Description
A sudden stop in capital flows is defined as a sudden slowdown in private capital inflows into emerging market economies, and a corresponding sharp reversal from large current account deficits into smaller deficits or small surpluses.
ABSTRACT
Title of dissertation: ESSAYS ON PREVENTING SUDDEN STOPS
Ceyhun Bora Durdu, Doctor of Philosophy, 2006
Dissertation directed by: Professor Enrique G. Mendoza
Department of Economics
Capital markets have witnessed a rash of ‘Sudden Stops’ during the last decade.
Policy proposals to prevent these crises include creating indexed bond markets and
providing price guarantees for emerging market assets. Chapter 1 explores the
macroeconomic implications of indexed bonds with a return indexed to the key
variables driving emerging market economies such as terms of trade or productivity.
We employ a quantitative model of a small open economy in which Sudden Stops are
driven by the ?nancial frictions inherent to world capital markets. While indexed
bonds provide a hedge to income ?uctuations and can undo the e?ects of ?nancial
frictions, they lead to interest rate ?uctuations. Due to this tradeo?, there exists a
non-monotonic relation between the “degree of indexation” (i.e., the percentage of
the shock re?ected in the return) and the overall e?ects of these bonds on macroe-
conomic ?uctuations. Therefore, indexation can improve macroeconomic conditions
only if the degree of indexation is less than a critical value. When the degree of
indexation is higher than this threshold, it strengthens the precautionary savings
motive, increases consumption volatility and impact e?ect of Sudden Stops. The
threshold degree of indexation depends on the volatility and persistence of income
shocks as well as the relative openness of the economy.
Chapter 2 explores the implications of asset price guarantees provided by an
international ?nancial organization on the emerging market assets. This policy is
motivated by the globalization hazard hypothesis, which suggest that Sudden Stops
caused by global ?nancial frictions could be prevented by o?ering foreign investors
price guarantees on emerging markets assets. These guarantees create a trade-
o?, however, because they weaken globalization hazard while creating international
moral hazard. We study this tradeo? using a quantitative, equilibrium asset-pricing
model. Without guarantees, margin calls and trading costs cause Sudden Stops
driven by a Fisherian de?ation. Price guarantees prevent this de?ation by propping
up foreign demand for assets. The e?ectiveness of price guarantees, their distor-
tions on asset markets, and their welfare implications depend critically on whether
the guarantees are contingent on debt levels and on the price elasticity of foreign
demand for domestic assets.
ESSAYS ON PREVENTING SUDDEN STOPS
by
Ceyhun Bora Durdu
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
2006
Advisory Commmittee:
Professor Enrique G. Mendoza, Chair/Advisor
Professor Bora?gan Aruoba
Professor Gurdip Bakshi
Professor Guillermo A. Calvo
Professor John Rust
Professor Carlos Vegh
c Copyright by
Ceyhun Bora Durdu
2006
DEDICATION
To my wife, Emine, my parents and my brother.
ii
ACKNOWLEDGMENTS
I am greatly indebted to all the people who have made this thesis possible.
First and foremost, I’d like to thank my advisor, Enrique Mendoza for his
patience and his continuous support throughout my graduate studies. Right from
the beginning, I learnt a lot from him; how to broaden my view and approach to
economic problems, how to get myself out from technicality into applicability and
intuition. His guidance shaped my ideas, helped me mature. He read every single
detail of my drafts and provided invaluable technical and editorial comments. He
always made himself available for help and advice. Every time I stumbled, I felt
his strong support that helped me stand up and “keep my eyes on the ball.” I am
greatly indebted for all this and his ever lasting friendship.
My special thanks also go to the other members of my core committee, Bora?gan
Aruoba, Guillermo Calvo, and John Rust. Their critiques and insightful comments
improved this thesis drastically. They raised excellent and thoughtful questions that
made me think harder and understand my work better. They also made themselves
available for help and advice anytime I needed. Having the opportunity to work
with such a special group of people has been invaluable.
I also thank Carlos Vegh for his help and support during this process, and join-
ing my committee. Gurdip Bakshi also kindly accepted to serve on my committee,
I owe my gratitude to him.
iii
I owe my deepest thanks to my beloved wife, my colleague, my companion
in this hard work, Emine. She shared every single happiness and disappointment
throughout my studies. She made important contributions to this thesis with our
productive conversations, with her comments on my drafts. She patiently listened
to my presentations over and over again. She stood beside me every time I faced an
obstacle.
I also thank my parents and my brother. They sacri?ced a lot during these
studies. But they never complained, and they have always supported me to pursue
what I have been passionate for and to produce an outcome that they can be proud
of.
Part of this thesis was completed while I visited the International Finance
Division of the Federal Reserve Board as a Dissertation Intern. I thank for their
hospitality and friendship, and my special thanks go to John Rogers, and Felipe
Zana.
This thesis has also bene?ted from the comments of several other people in-
cluding David Bowman, Christian Daude, Jon Faust, Dale Henderson, Ayhan K¨ose,
Marcelo Oviedo, the participants of the Inter University Conference at Princeton
University, Emerging Markets and Macroeconomic Volatility Conference at the Fed-
eral Reserve Bank of San Francisco, 2005 Midwest Macroeconomic Meetings, and
seminars participants at the Federal Reserve Board, the University of Maryland, the
Bank of England, the Bank of Hungary, Ko¸c University, Sabanc?University, Bilkent
University, TOBB ETU University, the Central Bank of Turkey, the Federal Reserve
Bank of Dallas and the Congressional Budget O?ce. I thank them here.
iv
TABLE OF CONTENTS
List of Tables vi
List of Figures vii
1 Are Indexed Bonds a Remedy for Sudden Stops? 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.1 The frictionless one-sector model . . . . . . . . . . . . . . . . 14
1.3.2 Two Sector Model with Financial Frictions . . . . . . . . . . . 22
1.3.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 31
1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2 Are Asset Price Guarantees Useful for Preventing Sudden Stops?: A Quan-
titative Investigation of the Globalization Hazard-Moral Hazard Tradeo?
(coauthored with Enrique G. Mendoza) 52
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.2 A Model of Globalization Hazard and Price Guarantees . . . . . . . . 57
2.2.1 The Emerging Economy . . . . . . . . . . . . . . . . . . . . . 58
2.2.2 The Foreign Securities Firm, the IFO & the Price Guarantees 61
2.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.3 Characterizing the Globalization Hazard-Moral Hazard Tradeo? . . . 63
2.4 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.4.1 Recursive Equilibrium and Solution Method . . . . . . . . . . 69
2.4.2 Deterministic Steady State and Calibration to Mexican Data . 71
2.4.3 Stochastic Simulation Framework . . . . . . . . . . . . . . . . 78
2.4.4 Baseline Results: Globalization Hazard and Sudden Stops
without Price Guarantees . . . . . . . . . . . . . . . . . . . . 80
2.4.5 Baseline Results: State-Contingent and Non-State-Contingent
Price Guarantees . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.5 Normative Implications and Sensitivity Analysis . . . . . . . . . . . . 88
2.5.1 Normative Implications of the Baseline Simulations . . . . . . 88
2.5.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 97
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Bibliography 116
v
LIST OF TABLES
1.1 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3 Previous Attempts of Indexed Bonds . . . . . . . . . . . . . . . . . . 38
1.4 Business Cycle Facts for Emerging Countries . . . . . . . . . . . . . . 39
1.5 Long Run Business Cycle Statistics of the One-Sector Model . . . . . 40
1.6 Returns and Natural Debt Limits . . . . . . . . . . . . . . . . . . . . 40
1.7 Variance Decomposition Analysis for Consumption . . . . . . . . . . 40
1.8 Long Run Business Cycle Statistics of the Two-Sector Model . . . . . 41
1.9 Initial Responses to a One-Standard-Deviation Endowment Shock . . 41
1.10 Sensitivity Analysis of the One-Sector Model . . . . . . . . . . . . . . 42
1.11 Sensitivity Analysis of the Two-Sector Model: Higher Share of Non-
tradable Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.1 Long Run Business Cycle Moments . . . . . . . . . . . . . . . . . . . 112
2.2 Payo?s of Domestic Agents and Foreign Traders in Baseline Simulations113
2.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.3 Sensitivity Analysis (Continued) . . . . . . . . . . . . . . . . . . . . . 115
vi
LIST OF FIGURES
1.1 Sudden Stops in Emerging Markets . . . . . . . . . . . . . . . . . . . 44
1.2 Deviations from Trend in Consumption and Ouput . . . . . . . . . . 45
1.3 Long Run Distributions of Bond Holdings in Non-Indexed Economies 46
1.4 Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock . . . . . . . . . . . . . . . . . 47
1.5 Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock . . . . . . . . . . . . . . . . . 48
1.6 Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock . . . . . . . . . . . . . . . . . 49
1.7 Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock . . . . . . . . . . . . . . . . . 50
1.8 Time Series Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1 Equilibrium in the Date t Equity Market . . . . . . . . . . . . . . . . 106
2.2 Ergodic Distributions of Domestic Equity and Bond Holdings . . . . 107
2.3 Ergodic Distributions of Domestic Equity and Bond Holdings . . . . 108
2.4 Consumption & Current Account-GDP Ratio Impact E?ects of a
Negative Productivity Shock in the Sudden Stop Region of Equity
& Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.5 Conditional Responses to a Negative, One-Standard-Deviation Pro-
ductivity Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
2.6 Equity Pricing Function in the Low Productivity State . . . . . . . . 111
vii
Chapter 1
Are Indexed Bonds a Remedy for Sudden Stops?
1.1 Introduction
Liability dollarization
1
and frictions in world capital markets have played a key
role in the emerging market crises or Sudden Stops of the last decade. Typically,
these crises are triggered by sudden reversals of capital in?ows that result in sharp
real exchange rate depreciations and collapses in consumption. Figures 1, 2, and
Table 4 document the Sudden Stops observed in Argentina, Chile, Mexico, and
Turkey in the last decade. For example in 1994, Turkey experienced a Sudden Stop
characterized by: 10% current account-GDP reversal, 10% consumption and GDP
drops relative to their trends, and 31% real exchange rate depreciation.
2
In an e?ort to remedy Sudden Stops, Caballero (2002, 2003) and Borensztein
and Mauro (2004) propose the issuance of state contingent debt instruments by
emerging market economies. Caballero’s proposal relies on the premise that crises in
some emerging economies are driven by external shocks (e.g., terms of trade shocks),
and that contrary to their developed counterparts, these economies have di?culty
absorbing these shocks due to imperfections in world capital markets. Most emerging
1
Liability dollarization refers to the denomination of debt in units of tradables (i.e., hard cur-
rencies). Liability dollarization is common in emerging markets, where debt is denominated in
units of tradables but partially leveraged on large non-tradables sectors.
2
See Figures 1 and 2, Table 4 for further documentation of these empirical regularities (see
Calvo et al. (2003) and Calvo and Reinhart (1999) for a more detailed empirical analysis).
1
countries could reduce aggregate volatility in their economies and cut precautionary
savings if they possessed debt instruments for which returns are contingent on the
external shocks that trigger crises.
3
He suggests creating an indexed bonds market
in which bonds’ returns are contingent on terms of trade shocks or commodity
prices.
4
Borensztein and Mauro (2004) argue that GDP-indexed bonds could reduce
the aggregate volatility and the likelihood of unsustainable debt-to-GDP levels in
emerging economies. Hence, they argue that these bonds can help these countries
avoid pro-cyclical ?scal policies.
This chapter introduces indexed bonds into a quantitative general equilibrium
model of a small open economy with ?nancial frictions in order to analyze the
implications of these bonds for macroeconomic ?uctuations and Sudden Stops. The
model incorporates ?nancial frictions proposed in the Sudden Stops literature (Calvo
(1998), Mendoza (2002), Mendoza and Smith (2005), Caballero and Krishnamurthy
(2001), among others). In particular, the economy su?ers from liability dollarization,
international debt markets impose a borrowing constraint in the small open economy.
This constraint limits debt to a fraction of the economy’s total income valued at
tradable goods prices. As established in Mendoza (2002), when the only available
instruments are non-indexed bonds, an exogenous shock to productivity or to the
terms of trade that renders the borrowing constraint binding triggers a Fisherian
debt-de?ation mechanism.
5
A binding borrowing constraint leads to a decline in
3
Precautionary savings refers to extra savings caused by ?nancial markets being incomplete.
Caballero (2002) points out that precautionary savings in emerging countries arise as excessive
accumulation of foreign reserves.
4
Caballero (2002) argues, for example, that Chile could index to copper prices, and that Mexico
and Venezuela could index to oil prices.
5
See Mendoza and Smith (2005), and Mendoza (2005) for further analysis on Fisherian debt-
2
tradables consumption relative to non-tradables consumption, inducing a fall in the
relative price of non-tradables as well as a depreciation of the real exchange rate
(RER). The decline in RER makes the constraint even more binding, creating a
feedback mechanism that induces collapses in consumption and the RER, as well as
a reversal in capital in?ows.
Our analysis consists of two steps. The ?rst step is to consider a one-sector
economy in which agents receive persistent endowment shocks, credit markets are
perfect but insurance markets are incomplete (henceforth frictionless one-sector
model). Second, we analyze a two sector model with ?nancial frictions that can
produce Sudden Stops endogenously through the mechanism explained in the previ-
ous paragraph. The motivation for the ?rst step is to simplify the model as much as
possible in order to understand how the dynamics of the model with indexed bonds
di?er from those of the one with non-indexed bonds.
6
In this frictionless one-sector
model, when the available instruments are only non-indexed bonds with a constant
exogenous return, agents try to insure away income ?uctuations with trade balance
adjustments. Since insurance markets are incomplete, agents are not able to attain
full-consumption smoothing, consumption is volatile, and correlation of consump-
tion with income is positive. Furthermore, agents try to self-insure by engaging in
precautionary savings. If the returns of the bonds are indexed to the exogenous
income shock only, the insurance markets are only “partially complete.” In order
to have complete markets, either full set of state contingent assets such as Arrow
de?ation.
6
This case can also be used to examine the role of indexed bonds in small open developed
economies such as Australia and Sweden, which have relatively large tradables sectors and better
access to international capital markets than most emerging market economies.
3
securities should be available (i.e., there are as many assets as the states of nature)
or the returns should be state contingent (i.e., contingent on both the exogenous
shock and the debt levels, see Section 1.3.1 for further discussion). Although in-
dexed bonds partially complete the market, the hedge provided by these bonds are
imperfect because they introduce interest rate ?uctuations. Assessing whether the
bene?ts (due to hedging) o?set the costs (due to interest rate ?uctuations) induced
by indexed bonds requires quantitative analysis.
Our quantitative analysis of the frictionless one-sector model establishes that
there exists a non-monotonic relation between the “degree of indexation” of the
bonds (i.e., the percentage of the shock that is passed on to the bonds’ return) and
the overall e?ects of these bonds on macroeconomic variables. Therefore, indexed
bonds can reduce precautionary savings, volatility of consumption and correlation
of consumption with income only if the degree of indexation is lower than a critical
value. If it is higher than this threshold (as with full indexation), indexed bonds
worsen these macroeconomic variables.
The changes in precautionary savings are driven by the changes in “catas-
trophic level of income.” Risk averse agents have strong incentives to avoid attain-
ing levels of debt that the economy cannot support when the income is at catas-
trophic level.
7
Because, otherwise agents would attain non-positive consumption
levels which in turn leads to in?nitely negative utility if such income levels realize.
The degree of indexation has a signi?cant e?ect on determining the state of nature
7
The largest debt that the economy can support to guarantee non-negative consumption in the
event that income is almost surely at its catastrophic level is referred as natural debt limit.
4
that de?nes catastrophic levels of income and whether these income levels are higher
or lower than what they would be without indexation. With higher degrees of in-
dexation, these income levels can be determined at a positive shock, because, for
example, if agents receive positive income shocks forever, they will receive higher
endowment income but will also pay higher interest rates. Our analysis shows that
for higher values of the degree of indexation, the latter e?ect is stronger, leading to
lower catastrophic income levels. This in turn creates stronger incentives for agents
to build up bu?er stock savings.
The e?ect of indexation on consumption volatility can be analyzed by de-
composing the variance of consumption. (Consider the budget constraint of such
an economy c
t
= (1 + ?
t
)y ? b
t+1
+ (1 + r + ?
t
)b
t
.
8
Using this budget constraint,
var(c
t
) = var(y
t
) + var(tb
t
) ? 2cov(tb
t
, y
t
)). On one hand, for a given income
volatility, indexation increases the covariance of trade balance with income (since
in good (bad) times indexation commands higher (lower) repayments to the rest of
the world), which lowers the volatility of consumption. On the other hand, index-
ation increases the volatility of trade balance (due to introduction of interest rate
?uctuations), which increases the volatility of consumption. Our analysis suggests
that at high levels of indexation, increase in the variance of trade balance dominates
the increase in the covariance of trade balance with income, which in turn increases
consumption volatility.
This tradeo? is also preserved in the two sector model with ?nancial frictions.
8
Here, b is bond holdings, r is risk free net interest rate, y is endowment income, ?
t
is the
income shock, and c is consumption.
5
In addition, in this model, the interaction of the indexed bonds with the ?nancial
frictions leads to additional bene?ts and costs. Speci?cally, when indexed bonds are
in place, negative shocks can result in a relatively small decline in tradable consump-
tion; as a result, the initial capital out?ow is milder and the RER depreciation is
weaker compared to a case with non-indexed bonds. The cushioning in the RER can
help to contain the Fisherian debt-de?ation process. While these bonds help relax
the borrowing constraint in case of negative shocks, this time, an increase in debt
repayment following a positive shock can lead to a larger need for borrowing, which
can make the borrowing constraint suddenly binding, triggering a debt-de?ation.
Quantitative analysis of this model suggests, once again, that the degree of indexa-
tion needs to be lower than a critical value in order to smooth Sudden Stops. With
indexation higher than this critical value, the latter e?ect dominates the former,
hence lead to more detrimental e?ects of Sudden Stops. We also ?nd that the
degree of indexation that minimizes macroeconomic ?uctuations and impact e?ect
of Sudden Stops depends on the persistence and volatility of the exogenous shock
triggering Sudden Stops, as well as the size of the non-tradables sector relative to
its tradables sector; suggesting that the indexation level that maximizes bene?t of
indexed bonds needs to be country speci?c. Because an indexation level that is
appropriate for one country in terms of its e?ectiveness at preventing Sudden Stops
may not be e?ective for another and may even expose to higher risk of facing Sudden
Stops.
Debt instruments indexed to real variables (i.e., GDP, commodity prices, etc.)
6
have not been widely employed in international capital markets.
9
As Table 1.3
shows, only a few countries issued these types of instruments in the past. In the early
1990s, Bosnia and Herzegovina, Bulgaria, and Costa Rica issued bonds containing
an element of indexation to GDP; at the same time, Mexico and Venezuela issued
bonds indexed to oil. Since the late 1990s, Bulgaria has already swapped a portion
of its debt with non-indexed bonds. France issued gold-indexed bonds in the early
1970s, but due to depreciation of the French Franc in subsequent years, the French
government bore signi?cant losses and halted issuance.
10
Although problems on the
demand side have been emphasized in the literature as the primary reason for the
limited issuance of indexed bonds, the supply of such bonds has always been thin,
as countries have exhibited little interest in issuing them. Our results may also help
to understand why it has been the case: countries may have been reluctant due to
the imperfect hedge that these bonds provide.
Several studies have explored the costs and bene?ts of indexed debt instru-
ments in the context of public ?nance and optimal debt management.
11
As men-
tioned above, Borensztein and Mauro (2004) and Caballero (2003) drew attention
to these instruments as possible vehicles to provide insurance bene?ts to emerging
countries. Moreover, Caballero and Panageas (2003) quanti?ed the potential wel-
fare e?ects of credit lines o?ered to emerging countries. They modelled a one-sector
model with collateral constraints where Sudden Stops are exogenous. They used
9
In terms of hedging perspective CPI-indexed bonds may not provide a hedge against income
risks, since in?ation is pro-cyclical.
10
The French government paid 393 francs in interest payments for each bond issued, far more
than the 70 francs originally planned (Atta-Mensah (2004)).
11
See, for instance, Barro (1995), Calvo(1988), Fischer (1975), Magil and Quinzii (1005), among
others
7
this setup to explore the bene?ts of these credit lines in terms of smoothing Sudden
Stops, interpreting them as akin to indexed bonds. This chapter contributes to
this literature by modelling indexed bonds explicitly in a dynamic stochastic gen-
eral equilibrium model where Sudden Stops are endogenous. Endogenizing Sudden
Stops reveals that the e?cacy of indexed bonds in terms of preventing these crises
depends on whether the bene?ts due to hedging outweigh the imperfections intro-
duced by these bonds. Depending on the structure of indexation, we show that they
can potentially amplify the e?ects of Sudden Stops.
