the same stochastic mean for the entrepreneurial consumption. Hence,
in comparing alternative policy rules, entrepreneurial consumption, however small it is, can be
neglected. See also Faia and Monacelli (2005) and references therein.
49
In particular, at the deterministic steady state, I do not assume any ad-hoc subsidy scheme
to undo distortions due to monopolistic competition, nor I assume a zero long-run in?ation that
undoes price dispersion. Moreover, credit distortions are e?ective in the deterministic long-run
as well. Such a subsidy scheme facilitates log-linearization around a zero-in?ation steady state.
Without that scheme, one need to rely on higher order approximation to the policy functions as
well as to the welfare. For further discussion, see Schmitt-Grohe and Uribe (2006).
36
?rst de?ne welfare in recursive form:
V
0,t
? U(C
t
, H
t
) +?E
t
V
0,t+1
(1.33)
and conduct second-order approximation to V
0,t
(as well as to the policy functions).
SGU (2006) show that an equivalent representation is
V
0,t
= V
0
+
1
2
?(V
0
) (1.34)
where V
0
is the welfare evaluated at the deterministic steady state, and ? is the
constant correction term capturing the second-order derivative of the policy function
for V
0,t
with respect to the variance of shocks. Hence, equation (1.34) provides
an approximation to the aggregate welfare at t = 0 taking into account the lack
of certainty at the stochastic steady state. Aggregate welfares for decentralized
economies are conditional on the deterministic steady state of the Ramsey planner’s
economy.
50
I will discuss Ramsey planner’s problem in detail in the next section.
For each policy alternative, I perform standard consumption-based welfare
comparisons. In particular, let the aggregate welfare associated with a policy regime
a be given by
V
a
0,t
? E
0
t=?
t=0
?
t
U(C
a
t
, H
a
t
) (1.35)
and the welfare attained by the Ramsey planner be given by
50
Decentralized economy starts from the Ramsey deterministic long-run equilibrium. As will be
evident below, this corresponds to setting deterministic long-run in?ation rate equal to zero.
37
V
r
0,t
? E
0
t=?
t=0
?
t
U(C
r
t
, H
r
t
) (1.36)
Let ? denote the percentage of consumption in Ramsey planner’s economy r
that the household is willing to give up to be as well of under regime a. ? then is
implicitly given by
V
a
0,t
= E
0
t=?
t=0
?
t
U((1 ??)C
r
t
, H
r
t
) (1.37)
A positive ?, for instance, implies that Ramsey economy dominates the decen-
tralized economy in welfare terms. To ?nd optimal policy rules, I search over policy
feedback coe?cients that minimize ?.
1.6 Optimal Monetary Policy
1.6.1 Sources of Ine?ciencies
The model economy has three features that lead to ine?cient outcomes compared
to a ?rst-best ?exible-price economy: the ?rst two are monopolistic competition
and price stickiness, standard distortions in New-Keynesian models. For a detailed
textbook discussion on these distortions, interested readers may refer to Gali (2008).
The third distortion is due to ?nancial frictions.
Monopolistic Competition. Since the retailers are assumed to have imperfectly
elastic demand for their di?erentiated products, they are endowed with some market
power and set prices above marginal cost. Under ?exible prices and no ?nancial
38
frictions, ?
?U(t)
?Ht
/
?U(t)
?Ct
= W
t
= MPL
t
1
X
, where X =
?1
> 1 is the desired gross
mark-up, and MPL is the marginal product of labor under no ?nancial frictions.
Note that under the ?rst-best economy, marginal rate of substitution should be
equal to marginal product of labor, MPL
t
. Since, in equilibrium, marginal rate of
substitution is increasing in hours and marginal product of labor is decreasing in
hours, the presence of monopolistic competition, X > 1, leads to an ine?ciently low
level of employment and output since MPL
t
1
X
< MPL
t
.
Price Stickiness. To study this distortion in isolation, assume that distortions
due to monopolistic competition is undone by an optimal wage subsidy, ? =
1
,
which is ?nanced by lump-sum taxes.
51
Note that economy’s average mark-up is
de?ned by P
t
/P
W
t
(up to a ?rst-order). Then, existence of price stickiness together
with the optimal subsidy scheme implies ?
?U(t)
?Ht
/
?U(t)
?Ct
= W
t
= MPL
t
X
Xt
which
violates the e?ciency condition under the ?rst-best economy that ?
?U(t)
?Ht
/
?U(t)
?Ct
=
MPL
t
, unless X
t
is equal to X at all times. Moreover, due to constant (and equal)
elasticity of substitution across the intermediate goods, consumers would be willing
consume equal amount of each intermediate good. However, if there exists price
dispersion across the goods, then consumer would optimally choose di?erent levels
of intermediate goods, which induces a welfare loss.
Compared to a second-best economy that features monopolistic competition
and ?nancial frictions, the distortion due to price stickiness is due to ? = 0 implying
that ¯ p
t
= 1 and hence S
t
is greater than one. S
t
> 1 leads to an ine?cient output
loss (see equation 1.24).
51
A wage subsidy of ? =
1
implies ?
?U(t)
?Ht
/
?U(t)
?Ct
= W
t
= MPL
t
1
X(1??)
= MPL
t
.
39
Financial Frictions. Note that in an economy with no ine?ciencies (?rst-best
economy),
?U(t)
?Ct
= ?E
t
R
k
t+1
_
?U(t+1)
?C
t+1
_
. Introducing ?nancial frictions creates a wedge
between expected return to capital and the risk-free rate, distorting households’
intertemporal decision. De?ning the wedge as R
t+1
= (1 ? ?
k
t+1
)R
k
t+1
, I next show
that the wedge depends on aggregate ?nancial conditions.
As shown in Appendix A1, the intermediaries’ zero-pro?t condition for the
next period is,
[1?F(?
t+1
)]Z
t+1
(?
t+1
; ?
t+1
)B
t+1
+(1?µ)
_
?
t+1
0
?
t+1
R
k
t+1
(?
t+1
; ?
t+1
)Q
t
K
t+1
dF(?
t+1
) = R
t+1
B
t+1
(1.38)
Substituting in ?
t+1
R
k
t+1
(?
t+1
; ?
t+1
)Q
t
K
t+1
= Z
t+1
(?
t+1
; ?
t+1
)B
t+1
, and
dividing by R
k
t+1
(?
t+1
; ?
t+1
)(Q
t+1
K
t+1
) yields
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
) =
R
t+1
R
k
t+1
(?
t+1
; ?
t+1
)
B
t+1
Q
t
K
t+1
(1.39)
The wedge is then given by
1 ??
k
t+1
=
_
Q
t
K
t+1
B
t+1
__
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
)
_
(1.40)
It is evident that ?uctuations in the wedge are due to movements in aggregate
40
?nancial conditions. The (inverse) of the ?rst term is an increasing function of the
leverage (
QtK
t+1
N
t+1
), and the second term is the net contractual share going to the
lenders.
1.6.2 Ramsey optimal policy problem
I assume that there is a benevolent planner at t = 0 that has been operating for an
in?nite number of periods. The planner is assumed commit to her decisions made
at some indeterminate point in the past. In this sense, I consider an optimal policy
problem from a timeless perspective (Woodford, 2003).
In Ramsey planner’s economy, there is no exogenous monetary policy rule. The
planner chooses the allocations, prices, and the policy rate to maximize aggregate
welfare, respecting the competitive equilibrium conditions. The planner has only
one policy tool, the short-run nominal interest rate.
Ramsey planner using a single policy tool to smooth the two wedges implies
that the Ramsey problem is incomplete (in the sense of Chari and Kehoe, 1999). As
evident from Section 1.6.1, a tax on return to capital would complete the system.
Moreover, equation (1.40) suggests that the proposed tax should smooth ?uctuations
in the leverage and net contractual share going to the lenders. In this regard,
interest-rate policy would be less e?ective if such a ?scal policy tool is introduced.
Further analysis is left to future work.
Formally, the Ramsey planner chooses state-contingent processes {C
t
, H
t
, H
e
t
, K
t
, I
t
,
N
t
, R
t
, AMC
t
, R
k
t
, ?
t
; ?
t
, x
1
t
, x
2
t
,W
t
, W
e
t
, R
k
t
, X
t
, ¯ p
t
, Q
t
, ?
t
, ?(?
t
, ?
t
), G(?
t
, ?
t
), ?
(?
t
, ?
t
),
41
G
(?
t
, ?
t
), ?(?
t
, ?
t
), k(?
t
, ?
t
), s(?
t
, ?
t
), r
n
t
, R
t
, ?
t
}
t=?
t=0
to maximize (1.32), subject to
the competitive equilibrium conditions (as presented in Appendix B, excluding the
monetary policy rule), R
t
? 1, for t > ??; given values of endogenous variables
(including the Lagrange multipliers associated with the competitive equilibrium con-
ditions) for t < 0, and exogenous stochastic processes {?
A
t
, ?
G
t
, and U
t
}
?
t=0
.
52
At the deterministic long-run equilibrium, the Ramsey planner can not achieve
?rst-best level of welfare. The planner has no policy tool (such as factor subsidies)
to undo distortions due to monopolistic competition. Moreover, since the policy rate
cannot a?ect the level of premium in the deterministic long-run, ?nancial frictions
can not be eliminated as well.
53
In the stochastic steady state, however, the policy
tool can be used to balance the ‘tension’ between the three distortions. As will be
suggested by the impulse responses, the optimal in?ation rate is not zero at all times
as would be in standard cashless New-Keynesian models with the aforementioned
factor subsidies.
1.6.2.1 Cyclical Volatilities
A standard result in Ramsey optimal policy literature is that the planner would
like to smooth wedges (which distorts intra- and/or inter-temporal decisions) to
maximize aggregate welfare.
54
Note from Section 1.6.1 that the wedges in the model
economy ?uctuate due to movements in the EFP and aggregate gross mark-up
52
The endogenous objects, ?(?
t
, ?
t
), G(?
t
, ?
t
), ?
(?
t
, ?
t
), G
(?
t
, ?
t
) are related to the debt-
contract problem. See Appendix A2 for details.
53
The premium, in the absence of aggregate shocks, is determined purely within the partial
equilibrium debt-contract framework.
54
Among many others, see Chari and Kehoe (1999), and Chugh and Arseneau (2010).
42
(respectively for each wedge). As shown in Table 1.4 below, the results suggest that
the cyclical volatility of EFP is reduced by 17%, and that of in?ation (which is
intrinsically linked to mark-up) by 28% compared to the decentralized economy.
In addition, EFP being smoother while leverage being rather equally volatile
in the planner’s economy suggests that the planner smooths the sensitivity of pre-
mium to the leverage. I analyze this point more in detail in the next subsection.
Table 1.4: Cyclical Volatilities (%-standard deviations)
Variable Decentralized Economy Planner’s Economy
Y 1.14 1.16
Real Variables C 0.95 0.96
I 2.90 2.86
Q 0.73 0.72
EFP 0.31 0.25
Net Worth 1.48 1.44
Financial Variables Debt 0.28 0.35
Leverage 1.36 1.33
Bankruptcy Rate 0.53 0.44
Monetary Variables Policy Rate 0.16 0.91
In?ation 0.30 0.22
1.6.2.2 Reducing the strength of ?nancial ampli?cation
In the dynamics, the Ramsey planner smoothes ?uctuations in EFP, lowering its
volatility by approximately 17% compared to the decentralized economy.
55
The
way the planner reacts to EFP can be understood by decomposing it into two
parts: sensitivity of EFP to the leverage, h(?
t+1
), and the leverage,
_
1 ?
Nt
QtK
t+1
_
.
56
Simulation-based h(.) for the decentralized economy gets stronger as the leverage
rises for the decentralized economy (see Figure 1.5). For the planner’s economy,
55
A complete stabilization, however, is not optimal since that would imply higher level of ?uc-
tuations in in?ation and hence higher distortions due to price dispersion.
56
See equation (1.7).
43
on the other hand, sensitivity is rather smooth.
57
Accordingly, the spread reacts
smoother in the Ramsey economy as leverage changes. In other words, the planner
achieves a lower strength of ?nancial ampli?cation.
Figure 1.5: Strength of Financial Ampli?cation (Planner’s Economy)
.14
.16
.18
.20
.22
.24
.26
The Elasticity under the Competitive Equilibrium
The Elasticity under the Ramsey Equilibrium
1.02 1.07 1.12
Leverage Ratio
T
h
e
E
l
a
s
t
i
c
i
t
y
o
f
E
F
P
1.6.2.3 Reducing the contribution of uncertainty on business cycles
There are striking di?erences in the contribution of uncertainty shocks on the volatil-
ity of real and ?nancial variables under the benchmark against the Ramsey planner’s
economy (Table 1.5). The relative contribution of uncertainty on the volatility of
most real and ?nancial variables is much lower under the Ramsey economy. On the
other hand, ?uctuations in policy rate, mark-up, price dispersion and in?ation are
driven substantially by uncertainty. In sum, the planner uses the policy rate almost
57
In particular, I ?rst obtain simulated series for the EFP and the leverage for the two economies
(where each economy is simulated for 3000 periods, and the ?rst 500 periods are omitted). Then I
sort the sample according to the leverage, and run an ordinary least squares log-log regression of
EFP on leverage for the ?rst 1000 observations. Then I roll the sample by one observation -with
a ?xed window size-, and obtain the estimate for the elasticity for this sample. Rolling the sample
further and obtaining the slope estimates give out the elasticity series in Figure 1.5.
44
solely due to uncertainty to lessen the contribution of uncertainty on business cycle
?uctuations.
Table 1.5: Variance Decomposition (Decentralized Economy vs. Ramsey Planner’s)
Variable Decentralized Economy Planner’s Economy
TFP+G Shocks Uncertainty Shocks TFP+G Shocks Uncertainty Shocks
Y 96.08 3.92 97.7 2.3
Real Variables C 98.73 1.27 96.05 3.95
I 81.67 18.33 96.54 3.46
Q 81.67 18.33 96.52 3.48
EFP 12.31 87.69 23.05 76.96
Net Worth 81.66 18.34 99.12 0.88
Financial Variables Debt 82.27 17.73 59.4 40.59
Leverage 81.66 18.34 96.96 3.04
Bankruptcy Rate 11.39 88.61 21.07 78.93
Monetary Variables Policy Rate 61.78 38.22 3.34 96.66
In?ation 61.78 38.22 8.8 91.21
Further Insights Mark-up 48.41 51.59 5.19 94.8
Price Dispersion 61.78 38.22 8.8 91.21
1.6.2.4 Impulse Responses
Figure 1.6 provides the impulse responses to a one-standard deviation increase in
productivity for the Ramsey economy (dashed line) against the benchmark decen-
tralized equilibrium (solid line). First, recall from Figure 1.2 that existence of ?nan-
cial ampli?cation dampens the response of in?ation to productivity shocks. Hence,
there is no inherent trade-o? for the planner in neutralizing the distortions due to
?nancial frictions and price dispersion. The planner, endowed with a single tool,
partially neutralizes price stickiness distortion, exerting negligible e?ect on the dy-
namics of ?nancial variables.
58
When the economy is driven by the uncertainty shock, however, there is a no-
ticeable di?erence between the dynamics of decentralized economy and the planner’s
economy (Figure 1.7). The planner would like to smooth ?uctuations in ?nancial
58
See Faia and Monacelli (2005) for a similar result.
45
Figure 1.6: Ramsey Impulse Responses to a 1 sd. increase in total factor
productivity
0 10 20 30 40
0
0.5
1
Output
0 10 20 30 40
0
0.5
1
Consumption
0 10 20 30 40
?0.1
0
0.1
Labor
0 10 20 30 40
0
1
2
3
Investment
0 10 20 30 40
?0.5
0
0.5
1
Asset Price
0 10 20 30 40
0
0.5
1
1.5
Net Worth
0 10 20 30 40
?1.5
?1
?0.5
0
Debt
0 10 20 30 40
?2
?1
0
1
Leverage Ratio
0 10 20 30 40
?10
?5
0
5
Premium (bpts)
0 10 20 30 40
?0.2
0
0.2
Bankruptcy Rate (ppts)
0 10 20 30 40
?0.5
0
0.5
Threshold Prod. (?)
0 10 20 30 40
?0.2
0
0.2
Mark-up
0 10 20 30 40
?0.5
0
0.5
In?ation Rate (ppts)
0 10 20 30 40
?0.2
0
0.2
Policy Rate (ppts)
0 10 20 30 40
?0.1
0
0.1
Real Rate (ppts)
Notes. Solid line: Decentralized economy. Dashed line: Ramsey Planner’s economy.
variables, yet at an expense of higher volatility in in?ation. The intuition lies on
the fact that the planner faces a trade-o? in eliminating ?nancial frictions and price
dispersion. For instance, in response to an unfavorable uncertainty shock, the plan-
ner would like to reduce the real rate to contain movements in the premium. On
the other hand, planner would like to increase the real rate to reduce ?uctuations
in in?ation. In equilibrium, ?nancial frictions, which are more pronounced under
uncertainty shocks, overwhelms price dispersion, and the planner at the margin
chooses to reduce the real rate.
Before studying optimal policy rules, note that it is the existence of price stick-
46
Figure 1.7: Ramsey Impulse Responses to a 1 sd. increase in uncertainty
0 10 20 30 40
?0.2
0
0.2
Output
0 10 20 30 40
?0.2
0
0.2
Consumption
0 10 20 30 40
?0.5
0
0.5
Labor
0 10 20 30 40
?1
?0.5
0
0.5
Investment
0 10 20 30 40
?0.5
0
0.5
Asset Price
0 10 20 30 40
?0.5
0
0.5
Net Worth
0 10 20 30 40
?0.5
0
0.5
Debt
0 10 20 30 40
?0.5
0
0.5
Leverage Ratio
0 10 20 30 40
?20
0
20
40
Premium (bpts)
0 10 20 30 40
?0.5
0
0.5
Bankruptcy Rate (ppts)
0 10 20 30 40
?0.2
0
0.2
Threshold Prod. (?)
0 10 20 30 40
?0.5
0
0.5
Mark-up
0 10 20 30 40
?0.2
0
0.2
In?ation (ppts)
0 10 20 30 40
?1
?0.5
0
0.5
Policy Rate (ppts)
0 10 20 30 40
?1
?0.5
0
0.5
Real Rate (ppts)
Notes. Solid line: Decentralized economy. Dashed line: Ramsey Planner’s economy.
iness that enables the planner to reduce strength of ?nancial ampli?cation (or reduce
the contribution of uncertainty on the business cycles). Without price stickiness,
the policy tool, short-term nominal interest rate, cannot a?ect the real interest rate
and hence real allocations in the economy. In turn, the policy would be ine?ective
in neutralizing the distortions.
59
59
To formally analyze this, I consider the model with only ?nancial market imperfections (hence
no monopolistic competition or price stickiness). The cyclical volatilities and cross-correlations are
provided in Tables 1.9 and 1.10 in the Appendix. Without price stickiness and given symmetric
retailers, there will be no price dispersion (hence no resulting ine?ciencies). In this regard, the
planner has no incentive to smooth ?uctuations in in?ation. Accordingly, in?ation ?uctuates
substantially in the planner’s economy (and leading to frequent violation of zero lower bound for
the interest rate, which I ignore for the sake of this experiment). On the other hand, the planner
would be willing to smooth ?uctuations in the inter-temporal wedge to improve aggregate welfare,
though, unable to do so since the policy rate cannot a?ect real allocations.
47
1.7 Optimal Simple and Implementable Policy Rules
The planner’s problem yields equilibrium behavior of the policy rate as a function
of the state of the economy. Implementing the planner’s policy, hence, requires
the policy maker to observe the equilibrium values of all endogenous state variables
(including lagrange multipliers associated with the equilibrium conditions). Even if
the policy maker could observe the state of the economy, the equilibrium may not
render a unique competitive equilibrium. Hence, it is of particular interest whether a
simple and implementable monetary policy rule that includes only a few observable
macroeconomic variables and that ensures a (locally) unique equilibrium can achieve
an aggregate welfare level virtually identical to that under the planner’s economy.
The monetary policy rule is assumed to have the following form:
log
_
1 +r
n
t
1 +r
n
_
= ?
r
log
_
1 +r
n
t?1
1 +r
n
_
+(1??
r
)
_
?
?
log
_
1 +?
t
1 +?
_
+?
Y
log
_
Y
t
Y
_
+?
F
log
_
F
t
F
__
(1.41)
where F stands for Financial, and denotes either asset price (Q) or external ?nance
premium (EFP). In search for optimal values of ?
r
, ?
?
, ?
Y
, and ?
F
, I restrict
(long-run) in?ation feedback coe?cient to be within [1,3], persistence parameter to
be within [0,1] and other policy rule coe?cients to be within [-3,3]. The lower bound
for ?
?
is to ensure equilibrium determinacy. The upper bound for ?
?
, and the range
of [-3,3] for ?
Y
and ?
F
are set from a practical policy making view.
60
60
To obtain policy rule coe?cients, I search over 50000 alternative policy rules and calculate
conditional welfare for each rule using equation (1.34). Then given the results suggested by the
grid search, I use simulated annealing algorithm to pinpoint the policy rule that maximizes welfare.
48
As suggested by Schmitt-Grohe and Uribe (2006), a stronger policy reaction
than what these bounds suggest might be di?cult to implement in an actual econ-
omy. Moreover, I discuss potential implications of a binding upper bound for in-
?ation feedback coe?cient on the optimal magnitude of responses based on welfare
loss results.
Responding to ?nancial variables.
Con?rming the conventional ?nding in the literature, if the economy is driven
by traditional ?rst-moment shocks, it is optimal not to respond to ?nancial variables
(column 5 in Table 1.6). Consider, for instance, a monetary authority reacting to
asset prices in response to productivity shocks. In particular, ?
r
, ?
?
, and ?
Y
are
set at their optimal values (?
r
= 0.540, ?
?
= 3, ?
Y
= 0), while ?
Q
is set at 0.25 (a
lean-against-the wind policy reaction).
61
Figure 1.8 suggests that such a reaction
to asset prices leads to higher ?uctuations in in?ation, which in turn creates higher
distortions due to relative price dispersion.
If the economy is driven by uncertainty shocks, optimal policy prescribes a
reaction to ?nancial variables. In particular, consider the impulse responses un-
der two alternative policy rules (the optimal policy rule and a Taylor rule (?
r
=
0.85, ?
?
= 1.5, ?
Y
= 0.5/4, ?
EFP
= 0)), versus the Ramsey economy.
62
Figure 1.9
shows that the optimal rules yield dynamics closer to the Ramsey economy.
63
Note
61
One can use a lean-on-the-wind policy reaction to asset prices (?
Q
< 0) as well. This would
just exacerbate the di?erence between optimal and the non-optimal rule.
62
I report the dynamics under the optimal rule with a reaction to premium (?
r
= 0, ?
?
=
2.94, ?
Y
= 0, and ?
EFP
= ?0.681). The optimal rule with a reaction to asset prices yields
virtually the same dynamics.
63
Similarly, one can show that such a response to ?nancial variables would decrease the sensitivity
of EFP to ?uctuations in leverage.
49
Figure 1.8: Responding to Asset Prices -productivity shocks-
0 20 40
0
0.5
1
Output
0 20 40
0
0.5
1
Consumption
0 20 40
0
1
2
3
Investment
0 20 40
?0.5
0
0.5
1
Asset Price
0 20 40
0
0.5
1
1.5
Net Worth
0 20 40
?1.5
?1
?0.5
0
Debt
0 20 40
?1.5
?1
?0.5
0
Leverage Ratio
0 20 40
?10
?5
0
Premium (bpts)
0 20 40
?0.2
?0.1
0
Bankruptcy Rate (ppts)
0 20 40
?1
?0.5
0
Threshold Prod. (?)
0 20 40
?0.1
0
0.1
0.2
Mark-up
0 20 40
?0.5
0
0.5
In?ation Rate (ppts)
0 20 40
?0.4
?0.2
0
Policy Rate (ppts)
0 20 40
?0.05
0
0.05
Real Rate (ppts)
Notes. Solid line: Policy rule with ?
Q
= 0.25 (other policy parameters are as in the optimal rule). Dashed
Line: Optimal Rule.
that although mark-up ?uctuates less under the optimal rule (compared to Ramsey
dynamics), it yields a lower aggregate welfare. The reason lies on the fact that the
premium ?uctuates less under Ramsey economy, implying milder ?uctuations in the
intertemporal wedge. Such a di?erence seems to o?set the welfare loss originated
from higher price dispersion under the Ramsey economy.
If the economy is driven by ?rst-moment as well as uncertainty shocks, then
it is optimal to respond to credit spreads but not to asset prices (Table 1.6). This
50
Figure 1.9: Responding to Asset Prices -uncertainty shocks-
0 5 10
?0.2
0
0.2
Output
0 5 10
?0.2
0
0.2
Consumption
0 5 10
?1
?0.5
0
0.5
Investment
0 5 10
?0.2
0
0.2
Asset Price
0 5 10
?0.5
0
0.5
Net Worth
0 5 10
?0.5
0
0.5
Debt
0 5 10
?0.5
0
0.5
Leverage Ratio
0 5 10
0
10
20
30
Premium (bpts)
0 5 10
0
0.2
0.4
Bankruptcy Rate (ppts)
0 5 10
?0.2
0
0.2
Threshold Prod. (?)
0 5 10
?0.5
0
0.5
Mark-up
0 5 10
?0.2
0
0.2
In?ation (ppts)
0 5 10
?1
?0.5
0
0.5
Policy Rate (ppts)
0 5 10
?1
?0.5
0
0.5
Real Rate (ppts)
Notes. Solid line: Optimal rule. Dashed line: Taylor rule (?
r
=0.85, ?
?
=1.5, and ?
Y
= 0.5/4). Dotted
Line: Ramsey economy.
is mainly due to credit spreads being driven mostly by uncertainty shocks, whereas
asset prices being driven mostly by productivity shocks (see Table 1.3). This is
inline with planner’s motive to mitigate ?uctuations in uncertainty as discussed in
the previous section. The optimal degree of response suggests that in response to a
1% increase in credit spreads, the policy rate should be reduced by 32 basis points.
The optimized rule with a reaction to credit spreads achieves a welfare elvel slightly
less than the strict in?ation stabilization.
Note also that the upper bound for in?ation is hit in this case (when all shocks
51
are present).
64
Since strict in?ation stabilization dominates the optimized rule in
welfare terms (though by a small margin), setting a higher upper bound for in?ation
would imply a higher optimal reaction to in?ation and a decrease in the optimal
magnitude of response to credit spreads. Eventually as one increases the upper
bound, the optimal magnitude of response to credit spreads would be driven down
to zero.
Figure 1.10: Welfare Surfaces (Benchmark Uncertainty versus High Uncertainty)
?3
?2.7
?2.4
?2.1
?1.8
?1.5
?1.2
?0.9
?0.6
?0.3
0
0.3
0.6
0.9
1.9
2.2
2.5
2.8
?132.8
?132.78
?132.76
?132.74
?132.72
?132.7
?132.68
?132.66
Response to Premium
Response to Inflation
C
o
n
d
i
t
i
o
n
a
l
W
e
l
f
a
r
e
Higher
Uncertainty
Benchmark
Uncertainty
For sensitivity analysis, I consider an alternative calibration for uncertainty
shocks (an increase in ?
U
to 0.25).
65
For brevity in the discussion that follows, I will
64
As argued above, the upper bound is set at 3 from a practical policy making view (Schmitt-
Grohe and Uribe, 2006).
65
In particular, I calibrate ?
U
to match the cyclical volatility of the spread between BAA-rated
corporate bond yield and 10-year constant maturity treasury bill, the most volatile spread among
the ones I consider. Joint calibration of ?
?
A, ?
?
G, and ?
U
now implies 0.00808, 0.00764, and
0.02506, respectively.
52
call this case as higher uncertainty. Under higher uncertainty, optimal policy pre-
scription suggests a stronger reaction to premium. In particular, the optimized rule
suggests ?
r
= 0, ?
?
= 3, ?
Y
= 0 and ?
EFP
= ?0.60 (Figure 1.10). Moreover, the
welfare surface under higher uncertainty not only shifts down and induces a stronger
reaction to the premium, but also shows more concavity around the optimal rule.
A zero policy response to the premium under higher uncertainty would then imply
a much higher welfare loss compared to an economy under benchmark uncertainty.
Figure 1.11: Welfare Surfaces (Responding to Uncertainty)
?3
?2.7
?2.4
?2.1
?1.8
?1.5
?1.2
?0.9
?0.6
?0.3
0
0.3
0.6
0.9
1.9
2.2
2.5
2.8
?134.4
?134.2
?134
?133.8
?133.6
?133.4
?133.2
?133
?132.8
?132.6
?132.4
Response to Uncertainty
Response to Inflation
C
o
n
d
i
t
i
o
n
a
l
W
e
l
f
a
r
e
?
Y
=0.1
?
Y
=0.2
?
Y
=0
To provide a further understanding on whether time-variation in cross-sectional
dispersion is welfare detrimental, I next consider normative implications of react-
ing to the uncertainty itself in the policy rule.
66
This point is especially relevant,
66
Note that the deterministic steady state value of the uncertainty shock is equal to zero. Hence,
the relevant part of the policy rule cannot be modi?ed as log deviation of U from its deterministic
value. I accordingly modify the relevant part as ...+?
F
(U).
53
since including asset prices or credit spreads in the policy rule counterfactually as-
sumes that the central bank cannot observe uncertainty. In contrast, the central
bank is able observe uncertainty, and importantly, would like to react directly to
uncertainty, since the Ramsey optimal policy results suggest that the planner would
like reduce the contribution of uncertainty on the business cycles. Welfare surfaces
suggests that policy maker is willing to react to the uncertainty directly in a simple
policy rule (Figure 1.11).
67
Moreover, the welfare surface remains concave for higher degrees of in?ationary
reaction. Essentially, the optimal policy rule that includes uncertainty fares even
better than the strict in?ation stabilization (although slightly), and yields a welfare
gain of 0.0026% in consumption terms.
68
In sum, I conclude that the time variation
in cross-sectional dispersion induce ine?ciencies in the economy. This is why it is
the credit spreads, ?uctuations in which are mostly driven by uncertainty shocks,
call for a negative response, whereas asset prices, ?uctuations in which are driven
mostly by ?rst-moment shocks, call for a zero response in the optimal policy rule.
Responding to in?ation.
Under ?rst-moment shocks, strict in?ation stabilization that completely elimi-
nates distortions due to relative price dispersion turns out to be the welfare-maximizing
67
With optimal policy rule coe?cients ?
r
= 0, ?
?
= 3, ?
Y
= 0 and ?
U
= ?0.20.
68
Interestingly, under this counterfactual scenario in which the policy maker could directly react
to an exogenous state variable, the economy under the optimal policy rule welfare dominates the
Ramsey economy slightly by 0.0022% in consumption terms. This is mainly due to approximating
welfare at t=0 (taking into account lack of certainty at the stochastic steady state). Since the rule
includes one of the exogenous state itself, the resulting correction term becomes closer to zero,
increasing the welfare signi?cantly, leading to this result. This result that the Ramsey planner
might be dominated (even slightly) by an optimal rule is a result also noted in Schmitt-Grohe and
Uribe (2006).
54
policy (Table 1.6). Comparing the impulse responses under strict in?ation stabiliza-
tion and that under Ramsey policy shows that the dynamics of real and ?nancial
variables are almost the same.
69
In a model with ?nancial frictions, the reason
why such an emphasis is given to price stickiness distortion manifests itself in the
simulated volatility of external ?nance premium. In particular, in response to ?rst-
moment shocks, ?uctuations in the premium is unrealistically low, suggesting an
unrealistic low degree of ?nancial ampli?cation. Hence, less emphasis is given to
mitigating ?nancial ampli?cation.
If the economy is driven by uncertainty shocks, the optimal policy allows for
mild ?uctuations in in?ation, inline with Ramsey policy ?ndings. Optimal rules
achieve a welfare higher than the strict in?ation stabilization.
If the economy is driven by all shocks, the price dispersion distortion becomes
more relevant (mainly due to ?rst-moment shocks), and the welfare attained under
the optimal rule is slightly less than that under strict in?ation stabilization (Table
1.6).
Responding to output gap.
If the economy is driven by ?rst-moment shocks, a positive response to out-
put gap exacerbates ?uctuations in average mark-up in the economy, leading to
much higher distortions due to price dispersion.
70
Consider, for instance, in Fig-
69
Shown in the Appendix Figure 1.1g in the Appendix. Curiously though, conditional on the
initial state being the deterministic Ramsey steady state, strict in?ation stabilization welfare dom-
inates the Ramsey economy though by only a negligible amount. A consumer in the Ramsey
economy would prefer a consumption subsidy of 3 ? 10
?7
% to be as well o? as under the strict
in?ation stabilization regime. See Schmitt-Grohe and Uribe (2006) for a similar result.
70
For a detailed discussion, see Schmitt-Grohe and Uribe (2006).
55
ure 1.17 in the Appendix, the model dynamics under the benchmark policy rule
(?
r
= 0.85, ?
?
= 2.309, ?
Y
= 0) and those under the calibrated rule (?
r
= 0.85, ?
?
=
2.309, ?
Y
= 0.593/4). It is evident that an output response reduces ?uctuations
in the premium, yet leads to much higher ?uctuations in average mark-up in the
economy. Welfare losses presented in Table 1.6 suggest that the distortion due to
increase in relative price dispersion outweighs the potential welfare gain from having
a smoother premium. Similarly, a comparison of Taylor rules (with no persistence)
shows that an output reaction of ?
Y
= 0.5 leads to a welfare loss equal to 0.4% in
consumption terms.
71
In response to uncertainty shocks, as evident from welfare surfaces (Figures
1.19 to 1.22 in the Appendix), responding to output gap becomes much less welfare
reducing. For a mild policy reaction to in?ation (such as ?
?
=1.5), a positive policy
response to output might even be welfare improving.
Gradualism in the policy.
The optimality of gradual policy reaction to (?rst-moment) disturbances has
also been recognized in the literature.
72
Such a result implies that monetary policy
should be backward looking. Nevertheless, welfare losses from acting proactively
is negligible. Comparing the optimized rules shows that decreasing the persistence
parameter ?
r
by approximately 0.1 induce a welfare loss less than one-thousandth
of a percentage in consumption terms. Moreover, for ?
?
= 1.5 as in the Taylor
71
In 2005$s, this welfare loss amounts to 24 billions dollars. To get this number, I ?rst calculate
the average real consumption expenditures on non-durables and services for 1989Q1-2009Q1, which
is approximately 6 trillion (in 2005$s). Calculating the fraction of 0.4% then yields the desired
number.
72
See for instance Schmitt-Grohe and Uribe (2006).
56
rule, an increase in the persistence to .85 from nil costs 0.003% of consumption.
Under uncertainty shocks, policy making should be pro-active (no gradual policy
reaction). Yet, welfare losses due to a milder persistence seems negligible. Consider
for instance an increase in the persistence from ?
r
= 0 to ?
r
= 0.85 in standard
Taylor rules reported in Table 1.6. The resulting welfare loss is around 0.003%.
Under a stronger anti-in?ationary stance, the loss would even be lower.
1.8 Further Discussion
The analysis so far shows that policy makers should contain business cycle ?uc-
tuations due to uncertainty, by either directly responding to uncertainty, or more
practically, by responding to credit spreads (which, themselves, are a good proxy
for uncertainty). In this section, with the caveat in mind that the model is rather
simplistic, I provide further insights on this result from a historical perspective.
First, note that the key equation in the ?nancial ampli?cation mechanism -
that relates the external ?nance premium (EFP) to the aggregate leverage ratio
(
QtK
t+1
N
t+1
)- can be expressed as a ‘collateral’ constraint. In particular,
EFP
t
?
R
k
t+1
R
t
=
_
1 ?
N
t+1
Q
t
K
t+1
__
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
)
_
?1
which implies that
AmountBorrowed
¸ .. ¸
Q
t
K
t+1
?N
t+1
=
_
_
1
1 ?EFP
t
_
[1 ?F(?
t+1
)] + (1 ?µ)
_
?
t+1
0
?
t+1
dF(?
t+1
)
_
?1
_
_
NetWorth
¸ .. ¸
N
t+1
57
Hence, ?rms can borrow a certain fraction of their net worth, the fraction
depending on aggregate ?nancial conditions in the economy.
How strong does the planner value marginally relaxing this constraint over the
actual business cycles? Technically, how does the Lagrange multiplier associated
with this constraint evolve over time?
To address this question, I use the stochastic processes for innovations to
TFP, government spending, and cross-sectional dispersion derived from actual US
data for the sample period 1989Q1 to 2009Q1. For uncertainty, I use three di?erent
measures, a macro-level measure, the implied stock market volatility (the VXO), and
two micro-level measures, cross-sectional dispersion of industrial TFP growth, and of
?rm-level stock returns’ growth.
73
For deriving each series of innovations, I estimate
an AR(1) process for cyclical TFP, government spending, and the dispersion series
(or the VXO). Actual series as well as details on the estimation are provided in
Appendix D.
Figure 1.12 suggests that planner’s willingness to relax the ?nancial constraint
shows a rapid deterioration starting in mid-2002 and eventually hits record low
levels by the end of 2006. When industry-level dispersion is used as a measure
of uncertainty, such rapid deterioration starts in 2001 and ceases by 2005. These
all indicate that the planner -who respects the competitive equilibrium conditions-
values relaxing the ?nancial constraint at a historically low level in the run up to
the recent crisis.
73
For the latter two, I use the data set provided by Bloom et al. (2010). You may refer to
http://www.stanford.edu/
~
nbloom/RUBC_data.zip
58
Figure 1.12: Shadow Value of Relaxing the Financial Constraint
1.2
1.4
1.6
1.8
2.0
2.2
2.4
2.6
2.8
1.7
1.8
1.9
2.0
2.1
2.2
2.3
2.4
2.5
90 92 94 96 98 00 02 04 06 08
Shadow Value (Uncertainty: Industry-Level)
Shadow Value (Uncertainty: Firm-Level)
Shadow Value (Uncertainty: VXO)
Moreover, marginal bene?t of relaxing the ?nancial constraint follows the dis-
persion (or the VXO) at a great extent.