12
This chapter is related to studies in several strands of macro and international
?nance literature. The model has several features common to the literature on
precautionary saving and macroeconomic ?uctuations (e.g., Aiyagari (1994), Hugget
(1993)). The chapter is also related to studies exploring business cycle ?uctuations
in small open economies (e.g., Mendoza (1991), Neumeyer and Perri (2005), Kose
(2002), Oviedo (2005), Uribe and Yue (2005)) from the perspective of analyzing how
interest rate ?uctuations a?ect macroeconomic variables. In addition to the papers
in the Sudden Stops literature, this chapter is also related to follow up studies to this
literature, including Calvo (2002), Durdu and Mendoza (2005), and Caballero and
Panageas (2003), which investigate the role of relevant policies in terms of preventing
Sudden Stops. Durdu and Mendoza (2005) explore the quantitative implications of
price guarantees o?ered by international ?nancial organizations on emerging market
assets. They ?nd that these guarantees may induce moral hazard among global
12
Krugman (1998) and Froot et al. (1989) emphasize moral hazard problems that GDP indexa-
tion can introduce. Here, we point out other adverse e?ects that indexation can cause even in the
absence of moral hazard.
8
investors, and conclude that the e?ectiveness of price guarantees depends on the
elasticity of investors’ demand as well as whether the guarantees are contingent on
debt levels. Similarly, in this chapter, we explore the potential imperfections that
can be introduced by the issuance of indexed bonds, and derive the conditions under
which such a policy could be e?ective in preventing Sudden Stops.
Our ?ndings are closely related to those of Magill and Quinzii (1995). They
compare the welfare e?ects of introduction of in?ation indexed bonds and point out
that while these bonds can eliminate the ?uctuations in purchasing power, they
introduce another risk that arise from relative price ?uctuations; suggesting that
economies might actually be worse o? with introduction of in?ation indexed bonds.
Earlier seminal studies that in ?nancial innovation literature such as Shiller
(1993) and Allen and Gale (1994) analyze how creation of new class of “macro
markets” can help to manage economic risks such as real estate bubbles, in?ation,
recessions, etc. and discusses what sorts of frictions can prevent the creation of
these markets. This chapter emphasizes possible imperfections in global markets,
and points out under which conditions issuance of indexed bonds may not improve
macroeconomic conditions for a given emerging market.
The rest of the chapter proceeds as follows. The next section describes the full
model environment. Section 1.3 presents the quantitative results of the frictionless
one-sector model, and the two-sector model with ?nancial frictions. We conclude
and o?er extensions in Section 1.4.
9
1.2 Model
In this section, we describe the general setup of the two sector model with
?nancial frictions. The model with non-indexed bonds is similar to Mendoza (2002).
Foreign debt is denominated in units of tradables and imperfect credit markets
impose a borrowing constraint that limits external debt to a share of the value of
total income in units of tradables (which therefore re?ects changes in the relative
price of non-tradables that is the model’s RER).
Representative households receive a stochastic endowment of tradables and
non-stochastic endowment of non-tradables, which are denoted (1 + ?
t
)y
T
and y
N
,
respectively. ?
t
is a shock to the world value of the mean tradables endowment
that could represent a productivity shock or a terms-of-trade shock. In our model,
? ? E = [?
1
< ... < ?
m
] (where ?
1
= ??
m
) evolves according to an m-state symmetric
Markov chain with transition matrix P. Households derive utility from aggregate
consumption (c), and maximize Epstein’s (1983) stationary cardinal utility function:
U = E
0
_
?
t=0
exp
_
?
t?1
?=0
? log(1 + c
t
)
_
u(c
t
)
_
. (1.1)
Functional forms are given by:
u(c
t
) =
c
1??
t
?1
1 ??
, (1.2)
c
t
(c
T
t
, c
N
t
) =
_
?(c
T
t
)
?µ
+ (1 ??)(c
N
t
)
?µ
¸
?
1
µ
. (1.3)
10
The instantaneous utility function (1.2) is in constant relative risk aversion
(CRRA) form with an inter-temporal elasticity of substitution 1/?. The consump-
tion aggregator is represented in constant elasticity of substitution (CES) form,
where 1/(1+µ) is the elasticity of substitution between consumption of tradables and
non-tradables and where ? is the CES weighing factor. exp
_
?
t?1
?=0
? log(1 + c
t
)
¸
is
an endogenous discount factor that is introduced to induce stationarity in consump-
tion and asset dynamics. ? is the elasticity of the subjective discount factor with
respect to consumption. Mendoza (1991) introduced preferences with endogenous
discounting to quantitative small open economy models, and such preferences have
since been widely used.
13
The households’ budget constraint is:
c
T
t
+p
N
t
c
N
t
= (1 +?
t
)y
T
+p
N
t
y
N
?b
t+1
+ (1 +r +??
t
)b
t
(1.4)
where b
t
is current bond holdings, (1 + r + ??
t
) is the gross return on bonds, and
p
N
t
is relative price of non-tradables. The indexation of the debt works as follows.
Consider a case in which there are high and low states for tradables income. The
return on the indexed bonds is low in the bad state and high in the good one, but
the mean of the return remains unchanged and equal to R.
14
When households’
13
As explained in Schmitt-Groh´e and Uribe (2003), preferences with constant discounting, where
rate of time preference is equal to real interest rate, introduces non-stationarity in consumption
and asset holdings. Schmitt-Groh´e and Uribe (2003) compares the quantitative implications of the
speci?cations used in the literature to resolve this problem. Kim and Kose (2003) also compares
quantitative implications of endogenous discounting with that of constant discounting.
14
Although return is indexed to terms of trade shock, our modeling approach potentially sheds
light on the implications of RER indexation, as well. In our model, the aggregate price index (i.e.,
the RER) is an increasing function of the relative price of non-tradables (p
N
), which is determined
at equilibrium in response to endowment shocks.
11
current bond holdings are negative, (i.e., when households are debtors) they pay
less (more) in the event of a negative (positive) endowment shock. The standard
assumption on modelling bonds’ return is to assume that indexation is one-to-one;
i.e., the return of indexed bonds is 1+r+?
t
(see for example Borensztein and Mauro
(2004)). Here, we consider a more ?exible setup by assuming a ?exible degree of
indexation by introducing a parameter ? ? [0, 1], which measures the degree of
indexation of the bonds. In particular, the limiting case ? = 0 yields the benchmark
case with non-indexed bonds, while ? = 1 is the full-indexation case. Notice that
? a?ects the variance of the bonds’ return (since var(1 + r + ??
t
) = ?
2
var(?
t
)).
As ? increases, the bonds provide a better hedge against negative income shocks,
but at the same time it introduces additional volatility by increasing the return’s
variance. As explained below, there is a critical degree of indexation beyond which
the distortions due to the increased volatility of returns outweigh the bene?ts that
indexed bonds introduce. In our quantitative experiments, we will characterize the
value of ?; at which, the bonds’ bene?ts are maximized.
To simplify notation, we denote bond holdings as b
t
regardless of whether
bonds are non-indexed or indexed. As mentioned above, when ? is equal to zero,
the bond boils down to a non-indexed bond with a ?xed gross return R = 1 + r.
This return is exogenous and equal to the world interest rate. When ? is greater
than zero, it is an indexed bond with a state contingent return; i.e., it (imperfectly)
hedges income ?uctuations.
In addition to the budget constraint, foreign creditors impose the following
borrowing constraint, which limits debt issuance as a share of total income at period
12
t not to exceed ?:
b
t+1
? ??
_
(1 +?
t
)y
T
+p
N
t
y
N
¸
. (1.5)
The borrowing constraint takes a similar form as those used in the Sudden Stops lit-
erature in order to mimic the tightening of the available credit to emerging countries
(see for example, Caballero and Krishnamurthy (2001), Mendoza (2002), Mendoza
and Smith (2005), Caballero and Panageas (2003)). As Mendoza and Smith (2005)
explain, although these types of borrowing constraints are not based upon a con-
tracting problem between lenders and borrowers, they are realistic in the sense that
they resemble the risk management tools used in international capital markets, such
as Value-at-Risk models employed by investment banks.
The optimality conditions of the problem facing households are standard and
can be reduced to the following equations:
U
c
(t)
_
1 ?
?
t
?
t
_
= exp [?? log(1 + c
t
)] E
t
_
(1 + r +??
t
)p
c
t
p
c
t+1
U
c
(t + 1)
_
(1.6)
1 ??
?
_
c
T
t
c
N
t
_
1+µ
= p
N
t
(1.7)
along with the budget constraint (1.4), the borrowing constraint (1.5), and the
standard Kuhn-Tucker conditions. ? and ? are the Lagrange multipliers of the
borrowing constraint and the budget constraint, respectively. U
c
is the deriva-
tive of lifetime utility with respect to aggregate consumption. p
c
t
is the CES price
index of aggregate consumption in units of tradable consumption, which equals
_
?
1
µ+1
+ (1 ??)
1
µ+1
(p
N
)
µ
µ+1
_
1+µ
µ
. Equation (1.6) is the standard Euler Equation
13
equating marginal utility at date t to that of date t +1. Equation (1.7) equates the
marginal rate of substitution between tradabales consumption and non-tradables
consumption to the relative price of non-tradables.
1.3 Quantitative Analysis
We explore the model’s dynamics in two steps. First, we examine the role
that indexed bonds play in a standard one-sector model in which the problem of
liability dollarization is excluded and there is no borrowing constraint. Then we
introduce the two frictions back as in the complete model described above in order
to examine the role that indexed bonds can play in reducing the adverse e?ects of
liability dollarization and preventing Sudden Stops.
1.3.1 The frictionless one-sector model
In the frictionless one-sector version of the model, indexed bonds with returns
indexed to the exogenous shock are not able to complete the market but just partially
completes it by providing the agents with the means to hedge against ?uctuations
in endowment income. If we call (1 + r + ??)b
t
?nancial income, the underlying
goal to complete the market would be to keep the sum of endowment and ?nancial
incomes constant and equal to the mean endowment income, i.e., (1+?
t
)y
T
+(1+r+
??)b
t
= y
T
. Clearly, we can keep this sum constant only if the bonds’ return is state
contingent (i.e., contingent on both the exogenous shock and the debt stock, which
requires R
t
(b, ?) = ?
?
t
y
T
b
t
or agents can trade Arrow securities (i.e., there are as many
14
assets as the number of state of nature). Hence, indexed bonds introduce a tradeo?:
on one hand it hedges income ?uctuations but on the other hand it introduces
interest rate ?uctuations. In order to analyze the overall e?ect of indexed bonds,
we solve the model numerically. The dynamic programming representation (DPP)
of the household’s problem in this case reduces to:
V (b, ?) = max
b
_
u(c) + (1 + c)
??
E [V (b
, ?
)]
_
s.t.
c
T
= (1 + ?)y
T
?b
+ (1 +r +??)b.
(1.8)
Here, the endogenous state space is given by B = {b
1
< ... < b
NB
}, which is
constructed using NB = 1, 000 equidistant grid points. The exogenous Markov
process is assumed to have two states for simplicity: E = {?
L
< ?
H
}. Optimal
decision rules, b
(b, ?) : E × B ? R, are obtained by solving the above DPP via a
value function iteration algorithm.
Calibration
The parameter values used to calibrate the model are summarized in Table 1.1.
The CRRA parameter ? is set to 2, the mean endowment y
T
is normalized to one,
and the gross interest rate is set to the quarterly equivalent of 6.5%, following the
values used in small open economy RBC literature (see for example Mendoza (1991)).
The steady state debt-to-GDP ratio is set to 35%, which is inline with the estimate
for the net asset position of Turkey (see Lane and Milesi-Ferretti (1999)). The
elasticity of the subjective discount factor follow from euler equation for consumption
15
evaluated at steady-state:
(1 + c)
??
(1 + r) = 1 ?? = log(1 + r)/ log(1 + ¯ c). (1.9)
The standard deviation of the endowment shock is set to 3.51% and the autocorre-
lation is set to 0.524, which are the standard deviation and the autocorrelation of
tradable output for Turkey given in Table 1.4.
Table 1.1: Parameter Values
? 2 relative risk aversion RBC parametrization
y
T
1 tradable endowment normalization
?
?
0.0351 tradable output volatility Turkish data
?
?
0.524 tradable output autocorrelation Turkish data
R 1.0159 gross interest rate RBC parametrization
? 0.0228 elasticity of discount factor steady state condition
Using the “simple persistence” rule, we construct a Markovian representation
of the time series process of output. The transition probability matrix P of the
shocks follows:
P(i, j) = (1 ??
?
)?
i
+?
?
I
i,j
(1.10)
where i, j = 1, 2; ?
i
is the long-run probability of state i; and I
i,j
is an indica-
tor function, which equals 1 if i = j and 0 otherwise, ?
?
is the ?rst order serial
autocorrelation of the shocks.
16
Simulation Results
We report long run values of the key macroeconomic variables, such as mean
bond holdings that is a measure of precautionary savings, volatility of consumption,
correlation of consumption with income, which measures to what extend income ?uc-
tuations a?ect consumption ?uctuations, and serial autocorrelation of consumption
which measures the persistence of consumption, of the model to highlight the e?ect
of indexation on consumption smoothing in Table 1.5. Without indexation (? = 0),
mean bond holdings are higher than the case with perfect foresight (?0.35) (which
is an implication of precautionary savings), volatility of consumption is positive,
and consumption is correlated with income.
Now we analyze how the results change when we index debt repayments to
endowment shocks. As Table 1.5 reveals, when the degree of indexation is in the
[0.015, 0.25) range, households engage in less precautionary savings (as measured
by the long run average of b) and the standard deviation of consumption declines
relative to the case in which there is no indexation. Moreover, in this range, correla-
tion of consumption with GDP falls slightly and its serial autocorrelation increases
slightly. These results suggests that when the degree of indexation is in this range,
indexation improves these macroeconomic variables from the consumption smooth-
ing perspective. However, when the degree of indexation is greater than 0.25, these
improvements reverse. In the full-indexation (? = 1) case, for example, the stan-
dard deviation of consumption is 4.8%, four times the standard deviation in the
no-indexation case. The persistence of consumption also declines at higher degrees
17
of indexation. The autocorrelation of consumption in the full indexation case is
0.886, compared to 0.978 in the no-indexation case and the high of 0.984 in the case
where ? = 0.10. Not surprisingly, the ranking of welfare is in line with the ranking
of consumption volatility, as the last row of Table 1.5 reveals. However, the absolute
values of the di?erences in welfare are quite small.
15
The above changes are driven by the changes in the ability to hedge income
?uctuations with indexed bonds. This hedging ability is a?ected by the degree of
indexation because the degree of indexation alter the incentives for precautionary
savings. In particular, it has a signi?cant e?ect on determining the state of nature
that de?nes the “catastrophic” level of income at which household reach their natural
debt limits. The natural debt limit (?) is the largest debt that the economy can
support to guarantee non-negative consumption in the event that income remain at
its catastrophic level almost surely, i.e.,
? = ?
(1 ??)y
T
r
. (1.11)
With non-indexed bonds, catastrophic level of income is realized at state of nature
with the negative endowment shock. When the debt approaches to the natural
debt limit, consumption approaches zero, which leads to in?nitely negative utility.
Hence, agents have strong incentives to avoid holding debt levels lower than natural
debt limit. In order to guarantee positive consumption almost surely in the event
that income remains at its catastrophic level, agents engage in strong precaution-
15
As pointed out by Lucas (1987), welfare implications of altering consumption ?uctuations in
these type of models are quite low.
18
ary savings. An increase (decrease) in this debt limit strengthens (weakens) the
incentives to save, since the level of debt that agents would try to avoid would be
higher (lower). With indexation, the natural debt limit can be determined at either
negative or positive realization of the endowment shock, depending on which yields
the lower income (determines the catastrophic level of income). To see this, notice
that using the budget constraint, when the shock is negative, we derive:
c
t
? 0 ?(1 ??)y ?b
t+1
+b
t
(1 +r ???) ? 0 ??
L
? ?
(1 ??)y
r ???
, if r ??? > 0.
(1.12)
Notice that for the ranges of values of ? where r ? ?? < 0, Equation 1.12 yields
an upper bound for the bond holdings; i.e., ?
L
? ?
(1??)y
r???
). Hence, in this range,
negative shock will not play any role in determining the natural debt limit. Again
using the budget constraint, positive endowment shock implies the following natural
debt limit:
c
t
? 0 ?(1 +?)y ?b
t+1
+b
t
(1 +r +??) ? 0 ??
H
? ?
(1 + ?)y
r +??
.
(1.13)
Combining these two equations, we get:
? =
_
¸
¸
_
¸
¸
_
max {?
(1??)y
r???
, ?
(1+?)y
r+??
}, if ? < r/?
?
(1+?)y
r+??
, if ? > r/?.
(1.14)
Further algebra suggest that when
1??
1+?
<
r???
r+??
or ? < r, natural debt limit is
19
determined at state of nature with a negative endowment shock and in this case,
??/?? < 0, i.e., increasing the degree of indexation decreases the natural debt limit
or weakens the precautionary savings incentive. However if
1??
1+?
>
r???
r+??
or ? > r,
??/?? > 0, i.e., increasing the degree of indexation increases the natural debt limit
or strengthens the precautionary savings incentive.
In Table 1.6, we numerically calculate these natural debt limits as functions
of the degrees of indexation, along with the corresponding returns in both states
(R
i
t
= 1 + r + ??
t
) and con?rm the analytical results derived above. When the
degree of indexation is less than 0.0159, the natural debt limit is determined by the
negative shock and decreases (i.e., the debt limit becomes looser) as we increase ?.
When ? is greater than 0.0159, it is determined by the positive shock and increases
(i.e., the debt limit becomes tighter) as we increase ? (we print the corresponding
limits darker in the table). In the full-indexation case, for example, this debt limit
is -20.09, whereas the corresponding value is -61.49 in the non-indexed case. In
other words, in the full-indexation case, positive endowment shocks decrease the
catastrophic level of income to one third of the value in the non-indexed case. This
in turn sharply strengthen precautionary savings motive.
In order to understand the role of indexation on volatility of consumption,
we perform a variance decomposition analysis. Higher indexation provides a better
hedge to income ?uctuations by increasing the covariance of the trade balance (tb
=b
? R
i
t
b) with income (since in good (bad) times agents pay more (less) to the
rest of the world). However, higher indexation also increases the volatility of the
trade balance. In order to pin down the e?ect of indexation on these variables, we
20
perform a variance decomposition using the following identity:
var(c
T
) = var(y
T
) + var(tb) ?2cov(tb, y
T
).
In Table 1.7, we present the corresponding values for the last two terms in the above
equation for each of the indexation levels.
16
Clearly, both the variance of the trade
balance and the covariance of the trade balance with income monotonically increase
with the level of indexation. However, the term var(tb) ?2cov(tb, y
T
) ?uctuates in
the same direction as the volatility of consumption, suggesting that at high levels
of indexation the rise in the variance of the trade balance o?sets the improvement
in the co-movement of the trade balance with income, i.e., the e?ect of increased
?uctuation in interest rate dominates the e?ect of hedging provided by indexation.
Hence, consumption becomes more volatile for higher degrees of indexation.
To sum up, when the degree of indexation is higher than a critical value (as
with full-indexation), the precautionary savings motive is stronger and the volatil-
ity of consumption is higher than in the non-indexed case. These results arise
because the natural debt limit is lower at higher levels of indexation and because
the increased volatility in the trade balance far outweighs the improvement in the
co-movement of the trade balance with income.
These results suggest that in order to improve macroeconomic variables, the
indexation level should be low. When ? is lower than 0.25, agents can better hedge
against ?uctuations in endowment income than when ? is at higher levels. In this
16
Since the endowment is not a?ected by changes in the indexation level, its variance is constant.
21
case, the precautionary savings motive is weaker, the volatility of consumption is
smaller, and consumption is more persistent. When ? is in the [0.10, 0.25] range, the
correlation of consumption with income approaches zero and the autocorrelation of
consumption nears unity. These values resemble the results that could be attained
in the full-insurance scenario, and suggest that partial indexation is optimal.
The results using a frictionless one-sector model shed light on the debate about
the indexation of public debt. Our ?ndings in this section suggest that the hedge
indexed bonds provide is imperfect and that indexation of the debt in a one-to-
one fashion may not improve macroeconomic variables. However, partial indexation
could prove bene?cial by mimicking outcomes that would arise under full insurance.
1.3.2 Two Sector Model with Financial Frictions
When we introduce liability dollarization and a borrowing constraint, the DPP
of the household’s problem becomes:
V (b, ?) = max
b
_
u(c) + (1 + c)
??