74
In this regard, uncertainty captures well
how strong the planner values relaxing the constraint. The reason lies on the fact
that uncertainty drives most of the ?uctuations in credit spread, the ease at which
borrowers are able to fund their projects.
1.9 Conclusion
This paper studies normative implications of uncertainty, or as also called in the
literature risk or dispersion shocks, on monetary policy. Uncertainty shocks, having
a direct e?ect on aggregate ?nancial conditions, prescribes that ?nancial variables
per se should matter for monetary policy making.
The results suggests that optimal policy is to contain business cycle ?uctua-
74
See Figure 1.25 in the Appendix for the dispersion or the VXO series.
59
tions due to uncertainty. Moreover, a higher uncertainty makes the planner more
willing to relax the ?nancial constraints. From a practical point of view, however,
the availability and the quality of information on the dispersion may not be available
in real time. Yet, since credit spreads can serve as a good proxy for uncertainty,
responding to credit spreads can be used as a general policy to have better aggre-
gate outcomes. The optimal degree of response is generally less than one-to-one
under various scenarios. A strict in?ation stabilization, compared to the optimal
rule, yields negligible welfare gains. Under ‘higher uncertainty’, the precise degree
to which the policy maker should respond to the spread rises.
Note however that there are many credit spreads in an actual economy, busi-
ness cycle properties of which, although mostly follow a common trend, might dif-
fer during abnormal times. Moreover, potential interaction between ?rst-moment
shocks and uncertainty can also be explored. To the extent ?rst-moment shocks (e.g.
productivity) lead to ?uctuations in cross-sectional dispersion, and accordingly, in-
duce more pronounced distortions in capital supply decisions, optimal policy would
still prescribe a response to credit spreads. The optimal magnitude of response,
though, requires a quantitative exercise. Besides, facing not a single but many mea-
sures of ?nancial stability, monetary authorities, in a real economy, is to conjecture
an optimal response to various types of disturbances (of real and ?nancial types) de-
pending on the quantity and the quality of the information available. These points
are left to future work.
60
Table 1.6: Simple Rules versus Optimal Policy (Baseline Calibration)
First-Moment Shocks ?
r
?
?
?
Y
?
F
?
r
?
?
?
Y
?
EFP
CEV (%)
Taylor Rules
0 1.5 0 0 0.190 0.126 1.180 0.131 0.0092
0 1.5 0.5/4 0 1.197 1.167 1.135 0.123 0.4015
0.85 1.5 0 0 0.169 0.375 1.088 0.101 0.0121
0.85 1.5 0.5/4 0 0.748 1.815 0.794 0.023 0.3050
Benchmark Rule
0.84 1.770 0 - 0.132 0.235 1.124 0.113 0.0022
0.84 1.770 0.640/4 - 0.710 1.482 0.863 0.027 0.2325
Strict In?ation Stabilization - - - - 0.067 0 1.177 0.131 0.000
Ramsey Policy - - - - 0.166 0.064 1.149 0.120 0
Optimized Rules
with Asset Price 0.540 3 0 0 0.092 0.043 1.174 0.129 0.0006
with Premium 0.445 3 0 0 0.093 0.039 1.175 0.130 0.0006
Uncertainty Shocks ?
r
?
?
?
Y
?
F
?
r
?
?
?
Y
?
EFP
CEV (%)
Taylor Rules
0 1.5 0 0 0.252 0.166 0.119 0.270 0.0063
0 1.5 0.5/4 0 0.170 0.078 0.111 0.268 0.0052
0.85 1.5 0 0 0.092 0.229 0.192 0.289 0.0100
0.85 1.5 0.5/4 0 0.042 0.078 0.132 0.275 0.0069
Benchmark Rule
0.84 1.770 0 - 0.094 0.189 0.175 0.285 0.0086
0.84 1.770 0.640/4 - 0.048 0.071 0.129 0.274 0.0062
Strict In?ation Stabilization - - - - 0.116 0 0.094 0.265 0.0033
Ramsey Policy - - - - 0.891 0.206 0.176 0.219 0
Optimized Rules
with Asset Price 0 2.947 0 0.281 0.082 0.042 0.087 0.264 0.0032
with Premium 0 2.921 0 -0.684 0.090 0.031 0.090 0.264 0.0032
First-Moment & Uncertainty Shocks ?
r
?
?
?
Y
?
F
?
r
?
?
?
Y
?
EFP
CEV (%)
Taylor Rules
0 1.5 0 0 0.316 0.208 1.186 0.300 0.0126
0 1.5 0.5/4 0 1.209 1.169 1.141 0.295 0.4037
0.85 1.5 0 0 0.192 0.440 1.105 0.306 0.0191
0.85 1.5 0.5/4 0 0.749 1.187 0.805 0.276 0.3090
Benchmark Rule
0.84 1.770 0 - 0.162 0.301 1.138 0.307 0.0107
0.84 1.770 0.640/4 - 0.712 1.484 0.873 0.275 0.2385
Strict In?ation Stabilization - - - - 0.133 0 1.181 0.296 0.0004
Ramsey Policy - - - - 0.907 0.216 1.162 0.250 0
Optimized Rules
with Asset Price 0 3 0 0 0.186 0.062 1.183 0.297 0.0016
with Premium 0 3 0 -0.325 0.169 0.050 1.181 0.296 0.0014
61
1.10 Appendix - Tables
1.11 Appendix - Figures
Figure 1.13: Long-run equilibria as a function of monopolistic competition
5 10 15 20
0.8
0.9
1
1.1
1.2
1.3
Output
5 10 15 20
0.45
0.5
0.55
0.6
0.65
Consumption
5 10 15 20
0.16
0.18
0.2
0.22
0.24
0.26
0.28
Investment
5 10 15 20
2
4
6
8
10
Total Debt
5 10 15 20
0
1
2
3
4
5
Net Worth
5 10 15 20
1
2
3
4
5
6
7
8
Leverage
5 10 15 20
0
0.5
1
1.5
2
2.5
3
3.5
Bankruptcy Rate (ppts)
5 10 15 20
0
50
100
150
200
250
Premium (bpts)
5 10 15 20
0
1
2
3
4
5
6
x 10
?4
Agg. Monitoring Costs
Notes. Dashed line: No ?nancial frictions (? 0), Solid line: Financial frictions (? = 0.263).
62
Figure 1.14: Long-run equilibria as a function of long-run in?ation
0 0.01 0.02 0.03
0.7
0.8
0.9
1
1.1
Output
0 0.01 0.02 0.03
0.35
0.4
0.45
0.5
0.55
0.6
Consumption
0 0.01 0.02 0.03
0.1
0.15
0.2
0.25
Investment
0 0.01 0.02 0.03
2
4
6
8
10
Total Debt
0 0.01 0.02 0.03
0
1
2
3
4
Net Worth
0 0.01 0.02 0.03
0
2
4
6
8
Leverage
0 0.01 0.02 0.03
0
1
2
3
4
Bankruptcy Rate (ppts)
0 0.01 0.02 0.03
?50
0
50
100
150
200
250
Premium (bpts)
0 0.01 0.02 0.03
?2
0
2
4
6
x 10
?4
Agg. Monitoring Costs
Notes. Dashed line: No ?nancial frictions (? 0), Solid line: Financial frictions (? = 0.263).
63
Table 1.7: Business Cycle Statistics -Decentralized Economy-
Real Variables Financial Variables Monetary Variables
Y C I Q EFP Net Worth Debt Leverage Bankruptcy Rate Policy Rate In?ation
Std. Dev (%) 1.14 0.95 2.90 0.73 0.31 1.48 0.28 1.36 0.53 0.16 0.30
Auto. corr. 0.73 0.75 0.72 0.72 0.66 0.72 0.93 0.70 0.66 0.85 0.32
Real Variables
Y 1 0.93 0.97 0.96 -0.50 0.96 0.53 -0.94 -0.48 -0.58 -0.44
C 1 0.86 0.85 -0.23 0.85 0.60 -0.81 -0.21 -0.81 -0.62
I 1 1.00 -0.68 0.99 0.47 -0.99 -0.67 -0.44 -0.34
Financial Variables
Q 1 -0.68 0.98 0.40 -0.99 -0.67 -0.42 -0.35
Premium 1 -0.69 -0.19 0.71 1.00 -0.28 -0.23
Net Worth 1 0.52 -0.98 -0.68 -0.42 -0.34
Debt 1 -0.36 -0.19 -0.62 -0.02
Leverage 1 0.70 0.33 0.37
Bankruptcy Rate 1 -0.29 -0.24
Monetary Variables
Policy Rate 1 0.54
In?ation 1
6
4
Table 1.8: Business Cycle Statistics -Planner’s Economy-
Real Variables Financial Variables Monetary Variables
Y C I Q EFP Net Worth Debt Leverage Bankruptcy Rate Policy Rate In?ation
Std. Dev (%) 1.16 0.96 2.86 0.72 0.25 1.44 0.35 1.33 0.44 0.91 0.22
Auto. corr. 0.71 0.71 0.71 0.71 0.66 0.72 0.83 0.71 0.66 -0.15 -0.37
Real Variables
Y 1 0.97 0.98 0.97 -0.44 0.98 0.46 -0.95 -0.42 -0.13 0.05
C 1 0.96 0.95 -0.34 0.98 0.47 -0.95 -0.32 -0.21 0.07
I 1 1.00 -0.54 0.99 0.46 -0.95 -0.52 -0.08 0.05
Financial Variables
Q 1 -0.55 0.98 0.40 -0.95 -0.53 -0.07 0.04
Premium 1 -0.46 -0.51 0.36 1.00 -0.52 0.20
Net Worth 1 0.44 -0.97 -0.44 -0.07 -0.01
Debt 1 -0.21 -0.51 -0.15 0.36
Leverage 1 0.34 0.04 0.11
Bankruptcy Rate 1 -0.53 0.20
Monetary Variables
Policy Rate 1 -0.85
In?ation 1
6
5
Table 1.9: Business Cycle Statistics (only ?nancial frictions) -Decentralized Economy-
Real Variables Financial Variables Monetary Variables
Y C I Q EFP Net Worth Debt Leverage Bankruptcy Rate Policy Rate In?ation
Std. Dev (%) 1.20 0.92 3.00 0.76 0.30 1.57 0.25 1.46 0.51 0.17 0.44
Auto. corr. 0.72 0.72 0.71 0.71 0.66 0.71 0.93 0.71 0.66 0.69 -0.05
Real Variables
Y 1 0.95 0.98 0.97 -0.51 0.98 0.46 -0.98 -0.49 -0.55 -0.33
C 1 0.90 0.89 -0.28 0.92 0.50 -0.90 -0.26 -0.78 -0.45
I 1 1.00 -0.65 0.99 0.42 -1.00 -0.63 -0.46 -0.29
Financial Variables
Q 1 -0.65 0.98 0.34 -1.00 -0.63 -0.44 -0.29
Premium 1 -0.63 -0.29 0.63 1.00 -0.34 -0.20
Net Worth 1 0.50 -0.99 -0.62 -0.48 -0.29
Debt 1 -0.37 -0.29 -0.33 0.02
Leverage 1 0.61 0.46 0.31
Bankruptcy Rate 1 -0.35 -0.21
Monetary Variables
Policy Rate 1 0.57
In?ation 1
6
6
Table 1.10: Business Cycle Statistics (only ?nancial frictions) -Planner’s Economy-
Real Variables Financial Variables Monetary Variables
Y C I Q EFP Net Worth Debt Leverage Bankruptcy Rate Policy Rate In?ation
Std. Dev (%) 1.20 0.92 3.01 0.76 0.30 1.57 0.25 1.47 0.51 3682330310.15 3646188341.77
Auto. corr. 0.72 0.72 0.71 0.71 0.66 0.71 0.93 0.71 0.66 0.43 0.43
Real Variables
Y 1 0.95 0.98 0.97 -0.51 0.98 0.45 -0.98 -0.49 0.15 0.10
C 1 0.90 0.89 -0.28 0.92 0.50 -0.90 -0.27 0.43 0.29
I 1 1.00 -0.65 0.99 0.42 -1.00 -0.63 0.05 0.02
Financial Variables
Q 1 -0.65 0.98 0.34 -1.00 -0.63 0.04 0.01
Premium 1 -0.63 -0.29 0.63 1.00 0.66 0.45
Net Worth 1 0.50 -0.99 -0.62 0.07 0.03
Debt 1 -0.37 -0.29 0.05 0.10
Leverage 1 0.62 -0.06 -0.02
Bankruptcy Rate 1 0.67 0.46
Monetary Variables
Policy Rate 1 0.43
In?ation 1
6
7
Figure 1.15: Impulse Responses to a 1 sd. increase in government spending
0 20 40
0
0.1
0.2
Output
0 20 40
?0.2
0
0.2
Consumption
0 20 40
?0.1
0
0.1
0.2
Labor
0 20 40
?0.5
0
0.5
Investment
0 20 40
?0.1
0
0.1
Asset Price
0 20 40
?0.1
0
0.1
Net Worth
0 20 40
?0.1
0
0.1
Debt
0 20 40
?0.1
0
0.1
Leverage Ratio
0 20 40
?1
?0.5
0
0.5
Premium (bpts)
0 20 40
?0.02
?0.01
0
0.01
Bankruptcy Rate (ppts)
0 20 40
?0.04
?0.02
0
Threshold Prod. (?)
0 20 40
?0.1
0
0.1
Mark-up
0 20 40
?0.1
0
0.1
In?ation Rate (ppts)
0 20 40
?0.1
0
0.1
Policy Rate (ppts)
0 20 40
?0.05
0
0.05
Real Rate (ppts)
Notes. Solid line: Financial ampli?cation, Dashed line: No ?nancial ampli?cation (EFP is
?xed). Unless otherwise noted, the responses are in terms of percentage deviation from the
respective deterministic steady states.
68
Figure 1.16: Strict In?ation Stabilization versus Ramsey Policy -productivity
shocks-
0 20 40
0
0.5
1
Output
0 20 40
0
0.5
1
Consumption
0 20 40
0
1
2
3
Investment
0 20 40
?0.5
0
0.5
1
Asset Price
0 20 40
0
0.5
1
1.5
Net Worth
0 20 40
?1.5
?1
?0.5
0
Debt
0 20 40
?2
?1
0
1
Leverage Ratio
0 20 40
?10
?5
0
5
Premium (bpts)
0 20 40
?0.2
0
0.2
Bankruptcy Rate (ppts)
0 20 40
?1
?0.5
0
0.5
Threshold Prod. (?)
0 20 40
?0.1
0
0.1
Mark-up
0 20 40
?0.1
0
0.1
In?ation Rate (ppts)
0 20 40
?0.1
0
0.1
Policy Rate (ppts)
0 20 40
?0.1
0
0.1
Real Rate (ppts)
Notes. Solid line: Strict in?ation stabilization. Dashed Line: Ramsey economy.
69
Figure 1.17: Responding to Output Gap -productivity shocks-
0 20 40
0
0.5
1
Output
0 20 40
0
0.5
1
Consumption
0 20 40
?1
?0.5
0
0.5
Labor
0 20 40
0
1
2
Investment
0 20 40
?0.5
0
0.5
Asset Price
0 20 40
0
0.5
1
1.5
Net Worth
0 20 40
?1
?0.5
0
Debt
0 20 40
?1
?0.5
0
0.5
Leverage Ratio
0 20 40
?10
?5
0
5
Premium (bpts)
0 20 40
?0.2
0
0.2
Bankruptcy Rate (ppts)
0 20 40
?0.5
0
0.5
Threshold Prod. (?)
0 20 40
0
0.5
1
Mark-up
0 20 40
?2
?1
0
In?ation Rate (ppts)
0 20 40
?1
?0.5
0
Policy Rate (ppts)
0 20 40
?0.5
0
0.5
1
Real Rate (ppts)
Notes. Solid line: Benchmark policy rule with a response to output gap (?
r
=0.84, ?
?
=1.770,
?
Y
= 0.640/4). Dashed Line: Benchmark policy rule (?
r
=0.84, ?
?
=1.770).
70
Figure 1.18: Responding to Output Gap -uncertainty shocks-
0 10 20 30 40
?0.2
0
0.2
Output
0 10 20 30 40
?0.2
0
0.2
Consumption
0 10 20 30 40
?1
?0.5
0
0.5
Investment
0 10 20 30 40
?0.5
0
0.5
Asset Price
0 10 20 30 40
?1
?0.5
0
0.5
Net Worth
0 10 20 30 40
?0.5
0
0.5
1
Debt
0 10 20 30 40
?0.5
0
0.5
Leverage Ratio
0 10 20 30 40
?20
0
20
40
Premium (bpts)
0 10 20 30 40
?0.5
0
0.5
Bankruptcy Rate (ppts)
0 10 20 30 40
?0.2
0
0.2
Threshold Prod. (?)
0 10 20 30 40
?0.5
0
0.5
Mark-up
0 10 20 30 40
?0.5
0
0.5
In?ation (ppts)
0 10 20 30 40
?1
?0.5
0
0.5
Policy Rate (ppts)
0 10 20 30 40
?1
?0.5
0
0.5
Real Rate (ppts)
Notes. Solid line: Taylor rule with policy intertia (?
r
=0.85, ?
?
=1.5, and ?
Y
= 0). Dashed
Line: Taylor rule with policy inertia and response to output gap (?
r
=0.85, ?
?
=1.5, and ?
Y
=
0.5/4). Dotted Line: Ramsey economy.
Figure 1.19: Welfare Surface -TFP and G Shocks-
?0.5
?0.2
0.1
0.4
0.7
1
1.3
1.6
1.9
1.6
1.9
2.2
2.5
2.8
?136.5
?136
?135.5
?135
?134.5
?134
?133.5
?133
?132.5
Response to Asset Price
Response to Inflation
C
o
n
d
it
io
n
a
l
W
e
lf
a
r
e
?
Y
=0.2
?
Y
=0.4
?
Y
=0
Notes. ?
r
is set at its optimal value.
71
Figure 1.20: Welfare Surface -Uncertainty Shock-
?0.5
?0.2
0.1
0.4
0.7
1
1.3
1.6
1.9
1.9
2.2
2.5
2.8
?132.705
?132.7
?132.695
?132.69
?132.685
?132.68
?132.675
?132.67
Response to Asset Price
Response to Inflation
C
o
n
d
it
io
n
a
l
W
e
lf
a
r
e
?
Y
=0.2
?
Y
=0
?
Y
=0.4
Notes. ?
r
is set at its optimal value.
Figure 1.21: Welfare Surface -All Shocks-
?0.5
?0.2
0.1
0.4
0.7
1
1.3
1.6
1.9
1.9
2.2
2.5
2.8
?136
?135.5
?135
?134.5
?134
?133.5
?133
?132.5
Response to Asset Price
Response to Inflation
C
o
n
d
i
t
i
o
n
a
l
W
e
l
f
a
r
e
?