E [V (b
, ?
)]
_
s.t.
c
T
= (1 + ?)y
T
?b
+ (1 + ??)Rb
c
N
= y
N
b
? ??
_
(1 + ?)y
T
+p
N
y
N
¸
.
(1.15)
As in the previous one-sector model, the endogenous state space is given by
B = {b
1
< ... < b
NB
}, and the exogenous Markov process is assumed to have two
states: E = {?
L
< ?
H
}. Optimal decision rules, b
(b, ?) : E × B ? R, are obtained
22
by solving the above DPP.
Solving the Model
We solve the stochastic simulations using value function iteration over a dis-
crete state space in the [-2.5, 5.5] interval with 1,000 evenly spaced grid points. We
derive this interval by solving the model repeatedly until the solution captures the
ergodic distribution of bond holdings. The endowment shock has the same Markov
properties described in the previous section. The solution procedure is similar to
that in Mendoza (2002). We start with an initial conjecture for the value function
and solve the model without imposing the borrowing constraint for each coordinate
(b, ?) in the state space, and check whether the implied b
satis?es the borrowing
constraint. If so, the solution is found and we calculate the implied value function
that is then used as a conjecture for the next iteration. If not, we impose the bor-
rowing constraint with equality and solve a system of non-linear equations de?ned
by the three constraints given in the DPP (1.15) as well as the optimality condition
given in Equation (1.7). Then, we calculate the implied value function using the
optimal b
, and iterate to convergence.
Calibration
We calibrate the model such that aggregates in the non-binding case match
the certain aggregates of Turkish data. In addition to the parameters used in the
frictionless one-sector model, we introduce the following parameters, the values of
23
which we summarize in Table 1.2.: y
N
is set to 1.3418, which implies a share of
non-tradables output in line with the average ratio of the non-tradable output to
tradable output in between 1987-2004 for Turkey; µ is set to 0.316, which is the
value Ostry and Reinhart (1992) estimate for emerging countries; the steady state
relative price of non-tradables is normalized to unity, which implies a value of 0.4027
for the CES share of tradable consumption (?), calculated by using the condition
that equates the marginal rate of substitution between tradables and non-tradables
consumption to the relative price of non-tradables (Equation (1.7)). The elasticity
of the subjective discount factor (?) is recalculated including these new variables
in the solution of the non-linear system of equations implied by the steady-state
equilibrium conditions of the model given in Equation (1.9). ? is set to 0.3 (i.e.
households can borrow up to 30% of their current income), which is found by solving
the model repeatedly until the model matches the empirical regularities of a typical
Sudden Stop episode at a state where the borrowing constraint binds with a positive
probability in the long run.
Table 1.2: Parameter Values
µ 0.316 elasticity of substitution Ostry and Reinhart (1992)
y
N
/y
T
1.3418 share of NT output Turkish data
p
N
1 relative price of NT normalization
? 0.3 constraint coe?cient set to match SS dynamics
? 0.4027 CES weight calibration
? 0.0201 elasticity of discount factor calibration
24
Simulation Results
The stochastic simulation results are divided into three sets. In the ?rst set,
which we refer to as the frictionless economy, the borrowing constraint never binds.
In the second set of results, which we refer to as the constrained economy, the
borrowing constraint occasionally binds and households can issue only non-indexed
bonds. In the last set, which we refer to as the indexed economy, borrowing con-
straint occasionally binds but households can issue indexed bonds.
Our results that compare the frictionless and constrained economies are anal-
ogous of those presented by Mendoza (2002). Hence, here we just emphasize the
results that are speci?c and crucial to the analysis of indexed bonds and refer the
interested reader to Mendoza (2002) for further details. Since at equilibrium, the
relative price of non-tradables is a convex function of the ratio of tradables consump-
tion to non-tradables consumption, a decline in tradables consumption relative to
non-tradables consumption due to a binding borrowing constraint leads to a decline
in the relative price of non-tradables, which makes the constraint more binding and
leads to a further decline in tradables consumption.
Figure 1.3 shows the ergodic distributions of bond holdings. The distribution
in the frictionless economy is close to normal and symmetric around its mean. Mean
bond holdings are -0.299, higher than the steady state bond holdings of -0.35; this
re?ects the precautionary savings motive that arises as a result of uncertainty and
the incompleteness of ?nancial markets. The distribution of bond holdings in the
constrained economy is shifted right relative to that of the frictionless economy.
25
Mean bond holdings in the constrained economy are 0.244, which re?ects a sharp
strengthening in the precautionary savings motive due to the borrowing constraint.
Table 1.8 presents the long-run business cycle statistics for the simulations.
Relative to the frictionless economy, the correlation of consumption with the trad-
ables endowment is higher in the constrained economy. In line with this stronger
co-movement, the persistence (autocorrelation) of consumption is lower in the con-
strained economy.
Behavior of the model can be divided into three ranges. In the ?rst range,
debt is su?ciently low that the constraint is not binding. In this case, the response
of the constrained economy to a negative endowment shock is similar to that of the
frictionless economy, and a negative endowment shock is smoothed by a widening
in the current account de?cit as a share of GDP. There is also a range of bond
holdings in which debt levels are too high. In this range, the constraint always
binds regardless of the endowment shock. However, at more realistic debt levels
where the constraint only binds when the economy su?ers a negative shock, the
model with non-indexed bonds roughly matches the empirical regularities of Sudden
Stops. This range, which we call the “Sudden Stop region” following Mendoza and
Smith (2005), corresponds to the 218-230th grid points.
In Figure 1.4, we plot the conditional forecasting functions of the frictionless
and constrained economies for tradables consumption, aggregate consumption, the
relative prices of non-tradables, and the current account-GDP ratios, in response to
a one-standard deviation endowment shock. These forecasting functions are condi-
tional on the 229th bond grid, which is one of the Sudden Stop states and has a
26
long-run probability of 0.47%, and they are calculated as responses of these variables
as percentage deviations from the long-run means of their frictionless counterparts.
17
As these graphs suggest, the response of the constrained economy is dramatic.
The endowment shock results in a 4.1% decline in tradable consumption. That
compares to a decline of only 0.9% in the frictionless economy. In line with the larger
collapse in the tradables consumption, the responses of aggregate consumption and
the relative price of non-tradables are more dramatic in the constrained economy
than in the frictionless economy. While households in the frictionless economy are
able to absorb the shock via adjustments in the current account (the current account
de?cit slips to 1.4% of GDP), households in the constrained economy cannot due to
the binding borrowing constraint (the current account shows a surplus of 0.02% of
GDP). These ?gures also suggest that the e?ects of Sudden Stops are persistent. It
takes more than 40 quarters for these variables to converge back to their long-run
means.
Figures 1.5, 1.6, and 1.7 compare the detrended conditional forecasting func-
tions of the constrained economy with that of the indexed economy to illustrate how
indexed bonds can help smooth Sudden Stop dynamics (the degrees of indexation
are provided on the graphs).
18
As Figure 1.5 suggests, when the degree of index-
ation is 0.05, indexed bonds provide little improvement over the constrained case;
indeed, the di?erence in the forecasting functions is not visible. When indexation
reaches 0.10, however, the improvements are minor yet noticeable. At this degree of
17
Bond holdings on this grid point are equal to -0.674, which implies a debt-to-GDP ratio of
30%.
18
These forecasting functions are detrended by taking the di?erences relative to the frictionless
case.
27
indexation, aggregate consumption rises 0.11%, tradables consumption rises 0.24%,
the relative price of non-tradables increases 0.30%.
With increases in the degree of indexation to 0.25 and 0.45, the initial ef-
fects are relatively small. Figure 1.6 suggests that the improvements in tradables
consumption are close to 1% and 1.8% when the degrees of indexation are 0.25
and 0.45, respectively. Figure 1.7 suggests that when the degree of indexation gets
higher, 0.7 and 1.0 for example, tradables consumption and aggregate consumption
fall below the constrained case after the fourth quarter and stay below for more
than 30 quarters despite the initially small e?ects of a negative endowment shock.
In other words, degrees of indexation higher than 0.45 in an indexed economy imply
more pronounced detrimental Sudden Stop e?ects than in a constrained economy.
Table 1.9 summarizes the initial e?ects of both a negative and a positive
shock conditional on the same grid points used in the forecasting functions. When
indexed bonds are in place, our results suggest that if the degree of indexation is
within [0.05, 0.25], indexed bonds help to smooth the e?ects of Sudden Stops. As
Table 1.9 suggests, when the degree of indexation is 0.05, indexed bonds provide
little improvement. As we increase the degree of indexation, the initial impact of
a negative endowment shock on key variables gets smaller. In this case, debt relief
accompanies a negative endowment shock, and this relief helps to reduce the initial
impact of a binding borrowing constraint. Hence, the depreciation in the relative
price of non-tradables is milder, which in turn prevents the Fisherian debt-de?ation.
Table 1.9 also suggests that although the smallest initial impact of a negative
endowment shock occurs when the degree of indexation is unity (full-indexation),
28
this level of indexation has signi?cant adverse e?ects if a positive shock realizes. In
this case, households must pay a signi?cantly higher interest rate over and above
the risk-free rate. Although the constrained economy is not vulnerable to a Sudden
Stop when there is a positive endowment shock, agents in such an economy face a
Sudden Stop due to a sudden jump in debt servicing costs.
Hence, our analysis suggests that household face a tradeo? when they engage
in debt contracts with high degrees of indexation. If the households are hit by
a negative endowment shock, highly indexed bonds can allow them to absorb the
shock without su?ering severely in terms of consumption. Such a shock might
trigger a Sudden Stop if households were to borrow instead via non-indexed bonds
(the initial e?ects are closest to the frictionless case when the degree of indexation
is one). However, if they receive a positive endowment shock, the initial e?ects
are larger in the indexed economy (where the degree of indexation equals 1) than
in the constrained economy (e.g., the impact on tradable consumption jumps from
-1.1% to -6.7%). Analyzing the results in columns 3-9, we conclude that degrees
of indexation in the [0.45, 1.0] interval lead to stronger Sudden Stop e?ects. If we
take the average of initial responses across the high and the low states in this range
of values, we ?nd that the minimum of these averages is attained when the degree
of indexation is 0.25, which suggests that households with concave utility functions
would attain a higher utility with this consumption pro?le than ones achieved with
indexation levels higher than 0.25.
In Figure 1.8, we plot the time series simulations of the frictionless, con-
strained, and indexed economies. These simulations are derived ?rst by generating
29
a random exogenous endowment shock process using the transition matrix, P, and
then by feeding these series into each of the respective economies. On the top left
graph, the dotted line is the tradable consumption series for the frictionless econ-
omy. The solid line is the series for the constrained economy. As the graphs reveal,
although patterns of consumption in each economy mostly move together, there are
cases (around periods 2000, 3600, 6500, 8800), where we observe sharp declines in
constrained economy. These declines correspond to Sudden Stop episodes. In these
cases, a consecutive series of negative endowment shocks make the constraint bind-
ing, which in turn triggers a debt-de?ation that ultimately leads to a collapse in
consumption.
When the return is indexed and the degree of indexation is 0.05 (top right
graph), the volatility of consumption is noticeably lower than in the constrained
case, and collapses in consumption during Sudden Stop episodes are milder. When
we increase the degree of indexation to 0.45, however, there is a signi?cant increase
in the volatility of consumption, and there are more frequent collapses. When the de-
gree of indexation is 1.0 (due to space limitations, we leave out the ?gures associated
with other degrees of indexation), we observe a spike in volatility and much more
frequent and sizeable collapses in consumption. These simulations illustrate that
when indexation is full, the e?ect on consumption can be signi?cantly negative, fur-
thermore that indexation can yield bene?ts in terms of consumption volatility only
if the degree of indexation is quite low.
Table 1.8 suggests that in addition to the tradeo? of gains in the low state
versus losses in the high state, there is also a short run versus long run tradeo?
30
with respect to issuing indexed bonds with high degrees of indexation. With higher
indexation levels, indexed bonds can generate substantial short-run bene?ts, but also
introduce more severe adverse e?ects in the long run; i.e., consumption volatility and
its co-movement with income increase with greater degrees of indexation. Consistent
with our ?ndings in the frictionless one-sector model, the value of indexation that
minimizes the co-movement of consumption with GDP and yields more persistent
consumption is low (in the range of [0.05, 0.1] for this calibration). These results
also suggest that, depending on the objectives, the optimal degree of indexation level
may vary. As we illustrated before, the level of indexation that would minimize the
e?ect of Sudden Stops is in the [0.25, 0.45] interval, whereas the one that minimizes
long-run ?uctuations is in the [0.05, 0.1] range. However, regardless of whether
we would like to smooth Sudden Stops or long-run ?uctuations, full-indexation is
undesirable.
1.3.3 Sensitivity Analysis
This section presents the results of analysis aimed at evaluating the robustness
of our results to several variations in model parameterization. Due to space limita-
tions, for the ?rst three sensitivity analysis we present result of the the frictionless
one-sector model. These results are summarized in Table 1.10.
We ?rst analyze the robustness of the results to changes in the number of
exogenous state variables. For this analysis, we use a seven-state Markov chain
that maintains the same autocorrelation and standard deviation of the shock as in
31
the previous setup. Note that the simple persistence rule can be employed only if
the number of exogenous state variables is two. In order to create the transition
matrix with seven exogenous states, we employ the method described in Tauchen
and Hussey (1991). The ?rst block in Table 1.10 presents key long-run statistics,
which are nearly identical to the ones presented in Table 1.5; in fact, for a given
indexation level, the statistics are the same out to two decimal points. Hence, we
conclude that our results are robust to the number of state variables used in the
Markov process.
Second, we increase the standard deviation of the exogenous endowment shock
to 4.5%. As Table 1.10 suggests, when bonds are not indexed, the precautionary
savings motive is stronger, consumption is more volatile, and consumption displays
greater correlation with income when we increase variation in the magnitude of
the exogenous endowment shock. Comparing Table 1.10 with Table 1.5 for the
indexed case, we conclude that the optimal indexation level that minimizes long-run
macroeconomic ?uctuations is in the [0.05, 0.1] interval in the former case, whereas
it is in the [0.1, 0.25] interval in the latter one. In other words, the optimal degree
of indexation decreases with increases in the volatility of the exogenous endowment
shock.
Next, we evaluate the changes in results that arise when we lower the autocor-
relation of the endowment shock. Compared to the baseline results given in Table
1.5, with an endowment shock autocorrelation of 0.4, agents engage in less pre-
cautionary savings. Furthermore, consumption volatility and its co-movement with
income are lower. When indexed bonds are in place, the lower the persistence of the
32
shock, the higher the degree of indexation that would minimize the co-movement of
consumption with income. For instance, when the indexation is 0.1, the correlation
of consumption with income is 0.07 when the autocorrelation of the shock is 0.4.
By comparison, at the same indexation level, the correlation of consumption with
income is 0.017 when the autocorrelation is 0.524.
As a ?nal robustness check, we examine the e?ect of having a larger non-
tradables sector. The results are summarized in Table 1.11. We set the y
N
/y
T
ratio
to 1.6, which implies that the degree of openness of the country is lower than in
the baseline case. Not surprisingly, the model in this case captures the empirical
regularities of an economy with less ?nancial integration. In particular, consump-
tion is more volatile than in the baseline case (for instance, the volatility of the
tradables consumption in the frictionless economy increases to 1.6%, compared to
the baseline value of 1.5%), and the co-movement of consumption with income is
stronger (the correlation of tradables consumption with income in the frictionless
economy increases to 0.75 from the baseline value of 0.69). When we compare the
initial responses of each of these economies to a one-standard-deviation endowment
shock, the response of the constrained economy with a higher share of non-tradable
output is stronger than that of the one with baseline parameters, which suggests
that the debt-de?ation process is more severe in the former economy. This result
is consistent with the empirical evidence on the relationship between the degree of
openness and the severity of Sudden Stops (see Calvo et al. (2003)). In order to
compare the optimal indexation levels across di?erent parameterizations, we com-
pare the average responses of these economies in the high and the low states to a
33
one-standard-deviation endowment shock. These results suggest that the minimum
average response is attained when the degree of indexation is 0.25, which is the
same degree of indexation in the baseline results. However, this result depends on
the coarseness of the indexation intervals with which we are solving the problem.
Economic intuition suggests that lower ?nancial integration would require higher
indexation levels to smooth exogenous shocks better.
The sensitivity analysis presented in this section suggests that the optimal
indexation level depends on the properties of the exogenous shock, including its
persistence and its volatility. Hence, the optimal degree of indexation needs to
be country speci?c, since it is highly likely that each emerging country receives
shocks with di?erent statistical properties.The ?ndings of this chapter suggest that
while indexed bonds might aid many countries in averting or at least mitigating the
e?ects of Sudden Stops in emerging markets, an indexation level appropriate for one
country might not be optimal for another.
1.4 Conclusion
Recent policy proposals argue that indexing the debt of emerging markets
could help prevent the sudden reversals of capital in?ows accompanied by real ex-
change rate devaluations that were typical of the emerging market crises of the
last decade. This chapter explores the quantitative implications of this policy in a
DSGE model. Debt is denominated in units of tradables, and international lenders
impose a borrowing constraint that limits debt to a fraction of national income. The
34
benchmark model with non-indexed bonds and credit constraints features Sudden
Stops as an equilibrium outcome that results from a debt-de?ation process, the feed-
back mechanism between liability dollarization and the borrowing constraint that
operates through the relative price of non-tradables.
We conducted our quantitative experiments to evaluate the e?ects of indexed
bonds in two steps. First, we studied the e?ects of bonds indexed to output in a
canonical one-sector small open economy model with varying degrees of indexation.
We found that the introduction of indexed bonds partially completes the insurance
market in such an economy, and whether they help to reduce precautionary savings,
the volatility of consumption, and the correlation of consumption with income de-
pends on the degree of indexation of the bond. When this degree is higher than a
critical threshold (as with the full indexation for example), indexation can, in fact,
make agents worse o?. Because increase in the variance of trade balance (due to
higher interest rate ?uctuations) outweighed the improvement in the covariance of
trade balance with income, which then led to higher volatility of consumption; and
natural debt limits became tighter, which then led to an increase in precautionary
savings.
In the second step, we analyzed the role of indexed bonds in smoothing Sud-
den Stops and RER ?uctuations. We found that indexed bonds can reduce the
initial capital out?ow in the event of an exogenous shock that otherwise trigger a
Sudden Stop in an economy with only non-indexed bonds. Indexed bonds can in
turn reduce the depreciation in the RER and break the Fisherian debt-de?ation
mechanism. However, once again, the bene?t of these bonds depends critically on
35
the degree of indexation. When the level of indexation is lower than a critical value,
indexed bonds weaken Sudden Stops. If indexation is higher than this critical value,
although indexed bonds can provide some temporary relief in the event of a negative
shock, the initial improvement is short lived. Moreover, in the event of a positive
shock, the economy is vulnerable to a Sudden Stop even though such a shock would
never trigger a Sudden Stop in an economy in which household facing borrowing
constraints can only issue non-indexed bonds. Because in this case, positive shock
commands higher repayment, which increases the need for larger borrowing, this in
turn can make the borrowing constraint suddenly binding, and triggering a debt-
de?ation.
To conclude, bonds on which the return is indexed in a one-to-one fashion (i.e.,
full-indexation) will not necessarily provide bene?ts to emerging countries. However,
indexed bonds with optimal degree of indexation can help these countries smooth
Sudden Stops. This optimal value depends on the persistence and the volatility
of the exogenous shocks a given country experiences, as well as the size of the
country’s non-tradables sector relative to the its tradables sector (i.e., the openness
of the country). Hence, in terms of policy implications, our analysis reveals that the
degree of indexation is a key variable that should optimally be chosen in order to
smooth Sudden Stops, and furthermore that this value should be country speci?c.
In our analysis, we assumed that investors are risk-neutral and that indexing
debt repayments would not require them to obtain more country speci?c informa-
tion. It may be the case that indexed returns may a?ect investors’ incentives to col-
lect more country speci?c information. The implications of introducing risk-averse
36
investors or informational costs in a dynamic setup are left for future research. The
model can also be used to explore the implications of indexation to relative price of
non-tradables, or to CPI, but it is left for further research. Analyzing if trading in
option or futures markets can help emerging countries for mitigating Sudden Stops
is an avenue of research. This would require a richer model, and it is left for further
research, as well. Another avenue for future research could be analyzing the im-
plications of indexed bonds on default probabilities. In order to carry out such an
analysis, indexed bonds could be introduced into “willingness to pay” models such
as those of Eaton and Gersovitz (1980) and Arellano (2004).