Y
=0.2
?
Y
=0.4
?
Y
=0
Notes. ?
r
is set at its optimal value.
72
Figure 1.22: Welfare Surface -Uncertainty Shock-
?3
?2.7
?2.4
?2.1
?1.8
?1.5
?1.2
?0.9
?0.6
?0.3
0
0.3
0.6
0.9
1.9
2.2
2.5
2.8
?132.69
?132.685
?132.68
?132.675
?132.67
?132.665
Response to Premium
Response to Inflation
C
o
n
d
it
io
n
a
l
W
e
lf
a
r
e
?
Y
=0
?
Y
=0.2
?
Y
=0.4
Notes. ?
r
is set at its optimal value.
Figure 1.23: Welfare Surface -All Shocks-
?3
?2.7
?2.4
?2.1
?1.8
?1.5
?1.2
?0.9
?0.6
?0.3
0
0.3
0.6
0.9
1.9
2.2
2.5
2.8
?132.72
?132.71
?132.7
?132.69
?132.68
?132.67
?132.66
Response to Premium
Response to Inflation
C
o
n
d
it
io
n
a
l
W
e
lf
a
r
e
Notes. ?
r
and ?
Y
are set at their optimal values. The welfare surfaces under ?
Y
= 0.2 or
?
Y
= 0.4 are not presented for presentation purposes. They are much lower than the one
presented.
73
1.12 Appendix - Competitive Equilibrium, Calibration and Further
Discussions
Appendix A1. Derivation of ex-post marginal real return to capital
The ex-post real marginal return to holding capital from t?1 to t for an entrepreneur
i is given by
R
i,k
t
=
?
1
Xt
Y
it
+?
it
Q
t
(1 ??)K
it
Q
t?1
K
it
(1.42)
= ?
it
1
Xt
?Yt
K
it
+Q
t
(1 ??)
Q
t?1
(1.43)
where Y
t
is the average wholesale production across the entrepreneurs (Y
it
=
?
it
Y
t
). Hence, the expected average return to capital across the entrepreneurs,
E
t?1
R
i,k
t
, is
E
t?1
_
R
i,k
t
_
= E
t?1
1
Xt
?Yt
K
it
+Q
t
(1 ??)
Q
t?1
(1.44)
under the assumption that E
t?1
?
it
= 1 and CRTS production technology. The
ex-post return to capital, R
k
t
(?
t
; ?
t
), therefore, is the right hand side of the above
equation without the expectation operator.
74
Appendix A2 - Debt Contract Problem
The intermediaries are assumed to operate in perfectly competitive markets, earning
zero pro?ts in equilibrium and perfectly diversifying any idiosyncratic risk. Hence,
the opportunity cost of funds that the intermediaries face is the economy-wide real
return of holding riskless government bonds from t ?1 to t, R
t
. The debt contract
problem should then satisfy that the intermediary earns his opportunity costs in
expected terms, i.e.
E
t?1
_
[1 ?F(?
it
)]Z
i
t
(?
t
; ?
t
)B
i
t
+ (1 ?µ)
_
?
it
0
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
dF(?
it
)
_
= R
t
B
i
t
(1.45)
The ?rst term inside the square brackets amounts to the total receipts that
the intermediary earns from the non-defaulting entrepreneurs. The second term is
the receipts from the defaulting entrepreneurs which amounts to the net wholesale
revenue (after proportional monitoring costs are incurred).
On the ?ip side, the expected return to holding capital for the entrepreneur is
given by
E
t?1
__
?
?
it
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
dF(?
it
) ?[1 ?F(?
it
)]?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
(1.46)
The ?rst term inside the square brackets is the expected total return to capital
(taking into account the probability that the entrepreneur i’s idiosyncratic produc-
75
tivity ?
it
is above the threshold level ?
it
). The second term is the amount that
the non-defaulting entrepreneur pays to the intermediary. Note that in the case of
no-default, the entrepreneur keeps the equity (?
it
??
it
)R
k
t
(?
t
; ?
t
)Q
t?1
K
it
.
Hence, the entrepreneur’s maximization problem is
max
K
it
,?
it
E
t?1
__
?
?
it
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
dF(?
it
) ?[1 ?F(?
it
)]?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
(1.47)
subject to
E
t?1
_
[1 ?F(?
it
)]Z
i
t
(?
t
; ?
t
)B
i
t
+ (1 ?µ)
_
?
it
0
?
it
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
dF(?
it
)
_
= R
t
B
i
t
(1.48)
The entrepreneur takes net worth and asset prices as given in the maximization
problem. Before deriving the ?rst-order necessary conditions, I will manipulate the
objective function and the constraint to make the problem more tractable.
After algebraic manipulation, the entrepreneur’s expected return to holding
capital can be expressed as
E
t?1
__
1 ?
_
?
it
_
?
?
it
dF(?
it
) +
_
?
it
0
?
it
dF(?
it
)
__
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
(1.49)
and the zero-pro?t condition as
76
E
t?1
___
?
it
_
?
?
it
dF(?
it
) +
_
?
it
0
?
it
dF(?
it
)
_
?µ
_
?
it
0
?
it
dF(?
it
)
_
R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
= R
t
B
i
t
(1.50)
Now let
?(?
it
) = ?
it
_
?
?
it
dF(?
it
) +
_
?
it
0
?
it
dF(?
it
(1.51)
and
G(?
it
) =
_
?
it
0
?
it
dF(?
it
) (1.52)
Then, the maximization problem can be expressed shortly as
max
Kt,?
it
E
t?1
_
1 ?(?(?
it
)) R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
(1.53)
subject to
E
t?1
_
(?(?
it
) ?µG(?
it
)) R
k
t
(?
t
; ?
t
)Q
t?1
K
it
_
= R
t
_
Q
t?1
K
i
t
?N
it
_
(1.54)
where 1 ? ?(?
it
) denotes the net share of contractual return going to the en-
trepreneur, and ?(?
it
) ? µG(?
it
) is the net contractual share of the lender. As
optimality conditions are presented in Appendix A3 of BGG (p.1385), then one can
show that ex-ante external ?nance premium is an increasing function of leverage.
77
Moreover, in simulating the model, unexpected changes in return to capital due
to aggregate shocks can be accommodated using partial-equilibrium debt contract
problem optimality conditions together with ex-post marginal real return to capital
(as de?ned in Appendix A1).
75
I now present the equilibrium debt contract optimality conditions where R
k
t+1
is assumed to known in advance and ?
i
is assumed to be log-normal. Let ?(?) =
_
?
0
?f(?)d? + ?
_
?
?
f(?)d? denote the expected payo? share of the lender. Note
that 1 ??
(?) = F(?) denotes the bankruptcy rate of entrepreneurs. Let µG(?) ?
µ
_
?
0
?f(?)d? denote the expected monitoring costs. Hence, the expected net payo?
share to the lender is ?(?) ?µG(?), and the normalized payo? to the entrepreneur
is 1 ??(?). Accordingly, the optimal contract problem is
max
K
t+1
,(?)
(1 ??(?))R
k
t+1
Q
t
K
t+1
subject to
(?(?) ?µG(?)) R
k
t+1
Q
t
K
t+1
= R
t
(Q
t
K
t+1
?N
t+1
)
The problem is easier to solve using k =
QtK
t+1
N
t+1
the capital-to-wealth ratio
(which is equal to one plus the leverage ratio -the ratio of external debt to the net
worth-) as the choice variable. Let s =
R
k
t+1
Rt
denote the external ?nance premium
75
Indeed, simulation results show that the ex-ante premium is an increasing function of leverage
(regardless of aggregate shocks), whereas the ex-post premium may or may not be an increasing
function of leverage, depending on various factors, one of which is the policy rule. A very aggressive
policy response to output gap, for instance, might induce a pro-cyclical ex-post premium.
78
over the riskless rate. Then, the problem becomes
max
k,(?)
(1 ??(?))sk
subject to
(?(?) ?µG(?)) sk = k ?1
Assuming an interior solution, the ?rst-order optimality conditions imply
?
(?) ??(?)(?(?) ?µG
(?)) = 0
?(?)s ??(?) = 0
(?(?) ?µG(?))sk ?(k ?1) = 0
where ? ? 1 ??(?) +?(?)(?(?) ?µG(?)).
76
Rearranging gives
s(?) =
?(?)
?(?)
76
A su?cient condition for an interior solution is
s <
1
?(?
?
) ?µG(?
?
)
? s
?
79
k(?) =
?(?)
1 ??(?)
and
?(?) =
?
(?)
?
(?) ?µG
(?)
.
BGG shows that s
(?) > 0 for s > 1 su?ciently low. Then,
k(?) = ?(s(?))
where ?
> 0. Using the expressions for the return to capital, the evolution of net
worth, and the parameters, one can deduce ?. The equation above implies that the
external ?nance premium depends inversely on the capital-to-net-worth ratio.
The algebraic expressions for ?(?) and ?(?) ? µG(?) can be derived by as-
suming that ? is log-normally distributed. In particular, let ln(?) ? N(?
1
2
?
2
?
, ?
2
?
).
Then using the central limit theorem, z ? (ln(?) +0.5?
2
)/? is distributed standard
normal. Hence, the set of equations characterizing the debt contract problem is
z = (log(?) + 0.5?
2
t
)/?
t
?(?) = ?(z ??
t
) +?(1 ??(z))
80
?(?) ?µG(?) = (1 ?µ)?(z ??
t
) +?(1 ??(z))
?
(?) = ?(z ??
t
) + (1 ?(?(z)) ?
?(z)
?
t
?
(?) ?µG
(?) = ?
(?) ?µ
?(z ??
t
)
??
t
?(?) =
?
(?)
?
(?) ?µG
(?)
k(?) = 1 + (?(?) ? (?(?) ?µG(?))/(1 ??(?))
s(?) = ?(?)/((1 ??(?)) ? k(?))
where k(?) is the equilibrium capital to wealth ratio (
QtK
t+1
N
t+1
), and s(?) is the ex-
ternal ?nance premium over the riskless rate.
81
Appendix A3. Retailers’ Problem
Let y
t
(j) be the output of retailer j, and Y
f
t
the ?nal good. We assume that the
?nal goods are produced via the following Dixit-Stiglitz aggregator with elasticity
of substitution :
Y
f
t
=
__
1
0
y
t
(j)
1?
1
_
1
1?
1
(1.55)
and sold at a price of P
t
which satis?es
P
t
=
__
1
0
P
t
(j)
1?
dj
_
1
1?
(1.56)
where P
t
(j) is the price of the retail good j. The demand for each retail good
satis?es the following iso-elastic demand curve:
y
t
(j) =
_
P
t
(j)
P
t
_
?
Y
f
t
(1.57)
The retailers, those who are allowed to change their prices, maximize their
pro?ts given this demand curve and given the price of wholesale goods. In particular,
let P
?
t
denote the price set by retailers who are allowed to change their price at t,
y
?
(j) be the demand given this price, and P
t
the aggregate price level for the ?nal
goods. Then, the retailers’ maximization problem is
max
P
?
t
E
t
?
s=t
?
t,s
?
s?t
P
?
t
?P
W
s
P
s
y
?
s
(j) (1.58)
82
subject to
y
?
s
(j) =
_
P
?
t
P
s
_
?
Y
f
s
?s ? t (1.59)
where ?
t,s
is the shareholders’ (households’) intertemporal elasticity of substitution
which is taken as given by the retailers.
Appendix A4. Deriving the New-Keynesian Phillips Curve in recursive
format
Let
x
1
t
= E
t
?
s=t
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
?
t
P
s
_
(1.60)
=
_
P
?
t
P
t
_
1?
Y
f
t
+E
t
?
s=t+1
?
t,s
?
s?t
_
P
?
t
P
s
_
1?
Y
f
s
=
_
P
?
t
P
t
_
1?
Y
f
t
+E
t
?
t,t+1
?
_
P
?
t
P
?
t+1
_
1?
E
t+1
?
s=t+1
?
t+1,s
?
s?t?1
_
P
?
t+1
P
s
_
1?
Y
f
s
=
_
P
?
t
P
t
_
1?
Y
f
t
+E
t
?
t,t+1
?
_
P
?
t
P
?
t+1
_
1?
x
1
t+1
De?ning ¯ p
t
=
P
?
t
Pt
, we have
83
= ¯ p
t
1?
Y
f
t
+E
t
?
t,t+1
?(1 +?
t+1
)
?1
_
¯ p
t
¯ p
t+1
_
1?
x
1
t+1
Similarly,
x
2
t
= E
t
?
s=t
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
w
s
P
s
_
(1.61)
=
_
P
?
t
P
t
_
?
Y
f
t
_
P
w
t
P
t
_
+E
t
?
s=t+1
?
t,s
?
s?t
_
P
?
t
P
s
_
?
Y
f
s
_
P
w
s
P
s
_
=
_
P
?
t
P
t
_
?
Y
f
t
_
P
w
t
P
t
_
+E
t
?
t,t+1
?
_
P
?
t
P
?
t+1
_
?
E
t+1
?
s=t+1
?
t+1,s
?
s?t?1
_
P
?
t+1
P
s
_
?
Y
f
s
_
P
w
s
P
s
_
=
_
P
?
t
P
t
_
?
Y
f
t
_
P
w
t
P
t
_
+E
t
?
t,t+1
?
_
P
?
t
P
?
t+1
_
?
x
2
t+1
= ¯ p
t
?
Y
f
t
1
X
t
+E
t
?
t,t+1
?(1 +?
t+1
)
_
¯ p
t
¯ p
t+1
_
?
x
2
t+1
84
Appendix A5. Deriving the Demand for the Final Goods
For any given level of demand for the composite consumption good C
t
, the demand
for each c
it
solves the problem of minimizing total expenditures,
_
1
0
P
it
c
it
di subject
to the aggregation constraint C
t
=
_
_
1
0
c
1?
1
it
di
_ 1
1?
1
, where P
it
is the nominal price
of variety c
it
. The solution to this problem yields the optimal demand for c
it
which
satis?es
c
it
=
_
P
it
P
t
_
?
C
t
(1.62)
where the aggregate price P
t
is
P
t
=
__
1
0
P
1?
it
di
_
1
1?
(1.63)
Similarly, the investment good I
t
is assumed to be a composite good made with
varieties i
it
, satisfying I
t
=
_
_
1
0
i
1?
1
it
di
_ 1
1?
1
. Then, capital producers minimize the
total expenditure of buying investment goods,
_
1
0
P
it
i
it
di, which implies a demand
for i
it
satisfying i
it
=
_
P
it
Pt
_
?
I
t
.
For a given level of G
t
, the government minimizes the total cost of absorbing
G
t
. Hence, the public demand for each retail good j is given by g
jt
=
_
P
jt
Pt
_
?
G
t
.
Appendix A6. Deriving S
t
in recursive format
Let 1?? measure of retailers choose a price level P
?
t
at the (symmetric) equilibrium,
and the remaining measure of retailers does not change their prices. Those who have
85
not changed their prices in the current period, however, might have been allowed to
change their prices (with probability 1 ??) and choose P
?
t?1
in the previous period.
Similarly going backwards, one can get a recursive representation for S
t
. Namely,
S
t
?
_
1
0
_
P
it
P
t
_
?
di
= (1 ??)
_
P
?
t
P
t
_
?
+?
_
_
(1 ??)
_
P
?
t?1
P
t
_
?
+ (1 ??)?
_
P
?
t?2
P
t
_
?
+...
_
_
= (1 ??)
_
P
?
t
P
t
_
?
+?
_
P
t?1
P
t
_
?
_
_
(1 ??)
_
P
?
t?1
P
t?1
_
?
+ (1 ??)?
_
P
?
t?2
P
t?1
_
?
+...
_
_
= (1 ??)
_
P
?
t
P
t
_
?
+?
_
P
t?1
P
t
_
?
S
t?1
= (1 ??) ¯ p
t
?
+??
S
t?1
(1.64)
Appendix B - Competitive Equilibrium
The competitive equilibrium for this economy is a set of endogenous objects {C
t
, H
t
, H
e
t
, K
t
, I
t
,
N
t
, R
t
, AMC
t
, R
k
t
, ?
t
; ?
t
, x
1
t
, x
2
t
,W
t
, W
e
t
, R
k
t
, X
t
, ¯ p
t
, Q
t
, ?
t
, ?(?
t
), G(?
t
), ?
(?
t
), G
(?
t
), ?(?
t
),
k(?
t
), s(?
t
)}
t=?
t=0
, given exogenous stochastic processes A
t
, G
t
, ?
t
, the long-run in?a-
86
tion ?, the parameters and the functional forms, such that the following block of
equations are satis?ed:
• The Households:
?U(t)
?C
t
= ?R
t
E
t
_
?U(t + 1)
?C
t+1
_
W
t
= ?
?U(t)
?Ht
?U(t)
?Ct
• The Evolution of Relative Price and the New-Keynesian Phillips Curve:
1 = ?(1 +?)
?1+
+ (1 ??) ¯ p
t
1?
x
1
t
= ¯ p
t
1?
Y
f
t
+E
t
?
t,t+1
?(1 +?
t+1
)
?1
_
¯ p
t
¯ p
t+1
_
1?
x
1
t+1
x
2
t
= ¯ p
t
?
Y
f
t
1
X
t
+E
t
?
t,t+1
?(1 +?
t+1
)
_
¯ p
t
¯ p
t+1
_
?
x
2
t+1
x
1
t
=
?1
x
2
t
• Aggregate Resource Constraint
87
Y
t
= C
t
+C
e
t
+I
t
+G
t
+AMC
t
Y
t
?C
e
t
?AMC
t
=
1
?
t
; ?
t
(F(K
t
, H
t
, H
e
t
) ?C
e
t
?AMC
t
)
?
t
; ?
t
= (1 ??)¯ p
?
t
+??
t
S
t?1
where
AMC
t
= µ ?
_
?
0
?F(?)R
k
t
Q
t?1
K
t
• The Optimal Contract Problem
z = (log(?) + 0.5?
2
t
)/?
t
?(?) = ?(z ??
t
) +?(1 ??(z))
?(?) ?µG(?) = (1 ?µ)?(z ??
t
) +?(1 ??(z))
88
?
(?) = ?(z ??
t
) + (1 ?(?(z)) ?
?(z)
?
t
?
(?) ?µG
(?) = ?
(?) ?µ
?(z ??
t
)
??
t
?(?) =
?
(?)
?
(?) ?µG
(?)
k(?) = 1 + (?(?) ? (?(?) ?µG(?))/(1 ??(?))
s(?) = ?(?)/((1 ??(?)) ? k(?))
where k(?) is the equilibrium capital to wealth ratio (
QtK
t+1
N
t+1
), and s(?) is the ex-
ternal ?nance premium over the riskless rate.
• Capital Accumulation and Investment Demand
E
t
R
k
t+1
= E
t
_
_
1
X
t+1
?Y
t+1
K
t+1
+ (1 ??)Q
t+1
Q
t
_
_
89
E
t
R
k
t+1
= R
t
s(?)
Q
t
=
_
?
_
I
t
K
t
_
_
?1
K
t+1
= (1 ??)K
t
+K
t
?
_
I
t
K
t
_
where ?
_
It
Kt
_
=
It
Kt
?
?
k
2
_
It
Kt
??
_
2
• Labor Demands
W
t
= (1 ??)?
Y
t
H
t
1
X
t
W
e
t
= (1 ??)(1 ??)
Y
t
H
e
t
1
X
t
H
e
t
= 1
• Evolution of Net Worth and Entrepreneurial Consumption
90
N
t+1
= ?
t
_
R
k
t
Q
t?1
K
t
?
_
R
t
+
AMC
t
Q
t?1
K
t
?N
t
_
? (Q
t?1
K
t
?N
t
)
_
+W
e
t
?
e
t
= (1 ??
t
)
_
R
k
t
Q
t?1
K
t
?E
t?1
R
k
t
B
t
_
• Exogenous Processes
log(A
t
) = ?
A
? log(A
t?1
) +?
A
t
log(G
t
) = (1 ??
G
)log(G) +?
G
log(G
t?1
) +?
G
t
log(?
t
) = (1 ??
?
)log(?) +?
?
log(?
t?1
) +U
t
• Monetary Policy Rule and the Fiscal Policy
log
_
1 +r
n
t
1 +r
n
_
= ?
r
log
_
1 +r
n
t?1
1 +r
n
_
+(1??
r
)
_
?
?
log
_
1 +?
t
1 +?
_
+?
Y
log
_
Y
t
Y
_
+?
F
log
_
F
t
F
__
where r
n
t
? 0, R
t
=
1+r
n
t
1+?
t+1
, 1 +? = ?(1 +r
n
), ? = 0 or = 1.0266
1/4
.
G
t
= T
t
91
Appendix C- Data De?nitions
The data is over the period 1989:Q1-2009:Q1, and is taken from Federal Reserve
St.Louis FRED. All the statistics are based on cyclical components of the variables
(based on HP ?lter with a smoothing parameter 1600). The cyclical volatility is
de?ned as the log-deviation of a variable from its HP-trend.
Consumption (C) de?ned as the sum of real personal consumption expendi-
tures of non-durable goods and services.
Investment (I) is the sum of real personal consumption expenditures on durables
and real gross domestic private investment.
Government Expenditures (G)- is de?ned as the real government consumption
expenditures and gross investment.
Real GDP (Y ) is the sum of C, I, and G as de?ned above.
Labor hours (H)- is the the average private labor hours times the total number
of workers.
External Finance Premium (EFP)- is the average of the (annualized) yield
spreads between (i) prime-lending rate and 6-month constant maturity treasury bill,
(ii) prime-lending rate and 3-month constant maturity treasury bill, (iii) Moody’s
BAA-rated and AAA-rated corporate bonds, (iv) Moody’s BAA-rated corporate
bond and 10-year constant maturity treasury bill.
92
Appendix D - Further Discussion
The actual processes for TFP, government spending, and uncertainty (measured
either at a macro- or micro-level) are given in Figures 1.24 and 1.25.
Figure 1.24: TFP and Real Government Spending (G)
.00048
.00052
.00056
.00060
.00064
.00068
90 92 94 96 98 00 02 04 06 08
TFP
1,700
1,800
1,900
2,000
2,100
2,200
2,300
2,400
2,500
2,600
90 92 94 96 98 00 02 04 06 08
Government Spending
Notes. G is de?ned as the real government consumption expenditures and gross investment.
Figure 1.25: VXO or Cross-Sectional Dispersion
10
20
30
40
50
60
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
VXO
.08
.10
.12
.14
.16
.18
.20
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Cross-sectional Dispersion (Firm-Level)
.010
.015
.020
.025
.030
.035
.040
.045
.050
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Cross-section Dispersion (Industry-Level)
Source: Bloom et al. (2010) and own calculations. At the ?rm-level, cross-sectional dispersion
in ?rms’ sales growth is reported. At the industry-level, cross-sectional dispersion of industrial
TFP growth is reported. The implied volatility is the Chicago Board of Options Exchange
VXO index of percentage implied volatility. I use the VXO, rather than the VIX, since the
VIX starts only after 1990. The correlation between the two series is above 0.99.
I use the log-linearly de-trended series in estimating the following AR(1) pro-
93
cesses for the period 1989Q1-2009Q1.
log(A
t
) = ?
A
? log(A
t?1
) +?
A
t
(1.65)
log(G
t
) = (1 ??
G
)log(G) +?
G
log(G
t?1
) +?
G
t
(1.66)
log(?
t
) = (1 ??
?
)log(?) +?
?
log(?
t?1
) +U
t
(1.67)
where ?
A
, ?
G
, ?
?
are the respective persistence parameters, G is the long-run
level of real government expenditures, ? is the long-run cross-sectional dispersion,
and ?
A
t
, ?
G
t
, and U
t
are the respective i.i.d Gaussian innovations. The estimated
parameters are given in Table 1.11.
Table 1.11: Estimated AR(1) Processes
Dependent Variable ? (Persistence) ?
?
(Std. of innovations) R
2
TFP 0.976 0.0066 0.848
G 0.955 0.0074 0.928
?
f
0.815 0.1145 0.615
?
i
0.823 0.1451 0.582
VXO 0.879 0.1859 0.728
Notes. A superscript f denotes cross-sectional dispersion of ?rm-level sales growth, i denotes cross-sectional
dispersion of industry-level TFP growth. See Bloom et al. (2010) for details on the data set.
The estimated shock processes are given in Figure 1.26.
94
Figure 1.26: TFP, Government Spending, and Uncertainty Shocks
-.03
-.02
-.01
.00
.01
.02
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Innovations to TFP
-.020
-.016
-.012
-.008
-.004
.000
.004
.008
.012
.016
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Innovations to Government Spending
-.4
-.2
.0
.2
.4
.6
.8
-.4
-.2
.0
.2
.4
.6
.8
1990 1992 1994 1996 1998 2000 2002 2004 2006 2008
Uncertainty (Industry-Level)
Uncertainty (Firm-Level)
Uncertainty (VXO)
Uncertainty
95
Chapter 2
Global and Regional Factors in Driving Emerging Markets’
Sovereign Risk Premium
2.1 Introduction
Sovereign credit risk is an important driver of emerging markets’ business cycles, as
studied by many papers including Blanchard (2004), Favero and Giavazzi (2004),
Neumeyer and Perri (2005), and Izquierdo et al. (2007). Large ?uctuations in credit
risk are often associated with swings in capital ?ows, creating challenges for policy
makers such as ensuring a stable exchange rate, maintaining in?ation or ?nancial
stability.
1
Given its relevance for business cycles as well as the challenges it poses,
understanding the nature of sovereign credit risk is of crucial importance for policy
makers in emerging markets.
In this paper, I study the nature of sovereign risk premia in emerging markets
by decomposing the premia into global, regional, and idiosyncratic factors using
dynamic factor modeling (DFM). Moreover, I assess how global ?nancial market
indicators often used in the literature to gauge global risk fare in explaining the
extracted latent global factor, accounting for potential regime changes. I also assess
estimated evolution of idiosyncratic factors by using easily identi?able idiosyncratic
1
See Blanchard (2004), Reinhart and Reinhart (2008), and Cardarelli et al. (2010) for policy
challenges for emerging markets due to ?uctuations in capital ?ows.
96
events, such as major political events or rating downgrades. Last, the contribution
of each factor to sovereign risk premium and potential policy implications are noted.
To measure sovereign credit risk, I use credit default swap (CDS) premia on
the external sovereign debt. A CDS is simply an asset that facilitates transfer of
default risk of one or more entities from one party to another. The premium re?ects
market expectation of a sovereign credit event, e.g. failure to pay, restructuring or
repudiation of the external debt, or even a drop in the borrower’s credit rating. I
use the CDS premia rather than another popular measure, the bond yield spreads,
since CDS markets are typically more liquid, and CDS premia provide a more direct
market-based measure of likelihood of a credit event, as argued by Pan and Singleton
(2008), Stultz (2010), and Ang and Longsta? (2011).
The data set includes a large set of emerging market economies with di?erent
geopolitical properties and credit risk, providing a good base to study common and
idiosyncratic risk factors. In selecting the countries, I require that countries have
su?ciently developed external debt markets, hence the information content is not
driven by idiosyncratic pricing of sovereign risk. For convenience, I choose those
included in the J.P. Morgan’s Emerging Market Bond Index (EMBI+ or EMBI
Global) for at least a year during the last decade.
2
The selection criteria is satis?ed
for 25 economies.
3
The sample includes 8 Latin American, 10 European, and 7
2
Instruments in the EMBI are required to have a minimum face value of $500 million and meet
certain liquidity criteria. EMBI+ has a more strict liquidity criteria than the EMBI Global.
3
The economies included are Argentina, Brazil, Bulgaria, Chile, China, Colombia, Croatia,
Greece, Hungary, Indonesia, Korea, Lithuania, Malaysia, Mexico, Panama, Peru, Philippines,
Poland, Romania, Russia, Thailand, Turkey, Ukraine, Venezuela, and Vietnam. I exclude African
economies, Egypt, Nigeria and South Africa, since having only 3 countries (especially for a re-
gion that exhibits weaker ?nancial and trade linkages compared to other regions) would not be
reasonable to use to extract the regional factor.
97
Asian countries. The list includes economies with a recent default/restructuring
(e.g. Argentina), restructuring (e.g. Greece), high in?ation (e.g. Venezuela), high
volume of commodity exports (e.g. Chile, Venezuela), high political instability
(e.g. Philippines), to name a few. The list in other words re?ects a wide range of
geopolitical features and risk patterns, hence suitable for studying common external
and idiosyncratic factors.
I use dynamic factor modeling (DFM) as it is well suited to study comove-
ment of macroeconomic series.
4
DFM is widely used in the literature on a variety
of topics, including constructing coincident macroeconomic indicators (Stock and
Watson, 1989), forecasting (Stock and Watson, 2002a, 2002b; Forni et al., 2005),
monetary policy analysis (Bernanke, Boivin and Eliasz, 2005; Stock and Watson,
2005; Forni and Gambetti, 2010), and international business cycles (Kose et al.,
2003, 2008; Del Negro and Otrok, 2008; Aruoba et al., 2011; Crucini et al., 2011).
This paper mainly follows the last strand. DFM can capture potential dynamics
of common driver(s), handles missing observations (through Kalman ?ltering), and
is immune to measurement errors. Last but not the least, and importantly for the
focus of this paper, it does not rely on restrictive assumptions about the choice of
variables that potentially re?ect global, regional or idiosyncratic factors.
The results suggest the following: First, emerging markets’ sovereign risk pre-
4
A pure bivariate correlation analysis, while providing a priori evidence, does not disentangle
the common versus the idiosyncratic factors, and misses potential persistence in common ?uctua-
tions. A simple principal component analysis (PCA) can extract the common factors, but cannot
handle missing observations. For instance, using PCA for our data set would imply using only one
third of the data set. Nor does it capture the persistence of common factors. Interested readers
may refer to Diebold and Rudebusch (1996), Breitung and Meier (2005), Bai and Ng (2008), and
Stock and Watson (2010) for literature surveys on DFM.
98
mium is mostly due to common external factors. On average, about 63% of the
movements in the sovereign risk premium is due to the global factor, and about
21% due to regional factors. There is, however, substantial heterogeneity among
the emerging markets. The contribution of external factors are substantially low
for economies that have experienced major idiosyncratic events, e.g. Greece, Philip-
pines. Moreover, there are a few economies that seem to decouple from regional
risk factors, e.g. Chile, Venezuela and Turkey, as the contribution of regional factor
is rather low for these economies. In addition, sovereign risk of largest economies
in the regions (e.g. Brazil and China) appears to move strongly with the regional
factor, potentially suggesting that these economies are by-and-large the driver of
regional comovement of sovereign risk premium.
Second, the extracted latent global risk factor can be explained fairly well by
global ?nancial variables considered. It appears that the global risk factor is best
re?ected by the CBOE’s VIX, a re?ection of investors’ risk sentiment, regardless
of the regimes. VIX explains around 87% of the global factor during ‘high stress’
times, and around 55% on average. As a re?ection of credit and liquidity risks in
global ?nancial markets, the TED spread (spread between London Interbank O?er
Rate (LIBOR) and 3-month US Treasury Bill) captures the global factor at a lesser
extent (20% on average). During high stress times, though, the TED spread explain
nearly half of the movements in the global factor. The yield spread between long-
term US Treasury notes has a lower power in explaining the global factor (of about
7% to 25%). Global ?nancial variables becoming much more powerful in explaining
the global risk factor during high-stress times indicates that volatility, credit and
99
liquidity risks are heightened substantially during the global crisis starting in late
2008. Furthermore, the results also suggest that in times of high stress, investors
seek for safe US assets, which contributes to a rise in emerging markets’ sovereign
risk.
Third, idiosyncratic factor matters, e.g. political instability, major idiosyn-
cratic economic events (isolated banking, currency, or debt crises, or rating down-
grades) matter for sovereign risk premium. For instance, nearly 60% of the move-
ments in Philippines’ sovereign risk premium is due to idiosyncratic factor which
can mostly be attributed to political instability. For Greece, political instability and
?scal solvency issues seem to contribute nearly 80% of the variations in her sovereign
risk premium.
Moreover, increasing concerns about the future of the Eurozone appear to
be a global risk factor in the recent era. In particular, I ?rst estimate a DFM
with a single factor and compare the estimated evolution of common factor with the
regional European factor estimated from the baseline two-factor DFM. The common
factor follows the European risk factor surprisingly well starting in June 2010. This
result suggest that the European debt crisis has gone beyond its boundaries and
become a global factor in driving sovereign risk premium.
The results so far are based on emerging markets. A natural question then is
how “global” is the estimated global factor? To address this question, I use a set of
35 developed and emerging market economies. Given recent ?scal solvency problems
in developed economies (e.g. Portugal, Spain, Italy, etc.), it may also be of interest
of its own studying sovereign risk of debt-crippled developed economies. Moreover,
100
I use higher frequency (weekly) to see whether using monthly frequency misses rel-
evant information. The results show that the evolution of common external factors
are by and large robust to including developed economies and using higher frequency.
This result suggests that emerging markets’ sovereign risk premium during the last
decade is not decoupled from how developed economies perform.
The contribution of this paper is two-fold: First, I study which ?nancial market
indicators best re?ect the global factor, and whether there are statistically signi?cant
regime changes in the relation. The relevance of global factors in driving emerging
markets’ sovereign risk is recognized in the literature. Numerous studies show that
global ?nancial market variables a?ect emerging markets’ sovereign risk signi?cantly.
For example, using global and local ?nancial market variables, Longsta? et al. (2011)
show that US ?nancial market variables are more signi?cant than the country-
speci?c variables in explaining changes in sovereign CDS. Ebner (2009) studies 11
central and eastern European economies’ bond spreads, using a large set of country-
speci?c variables, and proxies for external common factors. Common external factor,
as captured by market volatility, appears to a?ect the bond spreads signi?cantly.
Country-speci?c variables also matter, though less signi?cantly, for sovereign risk.
Yet, such analyses rely on restrictive assumptions about which variable captures the
global risk. Here I instead extract the global risk factor using DFM, and report the
contribution of global factor for each economy. Moreover, I assess how commonly
used global ?nancial market indicators fare in explaining the global risk factor.
5
5
To test whether there are regime changes in the relation, I employ Hansen’s (2000) threshold
estimation.
101
Second, I explicitly study regional risk factor. The analysis sheds light on
heterogeneity among the regions, and which economies (if any) are decoupled from
regional factors. Moreover, incorporating the regional risk factor provides a better
picture on the ‘true’ global risk factor. Recent experience has shown compelling
evidence that there exists noticeable heterogeneity in the sovereign risk among the
regions. For instance, European debt crisis unfolding in mid 2010 led to a surge in
European economies’ sovereign CDS, while having a less strong e?ect on Latin Amer-
ican economies. Moreover, economies with relatively sound fundamentals might be
decoupled from regional risk factors. These points are relatively unexplored in the
literature.
6
Closely related to my work, Longsta? et al. (2011) have pointed out that there
is a single common component explaining an average of 64% of the movements in
sovereign CDS (for a set of 26 economies).
7
They document that about two thirds of
the spread is due to default component, and on average, it is the default component
that is strongly linked to global ?nancial variables. Ciarlone et al. (2009) extracts a
single common factor driving bond spreads of 14 emerging markets. Using principal
factoring, they conclude that 85% of the variation in bond spreads is explained
by a single common factor. They report that the VIX is strongly signi?cant in
explaining the common factor, and it performs better than other ?nancial market
indicators considered. They also note country-speci?c fundamentals having a non-
6
Longsta? et al. (2011) report second and third principal components of sovereign risk as
potentially re?ecting regional factors, though do not study in detail. Existing literature focusing
on both the global and the regional factors are mostly related to business cycles, see for instance
Kose et al. (2003, 2008), Aruoba et al. (2011).
7
Of these, there are 23 emerging markets and 3 developed economies.
102
negligible e?ect on the spreads. This paper di?ers from these studies in several
respects. First, DFM provides a better picture of the relative contribution of each
factor on sovereign risk. The DFM is widely used in the literature ranging from
coincident macroeconomic indicators to international business cycles, though, to
my best knowledge, have not been employed using sovereign CDS spread data.
Second, I address whether global ?nancial market variables fare well in explaining
the global risk, and whether that depends on regime changes. Third, I explicitly
study the regional factor. Last, I use longer time span and more countries (and
further include developed economies for robustness).
The chapter proceeds as follows. Section 2.2 presents the the data and the
methodology. Section 2.3 presents the empirical results, Section 2.4 the relationship
between the global factor and ?nancial market indicators. Section 2.5 presents
robustness analysis, and Section 2.6 concludes.
2.2 Data and the Methodology
Credit default swaps enable transfer of credit risk from one party to another. Credit
event may be triggered due to failure to pay beyond any grace period allowed on
the obligation indenture; restructuring of the debt, altering the principal amount,
coupon, currency or maturity; repudiation/moratorium of the debt; or even a drop
if borrower’s credit rating.
8
A seller of a CDS contract (protection seller) receives
annual payments, but incurs the cost of a credit event. The buyer (protection buyer),
8
Note that bankruptcy/default is not taken as a credit event (as there is no international court
to force a sovereign to honor its premises), as typically around 40-50% of the debt is recovered (see
Reinhart and Rogo?, 2008). For a detailed de?nition of credit event, see Barclays (2010).
103
pays the premium and receives a payment equivalent to the loss in case of the credit
event. The CDS ‘spread’ is the annual amount that the protection buyer must pay
the protection seller till the maturity of the contract, expressed in percentage of the
notional amount. For instance, consider a protection buyer paying a spread of 500
basis points to insure $100 of debt. She would pay $5 per annum till the maturity of
the CDS contract to insure herself against a credit event of the reference entity (the
sovereign in our case).
9
Moreover, magnitude of the spread is intrinsically linked to
the likelihood of the sovereign default. Assuming that the loss associated with the
default is 60% and the maturity is ?ve years, the risk-neutral likelihood of default
is 12.5% for each year over the next 5 years.