37
Table 1.3: Previous Attempts of Indexed Bonds
Date Issued Indexation Clause Note
Argentina 1972-1989 CPI
Australia 1985-1988 CPI
Bosnia and
1990s GDP Issued as part of Brady Plan, VRRs
Herzegovina
Brazil 1964- CPI
Bulgaria 1990s GDP Issued as part of Brady Plan, VRRs
Colombia 1967- CPI
Costa Rica 1990s GDP Issued as part of Brady Plan, VRRs
Chile 1956- CPI
Israel 1955- CPI
France 1973 Gold
Debt servicing cost increased signi?cantly
due to depreciation of French Franc against gold
Mexico
1970s Oil Petro-bonos
1990s Oil Issued as part of Brady Plan, VRRs
1989- CPI
Turkey 1994- CPI
UK 1975- CPI
Venezuela 1990s Oil Issued as part of Brady Plan, VRRs
Sources: Borensztein and Mauro (2004), Campell and Shiller (1996), Kopcke and Kimball(1999),
Atta-Mensah (2004).
38
Table 1.4: Business Cycle Facts for Emerging Countries
Variable:x ?(x) ?(x)/?(Y ) ?(x) ?(x, Y ) Sudden Stop
Sudden Stop
relative to std.
Argentina 2002:1-2
GDP (Y) 4.022 1.000 0.865 1.000 -12.952 3.220
tradables GDP 4.560 1.134 0.667 0.923 -15.100 3.311
nontradables GDP 3.977 0.989 0.894 0.990 -12.169 3.060
consumption 4.475 1.113 0.830 0.975 -17.063 3.813
real exchange rate 15.189 3.777 0.754 0.454 -48.177 3.172
CA/Y 0.916 0.228 0.837 -0.802 1.353 1.476
Chile 1998:4-1999:1
GDP (Y) 2.093 1.000 0.731 1.000 -4.492 2.147
tradables GDP 1.833 0.876 0.473 0.762 -5.068 2.764
nontradables GDP 2.520 1.204 0.796 0.961 -4.840 1.921
consumption 4.184 1.999 0.748 0.898 -8.410 2.010
real exchange rate 0.007 0.003 0.649 0.372 -0.019 2.578
CA/Y 3.302 1.578 0.352 -0.512 10.932 3.311
Mexico 1994:4-1995:1
GDP (Y) 2.261 1.000 0.799 1.000 -7.440 3.290
tradables GDP 2.682 1.186 0.712 0.921 -8.976 3.347
nontradables GDP 2.189 0.968 0.832 0.978 -6.178 2.822
consumption 4.222 1.867 0.841 0.973 -11.200 2.653
real exchange rate 8.627 3.816 0.726 0.599 -32.844 3.807
CA/Y 0.698 0.309 0.831 -0.475 2.220 3.180
Turkey 1994:1-2
GDP (Y) 3.695 1.000 0.667 1.000 -10.383 2.001
tradables GDP 3.511 0.950 0.524 0.962 -10.925 3.112
nontradables GDP 4.021 1.088 0.680 0.982 -10.007 2.489
consumption 4.134 1.119 0.746 0.919 -10.098 2.443
real exchange rate 9.110 2.465 0.675 0.602 -31.630 3.472
CA/Y 2.744 0.743 0.633 -0.591 9.704 3.375
Source: Argentinean Ministry of Finance (MECON), Bank of Chile, Bank of Mexico, Central
Bank of Turkey, International Financial Statistics. The data cover periods 1993:Q1-2004:Q4 for
Argentina, 1986:Q1-2001:Q3 for Chile, 1987:Q1-2004:Q4 for Mexico, 1987:Q1-2004:Q4 for Turkey.
Data are quarterly seasonally adjusted real series. GDP and consumption data are logged and
?ltered using an HP ?lter with a smoothing parameter 1600. Real exchange rates are calculated
using the IMF de?nition (RER
i
= NER
i
×CPI
i
/CPI
US
for country i).
39
Table 1.5: Long Run Business Cycle Statistics of the One-Sector Model
Degree of Indexation (?)
0.00 0.015 0.02 0.05 0.10 0.25 0.45 0.70 1.0
E(b) -0.328 -0.349 -0.355 -0.385 -0.428 -0.042 0.522 1.458 2.026
?(cons) 1.243 1.242 1.240 1.236 1.209 1.474 2.119 3.291 4.731
?(tb/y) 3.486 3.516 3.527 3.590 3.674 4.211 4.820 5.724 6.755
?(cons, y) 0.186 0.160 0.151 0.097 0.017 -0.311 -0.409 -0.381 -0.304
?(tb/y, y) 0.936 0.937 0.937 0.939 0.945 0.943 0.916 0.849 0.752
?(cons) 0.978 0.980 0.980 0.981 0.984 0.909 0.870 0.876 0.886
?(tb/y) 0.549 0.549 0.548 0.546 0.541 0.542 0.562 0.601 0.646
welfare n.a. 0.0025 0.0034 0.0090 0.0146 -0.0032 -0.0092 -0.0120 -0.0136
Note: Standard deviations are in percent of the mean. Welfare gains are in percent and relative
to the non-indexed model.
Table 1.6: Returns and Natural Debt Limits
Degree of Indexation (?)
0.00 0.01 0.015 0.05 0.10 0.25 0.45 0.70 1.0
R
i
(L) 1.016 1.016 1.015 1.014 1.012 1.007 1.000 0.991 0.981
R
i
(H) 1.016 1.016 1.016 1.018 1.019 1.025 1.032 1.040 1.051
NDL(L) -61.487 -62.182 -62.894 -68.503 -78.431 -138.754 5440.508 106.131 48.760
NDL(H) -64.517 -63.819 -63.136 -58.642 -53.262 -41.767 -32.434 -25.353 -20.089
Note: First two rows are the corresponding gross returns in each states. In the last two rows, the
implied natural debt limits are printed bolder.
Table 1.7: Variance Decomposition Analysis for Consumption
Degree of Indexation (?)
0.00 0.015 0.02 0.05 0.10 0.25 0.45 0.70 1.0
?(cons) 1.243 1.242 1.240 1.236 1.209 1.474 2.119 3.291 4.731
var(tb) 12.241 12.463 12.540 13.008 13.638 17.707 22.903 31.959 44.788
cov(tb, y) 11.508 11.620 11.660 11.897 12.248 13.929 15.365 16.724 17.364
var(tb)
-10.775 -10.777 -10.781 -10.792 -10.857 -10.147 -7.827 -1.488 10.061
?2cov(tb, y)
40
Table 1.8: Long Run Business Cycle Statistics of the Two-Sector Model
Degree of Indexation (?)
F C 0.05 0.10 0.25 0.45 0.70 1.0
E(b) -0.299 0.244 0.122 0.276 0.594 1.599 2.328 2.516
?(c
T
) 1.530 1.268 1.251 1.389 1.851 2.835 3.914 5.266
?(c) 0.775 0.638 0.631 0.697 0.923 1.392 1.889 2.508
?(p
N
) 2.026 1.682 1.660 1.845 2.467 3.804 5.291 7.162
?(tb/y) 1.534 1.467 1.491 1.610 1.799 2.113 2.398 2.755
?(c
T
, y) 0.687 0.663 0.636 0.567 0.609 0.773 0.875 0.930
?(c, y) 0.687 0.664 0.637 0.567 0.608 0.770 0.870 0.924
?(p
N
, y) 0.687 0.663 0.636 0.567 0.609 0.774 0.877 0.933
?(tb/y, y) 0.512 0.648 0.646 0.548 0.290 -0.141 -0.404 -0.580
?(c
T
) 0.986 0.971 0.976 0.967 0.953 0.926 0.911 0.907
?(c) 0.986 0.971 0.976 0.967 0.953 0.925 0.909 0.903
?(p
N
) 0.986 0.971 0.976 0.967 0.953 0.927 0.912 0.909
?(tb/y) 0.581 0.546 0.540 0.546 0.572 0.609 0.631 0.661
Note: The ?rst column is the frictionless economy, the second column is the constrained economy,
and the rest of the columns are for the economy with borrowing constraint and indexed bonds
(with given degrees of indexation). Standard Deviations are in percent.
Table 1.9: Initial Responses to a One-Standard-Deviation Endowment Shock
Non-Indexed Degree of Indexation (?)
F C 0.05 0.10 0.25 0.45 0.70 1.0
A) Negative Shock
tradable consumption -0.907 -4.126 -4.007 -3.888 -3.531 -3.056 -1.657 -1.748
aggregate consumption -0.384 -1.780 -1.728 -1.676 -1.520 -1.312 -0.706 -0.745
relative price of non-tradables -1.197 -5.398 -5.244 -5.090 -4.626 -4.007 -2.179 -2.299
B) Positive Shock
tradable consumption -0.291 -1.095 -2.019 -2.138 -2.494 -2.970 -4.369 -6.691
aggregate consumption -0.120 -0.464 -0.862 -0.913 -1.068 -1.275 -1.887 -2.919
relative price of non-tradables -0.387 -1.444 -2.653 -2.808 -3.274 -3.895 -5.714 -8.716
Note: The ?rst column is the frictionless economy, the second column is the constrained economy,
and the rest of the columns are for the economy with borrowing constraint and indexed bonds (with
given degrees of indexation). Initial responses are calculated as percentage deviations relative to
the long-run mean of the frictionless economy.
41
Table 1.10: Sensitivity Analysis of the One-Sector Model
Degree of Indexation (?)
0.00 0.015 0.02 0.05 0.10 0.25 0.45 0.70 1.0
I. seven-state markov chain
E(b) -0.320 -0.345 -0.351 -0.369 -0.371 -0.083 0.548 1.459 1.968
?(cons) 1.246 1.245 1.244 1.243 1.258 1.487 2.147 3.319 4.776
?(cons, y) 0.182 0.154 0.144 0.079 0.031 -0.301 -0.410 -0.378 -0.293
?(cons) 0.970 0.971 0.971 0.974 0.982 0.906 0.869 0.870 0.869
II. ?
?
=0.045
E(b) -0.315 -0.335 -0.343 -0.359 -0.295 -0.017 0.908 1.741 2.064
?(cons) 1.567 1.566 1.566 1.560 1.576 1.919 2.899 4.372 6.226
?(cons, y) 0.208 0.173 0.160 0.085 -0.046 -0.270 -0.357 -0.307 -0.230
?(cons) 0.983 0.987 0.988 0.991 0.974 0.927 0.892 0.893 0.898
III. ?
?
=0.4
E(b) -0.335 -0.357 -0.361 -0.398 -0.477 -0.300 0.180 0.918 1.637
?(cons) 1.074 1.069 1.068 1.060 1.034 1.202 1.462 2.229 3.351
?(cons, y) 0.178 0.157 0.152 0.112 0.070 -0.167 -0.361 -0.367 -0.301
?(cons) 0.966 0.968 0.969 0.970 0.975 0.944 0.865 0.865 0.885
Note: Resulting transition matrix for seven-state markov chain is approximated using the method
described in Tauchen and Hussey (1991). Standard deviations are in percent.
42
Table 1.11: Sensitivity Analysis of the Two-Sector Model: Higher Share of Non-
tradable Output
Degree of Indexation (?)
F C 0.05 0.10 0.25 0.45 0.70 1.0
I. Long run statistics
E(b) -0.290 0.258 0.084 0.682 0.667 1.739 2.399 2.551
?(c
T
) 1.590 1.306 1.261 1.639 1.957 2.919 3.956 5.300
?(c) 0.822 0.671 0.649 0.836 0.994 1.457 1.941 2.565
?(p
N
) 2.105 1.734 1.672 2.182 2.609 3.920 5.351 7.211
?(c
T
, y) 0.749 0.716 0.691 0.664 0.714 0.844 0.913 0.951
?(c, y) 0.750 0.718 0.692 0.664 0.713 0.841 0.908 0.945
?(p
N
, y) 0.749 0.716 0.691 0.664 0.714 0.845 0.915 0.953
?(c
T
) 0.987 0.975 0.975 0.973 0.956 0.931 0.914 0.909
?(c) 0.987 0.976 0.976 0.974 0.956 0.930 0.911 0.905
?(p
N
) 0.987 0.975 0.975 0.973 0.957 0.932 0.915 0.911
II. Initial Responses
A)Negative Shock
tradable consumption -1.036 -4.254 -4.122 -3.991 -3.596 -3.070 -1.608 -1.623
aggregate consumption -0.395 -1.655 -1.603 -1.551 -1.395 -1.187 -0.616 -0.622
relative price of non-tradables -1.366 -5.565 -5.395 -5.224 -4.711 -4.025 -2.115 -2.135
B)Positive Shock
tradable consumption -0.420 -2.029 -2.156 -2.292 -2.686 -3.213 -4.675 -7.074
aggregate consumption -0.157 -0.780 -0.818 -0.883 -1.037 -1.244 -1.823 -2.788
relative price of non-tradables -0.557 -2.666 -2.985 -3.010 -3.525 -4.211 -6.111 -9.208
Notes: y
N
/y
T
ratio is set to 1.6 in this analysis. Standard deviations are in percent of the mean.
The ?rst column is the frictionless economy, the second column is the constrained economy, and
the rest of the columns are for the economy with borrowing constraint and indexed bonds (with
given degrees of indexation).
43
Figure 1.1: Sudden Stops in Emerging Markets
a. Current Account-GDP Ratio
b. Real Exchange Rate
-2
-1
0
1
2
3
93 94 95 96 97 98 99 00 01 02
Argentina
-12
-10
-8
-6
-4
-2
0
2
4
90 91 92 93 94 95 96 97 98 99 00 01
Chile
-3
-2
-1
0
1
2
88 90 92 94 96 98 00 02 04
Mexico
-8
-6
-4
-2
0
2
4
6
88 90 92 94 96 98 00 02 04
Turkey
20
40
60
80
100
120
93 94 95 96 97 98 99 00 01 02
Argentina
90
100
110
120
130
140
150
93 94 95 96 97 98 99 00 01 02
Chile
100
120
140
160
180
200
93 94 95 96 97 98 99 00 01 02
Mexico
80
90
100
110
120
130
140
93 94 95 96 97 98 99 00 01 02
Turkey
44
Figure 1.2: Deviations from Trend in Consumption and Ouput
a. Consumption
b. Output
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
93 94 95 96 97 98 99 00 01 02
Argentina
-0.10
-0.05
0.00
0.05
0.10
0.15
86 88 90 92 94 96 98 00
Chile
-0.15
-0.10
-0.05
0.00
0.05
0.10
88 90 92 94 96 98 00 02 04
Mexico
-0.15
-0.10
-0.05
0.00
0.05
0.10
88 90 92 94 96 98 00 02 04
Turkey
-0.15
-0.10
-0.05
0.00
0.05
0.10
93 94 95 96 97 98 99 00 01 02
Argentina
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
86 88 90 92 94 96 98 00
Chile
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
88 90 92 94 96 98 00 02 04
Mexico
-0.15
-0.10
-0.05
0.00
0.05
0.10
88 90 92 94 96 98 00 02 04
Turkey
45
Figure 1.3: Long Run Distributions of Bond Holdings in Non-Indexed Economies
?2 ?1 0 1 2 3 4
0
1
2
3
4
5
6
7
x 10
?3
Bond Holdings
Frictionless Economy
Costrained Economy
46
Figure 1.4: Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock
0 5 10 15 20 25 30 35 40
?1.8
?1.6
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
Aggregate Consumption
frictionless
constrained
0 5 10 15 20 25 30 35 40
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
Tradable Consumption
frictionless
constrained
0 5 10 15 20 25 30 35 40
?1.5
?1
?0.5
0
0.5
1
CAY Ratio
frictionless
constrained
0 5 10 15 20 25 30 35 40
?5.5
?5
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
Relative Price of NT
frictionless
constrained
Note: Forecasting functions are conditional on the 229th grid point of the bond holdings, which
implies a debt-to-GDP ratio of 30%. Solid and dashed lines are forecasting functions of the
frictionless, and constrained economies, respectively.
47
Figure 1.5: Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock
0 5 10 15 20 25 30 35 40
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
Aggregate Consumption
constrained
indexed, 0.05
indexed, 0.10
0 5 10 15 20 25 30 35 40
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Tradable Consumption
constrained
indexed, 0.05
indexed, 0.10
0 5 10 15 20 25 30 35 40
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
CAY Ratio
constrained
indexed, 0.05
indexed, 0.10
0 5 10 15 20 25 30 35 40
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Relative Price of NT
constrained
indexed, 0.05
indexed, 0.10
Note: Forecasting functions are conditional on the 229th grid point of the bond holdings, which
implies a debt-to-GDP ratio of 30%.
48
Figure 1.6: Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock
0 5 10 15 20 25 30 35 40
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
Aggregate Consumption
constrained
indexed, 0.25
indexed, 0.45
0 5 10 15 20 25 30 35 40
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Tradable Consumption
constrained
indexed, 0.25
indexed, 0.45
0 5 10 15 20 25 30 35 40
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
CAY Ratio
constrained
indexed, 0.25
indexed, 0.45
0 5 10 15 20 25 30 35 40
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Relative Price of NT
constrained
indexed, 0.25
indexed, 0.45
Note: Forecasting functions are conditional on the 229th grid point of the bond holdings, which
implies a debt-to-GDP ratio of 30%.
49
Figure 1.7: Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock
0 5 10 15 20 25 30 35 40
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
Aggregate Consumption
constrained
indexed, 0.7
indexed, 1.0
0 5 10 15 20 25 30 35 40
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Tradable Consumption
constrained
indexed, 0.7
indexed, 1.0
0 5 10 15 20 25 30 35 40
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
CAY Ratio
constrained
indexed, 0.7
indexed, 1.0
0 5 10 15 20 25 30 35 40
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Relative Price of NT
constrained
indexed, 0.7
indexed, 1.0
Note: Forecasting functions are conditional on the 229th grid point of the bond holdings, which
implies a debt-to-GDP ratio of 30%.
50
Figure 1.8: Time Series Simulation
1000 2000 3000 4000 5000 6000 7000 8000 9000
?10
?8
?6
?4
?2
0
2
4
6
8
10
Tradable consumption
frictionless
constrained
1000 2000 3000 4000 5000 6000 7000 8000 9000
?10
?8
?6
?4
?2
0
2
4
6
8
10
Tradable consumption
constrained
indexed,0.05
1000 2000 3000 4000 5000 6000 7000 8000 9000
?10
?8
?6
?4
?2
0
2
4
6
8
10
Tradable consumption
constrained
indexed,0.45
1000 2000 3000 4000 5000 6000 7000 8000 9000
?10
?8
?6
?4
?2
0
2
4
6
8
10
Tradable consumption
constrained
indexed,1.0
Note: Consumptions are in percentage deviations from their corresponding means. The ?rst
1,000 periods have been excluded from these graphs to focus on the data which are independent
of initial conditions.
51
Chapter 2
Are Asset Price Guarantees Useful for Preventing Sudden Stops?: A
Quantitative Investigation of the Globalization Hazard-Moral
Hazard Tradeo? (coauthored with Enrique G. Mendoza)
2.1 Introduction
The Sudden Stop phenomenon of emerging markets crises is characterized by
three stylized facts: sudden reversals of capital in?ows and current account de?cits,
collapses in output and private absorption, and large relative price corrections in
domestic goods prices and asset prices. A large fraction of the literature on this
subject is based on a hypothesis that Calvo (2002) labeled ”globalization hazard.”
According to this hypothesis, world capital markets are inherently imperfect, and
hence prone to display contagion and overreaction in asset positions and prices rel-
ative to levels consistent with ”fundamentals” (see Arellano and Mendoza (2003)
for a short survey of this literature). This argument suggests that an international
?nancial organization (IFO) could help prevent Sudden Stops by o?ering global
investors ex-ante price guarantees on the emerging-markets asset class. Calvo pro-
posed an arrangement for implementing this policy and compared it with other
arrangements that favor ex-post guarantees (including the IMF’s Contingent Credit
Line and Lerrick and Meltzer’s (2003) proposal).
Ex-ante price guarantees aim to create an environment in which asset prices
can be credibly expected to remain above the crash levels that trigger Sudden Stops
52
driven by globalization hazard. Calvo views this facility as akin to an open-markets
operation facility: it would exchange a liquid, riskless asset (e.g., U.S. T-bills) for an
index of emerging markets assets whenever the value of the index falls by a certain
amount, and would re-purchase the riskless asset when the index recovers. Market
participants would consider in their expectations that these guarantees would be
executed if a systemic ?re sale makes asset prices crash, and hence the guarantees
could rule out rational expectations equilibria in which Sudden Stops occur. If
globalization hazard is the only cause of Sudden Stops, and if the support of the
probability distribution of the shocks that causes them is known (i.e., if there are
no truly “unexpected” shocks), the facility would rarely trade.