10
I choose the CDS pricing data rather than another popular measure, bond
spreads, since the CDS markets are typically more liquid than the bond markets,
and CDS spreads provide a more direct measure of sovereign risk. Bond spreads, for
instance, are driven not only by sovereign risk, but also by ?uctuations in interest
rate and by illiquidity e?ects on sovereign debt prices.
11
Moreover, I choose the
sovereign CDS with 5-year maturity since it is generally the most liquid one among
other maturities.
12
9
Most CDS contracts are cash settled where an auction determines the market price of the dis-
tressed bond and thus the recovery value. In physical settlements, the CDS issuer receives the bond
in exchange for money. However, most contracts are cash settled, since physical delivery would
make the protection seller worse o? in case the corresponding bond market becomes illiquid. In
certain cases, the protection buyer could sell the bond at its par value, though if the corresponding
market had become illiquid, could sell any list of bonds or loans with equivalent seniority rights
depending on the contractual terms.
10
See Hull et al. (2005) for details on the derivation of default probability using CDS premium.
11
See Ang and Longsta? (2011), and Longsta? et al. (2011) for a similar discussion on why CDS
markets may be preferred over bonds market to measure sovereign credit risk.
12
See Pan and Singleton (2008) and Longsta? et al. (2011) for bid-ask spreads on a selective
number of emerging market sovereign CDSs.
104
The data set consists of a large set of emerging market economies with su?-
ciently developed external debt markets. For convenience, I choose those included
in the J.P. Morgan’s Emerging Market Bond Index (EMBI+ or EMBI Global) for
at least a year during the last decade. The selection criteria pick 25 economies:
Argentina, Brazil, Bulgaria, Chile, China, Colombia, Croatia, Greece, Hungary, In-
donesia, Korea, Lithuania, Malaysia, Mexico, Panama, Peru, Philippines, Poland,
Romania, Russia, Thailand, Turkey, Ukraine, Venezuela, and Vietnam.
13
The sam-
ple includes 8 Latin American, 10 European, and 7 Asian economies. The frequency
is monthly (monthly average), and the sample period covers October 2000 to Febru-
ary 2012. The starting period is due to data limitations, since the sovereign CDS
markets have been developed after 2000.
Table 2.1 presents the descriptive statistics of the data. The values are reported
in basis points. As evident from the starting dates of sovereign CDS trading, the
data become available for most of the countries by 2003 (20 economies).
14
The
data range widely across the countries. Average sovereign CDS ranges from 59
basis points (China) to 909 basis points (Argentina, which experienced an external
default along with banking and currency crises during 2001-2005), with standard
deviation ranging from 47 to 934 basis points. The CDS spread reaches as high as
4280 basis points for Ukraine (in late 2009), for which a default was imminent had
external funding not extended, while it is a mere 230 basis points for China. To
accompany Table 2.1, Figure 2.1 displays the evolution of sovereign CDSs during the
13
I exclude African economies, Egypt, Nigeria and South Africa.
14
Note that two economies with the same start date might have di?erent number of observations
(e.g. Colombia and Peru) due to missing observations.
105
sample period. The ?gure by itself suggests some degree of comovement in sovereign
risk: There is a noticeable jump in late 2008 and a re-surge in mid 2011 for most
economies.
Next, I present the DFM to extract the global, regional and idiosyncratic
components of sovereign risk. I assume that sovereign CDS pricing data, y
it
, have
the following factor structure:
y
it
= µ
i
+ ?
G
i
G
t
+ ?
R
i
R
t
+?
it
for i = 1, 2, ..., n (2.1)
where G
t
is the global factor a?ecting all the countries, and R
t
? (R
1
t
, R
2
t
, ..., R
k
t
)
are
the k regional factors. ?
G
i
and ?
R
i
? (?
1
i
, ?
2
i
, ..., ?
k
i
) are the factor loadings for global
and regional factors for country i. To separately identify the two common factors,
I assume that each regional factor a?ects only the countries in the corresponding
region. For a European country i, for example, the above equation simpli?es to
y
it
= µ
i
+ ?
G
i
G
t
+ ?
Europe
i
R
Europe
t
+?
it
(2.2)
?
i
captures all the variation in y
i
that is not captured by the common factors, re?ect-
ing idiosyncratic factors, and potentially, measurement errors. µ
i
is unconditional
mean of sovereign CDS for country i.
I assume that the factors follow a stationary autoregressive process of order
one, and are independent from each other:
G
t
= ?
G
1
G
t?1
+u
G
t
u
G
t
? i.i.d.N(0, 1) (2.3)
106
R
j
t
= ?
R
j
1
R
j
t?1
+u
R
j
t
u
R
j
t
? i.i.d.N(0, 1) j = 1, 2, ...k (2.4)
?
it
= ?
1
?
it?1
+?
it
?
it
? i.i.d.N(0, ?
2
i
) (2.5)
where E[?
it
?
js
] = 0 for i = j, and where G
0
and R
0
are uncorrelated with v
t
and u
t
for all t. The model above is a backbone DFM for a variety of DFMs used in the
literature. It is a simple version of DFM studied in, for instance, Kose et al. (2003)
(on international business cycles), Del Negro and Otrok (2008) (on the European
business cycles), and Stock and Watson (2008) (on the US housing market).
Identi?cation.
The identi?cation assumptions are as follows. First, the relative scale of the
model is indeterminate. Consider multiplying the common factor by ?,
F
t
= ?F
t
.
Also divide the factor loading by ?,
¯
? = ?/?. The scale of the model ?F
t
is
observationally equivalent to
¯
?
F
t
. To normalize the scale, I set global and regional
factor shock variances equal to one (Stock and Watson, 1993).
15
Second, the sign of the factor loadings and factors cannot be separately iden-
ti?ed. Consider setting ? above equal to -1. Similarly as above, ?F
t
is again
observationally equivalent to
¯
?
F
t
. As a remedy, I initialize factor loadings (for all
the factors) to be positive. Such a restriction identi?es the sign of the factors. Note
that scale and sign normalization has no e?ect on economic inferences such as the
15
Note that the scaling does not a?ect economic inferences such as the estimated evolution of
factors or variance decomposition. There might be applications for which the exact identi?cation
of F
t
is not sought, e.g. forecasting, yet, since I study the evolution of factors, such a scaling
assumption is necessary.
107
estimated evolution of factors and their contribution to the observable variables.
Third, common factors (global and regional factors) cannot be identi?ed sep-
arately. I make a natural assumption that, for a country i in region s, the factor
loadings on other regions are zero. That is, ?
j
i
is set equal to zero if i ? R
j
for all
j = 1, 2, . . . , k and for all i = 1, 2, . . . , n.
Number of Factors.
A modeling assumption made above is that the data generating process admits
two common factors, global and regional. Potentially, however, there can be many
common factors, e.g. one might include sub-regions as well. Although a conventional
way to see how many (independent) factors are needed to capture covariation in the
data su?ciently well is to obtain proportion of variance that is explained by each
common factor (through principle component analysis), it is not comparable to the
dynamic model above since there is only a single common factor, i.e. the global
factor, and the regional factors are common only those within the region. Hence, I
rather verify the relevance of global and regional factors by documenting whether
they account for a large portion of movements in sovereign risk premium for each
country.
Contribution of Factors.
The estimated fraction of volatility in y
i
that is explained by global and re-
gional factors can be calculated by simply applying the variance operator to each
signal equation. Using the fact that the factors are orthogonal to each other, the
fraction of movements in y
i
that is explained by the global factor is given by
108
(?
G
i
)
2
var(G)
var(y
i
)
(2.6)
and, similarly, the fraction of movements in y
i
that is explained by the regional
factor is given by
(?
R
i
)
2
var(R)
var(y
i
)
(2.7)
2.3 Empirical Results
The CDS series are ?rst standardized to have mean zero and standard deviation one
to ensure that an individual economy does not have a direct impact on the evolution
of factors. The model is then estimated by Gaussian maximum likelihood, where
the likelihood function is evaluated using the Kalman ?lter. The estimated state
variables are presented in the Appendix Figure 2.10.
The stationarity of the system is veri?ed through analyzing the estimated
model. The estimated autoregressive coe?cients for all the factors are below 1 (rang-
ing in between 0.08 to 0.99, with an average of 0.88). The estimates for smoothed
state disturbances and one-period-ahead signal disturbances are stationary (with
p-values 0.00) based on standard univariate or group unit root tests.
2.3.1 Evolution of Global and Regional Factors
Global Factor.
Figure 2.2 presents the evolution of global factor. The global factor captures
109
the common driver of sovereign CDS for all the emerging markets in the data set.
In reporting the factors, hereforth, I use October 2001 onwards to have the results
robust to initial state values and since the data become available for most of the
countries by this time. The estimated evolution of the global factor seems to follow
major economic events during the sample period. To shed light on the magnitude
of the global factor, note that the estimated standard deviation is roughly equal to
three.
The global factor hits unusually high levels during late 2002 and in late 2008,
consistent with the currency and banking crisis in Latin America and Turkey in
2001 and 2002, and with the US ?nancial turmoil started in late 2007. The sharp
increase in the global factor in October 2008 suggests that the recent US recession
have become a global risk factor after the Lehman Brothers’ collapse. Compared
to its pre-crisis levels, the factor rises by about four standard deviation. The ?gure
also suggests that proactive policy responses in advanced economies, –e.g. TARP,
CPFF, and in an international scale, extending swap lines among central banks,
IMF’s provision of short-term liquidity with looser terms for economies battered by
the ?nancial crises, e.g. Iceland, Ukraine, Hungary, Belarus, Romania, Mexico, to
name a few,– seem to avoid further increases in the global risk factor.
16
By late 2009, the global risk factor gets stabilized, though, around a level
higher than its pre-crisis level (about one standard deviation higher). It is only
16
To name a few, Ukraine signed a stand-by agreement with the IMF on Oct. 2008 to condi-
tionally receive $16.5 billion, Hungary on Nov. 2008 to receive $15 billion, Belarus on Jan. 2009
to receive $2.5 billion, and Romania on March 2009 to receive $27 billion (together with the EU,
WB, and EBRD). Through Flexible Credit Line, Mexico on March 2009 have secured $47 billion
line of (unconditional) credit from IMF.
110
after increased concerns about Italy and Spain rolling over its debt (hence concerns
about the Eurozone’s future) that the global factor starts to rise again (August
2011).
17
In the next section, I provide a further analysis on this recent episode.
Regional Factors.
Figure 2.3 presents the European, Latin American, and Asian regional risk
factors. The regional factor captures the comovement of the sovereign risk for the
economies within the region, and shows the pricing of sovereign risk independent
from global or idiosyncratic factors.
18
The estimated evolution of regional factors seems to follow major regional
economic events during the sample period. To shed light on the magnitude of
regional factors, note that the standard deviation is roughly 4 for the Latin American
and the Asian, and 4.5 for the European factor.
The European risk factor starts at a relatively high level in late 2001, mostly
due to Russian and Turkish ?nancial crisis. Then, as subsequent years and more
economies chime in the estimation, the regional factor becomes stable till the Lehman
Brother’s collapse in October 2008. Following October 2008, the European regional
factor surges. This surge implies that, the European factor feeds further risk to the
European economies (on top of the global factor). Moreover, European emerging
markets (on average) are hit more during this time compared to emerging markets
in other regions. This result might suggest that Europe has stronger ?nancial and
17
Note that Italy holds around 25% and Spain around 15%, in percent of total euro area gov-
ernment debt (on average for the last three years).
18
While this orthogonality assumption hinders potential spillover from other factors to the re-
gional factor, studying the spillover mechanism requires restrictive identi?cation assumptions, and
is not the focus of this paper. Note also that the orthogonality assumption is standard in the DFM
literature that studies global and regional factors (see, for instance, Kose et al. 2003; 2008).
111
trade linkages with the US (compared to other regions), though further investigation
is needed.
For the European regional risk factor, there are two distinctive episodes after
2009. The regional factor rises from mid-2009 to 2010 corresponding to the ?rst-
phase of European debt crisis, which is mostly limited to Greece and Ireland. The
second phase starts in mid-2011, exhibiting a surge in the regional risk. This period
corresponds to increased concerns about the future of Eurozone, as ?scal solvency
problems arouse for two large indebted economies in Euro area, Spain and Italy,
and further concerns about Greece.
Note that the second phase also coincides with the increase in the global factor,
potentially suggesting that the second phase in Europe goes beyond the boundaries,
and a?ects the sovereign risk of all the emerging markets. To shed further light on
this, I estimate a DFM with a single common factor (the single-factor DFM), and
plot the estimated common factor with the regional European factor (Figure 2.4).
19
The evolution of two series coincide surprisingly well for the recent era, suggesting
that concerns about the Eurozone become a global risk factor thereafter (after June
2010).
The Latin American factor, on the other hand, shows a di?erent risk pattern
than the European, noticeably for early 2000s and 2008 onwards. The factor is at
historically high levels during mid 2002, due to political instability in Brazil at the
time, contagious e?ects on the region of Argentina’s debt, currency, and banking
crises starting in 2001. The region enjoys a slowly decreasing risk, as the economies
19
For all the estimated factors in the single-factor DFM, see Appendix A2.
112
implement sound policies (and some follow IMF supported programs, e.g. Brazil
in 2002, and Colombia in 2003 and 2005). At the time global factor hits record
high levels in late 2008, the Latin American factor falls noticeably, suggesting that
the markets were pricing the Latin American economies’ sovereign risk lower than
the rest of the emerging markets. By 2010, the regional factor returns back to its
pre-crisis levels.
The Asian factor has an increasing pattern from 2003 till early 2008, poten-
tially due to Asian economies experiencing stable CDSs despite the decrease in the
global risk factor during this period. The nearly-discrete change in the regional
factor in 2008 happens to be earlier for Asian economies, coinciding with the start
of the US recession. The factor goes back to its pre-crisis levels by mid to late 2009,
and then keeps rising for the last three years.
Note that the regional factors are constructed to be orthogonal to each other
as well as to the global factor. However, estimation results suggest some degree of
correlation (Table 2.2). Two results emerge: First, regional factors are only slightly
correlated with the global factor, with the correlation ranging from -0.09 to 0.19,
inline with how the DFM is constructed. On the other hand, regional factors appear
to be correlated with each other, with the correlation ranging from -0.53 to 0.80.
The second result suggests that there are within-month spillovers across the regions.
This point is left to future work.
113
2.3.2 Contribution of Factors
Table 2.3 presents the contribution of global, regional and idiosyncratic factors to
the emerging economies’ sovereign CDSs.
A substantial portion of emerging markets’ sovereign risk is driven by external
factors (84%). On average, the global factor accounts for 63%, and the regional
factor 21% of the variations in sovereign risk. The contribution of external factors
di?ers widely across the economies. The global factor, for instance, accounts for as
low as 1% for Greece, and as high as 93% for Chile.
20
The wide range for the contribution of external factors can be due to di?erent
degrees of capital market openness across the economies. Moreover, one might
expect a higher contribution of external factors for more open economies. In Figure
2.6, I plot the Chinn-Ito capital account openness index (averaging over 2001-2010)
against the total contribution of external factors for all the countries.
21
For countries
with more open capital accounts, the contribution of external factors is higher.
The regional factor, on average, accounts for 21% of the ?uctuations in emerg-
ing markets’ sovereign risk. The contribution of which is highest for Brazil (82%)
20
Comparison of contributions across the economies should be handled with care, though. Con-
sider, for instance, two countries for which the contribution of global factor on her sovereign risk
premium is close (e.g. Ukraine versus Chile), while the former having a higher level of ?uctuations
in sovereign risk. A surge in global risk might push the former into a near default stage while
exerting comparatively negligible e?ect on the latter. In this sense, comparison should be made
along with country-speci?c macroeconomic conditions.
21
Chinn-Ito (2008) index is based on extracting the common factor for variables (i) indicating
presence of multiple exchange rates, (ii) indicating restrictions on current and capital account
transactions, and (iii) indicating the requirement of the surrender of export proceeds. The graph
shows the Chinn-Ito index against the contribution of external factor for all the economies with
the exceptions Greece and Argentina. I exclude Greece –which is a fairly open economy– whose
CDS is driven substantially by the idiosyncratic factor. Moreover, Argentina has defaulted for
nearly half of the sample period, and since the default was idiosyncratic, I set the contribution of
idiosyncratic factor at 50%.
114
in Latin America, Croatia (52%) in Europe, and China (20%) in Asia. It is no co-
incidence that Brazil’s and Chinese sovereign risk, of the largest economies in their
regions, move strongly with the regional factors. It is reasonable to think that these
economies are the main driver of regional risk, leading to a strong comovement with
the regional factor. For other economies with a high level of contribution of regional
risk factors, e.g. Colombia (67%), Peru (57%), Croatia (52%), they might possibly
be driven by (rather than drive) the regional factor. In these regards, the estimated
contribution of regional factors seems economically plausible.
The idiosyncratic factor, on average, accounts for 8% of the variations in
sovereign risk. The wide range applies to the idiosyncratic factor as well: it is
as high as 78% for Greece, 57% for Philippines, and nearly nil for Colombia and
Thailand.
To shed further light on the validity of evolution and contribution of factors,
next I study decomposition of sovereign CDS for four economies with di?erent credit
risk patterns: Chile, Greece, Philippines and Turkey (see Figure 2.5).
2.3.3 Idiosyncratic factor and four examples.
I choose four economies with ‘di?erent’ sovereign risk patterns: Chile, Greece,
Philippines and Turkey, di?erent in the sense that the contribution of each fac-
tor di?ers noticeably across these economies. The contribution of global factor is
highest for Chile (93%), that of the idiosyncratic factor is highest for Philippines in
Asia (57%), and for Greece in Europe (78%). The global and idiosyncratic factors
115
each share nearly half of the movements for Turkey. Moreover, Greece, Philippines
and Turkey have experienced idiosyncratic events that can be conveniently identi-
?ed (debt, in?ation, banking or political crisis) during the last decade, hence the
estimated evolution of idiosyncratic factors can be conveniently judged against.
It is also worth noting that the idiosyncratic factor should not be thought
as a sole re?ection of country-speci?c fundamentals commonly used in the related
literature (such as international reserves to imports, total external debt to real
GDP, imports to export ratios, to name a few). The idiosyncratic factor is orthog-
onal to global and regional factors, whereas country-speci?c variables (particularly
those pertaining to external balances) are most likely to be a?ected by global or
regional economic stance. Idiosyncratic factor, instead, can be interpreted as the
idiosyncratic nature of a sovereign’s credit risk, such as rule of law or institutional
quality, transparency in economic policy decisions and objectives, central bank in-
dependence, strength of business environment, e?ectiveness/e?ciency of the public
sector (in raising taxes, cutting spending, selling assets), default history, or robust-
ness/e?ectiveness of ?nancial sector.
22
Chile is one of the most stable and prosperous economies in the Latin American
region. Moreover, as a commodity-exporter, Chile has one of most sound sovereign
wealth fund in the world. The country enjoys one of the lowest public debt to GDP
ratio and in?ation rate in the region, e.g. of around 6% and 4-5% respectively as of
2011.
23
In line with these, the decomposition results suggest that Chilean sovereign
22
For variables which are potentially idiosyncratic, see for instance IMF (2010, p. 101).
23
To give a sense of these numbers, the largest economy in the region, Brazil, has a public debt
to GDP ratio of 60% and an in?ation rate of 9%.
116
risk is driven only negligibly by the Latin American-speci?c risk factors. Moreover,
due to its rather stable economy, the contribution of idiosyncratic factor is small
(7%). It is therefore mostly the global factor that drives the sovereign risk (however
comparatively small the movements are).
Greek credit risk, on the other hand, is driven only negligibly by the global
factor. After a long stable period, the Greek CDS rises after the Lehman Brother’s
collapse (as for all the emerging markets). Markets at the time seem to be pricing
the Greek sovereign risk lower than its global and regional counterparts, as re?ected
in the decline in the idiosyncratic factor. After 2009, there are three distinctive
surges in the Greek CDS, where each one is re?ected in the idiosyncratic factor.
The ?rst occurs in December 2009, coinciding with the announcement of debt to
GDP (of nearly 13%, which is to be revised later), and the downgrade of Greek
credit rating. It is only after the IMF and EU’s bailout package (of about $145bn)
that it slows down the increase in the sovereign risk. The second occurs in February
2011, in which the Greek authorities slammed EU and IMF o?cials’ overseeing
e?orts to reform its debt-crippled economy. The third occurs in July 2011, in which
Greek credit rating were downgraded by all the main three rating agencies to a
level associated with a substantial risk of default. These Greek-speci?c events are
captured by the evolution of its idiosyncratic factor.
Philippines’ sovereign risk is driven mostly by the idiosyncratic factor (57%),
where the idiosyncratic factor seems to capture phases of political instability in the
economy, e.g. a surge in the CDS due to increasing political tension till March
2003, the Oakwood mutiny in July 2003, and a relatively long-lived decline in the
117
CDS during a relatively calm political environment after July 2005. In other words,
political instability seems to contribute more than half of the Philippines’ sovereign
risk.
Turkish sovereign risk is driven mainly by global and idiosyncratic factors.
Despite strong trade and ?nancial linkages with Europe, the contribution of regional
European factor to Turkish sovereign risk is weak (of about 7%). Before 2005, the
idiosyncratic factor seems to capture political instability, e.g. resignation of eight
cabinet members in July 2002, elections in November 2002, political upheaval in
late 2003, all captured by a jump in the idiosyncratic factor. After a ?ve-year stable
period, the idiosyncratic factor declines in early 2008 till early 2009, suggesting that
Turkish sovereign risk is perceived to be lower than European emerging markets.
The idiosyncratic factor resumes back to its pre-crisis level by the end of 2010 (where
it had been for nearly 5 years). 2011 is characterized by a noticeable surge in
the idiosyncratic factor. Potential explanations might be increasing concerns about
current account de?cit to real GDP reaching record high levels through the year and
a jump in exchange rate volatility towards the end of the year. The idiosyncratic
factor starts to decline in 2012, suggesting that investors start to perceive Turkish
idiosyncratic risk at a lower level.
2.4 Interpreting the Global Risk Factor
The analysis so far sheds light on the evolution of global factor by associating it
with major ?nancial events. This section takes a formal stand. It provides an
118
understanding on the nature of global factor by linking it to global ?nancial market
indicators, taking into account potential regime changes in the relation.
I consider three ?nancial market indicators often quoted in the literature as
a way to gauge the stance of global ?nancial markets: the TED spread, the yield
spread between long-term Treasury notes (10- and 20-year Treasury notes), and
Chicago Board of Exchange’s Implied Volatility Index (VIX).
24
As discussed brie?y
below, these variables capture the strength of credit or liquidity risks, as well as
risk averseness in the US ?nancial markets. The evolution of these indicators are
provided in Figure 2.7.
The TED spread is the di?erence between the interest rate at which the US
government is able to borrow on a 3-month period (3-month U.S. Treasury bill), and
the rate at which banks are willing to lend to each other in a 3-month period (mea-
sured by 3-month USD LIBOR). The spread measures estimated risks that banks
pose on each other (compared to the likelihood of default of the US Treasury, which
is practically nil). The higher the perceived risk due to one or several banks having
liquidity or solvency problems, the higher the lending rate in interbank markets. In
this regard, the TED spread captures credit and liquidity risk in interbank markets.
Moreover, for periods of high risk averseness during which investors seek for ‘safe
havens’, the yield on risk-free rate would be pushed downward, resulting in a rise
in the spread. In this regard, in times of high credit/liquidity risks, a portion of
movements in the spread would be due to ‘?ight to quality’.
24
See Gonzales-Hermosillo (2008), and Gonzales-Hermosillo and Hesse (2009) for a thorough
analysis on ?nancial market indicators that are potentially global.
119
The yield spread between long-term US Treasury notes (e.g. 10- to 20-year
Treasury notes) re?ects how strong markets value the liquidity.
25
Since the two
bonds have essentially the same default risk, the yield spread re?ects expected aver-
age future yields (from 10 to 20 years) and a liquidity premium. To the extent the
former is stable, changes in the spread capture changes in liquidity premium. I use
the percentage change in the yield spread compared to the previous year.
The VIX, CBOE’s Volatility Index, re?ects the expected future volatility in
S&P500 (over the next 30 days) implied by the current index option prices. It
indicates how strong investors value insuring their portfolios (in a sense, capturing
investors’ fear gauge).
To explore potential regime changes in the relation between the global factor
and the ?nancial market indicators, I employ Hansen (2000)’s threshold regression
model.
26
I use the following threshold regression speci?cation:
?G
t
= ?
1
?x
t
+e
t
?G
t
? ? (2.8)
?G
t
= ?
2
?x
t
+e
t
?G
t
> ? (2.9)
where x
t
is one of the ?nancial market indicators mentioned above, ?x
t
= x
t
?x
t?1
,
?G
t
is the threshold variable used to split the samples into two groups or “regimes”,
and ? is the (endogenous) threshold parameter. The method is a sequential OLS
25
See Gonzales-Hermosillo (2008) for other potential variables to capture market liquidity risk.
Here I follow Gonzales-Hermosillo (2008), and use the yield spread between long-term US Treasury
notes.
26
I would like to thank Bruce Hansen for very helpful discussions on the methodology.
120
estimation, searching over all permissible ?s such that sum of squared errors of the
above system is minimized.
27
While the method determines the regimes endogenously, it may be the case
that the true data generating process admits a linear regression model, that is
H
0
: ?
1
= ?
2
cannot be rejected (hence no threshold e?ect). Testing H
0
, however,
is not straightforward since ? is not identi?ed under the null hypothesis. Hansen
(2000) introduces a heteroskedasticity-consistent bootstrap F-test procedure to test
the null of linearity. The procedure provides asymptotically correct p-values.
To further explore whether there are multiple regimes, I follow Hansen (2000)
and ?rst test whether there is a threshold in the whole sample. Then, given the
estimated threshold, I explore whether there are further thresholds within each
regime (sub-sample).
Table 2.4 presents the regression results, based on the whole sample as well
for each estimated regime.
Using the whole sample, VIX turns out to be the most powerful indicator in
27
In particular, ?rst write the equations above in a single equation form (by de?ning an indicator
variable). In particular, let I{q
i
? ?} be an indicator function that takes a value 1 if {.} is satis?ed
and 0 otherwise. And let x
i
(?) ? x
i
I{q
i
? ?}. Then the above model can be written as
y
i
= ?x
i
+?
n
x
i
(?) +e
i
(2.10)
where ? = ?
2
, and ?
n
= ?
2
??
1
. The least-squares estimators
´
?,
´
?, and ´?, jointly minimize
S
n
(?, ?, ?) =
i
(y
i
??x
i
+?
n
x
i
(?))
2
(2.11)
Conditional on ?, equation (10) is linear in ? and ?
n
. Conditional LS estimates
´
?(?) and
´
?(?)
can be obtained by regression y
i
on x
i
and x
i
(?). The conditional sum of squares is S
n
(?) ?
S
n
(
´
?(?),
´
?(?), ?). As shown in Hansen (2000), ´? can be de?ned uniquely as
´ ? = argmin
???n
S
n
(?) (2.12)
where ?
n
= ? ? {q
1
, ..., q
n
}.
121
explaining movements in the global factor (of about 58%). A rise in the VIX (a
decrease in investors’ risk appetite) leads to a statistically signi?cant increase in the
global factor. Similarly, a rise in the TED spread (an increase in credit/liquidity
risk) also induce a rise in the global factor. The TED spread can explain about 22%
of the movements in the global factor. The yield spread (the liquidity premium) has
the lowest explanatory power (of about 2%). Note that these results are based on
whole sample, and further investigation is needed as there are indeed regime changes
in the relation.
There are three regimes in the relation between the global factor and the ?nan-
cial market indicators: The high stress period (corresponding to large increases in
G
t
), the low-to-moderate stress period (corresponding to moderate changes in G
t
),
and the recovery period (corresponding to large declines in G
t
). These regimes are
determined based on estimated threshold values for ?G: ?
high
and ?
low
.
28
The two
thresholds are ‘statistically signi?cant’: the null of linearity is rejected at a 0.000
signi?cance level.
29
The estimated durations of these regimes are as follows: The
high stress period in sovereign risk markets seems to prevail for 6 to 11 months (de-
28
In particular, I ?rst test the signi?cance of the threshold in the whole sample, which splits the
sample into two regimes. The null of linearity is rejected with a p-value of 0.000. The threshold
value splits the sample into a small one (including 11 observations using the TED spread as the
independent variable, 6 observations using the yield spread, and 7 observations using the VIX),
and large one (including 113, 118 and 117 observations, respectively). I label the threshold that
splits the whole sample as ?
high
. I have not pursued splitting the small one into subsamples, as
that would imply excessively low degrees of freedom. I then test signi?cance of a threshold in
splitting the large sample, and the null of linearity is rejected at a p-value of 0.000. I label the
threshold splitting the large subsample as ?
low
.
29
For the likelihood ratio sequence used to construct the con?dence bands for the thresholds,
see Figure 2.13 in the Appendix. The likelihood ratio (LR) statistic gives out the change in sum of
squared errors under ? = ?
1
as compared to ? = ?
0
. The threshold estimate is where the sequence
reaches its minimum. The con?dence band limits are where the critical value intersects with the
LR sequence. The local minima in the ?rst graph sort of implies a second threshold, as further
validated by formal testing.
122
pending on which ?nancial market indicator is used). The low-to-moderate period
prevails for around 9 years. The estimated duration of this period seems to be rather
long, as this period captures a range of tranquil to moderately stressed periods in
the ?nancial markets. The recovery period, fast declines in the global risk, appears
to be for about 5 to 11 months.
The explanatory power of ?nancial market indicators is the highest under the
high-stress regime: The TED spread explains 49%, the yield spread 24%, and the
VIX 86% of the variations in the global factor. An increase in the TED spread,
which is potentially due to increased credit/liquidity risks in the interbank market
and ?ight to safe US assets, leads to a rise in the global factor. An increase in the
liquidity premium, which is captured by an increase in the yield spread, also implies
an increase in the global factor (though the e?ect is statistically insigni?cant). An
increase in the investors’ risk sentiment also leads to a rise in the global factor.
During the low-to-moderate stress period, all the three indicators explain the global
factor signi?cantly, though the explanatory power declines to 12%, 11%, and 35%,
respectively. Still, the investors’ risk sentiment (the VIX) stands out as the most
powerful indicator to explain the global factor. For the recovery period, ?nancial
market indicators are statistically insigni?cant in explaining the global risk (though
the point estimates with the expected sign). Fluctuations in the VIX explain 33% of
the movements in the global risk factor, the TED spread 19%, and the yield spread
7%.
The lessons I derive from the analysis are the following: First, investors’ risk
sentiment (or uncertainty about the US economy) is the single and most powerful
123
indicator of global risk factor a?ecting the emerging markets. Second, power of
?nancial market indicators in explaining the global factor depends on the state of
the global ?nancial markets. It is the high-stress period during which ?nancial
market variables have the highest explanatory power. Third, existence of ?ight
to safe US assets appears to be a relevant ingredient for the increase in emerging
markets’ sovereign risk premium in the recent era.
2.5 Robustness (Including Advanced Economies & Using Higher Fre-
quency)
How ‘global’ is the common driver of emerging markets’ sovereign risk? Given many
developed economies in Europe, how ‘European’ is the estimated European regional
risk factor? Does using monthly frequency (rather than a higher frequency) miss
important information? This section studies robustness of the results using a larger
sample (including advanced economies) and higher frequency (using weekly data).
I include all the economies for which the CDS trading exists for at least one
third of the sample period (October 2000 to February 2012). Additional countries
included are Belgium, France, Germany, Italy, Latvia, Netherlands, Portugal, Slo-
vakia, Spain and Sweden. Moreover, I use weekly (rather than monthly) average of
daily 5-year sovereign CDS data.
The estimated evolution of global factor is very similar to the one estimated
using the emerging markets alone (Figure 2.8).
30
As developed economies chimes
30
See Figure 2.12 in the Appendix for the estimated evolution of states. Note that estimated
idiosyncratic factors are inline with major economic events in these economies. Regarding the
124
in the estimation mostly after 2005, it is more fair to compare the evolutions after
2005. The global factor hits record high levels in late 2008, gets stabilized after
almost a year, and exhibits a further surge in mid 2011. While Latin American
and Asian regional factors follow similar patterns with the ones estimated before,
European regional risk factor is now noticeably higher due to including developed
economies (Figure 2.9).
2.6 Conclusion
This paper studies global, regional and idiosyncratic components of emerging mar-
kets’ sovereign credit risk premium, using a newly-developed data set, sovereign
credit default swaps. I use dynamic factor modeling to extract these components
rather than relying on restrictive assumptions on which variable would capture these
components. Moreover, I explore the performance of global ?nancial variables often
used in the literature to proxy global risk in explaining the extracted global risk
factor.
The results suggest that a large portion of emerging markets’ sovereign risk
premium is due to common external factors. On average, about 63% of the variations
in the sovereign risk is due to the global factor, and about 21% due to regional
factors. There is, however, substantial heterogeneity among the emerging markets.
Second, the global factor seems to be best re?ected by the CBOE’s VIX, a
idiosyncratic factor for the additional economies, for instance, the surge of the Italian CDS in mid
2011, of Portuguese and Spanish CDSs in 2010 are inline the unraveled ?scal solvency problems
in these economies at the time. Swedish idiosyncratic factor keeps declining during the last few
years, inline with the Swedish ?scal performance (maintaining very low levels of public debt to
GDP).
125
re?ection of investors’ risk sentiment, regardless of the regimes considered (high-
stress, low-to-moderate stress, or recovery regimes). VIX explains around 87% of
the global factor during high stress times, and of around 55% on average, while the
TED spread 50% during high stress times, and 20% on average. Furthermore, the
results also suggest that in times of high stress, investors seek for safe US assets,
which contributes to a rise in emerging markets’ sovereign risk. The yield spread
between long-term US Treasury notes which by-and-large re?ects liquidity premium
has a lower power in explaining the global factor (of about 7% to 25%).
Third, concerns about the future of Eurozone appear to go beyond the regional
boundaries, and become a global risk factor after June 2010. Estimating a DFM
with a single common driver, the results show that the common driver follows the
European risk factor surprisingly well starting in June 2010.
The evolution of common factors are by and large robust to including de-
veloped economies and using higher frequency. This result suggests that emerging
markets’ sovereign risks are not decoupled from how the developed economies per-
form.
For future research, linking the regional factors to ?nancial market variables
in central economies would shed further light on the nature of regional factors.
Moreover, to provide a further understanding on the contribution of regional factors,
one can partition economies within the regions using clustering methods. These
points are left to future research.
126
2.7 Appendix - Kalman Filter
Let y
t
denote an (nx1) vector of variables that are observable at t, and be driven
by a (kx1) vector of latent (unobserved) variables, s
t
. The dynamics of y
t
can
be represented by a state-space representation given by the following system of
equations:
y
t
= As
t
+u
t
[Signal equation] (2.13)
s
t+1
= Bs
t
+v
t+1
[State equation] (2.14)
where u
t
? N(0, R) and v
t
? N(0, Q), with E[u
t
u
?
] = R and E[v
t
v
?
] = Q if t = ?,
and 0 if t = ?. The matrices A, B, R, and Q have the dimensions nxk, kxk, nxn,
and kxk, respectively. Moreover, the disturbances u
t
and v
t
are assumed to be
uncorrelated at all lags, E[v
t
u
?
] = 0 ? t and ?. Also, the initial value of s
t
, s
1
, is
assumed to be uncorrelated with v
t
and u
t
?t.
The Kalman ?lter is an iterative algorithm whereby an initial estimate of the
latent factors is obtained from the state equation. This estimate is then used to
compute an estimate of the observable variables, y
t
. Using the observed and the
estimated values of y
t
, s
t
is updated through the Kalman gain.
In particular, denote conditional means of y
t
and s
t
by
y
t|t?1
= E
t?1
[y
t
] = As
t|t?1
(2.15)
127
s
t|t?1
= E
t?1
[s
t
] = Bs
t?1|t?1
(2.16)
and the conditional variables by
V
t|t?1
= E
t?1
[(y
t
?y
t|t?1
)(y
t
?y
t|t?1
)
] = AP
t|t?1
A
+R (2.17)
P
t|t?1
= E
t?1
[(s
t
?s
t|t?1
)(s
t
?s
t|t?1
)
] = BP
t?1|t?1
B
+Q (2.18)
Given s
1|0
and P
1|0
, one can deduce the adjustment to the factor estimate using the
observables. That is,
s
t|t
?s
t|t?1
= P
t|t?1
A
V
?1
t|t?1
(y
t
?y
t|t?1
) (2.19)
P
t|t
?P
t|t?1
= P
t|t?1
A
V
?1
t|t?1
AP
t|t?1
(2.20)
where G
t
= P
t|t?1
A
V
?1
t|t?1
is the Kalman gain, the adjustment to the latent factor
given the di?erence between the actual and estimated values of observables.