A potentially important drawback of ex-ante price guarantees is that they in-
troduce moral hazard incentives for global investors. Everything else the same, the
introduction of the guarantees increases the foreign investors’ demand for emerg-
ing markets assets, since the downside risk of holding these assets is transferred
to the IFO providing the guarantees. This can be a serious drawback because a
similar international moral hazard argument has been forcefully put forward as an
alternative explanation of Sudden Stops (see the Meltzer Commission report and
Lerrick and Meltzer (2003)).
1
Proponents of this view argue that Sudden Stops are
induced by excessive indebtedness of emerging economies driven by the expectation
of global investors that IFOs will bail out countries in ?nancial di?culties. Based
1
Part of the literature on Sudden Stops focuses on domestic moral hazard problems caused
by government guarantees o?ered to domestic agents (see, for example, Krugman (2000)). This
chapter focuses instead on Sudden Stops triggered by globalization hazard, and on the tradeo?
between this hazard and the international moral hazard created by o?ering price guarantees to
global investors.
53
on this premise, Lerrick and Meltzer proposed the use of ex-post price guarantees to
be o?ered by an IFO to anchor the orderly resolution of a default once it has been
announced and agreed to with the IFO. The IFO would determine the crash price
of the asset in default and would require the country to commit to re-purchase the
asset at its crash price (making the arrangement credible by committing the IFO
to buy the asset at a negligible discount below the crash price if the country were
unable to buy it).
The tensions between the globalization hazard and moral hazard hypothe-
ses, and their alternative proposals for using price guarantees, re?ect an important
tradeo? that ex-ante price guarantees create. On one hand, ex-ante price guaran-
tees could endow IFOs with an e?ective tool to prevent and manage Sudden Stops
driven by globalization hazard. On the other hand, ex-ante guarantees could end up
making matters worse by strengthening international moral hazard (even if it were
true that globalization hazard was the only cause of Sudden Stops in the past).
The goal of this chapter is to study the globalization hazard-moral hazard
tradeo? from the perspective of the quantitative predictions of a dynamic, stochastic
general equilibrium model of asset pricing and current account dynamics. The model
is based on the globalization hazard setup of Mendoza and Smith (2004). This
chapter adds to their framework an IFO that o?ers ex-ante guarantees to foreign
investors on the asset prices of an emerging economy. We are interested in particular
in studying how the guarantees a?ect asset positions, asset price volatility, business
cycle dynamics, and the magnitude of Sudden Stops.
Asset price guarantees have not received much attention in quantitative equi-
54
librium asset pricing theory, with the notable exception of the work by Ljungqvist
(2000), and these guarantees have yet to be introduced into the research program
dealing with quantitative models of Sudden Stops. The theoretical literature and
several policy documents on Sudden Stops have examined various aspects of the
globalization hazard and international moral hazard hypotheses separately. From
this perspective, one contribution of this chapter is that it studies the interaction
between these two hypotheses in a uni?ed dynamic equilibrium framework.
The two ?nancial frictions that we borrow from Mendoza and Smith (2004)
to construct a model in which globalization hazard causes Sudden Stops are: (a) a
margin constraint on foreign borrowing faced by the agents of an emerging economy,
and (b) asset trading costs incurred by foreign securities ?rms specialized in trading
the equity of the emerging economy.
2
These frictions are intended to represent the
collateral constraints and informational frictions that have been widely studied in
the Sudden Stops literature (see, for example, Calvo (1998), Izquierdo (2000), Calvo
and Mendoza (2000a, 2000b), Caballero and Krishnamurty (2001), and Mendoza
(2004)).
The model introduces asset price guarantees in the form of ex-ante guarantees
o?ered to foreign investors on the liquidation price (or equivalently, on the return)
of the emerging economy’s assets. Thus, these guarantees are akin to a ”put option”
with minimum return. An IFO o?ers these guarantees and ?nances them with a
lump-sum tax on foreign investors’ pro?ts. Hence, forward-looking equity prices
2
These two frictions are modeled following the closed-economy analysis of Aiyagari and Gertler
(1999).
55
re?ect the e?ects of margin constraints, trading costs and ex-ante price guarantees.
The setup of the price guarantees is similar to the one proposed in Ljungqvist’s
(2000) closed-economy, representative-agent analysis, but framed in the context of
what is e?ectively a two-agent equilibrium asset-pricing model with frictions.
Price guarantees have di?erent implications depending on the level at which
they are set. If they are set so low that they are never executed, globalization
hazard dominates and the model yields the same Sudden Stop outcomes of the
Mendoza-Smith model. If they are set so high that they are always executed, the
model yields equilibria highly distorted by international moral hazard. Hence, the
interesting range for studying the globalization hazard-moral hazard tradeo? lies
between these two extremes. The quantitative analysis shows that guarantees set
slightly above the model’s “fundamentals” price (by 1/2 to 1 percent) contain the
Sudden Stop e?ects of globalization hazard and virtually eliminate the probability of
margin calls in the stochastic steady state. If the guarantee is non-state-contingent,
however, the guarantee is executed often (with a long-run probability of about 1/3)
and the model predicts persistent overvaluation of asset prices above the prices
obtained in a frictionless environment. A guaranteed price set at the same level but
o?ered only at high levels of external debt is executed much less often (with a long
run probability below 1/100) and it is equally e?ective at containing Sudden Stops
without inducing persistent asset overvaluation.
Analysis of the normative implications of the model shows that, when the
elasticity of foreign demand for domestic assets is high, the guarantees improve
domestic welfare measured from initial conditions at a Sudden Stop state, with
56
negligible changes in long-run welfare levels. At the same time, the value of foreign
traders’ ?rms measured in a Sudden Stop state falls slightly, while their long-run
average rises sharply. In this case the balance tilts in favor of using price guarantees
to contain globalization hazard. On the other hand, when the elasticity of foreign
demand for domestic assets is low, higher price guarantees are needed to prevent
Sudden Stops, and as a result large moral hazard distortions reduce domestic welfare
gains at Sudden Stop states and enlarge average welfare losses in the stochastic
steady state. In this case, price guarantees can be a misleading policy instrument
that yields a short-term improvement in macroeconomic indicators and welfare at
the expense of a long-term welfare loss.
The chapter is organized as follows. Section 2.2 presents the model and char-
acterizes the competitive equilibrium in the presence of margin constraints, trading
costs and ex-ante price guarantees. Section 2.3 studies key properties of this equi-
librium that illustrate the nature of the globalization hazard-moral hazard tradeo?.
Section 2.4 represents the model’s competitive equilibrium in a recursive form suit-
able for quantitative analysis and examines a set of baseline results. Section 2.5
conducts normative and sensitivity analyses. Section 2.6 concludes.
2.2 A Model of Globalization Hazard and Price Guarantees
Consider a small open economy (SOE) inhabited by a representative household
that rents out labor and a time-invariant stock of capital to a representative ?rm.
Households can trade the equity of this ?rm with a representative foreign securities
57
?rm specialized in trading the economy’s equity, and can also access a global credit
market of one-period bonds. In addition, an IFO operates a facility that guarantees
a minimum sale price to foreign traders on their sales of the emerging economy’s
equity. Dividend payments on the emerging economy’s equity are stochastic and
vary in response to exogenous productivity shocks. Markets of contingent claims are
incomplete because trading equity and bonds does not allow domestic households to
fully hedge domestic income uncertainty, and the credit market is imperfect because
of margin constraints and trading costs.
2.2.1 The Emerging Economy
The representative ?rm inside the SOE produces a tradable commodity by
combining labor
and a time-invariant stock of physical capital (k) using a Cobb-
Douglas technology: exp(?
t
)F(k, n), where ?
t
is a Markov productivity shock. This
?rm participates in competitive factor and goods markets taking the real wage (w)
as given. Thus, the choice of labor input consistent with pro?t maximization yields
standard marginal productivity conditions for labor demand and the rate of dividend
payments (d):
w
t
= exp(?
t
)F
n
(k, n
t
) (2.1)
d
t
= exp(?
t
)F
k
(k, n
t
) (2.2)
Households choose stochastic sequences of consumption (c), labor supply, equity
holdings (?), and foreign bond holdings (b) so as to maximize the following utility
58
function:
U(c, n) = E
0
_
?
t=0
exp
_
?
t?1
?=0
?(c
?
?h(n
?
))
_
u(c
t
?h(n
t
))
_
(2.3)
This utility function is a time-recursive, intertemporal utility index with an endoge-
nous rate of time preference that introduces an “impatience e?ect” on the marginal
utility of consumption (i.e., changes in ct alter the subjective discount rate applied
to future utility ?ows). Utility functions with this feature are commonly used in
small open economy models to obtain well-de?ned long-run equilibria for holdings of
foreign assets.
3
As Section 2.3 shows, in models with credit constraints these prefer-
ences are also critical for supporting long-run equilibria in which credit constraints
can bind.
The period utility function u(·) is a standard, concave, twice-continuously
di?erentiable utility function. The function ?(·) is the time preference function,
which is also concave and twice-continuously di?erentiable. The argument of both
functions is a composite good de?ned by consumption minus the disutility of labor
c ? h, where h(·) is an increasing, convex, continuously-di?erentiable function.
Greenwood, Hercowitz and Hu?man (1988), GHH, introduced this composite good
as a way to eliminate the wealth e?ect on labor supply. As in Mendoza and Smith
(2004), this property of preferences, together with conditions (2.1) and (2.2), sepa-
rates the determination of equilibrium wages, dividends, labor and output from the
equilibrium allocations of consumption, saving and portfolio choice.
3
See Arellano and Mendoza (2003) for further details on this issue.
59
The household maximizes lifetime utility subject to the following budget con-
straint:
c
t
= ?
t
kd
t
+w
t
n
t
+q
t
(?
t
??
t+1
)k ?b
t+1
+b
t
R (2.4)
where ?
t
and ?
t+1
are beginning- and end-of-period shares of capital owned
by households, q
t
is the price of equity, and R is the world real interest rate (which
is kept constant for simplicity).
Foreign debt contracts feature a collateral constraint in the form of a margin
clause that limits the debt not to exceed the fraction ? of the market value of the
SOE’s equity holdings:
b
t+1
? ??q
t
?
t+1
k, 0 ? ? ? 1 (2.5)
Margin clauses of this form are widely used in international capital markets. In
some instances they are imposed by regulators with the aim of limiting the exposure
of ?nancial intermediaries to idiosyncratic risk in lending portfolios, but they are
also widely used by investment banks and other lenders to manage default risk
(either in the form of explicit margin clauses attached to speci?c securities o?ered
as collateral, or as implicit margin requirements linked to the volatility of returns of
an asset class like those implied by value-at-risk collateralization). Margin clauses
are a particularly e?ective collateral constraint (compared to the classic constraint
of Kiyotaki and Moore (1997) that limits debt to the discounted liquidation value of
assets one period ahead) because: (a) custody of the securities o?ered as collateral
60
is surrendered at the time the credit contract is entered and (b) margin calls to
make up for shortfalls in the market value of the collateral are automatic once the
value of the securities falls below the contracted value.
Households in the small open economy also face a short-selling constraint in
the equity market: ?
t+1
? ? with ??< ? < 1 for all t. This constraint is necessary
in order to make the margin constraint non-trivial. Otherwise, any borrowing limit
in the bond market implied by a binding margin constraint could always be undone
by taking a su?ciently short equity position.
2.2.2 The Foreign Securities Firm, the IFO & the Price Guarantees
The representative foreign securities ?rm obtains funds from international in-
vestors and specializes in investing them in the SOE’s equity. This ?rm maximizes
its net present value discounted at the discount factor of its international clients
(i.e., the world interest rate). Thus, the foreign traders’ problem is to choose ?
?
t+1
,
for t = 1, ..., ?, so as to maximize:
D = E
0
_
?
t=0
R
?t
?
t
_
,
?
t
? k
_
?
?
t
d
t
?
_
q
t
?
?
t+1
?max(q
t
, ˜ q
t
)?
?
t
_
?q
t
_
a
2
_
_
?
?
t+1
??
?
t
+?
_
2
?T
?
t
_
.
(2.6)
The total net return of the foreign securities ?rm (?
t
) is the sum of: (a)
dividend earnings on current equity holdings (k?
?
t
d
t
), minus (b) the value of equity
trades, which is the di?erence between equity purchases q
t
k?
?
t+1
and equity sales
max(q
t
, ˜ q
t
)k?
?
t
executed at either the market price q
t
or the guaranteed price ˜ q
t
,
61
whichever is greater, minus (c) trading costs, which include a term that depends on
the size of trades (?
?
t+1
??
?
t
) and a recurrent trading cost (theta), minus (d) lump
sum taxes paid to the IFO (kT
?
t
). Trading costs are speci?ed in quadratic form, so
a is a standard adjustment-cost coe?cient.
The IFO buys equity from the foreign traders at the guaranteed price and sells
it at the equilibrium price. Thus, the IFO’s budget constraint is:
T
?
t
= max(0, (˜ q
t
?q
t
)?
?
t
) (2.7)
If the guarantee is not executed, the tax is zero. If the guarantee is executed, the
IFO sets the lump-sum tax to match the value of the executed guarantee (i.e., the
extra income that foreign traders earn by selling equity to the IFO instead of selling
it in the equity market). Since the return on equity is R
q
t
? [d
t
+q
t
] /q
t
? 1, the
IFO’s o?er to guarantee the date-t price implies a guaranteed return on the emerging
economy’s equity
˜
R
q
T
= [˜ q +d
t
]/q
t?1
.
2.2.3 Equilibrium
A competitive equilibrium is given by stochastic sequences of prices and allo-
cations such that: (a) households maximize the utility function (2.3) subject to the
constraints (2.4) and (2.5) and the short-selling constraint, taking prices, wages and
dividends as given, (b) domestic ?rms maximize pro?ts so that equations (2.1) and
(2.2) hold, taking wages and dividends as given, (c) foreign traders maximize (2.6)
taking the price of equity, the price guarantees and lump-sum taxes as given, (d)
62
the budget constraint of the IFO in equation (2.7), holds and (e) the equity market
clears (i.e., ?
t
+?
?
t
= 1 for all t).
2.3 Characterizing the Globalization Hazard-Moral Hazard Tradeo?
The tradeo? between the globalization hazard introduced by the distortions
that margin constraints and trading costs create and the moral hazard introduced by
distortions due to price guarantees can be illustrated with the optimality conditions
of the competitive equilibrium. Consider the ?rst-order conditions of the domestic
household’s maximization problem:
U
c
(c, n) = ?
t
(2.8)
h
(n
t
) = w
t
(2.9)
q
t
(?
t
??
t
?) = E
t
[?t + 1(d
t+1
+q
t+1
)] + ?
t
(2.10)
?
t
??
t
= E
t
[?
t+1
R] (2.11)
U
c
(c, n) is the derivative of the SCU function with respect to c
t
(which includes the
impatience e?ect), and ?
t
, ?
t
and ?
t
are the Lagrange multipliers on the budget
constraint, the margin constraint, and the short-selling constraint respectively.
Condition (2.8) has the standard interpretation: at equilibrium, the marginal
utility of wealth equals the lifetime marginal utility of consumption. Condition
(2.9) equates the marginal disutility of labor with the real wage. This is the case
because the GHH composite good implies that the marginal rate of substitution
63
between c
t
and n
t
is equal to the marginal disutility of labor h
(n
t
), and thus is
independent of c
t
. It follows from this result that condition (2.9) together with (2.1)
and (2.2) determine the equilibrium values of n
t
, w
t
and d
t
as well as the equilibrium
level of output. These “supply-side” solutions are independent of the dynamics of
consumption, saving, portfolio choices and equity prices, and are therefore also
independent of the distortions induced by ?nancial frictions and price guarantees.
This result simpli?es signi?cantly the numerical solution of the model. Mendoza
(2004) studies the implications of margin constraints in a small-open-economy model
with endogenous investment in which ?nancial frictions a?ect dividends, investment
and the Tobin Q, but abstracting from international equity trading.
Conditions (2.10) and (2.11) are Euler equations for the accumulation of equity
and bonds respectively. As in Mendoza and Smith (2004), these conditions can be
combined to derive expressions for the forward solution of equity prices and the
excess return on equity from the perspective of the emerging economy. The forward
solution for equity prices is:
q
t
= E
t
_
?
i=0
_
i
j=0
_
1 ?
?
j+1
?
j+1
?
_
?1
_
M
t+1+i
d
t+1+i
_
(2.12)
where M
t+1+i
? ?
t+1+i
/?
t
, for i = 0, ..., ?, is the marginal rate of substitution
between c
t+1+i
and c
t
. The excess return on domestic equity is:
E
t
_
R
q
t+1
¸
?R =
?
t
(1 ??) ?
?
t
q
t
?COV
t
(?
t+1
, R
q
t+1
)
E
t
[?
t+1
]
(2.13)
64
Given these results, the forward solution for equity prices can also be expressed as:
q
t
= E
t
_
?
i=0
_
i
j=0
_
R
q
t+1+j
_
?1
_
d
t+1+i
_
(2.14)
Expressions (2.12)-(3.14) show the direct and indirect e?ects of margin calls on
domestic demand for equity and excess returns. The direct e?ect of a date-t margin
call is represented by the term ?
t
(1??) in (2.13), or the term ?
t
? in (2.12): When a
margin call occurs, domestic agents “?re sale” equity in order to meet the call and
satisfy the borrowing constraint. Everything else the same, this e?ect lowers the
date-t equity price and increases the expected excess return for t+1. The indirect
e?ect of the margin call is re?ected in the fact that a binding borrowing limit makes
“more negative” the co-variance between the marginal utility of consumption and
the rate of return on equity (since a binding borrowing limit hampers the households’
ability to smooth consumption). These direct and indirect e?ects increase the rate
at which future dividends are discounted in the domestic agents’ valuation of asset
prices, and thus reduce their demand for equity. Interestingly, the date-t equity
price along the domestic agents’ demand curve is reduced by a margin constraint
that is binding at date t or by any expected binding margin constraint in the future.
As a result, equity prices and the domestic demand for equity can be distorted by
the margin requirements even in periods in which the constraint does not bind.
In a world with frictionless asset markets, domestic agents facing margin calls
could sell assets in a perfectly-competitive market in which the world demand for
the emerging economy’s assets is in?nitely elastic at the level of the fundamentals
65
price. Margin calls would trigger portfolio reallocation e?ects without any price
movements. However, in the presence of frictions that make the world demand for
the emerging economy’s assets less than in?nitely elastic, the equilibrium asset price
falls. Since households were already facing margin calls at the initial price, this price
decline tightens further the margin constraint triggering a new round of margin calls.
This downward spiral in equity prices is a variant of Fisher’s (1933) debt-de?ation
mechanism, which magni?es the direct and indirect e?ects of the margin constraint.
The foreign demand for the emerging economy’s assets is less than in?nitely
elastic because of the trading costs that foreign traders pay. De?ne the fundamentals
price as the conditional expected value of dividends discounted at the world interest
rate q
f
t
? E
t
_
?
i=0
R
?(t+1+i)
d
t+1+i
_
. The ?rst-order condition for the optimization
problem of foreign traders implies then:
_
?
?
t+1
??
?
t
_
=
1
a
_
q
f
t
q
t
?1 +
E
t
_
?
i=1
R
?(t+i)
(max(q
t+i
, ˜ q
t+i
) ?q
t+i
)
¸
q
t
_
?? (2.15)
The foreign traders’ demand for the emerging economy’s assets is an increas-
ing function of: (a) the percent deviation of qt f relative to qt (with an elasticity
equal to 1/a) and (b) the expected present discounted value of the “excess prices”
induced by the price guarantees in percent of today’s equity price. The ?rst e?ect
re?ects the in?uence of the per-trade trading costs. If a = 0 and there are no price
guarantees, the foreign traders’ demand function is in?nitely elastic at q
f
. The
second e?ect is the international moral hazard e?ect of the guarantees, which acts
as a demand shifter on the foreign traders’ demand function. Foreign traders that
66
expect price guarantees to be executed at any time in the future have a higher de-
mand for domestic assets at date t than they would in a market without guarantees.
The recurrent trading costs are also a demand shifter (the foreign traders’ demand
function is lower the higher is ? ).
In light of the previous results, the tradeo? between globalization hazard and
international moral hazard can be summarized as follows. Suppose the date-t as-
set price in a market without margin constraints and without price guarantees is
determined at the intersection of the domestic agents’ and foreign traders’ demand
curves (HH and FF respectively) at point A in Figure 2.1.
The demand function of foreign traders is simply equation (2.15), shown in
Figure 2.1 as a linear function for simplicity and as an upward sloping curve because
the horizontal axis measures ?, which is the complement of ?
?
. This FF curve is
relatively ?at to approximate a situation with low per-trade costs. There is no
closed-form solution for HH, so the curve depicted is intended only to facilitate
intuition. HH is shown as a downward-slopping curve but, since domestic agents
respond to wealth, intertemporal-substitution and portfolio-composition e?ects in
choosing their equity holdings, HH can be downward or upward slopping depending
on which e?ect dominates.
Suppose that a margin call hits domestic agents because an adverse shock
hits the economy when their debt is su?ciently high relative to the value of their
assets. As a result, HH shifts to HH
. In Figure 2.1, HH
represents the “?nal”
demand function, including the magni?cation e?ect of the Fisherian debt-de?ation
mechanism. Without price guarantees, the date-t equilibrium price would fall to
67
point B. This is the “Sudden Stop scenario,” in which margin calls result in lower
asset prices and reversals in consumption and the current account. Enter now an
IFO that sets a price guarantee higher than the market price at B. The international
moral hazard e?ect shifts the foreign traders’ demand curve to FF
and the new
date-t market price is determined at point C, which yields the fundamentals price.
The scenario depicted here is an ideal one in which the IFO is assumed to know
exactly at what level to set the guaranteed price so as to stabilize the market price
at the fundamentals level. In contrast, if the guarantee is set below the price at
B, it would have no e?ect on the Sudden Stop equilibrium price, and thus price
guarantees would be irrelevant. If the guarantee is set too high, it can lead to a
price higher than the fundamentals price (with the overpricing even larger than the
underpricing that occurs at B). Hence, ex-ante price guarantees do not necessarily
reduce the volatility of asset prices (as Ljungqvist’s (2000) ?ndings showed).
From the perspective of the dynamic stochastic general equilibrium model,
Figure 2.1 is a partial equilibrium snapshot of the date-t asset market. The forward-
looking behavior of domestic households and foreign traders implies that changes
that a?ect the date-t asset market spillover into the market outcomes at other dates
and vice versa. For example, the price guarantee may not be in force at t but the
expectation of executing future price guarantees will shift upward the FF curve at
t. Similarly, the margin constraint may not bind at t, but the expectation of future
margin calls is enough to shift the date-t HH curve. Given the lack of closed-form
solutions for equilibrium allocations and prices, the only way to study the e?ects
of price guarantees on the dynamics of consumption, the current account, asset
68
holdings, and asset prices is by exploring the model’s quantitative implications via
numerical simulation.
2.4 Quantitative Analysis
2.4.1 Recursive Equilibrium and Solution Method
In the recursive representation of the equilibrium, the state variables are the
current holdings of assets and bonds in the emerging economy, ? and b, and the
realization of the productivity shock e. The state space of asset positions spans
the discrete grid of NA nodes A = ?
1
< ?
2
< < ?
NA
with ?
1
= ?, and the state
space of bonds spans the discrete grid of NB nodes B = b
1
< b
2
< < b
NB
. The
endogenous state space is de?ned by the discrete set Z = A × B of NA × NB
elements. Productivity shocks follow a stationary, two-point Markov chain with
realizations E = ?
L
< ?
H
. Equilibrium wages, dividends, labor and output are
determined by solving the supply-side system given by equations (2.1), (2.2), (2.9)
and the production function. The solutions are given by functions that depend only
on ?: w(?), d(?), n(?) and F(?).
The numerical solution of the recursive equilibrium is obtained using a modi-
?ed version of Mendoza and Smith’s (2004) quasi-planning problem algorithm. The
algorithm starts with a conjecture for the function
ˆ
G(?, b, ?) : E×Z ?R
+
, which re-
turns the expected present discounted value of “excess prices” for any triple (?, b, ?)
in the state space. Given this conjecture, the optimal decision rules for equity and
bond holdings of domestic agents, are obtained by solving the following dynamic
69
programming problem:
V (?, b, ?) = max
?
,b
?A×B
{u(c ?h(n(?))) + exp(??(c ?h(n(?))))E[V (?
, b
, ?
)]}
(2.16)
subject to:
c = ?kd(?) +w(?)n(?) +
q
f
(?) +
ˆ
G(?, b, ?)
1 + a? +a(? ??
)
k(? ??
) ?b
+bR (2.17)
b
? ??
q
f
(?) +
ˆ
G(?, b, ?)
1 + a? +a(? ??
)
?
k (2.18)
Note that equity prices in (2.19) and (2.20) were replaced with the prices along the
demand curve of foreign traders by imposing equity market clearing and solving for
equity prices using (2.15).
The decision rule for equity holdings is plugged into equation (2.15) to derive
an “actual” asset pricing function (for the given conjecture
ˆ
G(?, b, ?)). The decision
rules for bonds and equity, the guaranteed prices, and this “actual” pricing function
are then used to solve for the “actual” function. The conjectured and actual G func-
tions are then combined to create a new conjecture using a Gauss-Siedel rule, and the
procedure starts again with the Bellman equation (2.18). The process is repeated
until
ˆ
G(·) and G(·) converge, so that the function
ˆ
G(?, b, ?) that is taken as given in
the dynamic programming problem is consistent with the function G(?, b, ?) implied
by the asset pricing function and decision rules that are endogenous outcomes of
that problem.
70
The drawback of this method is that it assumes that the emerging economy
internalizes the demand function of foreign traders. As a result, the equilibrium of
problem (2.18) is equivalent to a competitive equilibrium for a variant of the model
with a proportional tax or subsidy on asset returns, with tax revenues rebated as a
lump-sum transfer. In the simulations we discuss below, however, the implied taxes
are negligible: The maximum taxes in absolute values range between 0.08 (0.4) and
0.2 (0.8) percent when a = 0.2(2). The average tax in absolute value is 0.03 (0.3)
percent in the simulations with a = 0.2(2).
2.4.2 Deterministic Steady State and Calibration to Mexican Data
The functional forms that represent preferences and technology are the follow-
ing:
F(k, n
t
) = k
(1??)
n
?
t
, 0 ? ? ? 1 (2.19)
u(c
t
?h(n
t
)) =
[c
t
?h(n
t
)]
1??
?1
1 ??
, ? > 1 (2.20)
?(c
t
?h(n
t
)) = ?[Ln(1 + c
t
?h(n
t
))], 0 < ? ? ? (2.21)
h(n
t
) =
n
?
t
?
, ? > 1 (2.22)
? is the labor income share, ? is the coe?cient of relative risk aversion, ? is the
elasticity of the rate of time preference with respect to 1 + c
t
? h(n
t
), and ? sets
the wage elasticity of labor supply (which is equal to 1/(? ? 1)). The condition
0 < ? ? ? is required to limit impatience e?ects and obtain a well-de?ned limiting
distribution of foreign bonds (see Arellano and Mendoza (2003) for details).
71
The calibration strategy di?ers markedly from the one in Mendoza and Smith
(2004). They normalize the capital stock to k=1 and let the steady-state equity price
adjust to the value implied by the asset pricing condition, given a set of parameter
values taken directly from the data or set to enable the model to match ratios of
national accounts statistics. Here, we normalize instead the steady-state equity
price so that the capital stock matches the deterministic, steady-state capital stock
of a typical RBC-SOE model calibrated to Mexican data (see Mendoza (2004)).
The steady state of this RBC-SOE model is a frictionless, neoclassical stationary
equilibrium. Calibrating to this frictionless equilibrium helps focus the analysis
on the use of price guarantees to prevent Sudden Stops triggered by margin calls
that hit the economy only when it is highly leveraged (and hence o? the long-run
equilibrium).
The risk aversion parameter is set at ? = 2 in line with values often used in
RBC-SOE studies. The parameter values that enter into the supply-side system are
determined as follows. The labor share is set at ? = 0.65, in line with international
evidence on labor income shares. The Mexican average share of labor income in
value added in an annual sample for 1988-2001 is 0.34, but values around 0.65 are
the norm in several countries and there is concern that the Mexican data may mea-
sure inaccurately proprietors income and other forms of labor income (see Mendoza
(2004) for details). The real interest rate is set at 6.5 percent, which is also a value
widely used in the RBC literature. Since the model is set to a quarterly frequency,
this implies R = 1.065
1/4
. The labor disutility coe?cient is set to the same value
as in Mendoza and Smith (2004), ? = 2, which implies a unitary wage elasticity of
72
labor supply.
As in a typical RBC calibration exercise, the calibration is designed to yield
a set of parameter values such that the model’s deterministic steady state matches
actual averages of the GDP shares of consumption (sc), investment (si), govern-
ment purchases (sg) and net exports (snx). In the Mexican data, these shares are
sc = 0.684, si = 0.19, sg = 0.092, and snx = 0.034. Since the model does not
have investment or government purchases, their combined share (0.282) is treated
as exogenous absorption of output equivalent to 28.2 percent of steady-state GDP.
In the stochastic simulations we keep the corresponding level of these expenditures
constant at 28.2 percent of the value obtained for steady-state output in the cali-
bration.
The typical RBC-SOE model features a standard steady-state optimality con-
dition that equates the marginal product of capital net of depreciation with the
world interest rate, and a standard law of motion of the capital stock that relates
the steady-state investment rate to the steady-state capital-output ratio. Given
the values of si, ?, ? and R, these two steady-state conditions yield values of the
depreciation rate (dep) and the capital-output ratio (sk). On an annual basis, the
resulting depreciation rate is 7.75 percent and sk is about 2.5.
In a deterministic steady state of the model of Section 2 in which the credit
constraint does not bind and there are no price guarantees, the equity price is
q = q
f
= d/(R?1). Given the RBC-SOE calibration criterion that the steady-state
marginal product of capital net of depreciation equals the net world interest rate, q
f
can be re-written as F
k
(k, n)/(F
k
(k, n) ?dep). With the Cobb-Douglas production
73
function this reduces to q
f
= (1 ??)/(1 ?? ?si). Thus, the requirement that the
model’s dividend rate must match a typical RBC-SOE calibration implies that the
steady-state equity price is determined by si and g. With the parameter values set
above we obtain q
f
= 2.19.
Given the values of ?, ?, R, and q
f
the steady-state solutions for n, w, k, and
F(k, n) follow from solving the supply-side system conformed by (2.1), (2.2), (2.9)
and (2.21). The resulting steady-state capital stock is k = 79. By construction, this
capital stock is also consistent with the estimated capital-output ratio of 2.5 and
the observed Mexican investment rate of 0.19.
The parameters that remain to be calibrated are the time-preference elasticity
coe?cient b and the ?nancial frictions parameters a, ? and k. The value of ? is
derived from the consumption Euler equation as follows. In the deterministic sta-
tionary state of the model there are no credit constraints and hence the endogenous
rate of time preference equals the real interest rate:
_
1 + scF(k, n) ?
n
?
?
_
?
= R (2.23)
Given the values of R, ?, n, F(k, n) and sc, this condition can be solved for the
required value of ?. The solution yields ? = 0.0118. The total stock of do-
mestic savings at steady state follows then from the resource constraint as s =
[c ?F(k, n)(si +sg) ?wn]/(R ?1) = ?q
f
k +b.
Up to this point the calibration followed the typical RBC-SOE deterministic
calibration exercise. A problem emerges, however, when we try to determine the
74
composition of the savings portfolio because the allocation of savings across bonds
and equity is undetermined. Any portfolio (?, b) ? A × B is consistent with the
RBC-SOE deterministic steady state as long as it supports the unique steady-state
level of savings (i.e., ?q
f
k + b = s) and the margin and short-selling constraints
do not bind (b > ?k?q
f
k and ? > ?). Moreover, given the values of s, q
f
and k
implied by the calibration, it follows from the de?nition of savings that there is only
a small subset of portfolios in which the economy borrows in the bond market (i.e.,
portfolios with b < 0) in the set of multiple steady-state portfolios. Debt portfolios
require ? > 0.9. If domestic agents own less than 90 percent of k, their steady-state
bond position is positive and grows larger the smaller is a. This also implies that it
will take low values of ? to make the margin constraint bind. In particular, setting
the upper bound of ? at 100 percent, it takes ? ? 0.10 for the margin constraint to
bind for at least some of the multiple steady-state pairs of (?, b). These low values of
? can be justi?ed by considering that the margin constraint represents the fraction
of domestic capital that is useful collateral for external debt. Several studies in the
Sudden Stops literature provide arguments to suggest that this fraction is small (see,
for example, Caballero and Krishnamurty (2001)).
The stochastic RBC-SOE without credit constraints has the additional un-
appealing feature that it can lead to degenerate long-run distributions of equity
and bonds in which domestic agents hold the smallest equity position (?) and use
bonds to engage in consumption smoothing and precautionary saving. The reason is
that, without credit constraints and zero recurrent trading costs, risk-averse domes-
tic agents demand a risk premium to hold equity while risk-neutral foreign traders
75
do not.
4
Hence, domestic agents end up selling all the equity they can to foreign
traders, although the process takes time because of the trading costs that foreign
traders pay.
To circumvent the problems of portfolio determination in the deterministic and
stochastic RBC-SOE steady states, we calibrate the values of the ?nancial frictions
parameters (?, q and k) so that the allocations and prices obtained with the deter-
ministic RBC-SOE steady state can be closely approximated as the deterministic
steady state of an economy with negligible (but positive) recurrent trading costs
and a margin constraint that is just slightly binding. This calibration scenario is
labeled the “nearly frictionless economy”(NFE).
The deterministic steady state of the NFE has well-de?ned, unique solutions
for bond and equity positions. In particular, foreign traders hold a stationary equity
position at the price q = q
f
/(1 + a?). Since this price is less than q
f
, which is
the price at which the return on domestic equity equals R, it follows that at this
lower price R
q
> R. Thus, foreign traders now require an equity premium to
hold a stationary equity position. The ratio of the Lagrange multipliers of the
domestic agent’s margin constraint and budget constraint can then be found to be
?/? = (R
q
? R)/(R
q
? R?). In addition, since the margin constraint binds, bond
holdings must satisfy b = ???qk, and hence a unique stationary domestic equity
position can be obtained from the steady-state consumption Euler equation. This
4
With ? = 0 and no price guarantees, equation (2.15) implies that foreign traders attain a
stationary equity position when the equity price equals the fundamentals price, and the latter
implies a stationary asset return equal to R. Thus, at this steady state foreign traders hold equity
at zero equity premium.
76
is the value of a that solves the following expression:
_
1 + ?kd +wn ??q?k(R ?1) ?
n
?
?
_
?
=
R
1 ?(?/?)
(2.24)
Equation (26) illustrates the key role of the endogenous rate of time preference in
supporting deterministic stationary equilibria with binding credit limits: it allows
the rate of time preference to adjust so as to make the higher long-run consumption
level, implied by the fact that the credit constraint prevents domestic agents from
borrowing as they desire in the transition to steady state, to be consistent with the
higher e?ective long-run real interest rate also implied by the credit constraint. The
recurrent trading cost is also critical. With ? = 0, a stationary equity position for
foreign traders requires a price equal to q
f
and a return on equity equal to R, but
the latter implies that ?/? = 0, so the borrowing constraint could not bind.
In the NFE steady state, the values of a, ? and kappa are set to support a
deterministic steady state with a binding borrowing constraint that satis?es the
following conditions: (1) the debt-GDP ratio is in line with Mexican data, (2)
the allocations, factor payment rates and the equity price are nearly identical to
those obtained for the frictionless RBC-SOE deterministic steady state, and (3) the
elasticity of the foreign trader’s demand curve is relatively high. The values of the
?nancial frictions parameters are: a = 0.2, ? = 0.001 and ? = 0.03. With these
parameter values, and the values set earlier for ?, ?, ?, and R, the NFE steady
state yields values of c, s, n, w, d, q, and R
q
nearly identical to those of the RBC-
SOE deterministic steady state, but the NFE also has unique portfolio allocations
77
of ? = 0.931 and b = ?4.825 (which implies a debt-GDP ratio of about 0.62).
2.4.3 Stochastic Simulation Framework
The stochastic simulations are solved over a discrete state space with 78 evenly-
spaced nodes in the equity grid and 120 evenly-spaced nodes in the bonds grid. The
lower bound for equity is set at c=0.84, so the equity grid spans the interval [0.84,1].
These equity bounds, together with the maximum equity price de?ned in (2.17) and
the margin constraint, set the lower bound for bonds as ??q
max
k = ?5.2. This
is the largest debt that the SOE could leverage by holding the largest possible
equity position at the highest possible price. The upper bound of bonds is found
by solving the model repeatedly starting with an upper bound that supports steady
state savings with the equity position at its lowest, and then increasing the upper
bound until the grid captures the support of the ergodic distribution of bonds. The
resulting grid spans the interval [-5.2,25.7]. The segment of debt positions inside
this interval is relatively small, re?ecting the fact that, despite the frictions induced
by asset trading costs, domestic agents still have a preference for riskless bonds as
a vehicle to smooth consumption and build a bu?er stock of savings.
A lower bound on domestic equity holdings of 84 percent seems much higher
than the conventional short-selling limit set at 0 but it is consistent with the national
aggregates targeted in the calibration. In Mexico, the 1988-2000 average ratio of
stock market capitalization to GDP was 27.6 percent. Since the calibration produced
an estimate of the capital-output ratio of about 2.5, the shares of publicly traded
78
?rms constitute just 11 percent of the capital stock. A large fraction of Mexico’s
capital is owned by non-publicly-traded ?rms and by owners of residential property,
and thus does not have a liquid market in which shares are traded with foreign
residents. In general, it is hard to argue that a large fraction of the physical capital
of most emerging economies has a liquid international market. Moreover, the result
from the calibration showing that bond positions become positive and unrealistically
large for ? < 0.9 also argues for a high value of ?.
Productivity shocks are modeled as a two-point, symmetric Markov process
that follows the “simple persistence” rule. The two points of the Markov chain and
the transition probability matrix are set so that the model mimics the standard
deviation and ?rst-order autocorrelation of the quarterly cyclical components of
Mexico’s GDP reported in Mendoza (2004) – 2.64 percent and 0.683 respectively.
This requires a Markov process of productivity shocks with a standard deviation
(?
?
) of 1.79 percent and a ?rst-order autocorrelation coe?cient (?
?
) of 0.683. The
simple persistence rule implies then that the two points of the Markov chain are
-?
L
= ?
H
= 0.0179 and these two states a long-run probability of . The transition
probability of remaining in either state is given by (1 ? ?
?
) + ?
?
= 0.8415 and the
transition probability of shifting across states is (1 ??
?
) = 0.1585.
79
2.4.4 Baseline Results: Globalization Hazard and Sudden Stops with-
out Price Guarantees
The baseline results include four simulations: (1) the NFE case, (2) the econ-
omy with binding margin requirements (BMR), which uses a margin coe?cient set
at ? = 0.005, (3) a simple price-guarantees policy that sets a single, non-state-
contingent guaranteed price (NSCG) for all dates and states, and (4) an economy
with the same guaranteed price but as a state-contingent guarantee (SCG) that
applies only in a subset of the state space.
The key result that emerges from comparing the NFE and BMR economies is
that the ?nancial frictions representing globalization hazard in the model do cause
Sudden Stops when the ratio of debt to the market value of equity is high and the
equity market has enough liquidity (i.e., domestic agents are not at their short-
selling limit). Since this result echoes ?ndings from Mendoza and Smith (2004), we
keep the presentation short and refer the reader to their article for details.
Figures 2 shows the long run distributions of equity and bonds for the four
simulations. Comparing the bond distributions of the NFE and BMR simulations,
the e?ect of the margin constraint is evident. The distribution is biased to the
left in the two economies but it shifts markedly to the right in the BMR case.
The opposite occurs with the distribution of equity. The bias to the left in the
distribution of equity re?ects the incentive that risk-averse domestic agents have
to sell equity to risk-neutral foreign traders. Binding margin constraints shift the
equity distribution further to the left because of the equity ?re sales triggered by
80
margin calls. These shifts in the distributions of equity and bonds also re?ect the
outcome of precautionary saving. Domestic agents, aware of the imperfections of
?nancial markets, have an incentive to build up a bu?er stock of savings so as to
minimize the risk of large declines in consumption, and in doing so they also lower
the risk of facing states in which margin constraints bind in the long run (Figure 2
shows that the long run distribution of bonds of the BMR economy rules out states
with very large debt positions). Still, Table 1 shows that the long-run probability
of binding margin constraints is about 4 percent. Sudden Stops are therefore rare
but non-zero probability events in the stochastic steady state (although many of the
states in which margin constraints bind in the long run do not trigger Sudden Stops,
as explained below). Note also that margin constraints cause a portfolio reallocation
of savings from equity into bonds. Table 1 shows that the long-run average of the
bonds-output ratio increases from 18 percent in the NFE to 50 percent in the BMR
economy.