Initial values s
1|0
and P
1|0
are given by
s
1|0
= 0 (2.21)
vec(P
1|0
) = (I
kxk
?(B ?B))
?1
vec(Q) (2.22)
128
2.8 Appendix - Tables and Figures
129
Table 2.1: Descriptive Statistics for Sovereign Credit Default Swap (10/2000 -
4/2012)
Mean Std. Dev. Minimum Median Maximum Start N
Argentina 909.24 933.95 193.55 616.56 4271.17 6/2005 81
Brazil 476.22 659.90 65.68 177.12 3549.73 10/2001 125
Bulgaria 220.68 169.98 13.86 207.65 641.30 10/2000 137
Chile 70.20 55.03 12.98 61.43 259.14 1/2003 110
China 59.35 47.77 10.65 40.70 230.22 1/2003 110
Colombia 250.75 165.22 76.07 164.61 825.31 1/2003 110
Croatia 183.01 142.75 15.77 128.00 536.20 10/2000 137
Greece 285.91 603.89 5.46 13.93 3515.85 3/2003 104
Hungary 147.41 166.78 12.71 42.41 635.71 3/2002 120
Indonesia 230.84 141.00 100.90 193.63 805.69 10/2004 86
Korea 88.44 79.51 15.15 69.65 414.03 2/2002 121
Lithuania 313.15 174.72 6.00 285.65 765.38 12/2006 47
Malaysia 87.15 62.50 13.84 78.06 276.18 10/2001 125
Mexico 144.29 88.05 30.28 117.09 411.81 10/2001 125
Panama 171.28 84.07 65.20 143.37 435.00 10/2001 100
Peru 188.38 100.77 65.30 151.92 555.91 10/2003 101
Philippines 289.35 143.54 101.39 231.83 620.28 4/2002 119
Poland 77.86 76.38 8.34 46.87 360.63 10/2000 137
Romania 210.44 162.88 17.68 192.69 711.58 10/2002 113
Russia 283.35 252.89 39.42 189.68 1015.50 10/2000 137
Thailand 91.04 61.82 27.03 83.30 302.43 4/2002 118
Turkey 404.22 289.85 134.40 268.34 1212.50 10/2000 137
Ukraine 659.07 798.73 131.80 353.50 4280.02 8/2004 91
Venezuela 811.84 592.91 132.69 694.44 2824.82 1/2003 110
Vietnam 240.23 130.21 58.66 249.03 501.09 5/2006 67
Notes. The values are based on monthly average of daily 5-year sovereign CDS spreads. The
spreads are in basis points.
Table 2.2: Cross-correlations between Common External Factors
Global Europe Latin America Asia
Global 1
Europe 0.10 1
Latin America 0.19 -0.53 1
Asia -0.09 0.80 -0.61 1
130
Table 2.3: Contribution of Factors to the Sovereign CDS
Global Regional Idiosyncratic
Argentina
a
0.92 0.05 0.04
Brazil 0.11 0.82 0.07
Bulgaria 0.79 0.17 0.04
Chile 0.93 0.00 0.07
China 0.77 0.20 0.03
Colombia 0.33 0.67 0.00
Croatia 0.47 0.52 0.02
Greece 0.01 0.21 0.78
Hungary 0.44 0.18 0.38
Indonesia 0.85 0.00 0.14
Korea 0.78 0.05 0.17
Lithuania 0.82 0.08 0.10
Malaysia 0.81 0.16 0.03
Mexico 0.85 0.08 0.07
Panama 0.60 0.39 0.01
Peru 0.41 0.56 0.03
Philippines 0.41 0.02 0.57
Poland 0.36 0.33 0.30
Romania 0.53 0.29 0.18
Russia 0.85 0.01 0.14
Thailand 0.73 0.27 0.00
Turkey 0.51 0.07 0.43
Ukraine 0.91 0.01 0.08
Venezuela 0.69 0.01 0.30
Vietnam 0.74 0.06 0.19
Average 0.63 0.21 0.17
Median 0.73 0.16 0.08
Notes. Values in bold correspond to those above the median.
a
The values for Argentina are based on a rather recent period (Argen-
tinean CDS trading starts in 2005 after a 4-year default period). As there
is no data for the default period, Argentinean CDS seems to be driven only
negligibly by the idiosyncratic factor, though the default itself is mostly
idiosyncratic.
131
Table 2.4: Global Factor - Global Financial Market Indicators
?TED Spread ?T-Bill Spread (20y-10y) ?VIX
? 1.811
??
0.002
??
0.160
??
Whole [1.210,2.411] [0.000,0.004] [0.158,0.162]
Sample R
2
0.225 0.021 0.585
N 124 124 124
Regime 1 ? 2.556
??
0.0261 0.213
??
(High Stress) [0.301,5.991] [-0.031,0.080] [0.125,0.295]
(?G > ?
high
) R
2
0.493 0.244 0.858
N 11 6 7
?
high
0.675
††
1.036
††
0.947
††
[0.613,1.111] [1.036,1.116] [0.947,1.111]
Regime 2 ? 0.535
??
0.002
??
0.067
??
(Low-to-moderate Stress) [0.219,0.851] [0.000,0.003] [0.042,0.089]
(?
low
? ?G ? ?
high
) R
2
0.116 0.115 0.351
N 106 107 112
?
low
?1.096
††
?0.772
††
?1.338
††
[-1.139,-1.096] [-1.353,-0.638] [-1.353,-0.354]
Regime 3 ? 3.707 0.004 0.237
(Recovery) [-0.124,7.539] [-0.006,0.014] [-0.10,0.49]
(?G < ?
low
) R
2
0.192 0.073 0.331
N 7 11 5
Notes.
??
indicates signi?cance level at 1%. †† indicates the null of linearity is rejected at a 1% level. The TED spread
is the di?erence between the 3-month U.S. Treasury bill and 3-month USD LIBOR. The VIX is the Chicago Board of
Options Exchange index of percentage implied volatility.
1
3
2
Figure 2.1: 5-year Sovereign CDS Spreads
0
500
1,000
1,500
2,000
2,500
3,000
00 01 02 03 04 05 06 07 08 09 10 11
ARGENTINA BRAZIL BULGARIA
CHILE CHINA COLOMBIA
CROATIA GREECE HUNGARY
INDONESIA KOREA LITHUANIA
MALAYSIA MEXICO PANAMA
PERU PHILIPPINES POLAND
ROMANIA RUSSIA THAILAND
TURKEY UKRAINE VENEZUELA
VIETNAM
Brazil: 3550 bp
Argentina: 4271 bp
Ukraine: 4280 bp
Greece: 3516 bp
133
Figure 2.2: Global Factor and Major Events
-4
-2
0
2
4
6
8
10
12
01 02 03 04 05 06 07 08 09 10 11
Lehman Brothers
files for bankruptcy
(9/2008)
TARP; CPFF; TALF;
extending PDCF, AMLF, TSLF;
swap lines among major CBs;
IMF’s liquidity facility
(10/11/12 2008)
Fed’s extension of
liquidity facilities
(AMLF, CPFF,
PDCF, TSLF)
(6/2009)
Freddie Mac
announces
not buying
most risky MBSs
(2/2007)
1st bailout package
of 110bn to Greece
(5/2010)
Increased concerns
about Italy and Spain
(8/11)
3rd Greek
bailout (10/11)
Latin American Crisis
(Brazil: Debt Crisis, Elections, 6/2002)
(Argentina*: Default, Inflation
and Banking Crises, 2001-)
(Uruguay*: Banking Crisis, 7/2002-)
(contagious effects on the region)
____________________
IMF Programs-
(Brazil: 2001-2002)
(Argentina: 2001-2005)
(Colombia: 2003, 2005)
Abbreviations. AMLF: Asset-Backed Commercial Paper Money Market Mutual Fund Liquidity
Facility. CPFF: Commercial Paper Funding Facility. PDCF: Primary Dealer Credit Facility.
MBS: Mortgage-backed security. TARP: Troubled Asset Relief Program. TALF: Term Asset-
Backed Securities Loan Facility. TSLF: Term Securities Lending Facility.
134
Figure 2.3: Sovereign CDS and Regions
-2
-1
0
1
2
3
4
5
6
-12
-8
-4
0
4
8
12
16
20
01 02 03 04 05 06 07 08 09 10 11
BULGARIA CROATIA
GREECE HUNGARY
LITHUANIA POLAND
ROMANIA RUSSIA
TURKEY UKRAINE
European Factor (RHS) Global Factor (RHS)
-2
-1
0
1
2
3
4
5
-10
-5
0
5
10
15
20
25
01 02 03 04 05 06 07 08 09 10 11
ARGENTINA BRAZIL
CHILE COLOMBIA
MEXICO PANAMA
PERU VENEZUELA
Latin American Factor (RHS) Global Factor (RHS)
-2
-1
0
1
2
3
4
5
-12
-8
-4
0
4
8
12
16
01 02 03 04 05 06 07 08 09 10 11
CHINA INDONESIA
KOREA MALAYSIA
PHILIPPINES THAILAND
VIETNAM Asian Factor (RHS)
Global Factor (RHS)
135
Figure 2.4: Common Factor versus the European Factor
-15
-10
-5
0
5
10
15
20
25
01 02 03 04 05 06 07 08 09 10 11
Common Factor (Single-Factor DFM)
European Factor (Two-Factor DFM)
6/2010
10/2008
136
Figure 2.5: Decomposing Sovereign CDS
-2
-1
0
1
2
3
4
-10
-5
0
5
10
15
20
01 02 03 04 05 06 07 08 09 10 11
Chilean CDS, Standardized (LHS)
Global Factor (RHS)
Regional Factor, Latin America (RHS)
Idiosyncratic Factor (LHS)
Contribution of Factors:
Global: 93%
Regional: 0%
Idiosyncratic: 7%
-1
0
1
2
3
4
5
6
-8
-4
0
4
8
12
16
20
01 02 03 04 05 06 07 08 09 10 11
Greek CDS, Standardized (LHS)
Global Factor (RHS)
Regional Factor, Europe (RHS)
Idiosyncratic Factor (LHS)
Contribution of Factors:
Global: 1%
Regional: 21%
Idiosyncratic: 78%
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
2.0
2.5
-12
-8
-4
0
4
8
12
16
20
01 02 03 04 05 06 07 08 09 10 11
Philippines’ CDS, Standardized (LHS)
Global Factor (RHS)
Regional Factor, Asia (RHS)
Idiosyncratic Factor (LHS)
Contribution of Factors:
Global: 41%
Regional: 2%
Idiosyncratic: 57%
-2
-1
0
1
2
3
4
-8
-4
0
4
8
12
16
01 02 03 04 05 06 07 08 09 10 11
Turkey’s CDS - Standardized (LHS)
Global Factor (RHS)
Regional Factor, Europe (RHS)
Idiosyncratic Factor (LHS)
Contribution of Factors:
Global: 51%
Regional: 7%
Idiosyncratic: 43%
1
3
7
Figure 2.6: Chinn-Ito Index versus the Contribution of External Factors
Figure 2.7: Financial Market Indicators
-1
0
1
2
3
4
5
10
20
30
40
50
60
70
01 02 03 04 05 06 07 08 09 10 11
TED Spread (LHS)
Yield Spread (annual %-change) (LHS)
VIX (RHS)
138
Figure 2.8: Global Factor -Including Developed Economies-
-10
-5
0
5
10
15
20
25
30
-4
-2
0
2
4
6
8
10
12
01 02 03 04 05 06 07 08 09 10 11
Global Factor (including developed economies) (LHS)
Global Factor (emerging markets) (RHS)
Figure 2.9: European Regional Risk Factor -Including Developed Economies-
-10
0
10
20
30
40
01 02 03 04 05 06 07 08 09 10 11
European Regional Risk Factor (emerging markets)
European Regional Risk Factor (including developed economies)
139
Figure 2.10: Smoothed States -Two-Factor DFM-
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Argentina Idiosyncratic Factor
-1.2
-0.8
-0.4
0.0
0.4
0.8
01 02 03 04 05 06 07 08 09 10 11
Brazil Idiosyncratic Factor
-.8
-.4
.0
.4
.8
01 02 03 04 05 06 07 08 09 10 11
Bulgaria Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Chile Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
01 02 03 04 05 06 07 08 09 10 11
China Idiosyncratic Factor
-.4
-.2
.0
.2
.4
01 02 03 04 05 06 07 08 09 10 11
Colombia Idiosyncratic Factor
-.8
-.4
.0
.4
.8
01 02 03 04 05 06 07 08 09 10 11
Croatia Idiosyncratic Factor
-4
-2
0
2
4
6
01 02 03 04 05 06 07 08 09 10 11
Greece Idiosyncratic Factor
-2
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Hungary Idiosyncratic Factor
-2
-1
0
1
2
3
01 02 03 04 05 06 07 08 09 10 11
Indonesia Idiosyncratic Factor
-3
-2
-1
0
1
01 02 03 04 05 06 07 08 09 10 11
Korea Idiosyncratic Factor
-2
-1
0
1
01 02 03 04 05 06 07 08 09 10 11
Lithuania Idiosyncratic Factor
-.8
-.4
.0
.4
.8
01 02 03 04 05 06 07 08 09 10 11
Malaysia Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
01 02 03 04 05 06 07 08 09 10 11
Mexico Idiosyncratic Factor
-0.8
-0.4
0.0
0.4
0.8
1.2
01 02 03 04 05 06 07 08 09 10 11
Panama Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Peru Idiosyncratic Factor
-2
-1
0
1
2
3
01 02 03 04 05 06 07 08 09 10 11
Philippines Idiosyncratic Factor
-3
-2
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Poland Idiosyncratic Factor
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Romania Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Russia Idiosyncratic Factor
-.4
-.2
.0
.2
.4
01 02 03 04 05 06 07 08 09 10 11
Thailand Idiosyncratic Factor
-3
-2
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Turkey Idiosyncratic Factor
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Ukraine Idiosyncratic Factor
-1
0
1
2
01 02 03 04 05 06 07 08 09 10 11
Venezuela Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
1.5
01 02 03 04 05 06 07 08 09 10 11
Vietnam Idiosyncratic Factor
-5
0
5
10
15
01 02 03 04 05 06 07 08 09 10 11
Global Factor
-10
0
10
20
30
01 02 03 04 05 06 07 08 09 10 11
Latin America Factor
-10
0
10
20
01 02 03 04 05 06 07 08 09 10 11
Europe Factor
-12
-8
-4
0
4
8
12
01 02 03 04 05 06 07 08 09 10 11
Asia Factor
1
4
0
Figure 2.11: Smoothed States -Single-Factor DFM-
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Argentina Idiosyncratic Factor
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Brazil Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
03 04 05 06 07 08 09 10 11
Bulgaria Idiosyncratic Factor
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Chile Idiosyncratic Factor
-0.5
0.0
0.5
1.0
1.5
2.0
03 04 05 06 07 08 09 10 11
China Idiosyncratic Factor
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Colombia Idiosyncratic Factor
-2
-1
0
1
2
03 04 05 06 07 08 09 10 11
Croatia Idiosyncratic Factor
-2
0
2
4
6
03 04 05 06 07 08 09 10 11
Greece Idiosyncratic Factor
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Hungary Idiosyncratic Factor
-2
0
2
4
6
03 04 05 06 07 08 09 10 11
Indonesia Idiosyncratic Factor
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Korea Idiosyncratic Factor
-300
-200
-100
0
100
03 04 05 06 07 08 09 10 11
Lithuania Idiosyncratic Factor
-1.2
-0.8
-0.4
0.0
0.4
0.8
1.2
03 04 05 06 07 08 09 10 11
Malaysia Idiosyncratic Factor
-3
-2
-1
0
1
2
03 04 05 06 07 08 09 10 11
Mexico Idiosyncratic Factor
-4
-2
0
2
4
6
03 04 05 06 07 08 09 10 11
Panama Idiosyncratic Factor
-4
-2
0
2
4
6
03 04 05 06 07 08 09 10 11
Peru Idiosyncratic Factor
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Philippines Idiosyncratic Factor
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Poland Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
03 04 05 06 07 08 09 10 11
Romania Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
03 04 05 06 07 08 09 10 11
Russia Idiosyncratic Factor
-1.5
-1.0
-0.5
0.0
0.5
1.0
03 04 05 06 07 08 09 10 11
Thailand Idiosyncratic Factor
-6
-4
-2
0
2
4
03 04 05 06 07 08 09 10 11
Turkey Idiosyncratic Factor
-1
0
1
2
3
4
03 04 05 06 07 08 09 10 11
Ukraine Idiosyncratic Factor
-2
-1
0
1
2
3
03 04 05 06 07 08 09 10 11
Venezuela Idiosyncratic Factor
-50
0
50
100
03 04 05 06 07 08 09 10 11
Vietnam Idiosyncratic Factor
-20
-10
0
10
20
30
03 04 05 06 07 08 09 10 11
Global Factor
1
4
1
Figure 2.12: Smoothed States -Two-Factor DFM- (Including Developed Economies and Weekly Frequency)
-2
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Argentina Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Belgium Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Brazil Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
2000 2002 2004 2006 2008 2010
Bulgaria Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
2000 2002 2004 2006 2008 2010
Chile Idiosyncratic Factor
-0.8
-0.4
0.0
0.4
0.8
1.2
2000 2002 2004 2006 2008 2010
China Idiosyncratic Factor
-.8
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Colombia Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Croatia Idiosyncratic Factor
-.4
-.2
.0
.2
.4
2000 2002 2004 2006 2008 2010
France Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Germany Idiosyncratic Factor
-4
-2
0
2
4
6
2000 2002 2004 2006 2008 2010
Greece Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Hungary Idiosyncratic Factor
-2
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Indonesia Idiosyncratic Factor
-.8
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Italy Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Latvia Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Lithuania Idiosyncratic Factor
-.8
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Malaysia Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
2000 2002 2004 2006 2008 2010
Mexico Idiosyncratic Factor
-3
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Netherlands Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
2000 2002 2004 2006 2008 2010
Panama Idiosyncratic Factor
-1.0
-0.5
0.0
0.5
1.0
1.5
2000 2002 2004 2006 2008 2010
Peru Idiosyncratic Factor
-2
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Philippines Idiosyncratic Factor
-3
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Poland Idiosyncratic Factor
-2
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Portugal Idiosyncratic Factor
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Romania Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Russia Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
South Korea Idiosyncratic Factor
-1
0
1
2
3
2000 2002 2004 2006 2008 2010
Slovakia Idiosyncratic Factor
-.8
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Spain Idiosyncratic Factor
-2
0
2
4
2000 2002 2004 2006 2008 2010
Sweden Idiosyncratic Factor
-.4
.0
.4
.8
2000 2002 2004 2006 2008 2010
Thailand Idiosyncratic Factor
-2
0
2
4
2000 2002 2004 2006 2008 2010
Turkey Idiosyncratic Factor
-2
0
2
4
2000 2002 2004 2006 2008 2010
Ukraine Idiosyncratic Factor
-1
0
1
2
3
4
2000 2002 2004 2006 2008 2010
Venezuela Idiosyncratic Factor
-2
-1
0
1
2
2000 2002 2004 2006 2008 2010
Vietnam Idiosyncratic Factor
-10
0
10
20
30
2000 2002 2004 2006 2008 2010
Global Factor
-20
0
20
40
60
2000 2002 2004 2006 2008 2010
Latin American Factor
-20
0
20
40
60
2000 2002 2004 2006 2008 2010
European Factor
-20
-10
0
10
20
2000 2002 2004 2006 2008 2010
Asian Factor
1
4
2
Figure 2.13: Con?dence Interval Construction for the Thresholds (using the VIX)
?4 ?2 0 2 4 6 8
0
10
20
30
40
50
60
Threshold Variable:? G
L
ik
e
lih
o
o
d
R
a
t
io
S
e
q
u
e
n
c
e
in
?
LRN(?)
95% Critical
?4 ?3.5 ?3 ?2.5 ?2 ?1.5 ?1 ?0.5 0 0.5 1
0
5
10
15
20
25
30
35
40
45
50
Threshold Variable:? G
L
ik
e
lih
o
o
d
R
a
t
io
S
e
q
u
e
n
c
e
in
?
LRN(?)
95% Critical
143
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