Financial frictions have negligible e?ects on business cycle moments (see Table
2.1). Hence, as in Mendoza and Smith (2004), we study Sudden Stops by examining
the model’s dynamics in the high-debt region of the state space in which the margin
constraint binds (i.e., the “Sudden Stop region”). Figure 2.3 shows the date-0
responses (or impact e?ects) of consumption, and the current account-GDP ratio
(ca/y) to a negative, one-standard-deviation productivity shock for (?, b) pairs in
the Sudden Stop region, measured in percent of the long-run mean of each variable.
The Sudden Stop region includes the ?rst 25 nodes of the B grid and all 72 nodes
of the A grid.
81
Figure 3 suggests that there are two key factors driving impact e?ects in the
Sudden Stop region: (1) The leverage ratio, de?ned as the ratio of debt to the
market value of equity, and (2) The liquidity of the equity market, de?ned as the
di?erence between ? and ?. Sudden Stops with large reversals in c and ca/y occur
when the leverage ratio is high, but given high leverage the impact on asset prices
is di?erent depending on asset market liquidity. If the asset market is illiquid, the
Sudden Stop can feature negligible asset price declines because domestic agents are
close to ? and hence have little equity to sell (see Figure 2.5a), but if there is some
liquidity in the asset market, the Sudden Stop in c and ca/y is accompanied by a
fall in q. In contrast, when the leverage ratio is su?ciently low and the asset market
is su?ciently liquid, the drop in consumption and the current account reversal are
small (nearly as small as in the NFE case) but the drop in asset prices is larger.
In this case, domestic agents liquidate more equity and trigger larger asset price
collapses, but they do so in order to swap their limited borrowing ability via bonds
for equity sales so as to minimize the drop in consumption. This pattern of larger
current account corrections coinciding with smaller asset price collapses ?ts the
observations of some emerging markets crises. The current account reversal in the
?rst quarter of 1995 in Mexico was 5.2 percent of GDP but the drop in real equity
prices was nearly 29 percent. In contrast, in Korea the current account reversal in
the ?rst quarter of 1998 was twice as large but the asset price drop was just 10
percent.
Figure 2.4 illustrates Sudden Stop dynamics using the conditional forecasting
functions of c, q and ca/y. The ?rst two are shown as percentages of their long-run
82
averages in the NFE and the last is shown as the percentage points di?erence relative
to the long-run average in the NFE. These forecasting functions represent non-linear
impulse response functions to a negative, one-standard-deviation productivity shock
conditional on initial positions of equity and bonds inside the Sudden Stop region.
The Figures plot two sets of forecasting functions, one for a high leverage initial
state, at which ? = 0.938 and b = ?4.68 (with debt ratio of 60 percent of GDP
and a leverage ratio of 3 percent of GDP), and one for a low leverage state with the
same a but b = ?3.38 (with a debt ratio of 43 percent of GDP and a leverage ratio
of 2 percent of GDP). Since these initial states are distant from the corresponding
long-run averages, the data in the Figures were adjusted to remove low-frequency
transitional dynamics driven by the convergence of bonds and equity to their long-
run means. Given that c, q and ca/y have nearly identical long-run averages in the
four baseline experiments (except for the mean of q in the NSCG economy, which
is higher), the forecasting functions were detrended by taking di?erences relative to
the NFE forecasting functions.
The impact e?ects in the initial date of the forecasting functions of the BMR
economy di?er sharply across the high and low leverage states, and those of the high
leverage state deviate signi?cantly from those of the NFE (or from zero in terms
of Figure 2.4, since the data are plotted as di?erences relative to the NFE). In the
high leverage state of the BMR economy, the negative shock triggers a Sudden Stop
driven by the mechanisms described in Section 2.3: Domestic agents sell equity to
meet margin calls and trigger a Fisherian de?ation that reduces further their ability
to borrow. The net result is that, on impact, a one-standard-deviation shock to
83
productivity causes c and q to drop by 1.5 and 0.4 percent more than in the NFE
respectively and ca/y to rise by about 1 percentage point of GDP. In the low leverage
state, domestic agents are better positioned to smooth consumption by substituting
debt for equity to ?nance a current account de?cit. As a result, the responses of c
and ca/y in the BMR economy are nearly identical to those in the NFE, so their
detrended forecasting functions hover around zero. This occurs even though the
sales of equity still make q fall by about the same amount as in the high leverage
scenario. Notice also that the drop in asset prices is small relative to observed
Sudden Stops, but very large relative to the standard deviation of asset prices in
the NFE.
One caveat about the plots in Figure 2.4: The initial bond and equity positions
used to generate them yield outcomes consistent with Sudden Stops, but the set of
impact e?ects that the model predicts for all initial conditions inside the Sudden
Stop region are shown in Figures 2.3. As these Figures show, the Sudden Stop re-
gion includes scenarios with much larger consumption and current-account reversals
than those shown in Figure 2.4, as well as scenarios in which there is little di?erence
between the BMR and NFE because the asset market is su?ciently liquid to main-
tain a similar current account de?cit by selling equity when the margin constraint
binds. Precautionary saving implies, however, that all the scenarios with very large
reversals in consumption have zero probability in the long run. Notice also that,
since the Sudden Stop region includes instances in which the margin constraint binds
but ?re sales of assets prevent a sharp current account reversal, the probability of
binding margin constraints is not identical to the probability of Sudden Stops.
84
Figure 2.4 suggests that Sudden Stops in the model are short-lived. The
responses of the BMR economy converge to those of the NFE in about 4 quarters.
Mendoza and Smith (2004) obtained Sudden Stops with more persistence using
higher per-trade costs, which hamper the foreign traders’ ability to adjust equity
holdings.
2.4.5 Baseline Results: State-Contingent and Non-State-Contingent
Price Guarantees
The price guarantees are set above the fundamentals price in the low produc-
tivity state.
5
This is motivated by a theoretical result that holds for stationary
decision rules (i.e., ?
t+1
= a
t
, b
t+1
= b
t
) and equilibrium equity prices in the high
productivity state that exceed a time- and state-invariant guaranteed price. Under
these assumptions, we can show that G(?, b, ?
L
) = z
_
˜ q ?
q
f
(?
L
)
1+a?
_
, where z is a posi-
tive fraction that depends on R, a, ? and the transition probabilities of the shocks.
Hence, ˜ q >
q
f
(?)
1+a?
is a necessary condition for the guarantees to be executed at least
in some states.
The non-state-contingent price guarantee is set of a percentage point above
the fundamentals price in the low productivity state (2.185). Hence, the guaranteed
price is 2.196. This guarantee is o?ered in all states (?, b, ?) in the NSCG economy.
In contrast, the SCG economy provides the same guaranteed price only for (a,b)
pairs inside the Sudden Stop region.
5
Note that incomplete asset markets and the risk-averse nature of domestic agents imply that
equilibrium prices in the NFE di?er from the fundamentals price that discounts dividends at the
risk-free rate.
85
Figure 2.2 shows that, relative to the BMR case, the non-state-contingent
guarantee shifts the distribution of equity (bonds) markedly to the left (right). The
long-run average of the expected present value of excess prices (i.e., the long-run
average of G ) is 0.01, which is about of a percent above the mean equity price
in the stochastic stationary state. Comparing long-run moments across Panels I,
II and III of Table 1, the main change in the NSCG simulation is the reduction
in the probability of binding margin constraints. The probability is almost zero
with price guarantees, compared with 4 percent in the BMR economy. The long-
run moments of the model’s endogenous variables vary slightly with the non-state-
contingent guarantee. Asset-price ?uctuations display less variability, persistence
and co-movement with output in the NSCG economy relative to the NFE and BMR
cases. The mean equity price increases by 0.053 percent, slightly more than the
percent di?erence between the guaranteed price and the fundamentals price of the
low productivity state. The coe?cient of variation of consumption falls by about
1/5 of a percentage point and the variability of the current account and the trade
balance increase slightly. Consumption also becomes less correlated with GDP.
The e?ects of the price guarantee on Sudden Stop dynamics are shown in
Figure 2.4. Price guarantees are an e?ective policy for containing Sudden Stops.
Comparing the NSCG and BMR economies in the high leverage state, the initial
consumption and current account reversals are smaller in the NSCG economy, and
the drop in equity prices turns into an increase of about 1/2 of a percentage point.
In the low leverage state, the increase in equity prices in the NSCG economy is
slightly larger than in the high leverage state, and we now obtain an increase in
86
consumption and a widening of the current account de?cit at date 0. The price
guarantee results in a price of equity at date 0 that is 2/3 of a percentage point
higher in the NSCG than in the BMR economy in both the high and low leverage
states. The price guarantee is executed in both states of the NSCG economy.
Figure 5 plots the levels of equity prices in the low productivity state of the
NFE, BMR and NSCG economies for all equity and bond positions. The plots
show that the non-state-contingent guarantee not only results in higher prices in
the Sudden Stop region, but it actually increases prices in all states. In fact, the
guarantee produces signi?cantly higher asset prices in the NSCG economy than in
either the NFE or BMR economies in states well outside the Sudden Stop region.
This is a potentially important drawback of non-state-contingent price guarantees:
they distort asset prices even when the economy is in states where it is far from
vulnerable to Sudden Stops.
One alternative to remedy the drawbacks of non-state-contingent price guar-
antees is to consider state-contingent guarantees. Figure 2.2 shows that the SCG
economy yields a long-run distribution of equity (bonds) that is less skewed to the
left (right) than in the NSCG economy. Table 1 shows that the changes in the long-
run business cycle moments of the SCG economy relative to the NFE and BMR cases
are qualitatively similar to those noted for the NSCG economy but the magnitude
of the changes is smaller. The SCG economy still features near-zero percent prob-
ability of observing states of nature in which the margin constraint binds. Hence,
the state-contingent guarantee is as e?ective as the non-state-contingent guarantee
at eliminating the possibility of hitting states with binding margin requirements in
87
the long run.
Figure 2.4 shows that, in both the high and low leverage states, the SCG
economy features nearly identical date-0 responses in consumption and the current
account as the NSCG economy and a slightly smaller recovery in asset prices. After
date 0, the SCG economy converges faster to the dynamic paths of the NFE economy.
Finally, a comparison of the middle and bottom plots of Figure 5 shows that the SCG
economy yields higher asset prices mainly in the Sudden Stop region of the state
space. Thus, state contingent guarantees induce smaller distortions on asset demand
and asset prices than the non-state-contingent guarantees, particularly outside the
Sudden Stop region, yet they have similar e?ects in terms of their ability to prevent
Sudden Stops.
2.5 Normative Implications and Sensitivity Analysis
2.5.1 Normative Implications of the Baseline Simulations
We study next the normative implications of the baseline simulations by ex-
amining how domestic welfare and the value of foreign securities ?rms varies across
the NFE, BMR, NSCG and SCG simulations. Welfare costs, W(?, b, ?), are mea-
sured by computing compensating variations in date-0 consumption that equate
expected lifetime utility in the BMR, NSCG and SCG economies with that of the
NFE for any triple (?, b, ?) in the state space. Welfare e?ects are typically com-
puted as compensating variations that apply to consumption at all dates, but in
principle both measures are useful for converting ordinal units of utility into the
88
cardinal units needed for quantitative welfare comparisons. The two measures yield
identical welfare rankings for the four experiments, but the measure based on date-0
consumption highlights better the welfare costs of Sudden Stops and the potential
bene?ts of price guarantees because large deviations from the consumption dynam-
ics of the NFE occur only in Sudden Stop states (in which bond and equity positions
are distant from their long-run averages).
The model belongs to the class of models in which capital markets are used
to smooth consumption over the business cycle. Hence, since it is well-known that
the welfare cost of ”typical” consumption ?uctuations is small in these models, the
mean welfare costs of deviating from the NFE (E[W(?, b, ?)]) computed with the
ergodic distribution) should be small. As Table 2.2 shows, welfare comparisons
based on date-0 consumption preserve this result. Agents in the BMR, NSCG and
SCG economies incur average welfare losses relative to the NFE equivalent to cuts
of less than 0.07 percent in c
0
. This is also in line with Mendoza’s (1991) results
showing trivial welfare costs for giving up access to world capital markets in an
RBC-SOE model.
The situation is very di?erent when comparing welfare conditional on Sudden
Stop states. Since the Bellman equation implies that lifetime utility as of date 0
can be expressed as V (t) = u(t) +exp(?v(t))Et[V (t + 1)], Table 2 decomposes the
total welfare cost into a short-run cost (i.e., the percent change in c
0
that equates
u(0) in the distorted economies with that of the NFE) and a long-run cost (i.e., the
percent change in c0 that equates exp(?v(0))E
0
[V (1)] in the distorted economies
with that of the NFE). The Table also lists the rate of time preference, exp(?v(0)),
89
to show that changes in the endogenous subjective discount are irrelevant for the
welfare analysis.
In the high leverage Sudden Stop state, which is the one that in the BMR
economy produces dynamics closer to those of observed Sudden Stops, the short-run
welfare costs show that domestic agents are worse o? in the BMR, NSCG and SCG
economies than in the NFE. The welfare cost is 1.4 percent for the BMR economy
and 0.9 and 1 percent for the NSCG and SCG economies respectively. This ranking
re?ects the fact that declines in date-0 consumption, and hence u(0), are smallest
in the NFE because it provides the best environment for consumption smoothing,
followed by the economies in which price guarantees help contain Sudden Stops.
The long-run costs are negative (i.e., domestic agents make welfare gains) be-
cause consumption after date 0 increases at least temporarily in the BMR, NSCG
and SCG economies. In the high leverage case of the BMR economy, the binding
credit constraint tilts the consumption pro?le by reducing consumption at date 0
and increasing it later, resulting in a long-run welfare gain of about 1 percent. Con-
sumption tilting is also at work in the NSCG and SCG economies, but in addition
the higher (distorted) asset prices lead to higher consumption relative to both the
BMR and the NFE for three quarters beyond the initial date (see Figure 4). This
expansion of consumption in the economies with price guarantees is driven in turn
by larger current account de?cits, which are ?nanced by equity sales at higher prices.
After date 0, domestic agents set to rebalance their portfolios from equity into bonds
gradually, but in economies with price guarantees the capital in?ows from equity
sales exceed the out?ows from bond purchases in the early periods of transition thus
90
producing larger external de?cits. This leads to long-run welfare gains in the high
leverage NSCG and SCG economies (1.9 and 1.3 percent respectively) that are large
enough to o?set the short-run costs, so that domestic agents obtain total welfare
gains of 1 percent in the NSCG and 0.3 percent in the SCG. These results show that
the asset price changes induced by price guarantees represent non-trivial distortions
relative to the NFE. Moreover, as we show below, the same distortions that increase
domestic welfare in the high leverage Sudden Stop states of the NSCG and SCG
economies reduce the value of foreign traders’ ?rms in those states.
At equilibrium, the foreign traders’ net returns can be written as:
ˆ ?(?, b, ?) ? k{[(1 ??)d(?)] ?[q(?, b, ?)(? ? ˆ ?
(?, b, ?))]?
_
q(?, b, ?)
_
a
2
_
(? ? ˆ ?
(?, b, ?) + ?)
2
_
}
(2.25)
The three terms in square brackets in the right-hand-side of this expression represent
the foreign traders’ dividend earnings, the net value of their trades, and the trading
costs they incur. Notice that, since the budget constraint of the IFO holds, the lump
sum taxes paid by foreign traders cancel with the value of the executed guarantees.
Thus, price guarantees distort the traders’ optimality condition with the moral
hazard e?ect identi?ed in (2.15) without direct income e?ects.
The payo? of foreign traders D is the expected present discounted value of
the stream of net returns. In the recursive representation of the equilibrium, this
present value of returns is a function D(?, b, ?), and hence we can compute long-run
averages of net returns, E[D(?, b, ?)], and values of D(?, b, ?) conditional on Sudden
91
Stop states. Since the model has a well-de?ned stochastic steady state, the long-run
mean of net returns is given by E[D] = kE[ˆ ?]R(R ?1)
?1
.
Table 2.2 shows that, relative to the NFE, E[D] and are 14.5 percent higher
in the BMR economy and 52.6 and 42.5 percent higher in the NSCG and SCG
economies respectively. Thus, from the perspective of the long-run average of the
value of their ?rms, foreign traders are better o? in the BMR economy and signif-
icantly better o? in the economies with price guarantees than in the NFE. Table
2.2 also shows that this is the case mainly because of the increased average equity
holdings of foreign traders in the BMR, NSCG and SCG economies, and the corre-
sponding increase in their average dividend earnings. The contribution of changes
in the value of trades to changes in E[D] and is zero by de?nition (since the un-
conditional means of at and ?
t+1
are identical) and the contribution of changes in
trading costs is negligible. Foreign traders build up a larger equity position in the
BMR economy as a result of the rebalancing of the portfolio of domestic agents
from equity into bonds shown in Figure 2.2, and also because in some states foreign
traders buy assets at crash prices (i.e., when domestic agents ?re sale assets to meet
margin calls). Foreign traders are much better o? when price guarantees are in
place because the price guarantees are equivalent to a guaranteed minimum return,
which reduces sharply the downside risk of holding equity and results in even larger
domestic portfolio reallocations from equity into bonds.
The result that the payo? of foreign traders is signi?cantly higher on average
in the long run with price guarantees hides the fact that, when evaluated conditional
on a Sudden Stop state, the payo? of foreign traders is lower in economies with price
92
guarantees. Table 2.2 shows that the ranking of foreign traders’ payo?s obtained
by comparing D(?, b, ?) across Sudden Stop states with low or high leverage is the
opposite from the one obtained by comparing E[D]. Relative to the NFE, the
present value of pro?ts is nearly unchanged in the BMR economy and it falls in the
high and low leverage states of the economies with price guarantees (by about 0.7
and 0.3 percent in the NSCG and SCG economies respectively). The latter occurs
because in the NSCG and SCG economies the increase in the long-run average of net
returns (E[ˆ ?]) is not su?cient to o?set the short-run decline in returns (ˆ ?(?, b, ?))
that occurs at date 0 when a Sudden Stop hits (see Table 2.2). In turn, this decline
in net returns at date 0 is almost entirely driven by changes in the value of trades.
The value of trades in the high (low) leverage state rises from 0.36 in the NFE to
3.93 (3.22) in the BMR economy and to about 3.95 (3.24) in the NSCG and SCG
economies. In the BMR economy, the increase re?ects the domestic agents’ ?re sales
of equity to meet margin calls. The equity price falls, and when it falls foreign traders
demand more equity and the value of their trades increases. In the economies with
price guarantees, the moral hazard distortion exacerbates this e?ect by increasing
the foreign traders’ equity demand and producing equilibrium prices higher than in
the BMR economy. In line with the increase in trading values, trading costs rise
sharply from the NFE economy to the other economies, but their absolute amounts
remain small. Dividend earnings do not change because date-0 equity holdings are
the same in all four economies and the dividends of domestic ?rms are independent
of ?nancial frictions and price guarantees.
In principle, the present value of foreign traders’ net returns conditional on
93
a Sudden Stop state could be higher or lower with price guarantees than without
depending on whether the short-run e?ect lowering date-0 net returns is weaker or
stronger than the long-run e?ect increasing average net returns. The strength of
these e?ects depends in turn on how much and how fast equilibrium equity positions
and equity prices move, which depends on the parameters driving the demand for
equity of domestic agents and foreign traders. According to Table 2, however, the
substantial increases in the average payo? of foreign traders (E[D]) in the NSCG
and SCG economies exceed by large margins the small reductions in D(?, b, ?) to
which foreign traders are exposed with very low probability in the long run.
To analyze the distributional implications of price guarantees, consider the
“resource constraint” implied by the households’ budget constraint and the traders’
net returns:
c = ?F(k, n) ?[k?
?
d ?b(R ?1)] + [qk (?
?
??
?
) ?(b
?b)] (2.26)
As noted earlier, the long-run averages of consumption in the NFE, BMR,
NSCG and SCG economies are nearly identical (see Table 1). On the other hand,
Table 2.2 shows that the long-run average of the foreign traders’ dividend earnings is
higher in the latter three than in the NFE. Taking the long-run average of equation
(28), it follows from these two observations that domestic agents can sustain similar
long-run average consumption levels because their average savings remain nearly
unchanged: The drop in dividend earnings on equity is nearly o?set by increased
interest income from bonds. Thus, the baseline results suggest that globalization
94
hazard and price guarantees, as modeled in this chapter, do not alter the long-run
average shares of global income and wealth across the small open economy and the
rest of the world. Foreign traders receive a larger share of domestic GDP but GNP
is una?ected because domestic agents increase bond holdings and thus collect more
interest income from abroad. The independence of GDP from ?nancial frictions and
price guarantees is a strong assumption that plays a key role in this result. The
SOE assumption also plays a role because it allows the domestic portfolio swap of
equity for bonds to occur without increasing the price of these bonds, which would
lower the world interest rate.
Short-run distributional e?ects at a Sudden Stop state are di?erent. GNP
and GDP are unchanged across the four simulations, but there is a redistribution of
world income via the current account. Relative to the NFE, foreign traders transfer
income to domestic households in the BMR, NSCG and SCG economies, as the
value of trades in the third term of the right-hand-side of (28) increases because
domestic agents ?re-sale equity to meet margin calls. But whether the domestic
economy receives more or less income from the rest of the world as a whole depends
on whether the ?re sale of assets can prevent the current account reversal, which
in turn depends on the leverage ratio and the liquidity of the asset market. Table
2.2 shows that ˆ ?(?, b, ?) falls at date 0 in the high and low leverage states, but
Figure 2.4 shows that the reversal in ca/y is larger in the former. Thus, the high
leverage state features a redistribution of income from foreign traders to domestic
agents via the equity market, but the larger current account reversal indicates that
this redistribution is more than o?set by the loss of access to the credit market,
95
so that the domestic economy reduces the share of world output that it absorbs.
In contrast, in the low leverage state the current account de?cit remains close to
the level of the NFE and hence the domestic economy maintains its share of world
output. These results hold across the BMR, NSCG and SCG economies compared
to the NFE but the e?ects are stronger in the economies with price guarantees.
The above results show that, comparing long-run averages of the payo?s of
domestic agents and foreign traders, foreign traders are signi?cantly better o? in
the economies with price guarantees than in the NFE or BMR economies, while
domestic agents are nearly indi?erent. This suggests that price guarantees could
be close to a win-win situation, but this result has some caveats. In particular,
domestic agents are nearly indi?erent between the long-run outcomes of the four
economies because of the trivial cost of consumption ?uctuations in models of the
class examined here, and foreign traders make large gains in the BMR, NSCG and
SCG economies because their dividend earnings are una?ected by ?nancial frictions.
Interestingly, in the short run and starting at a Sudden Stop state, the moral hazard
distortion of economies with price guarantees yields persistently higher asset prices
that redistribute income from foreign traders to domestic agents by more than is
needed if the aim were just to recover the outcome of the NFE (hence making
domestic agents better o? and foreign traders worse o?). Still, foreign traders are
much better o? in the long run because the large increase in E[D] in the NSCG and
SCG economies dwarfs the small, near-zero-probability reduction in D(?, b, ?) for
Sudden Stop states.
96
2.5.2 Sensitivity Analysis
Table 2.3 reports the results of a sensitivity analysis that evaluates the ro-
bustness of the baseline results to the following parameter changes: Columns (II)
and (III), larger and more persistent productivity shocks (?
?
=0.024 and ?
?
=0.8),
Column (IV), higher price guarantees (1 percent above q
f
(?
L
)), Column (V), higher
recurrent trading costs (? =0.01), and Column (VI), higher per-trade costs (a =2).
Column (I) reproduces the baseline results. The Table shows panels with results for
the BMR, NSCG and SCG economies for all six scenarios. In each case, three sets
of results are listed: (a) Sudden Stop e?ects as measured by the detrended, date-0
forecasting functions conditional on the high leverage state, (b) key moments of the
ergodic distribution, and (c) changes in the payo?s of domestic agents and foreign
traders, relative to the corresponding NFE simulation, for the high leverage Sudden
Stop state and in the long-run averages.
Consider ?rst the BMR panel. Columns (I)-(VI) show that the results of the
comparison of the baseline NFE and BMR economies are robust to the parameter
changes considered. Increases in se and re result in small changes in Columns (II)
and (III) relative to Column (I). The exceptions are the probability of binding margin
constraints, which rises (falls) to 4.2 (2.3) percent when re (?
?
) increases, and the
long-run average of the value of the foreign traders’ ?rms, which falls to 12.2 and
4.4 percent in Columns (II) and (III) respectively. The changes in the probability
of margin calls result from portfolio rebalancing e?ects. More persistent (variable)
shocks increase (reduce) slightly the long-run average of domestic equity holdings,
97
and have the opposite e?ects on bond holdings. As a result, the economy with more
persistent (variable) shocks is more (less) likely to hit low bond positions (i.e., high
debt positions) in which the margin constraint binds.
Consider ?rst the BMR panel. Columns (I)-(VI) show that the results of the
comparison of the baseline NFE and BMR economies are robust to the parameter
changes considered. Increases in se and re result in small changes in Columns (II)
and (III) relative to Column (I). The exceptions are the probability of binding margin
constraints, which rises (falls) to 4.2 (2.3) percent when ?
?
(?
varepsilon
) increases, and
the long-run average of the value of the foreign traders’ ?rms, which falls to 12.2 and
4.4 percent in Columns (II) and (III) respectively. The changes in the probability
of margin calls result from portfolio rebalancing e?ects. More persistent (variable)
shocks increase (reduce) slightly the long-run average of domestic equity holdings,
and have the opposite e?ects on bond holdings. As a result, the economy with more
persistent (variable) shocks is more (less) likely to hit low bond positions (i.e., high
debt positions) in which the margin constraint binds.
In line with the ?ndings of Mendoza and Smith (2004), Columns (V) and (VI)
show that BMR economies with higher ? or higher a display larger Sudden Stops,
with the latter showing stronger e?ects. The long-run probability of margin calls
is also sharply higher in these economies, reaching 16.7 percent with q = 0.01 and
19.4 percent with a =2. The BMR economy with a =2 is the only scenario in
Table 3 that can account for large consumption and current account reversals and
large drops in asset prices, as in actual Sudden Stops. This scenario also results in
increased long-run variability in consumption and asset prices, and sharply higher
98
domestic welfare costs.
Comparing now Columns (I)-(VI) across the BMR, NSCG and SCG panels,
we ?nd that price guarantees always work to virtually eliminate the long-run prob-
ability of binding margin constraints. On the other hand, the long-run probability
of executing the guarantees is high in the NSCG economy, ranging between 29 and
34 percent in all scenarios except the one with higher sigma
?
, in which it falls to
15 percent. In contrast, the probability of executing the guarantees in the SCG
economy is below 1 percent in all the scenarios except those with ? =0.01 and a
=2, in which it reaches 6 and 3.2 percent respectively. Thus, state-contingent guar-
antees are as e?ective as non-state-contingent guarantees at reducing the long-run
probability of margin calls, with the advantage that in the SCG economy the IFO
would be trading much less frequently.
A comparison of Columns (I) and (IV) shows that rising the guaranteed price
1 percent above q
f
(?
L
), twice as large than in the baseline, the NSCG and SCG
economies dampen the Sudden Stops of the BMR economy even more than in the
baseline. With the higher price guarantee in Column (IV), the fall in c is just 0.5
(0.6) percent in the NSCG (SCG), compared to 0.8 (0.9) percent in the correspond-
ing baseline simulations. Similarly, the reversal in ca/y in the NSCG (SCG) is just
0.3 (0.4) percentage points of GDP in Column (IV), compared to 0.6 (0.7) in Col-
umn (I). On the other hand, the economies with higher guarantees prop up asset
prices in the Sudden Stop state even more than in Column (I), with price increases
of 0.7 (0.6) percent in the NSCG (SCG) economy. The domestic welfare gain in the
high leverage Sudden Stop state increases to 2.4 (0.9) percent in Column (IV) of
99
the NSCG (SCG) economy, compared to 1 (0.3) percent in the corresponding base-
line simulations, while the long-run welfare losses remain nearly unchanged across
Columns (I) and (IV). At the same time as the domestic welfare gains in the Sudden
Stop state grow, the decline in the payo? of the foreign traders in the same state
grows from 0.7 (0.3) percent in the NSCG (SCG) baseline to 1.4 (0.9) percent in
the NSCG (SCG) with higher guarantees. In contrast, the long-run average of the
traders’ payo? increases with the higher guarantees. Thus, the results regarding the
e?ects of price guarantees obtained with the baseline simulations are qualitatively
similar to those obtained with higher guarantees, but quantitatively the higher guar-
antees induce larger moral hazard distortions, which result in weaker Sudden Stops
but larger redistribution e?ects across foreign traders and domestic agents.
Column (VI) shows that, if the baseline level of price guarantees is applied to an
economy with higher per-trade asset trading costs, the price guarantees still work to
weaken the real e?ects of Sudden Stops relative to those in the BMR economy. With
a =2, however, the guarantee set 0.5 percent above q
f
(?
L
) is insu?cient to prevent
marked reversals in c and ca/y and a sharp drop in q. Consequently, domestic agents
su?er a substantial welfare loss of 1.5 (2.6) percent in the high leverage Sudden
Stop state of the NSCG (SCG) economy, instead of the small gains obtained in the
corresponding baseline simulations with a=0.2. Moreover, the long-run average of
welfare costs increases about 5 (2) times in the NSCG (SCG) economy with a=2
relative to the same simulations with a=0.2. Interestingly, the payo? of the foreign
traders in the high leverage Sudden Stop state is larger in the NSCG and SCG
economies with a=2 than in their baseline counterparts with a=0.2. In fact, in the
100
SCG economy with a=2 the value of the foreign traders’ ?rm in the high leverage
state is even higher than that in the corresponding NFE economy.
The above results show that, for a given guaranteed price, there can be a
su?ciently high value of a such that the mix of globalization hazard and international
moral hazard yields outcomes in which domestic agents su?er large welfare losses at
Sudden Stops, but still these losses are smaller than in the BMR economy without
guarantees. Moreover, for given a, higher guarantees dampen Sudden Stops more
and produce welfare gains at Sudden Stop states. These ?ndings suggest that price
guarantees should be higher the higher are trading costs. The results also show,
however, that economies with higher a face higher long-run averages of welfare costs
with price guarantees than without them (the cost is 1/3 of a percent in the NSCG
panel of Column (VI), compared to 1/10 of a percent in the corresponding BMR). In
addition, economies with higher guarantees and the baseline value of a yield larger
long-run welfare losses (see Column IV). Thus, if per-trade trading costs are high,
increasing price guarantees makes domestic agents better o? at Sudden Stop states
by weakening more the e?ects of globalization hazard, but the stronger e?ects of
international moral hazard makes them worse o? on average in the long run.
The ?ndings of the sensitivity analysis suggest that the size of per-trade costs
is crucial for the e?ectiveness of price guarantees and the globalization hazard-
moral hazard tradeo?. Mendoza and Smith (2004) showed that this parameter
is also crucial for the model’s ability to account for asset price collapses of the
magnitude observed in Sudden Stops, and documented empirical evidence of trading
costs roughly in line with the model’s predictions. Nevertheless, the crucial feature
101
is not the magnitude of a per se but the elasticity of world demand for the SOE’s
equity, which can be in?uenced by factors other than trading costs. The ?ndings
of this chapter suggest that, if this elasticity is high, it is relatively easy to set up
state-contingent price guarantees that reduce the probability of margin calls, undo
the Sudden Stop e?ects of globalization hazard, and make domestic agents better
o? at Sudden Stop states with negligible e?ects on foreign traders’ returns in those
states, and with trivial implications for the long-run welfare of domestic agents. On
the other hand, as the elasticity falls, price guarantees still weaken Sudden Stops
but the globalization hazard-moral hazard tradeo? can have negative consequences
for domestic welfare.
2.6 Conclusions
This chapter shows that, in the presence of globalization hazard caused by
world capital market frictions, providing ex-ante price guarantees on emerging mar-
kets assets can be an e?ective means to contain Sudden Stops. The same theory
predicts, however, that these guarantees create a form of international moral hazard
that props up the foreign investors’ demand for emerging markets assets. Hence, ex-
ante price guarantees create a tradeo? between the bene?ts of undoing globalization
hazard and the costs of international moral hazard.
The chapter borrows from Mendoza and Smith (2004) a dynamic, stochastic
equilibrium model of asset prices in which the sources of globalization hazard are
collateral constraints and asset trading costs. Collateral constraints are modeled as
102
margin constraints that limit the ability of domestic agents to leverage foreign debt
on equity holdings. Asset trading costs are incurred by foreign traders and take the
form of per-trade costs and recurrent costs. In this environment, typical realizations
of productivity shocks trigger margin calls when the economy’s debt is su?ciently
large relative to the value of its equity. Margin calls lead to ?re sales of equity and a
Fisherian de?ation of asset prices. If domestic asset markets are relatively illiquid,
the result is a Sudden Stop with reversals in consumption and the current account
and a fall in asset prices.
This chapter introduced into the Mendoza-Smith model an IFO that o?ers
foreign traders ex-ante guarantees to buy the emerging economy’s assets at pre-
announced minimum prices. The resulting international moral hazard distortion in-
creases the foreign traders’ demand for the emerging economy’s assets by an amount
that depends on the traders’ conditional expected present value of the excess of guar-
anteed prices over market prices.
The chapter’s quantitative analysis, based on a calibration to Mexican data,
showed that guaranteed prices set to 1 percent above the fundamentals price in a
low productivity state reduce signi?cantly the Sudden Stop e?ects of globalization
hazard, and eliminate the long-run probability of margin calls. If the guarantee is
non-state-contingent, however, the IFO trades often (with a long-run probability of
executing the guarantee of about 1/3), and there is persistent asset overvaluation
above the prices obtained without globalization hazard. The IFO trades much less
often, with a long run probability below 1/100, if the same guaranteed price is
o?ered as a state-contingent guarantee that applies only at high debt levels. These
103
state-contingent guarantees are just as e?ective at containing Sudden Stops and
they do not cause persistent asset overvaluation.
The e?ectiveness of price guarantees to prevent Sudden Stops and increase
social welfare hinges on the relative magnitudes of globalization hazard and inter-
national moral hazard. The price elasticity of world demand for domestic assets,
which in the model depends on the size of per-trade costs, is the key determinant
of both. The Fisherian de?ation that governs globalization hazard depends on how
much prices have to fall for foreign traders’ to accommodate the ?re sales of domes-
tic assets. The moral hazard distortion increases foreign demand for domestic assets
by an amount proportional to the price elasticity of this demand. With per-trade
costs that yield an elasticity of 5, guaranteed prices set to 1 percent above the low-
productivity fundamentals price result in domestic welfare gains when the economy
hits a Sudden Stop, with negligible changes in long-run welfare. The value of for-
eign traders’ ?rms in a Sudden Stop state falls slightly but its long-run average rises
sharply. Hence, in this case the bene?ts of price guarantees to contain globalization
hazard outweigh the costs of international moral hazard.
These results are reversed when per-trade costs yield an elasticity of world
demand for domestic equity of . In this case, globalization hazard causes larger
Sudden Stops and higher price guarantees are needed to contain them. However,
even with guarantees set at to 1 percent above the low-productivity fundamentals
price, which cannot prevent reversals in consumption and the current account, the
moral hazard distortion is magni?ed signi?cantly. Welfare gains for the emerging
economy at Sudden Stop states are smaller, and the economy su?ers non-trivial
104
welfare losses in the stochastic steady state. In this case, price guarantees yield
a short-term improvement in macroeconomic indicators and welfare because they
weaken globalization hazard, but international moral hazard outweighs this bene?t
and causes a long-run welfare loss. This outcome can be altered increasing guaran-
teed prices (to fully o?set Sudden Stop e?ects) and adjusting their state-contingent
structure (to weaken the moral hazard distortion) at the same time.
The challenge to the IFO is to design ex-ante price guarantees that can yield
better outcomes than those obtained without an instrument to contain Sudden
Stops. The ?ndings of our quantitative analysis illustrate the complexity of this
task. An e?ective system of price guarantees requires a ”useful” quantitative model
of asset prices that can explain the features of Sudden Stops and provide assessments
of the e?ects of the guarantees taking into account how they a?ect the optimal plans
of forward-looking agents. This challenge also applies to ex-post price guarantees.
The Lerrick-Meltzer and IMF proposals assume that a “useful” model sets sus-
tainable levels of external debt and the “normal” and crash prices of an emerging
economy’s assets. This chapter makes some progress towards developing models that
can be used for these purposes, but clearly there is a lot left for further research.
105
Figure 2.1: Equilibrium in the Date t Equity Market
?
t+1
?
t+1
*
q
t
HH
HH’
FF
FF’
A
B
C
D
106
Figure 2.2: Ergodic Distributions of Domestic Equity and Bond Holdings
0.00
0.02
0.04
0.06
0.08
10 20 30 40 50 60 70 80 90 100 110 120
0.00
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50 60 70 80 90 100 110 120
0.00
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50 60 70
NFE BMR
0.00
0.05
0.10
0.15
0.20
0.25
0.30
10 20 30 40 50 60 70
NSCG SCG
Bonds Bonds
Domestic Equity Domestic Equity
Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements,
NSCG is economy with binding margin requirements and non-state-contingent guarantees, and
SCG is economy with binding margin requirements and state-contingent guarantees.
107
Figure 2.3: Ergodic Distributions of Domestic Equity and Bond Holdings
0.00
0.02
0.04
0.06
0.08
10 20 30 40 50 60 70 80 90 100 110 120
0.00
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50 60 70 80 90 100 110 120
0.00
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50 60 70
NFE BMR
0.00
0.05
0.10
0.15
0.20
0.25
0.30
10 20 30 40 50 60 70
NSCG SCG
Bonds Bonds
Domestic Equity Domestic Equity
Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements,
NSCG is economy with binding margin requirements and non-state-contingent guarantees, and
SCG is economy with binding margin requirements and state-contingent guarantees.
108
Figure 2.4: Consumption & Current Account-GDP Ratio Impact E?ects of a Neg-
ative Productivity Shock in the Sudden Stop Region of Equity & Bonds
5
10
15
20
25
5
10
15
20
25
?80
?60
?40
?20
b (grid position)
NFE
? (grid position)
%
d
e
v
i
a
t
i
o
n
f
r
o
m
m
e
a
n
5
10
15
20
25
5
10
15
20
25
?80
?60
?40
?20
b (grid position)
BMR
? (grid position)
%
d
e
v
i
a
t
i
o
n
f
r
o
m
m
e
a
n
5
10
15
20
25
5
10
15
20
25
0
20
40
b (grid position)
NFE
? (grid position)
%
d
e
v
i
a
t
i
o
n
f
r
o
m
m
e
a
n
5
10
15
20
25
5
10
15
20
25
0
20
40
b (grid position)
BMR
? (grid position)
%
d
e
v
i
a
t
i
o
n
f
r
o
m
m
e
a
n
a. Consumption Impact Effect
b. Current Account?GDP Ratio Impact Effect
Note: The values are in percent deviations from long run average for consumption impact e?ects,
and percentage point di?erence for current account-GDP ratio impact e?ects.
109
Figure 2.5: Conditional Responses to a Negative, One-Standard-Deviation Produc-
tivity Shock
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18
consumption
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18
equity price
-0.8
-0.4
0.0
0.4
0.8
1.2
2 4 6 8 10 12 14 16 18
current account-GDP ratio
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18
consumption
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18
equity price
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
2 4 6 8 10 12 14 16 18
BMR NSCG SCG
current account-GDP ratio
High Leverage State1/ Low Leverage State2/
1/ Forecasting functions of each variable’s equilibrium Markov process conditional on initial states
?=0.938 and b=-4.68, which imply a leverage ratio of 0.029 and a debt/GDP ratio of 0.597.
2/ Forecasting functions of each variable’s equilibrium Markov process conditional on initial states
?=0.938 and b=-3.38, which imply a leverage ratio of 0.021 and a debt/GDP ratio of 0.43
110
Figure 2.6: Equity Pricing Function in the Low Productivity State
20
40
60
80
100
120
20
40
60
2.175
2.18
2.185
2.19
2.195
b (grid position)
equity price
? (grid position)
20
40
60
80
100
120
20
40
60
2.175
2.18
2.185
2.19
2.195
b (grid position)
equity price
? (grid position)
20
40
60
80
100
120
20
40
60
2.175
2.18
2.185
2.19
2.195
b (grid position)
equity price
? (grid position)
Note: The top graph is the Economy with Binding Margin Requirements. The bottom left graph
is the Economy with Non-State-Contingent Guarantees. The bottom right graph is the Economy
with State-Contingent Guarantees
111
Table 2.1: Long Run Business Cycle Moments
Variable mean std. dev. std. dev. correlation ?rst order
(in %) rel. to GDP with GDP autocorr.
I. NFE
GDP 7.833 2.644 1.000 1.000 0.683
consumption 5.366 2.185 0.826 0.853 0.770
current account/GDP 0.000 1.347 0.509 0.979 0.660
trade balance/GDP 0.315 0.948 0.358 0.564 0.811
equity price 2.187 0.121 0.046 0.961 0.606
foreign debt-GDP ratio 0.177 56.694 21.442 -0.076 0.997
debt-equity ratio 0.010 2.888 1.092 0.000 0.001
II. BMR Economy (probability of binding margin constraints = 3.973%)
GDP 7.833 2.644 1.000 1.000 0.683
consumption 5.365 2.186 0.827 0.856 0.771
current account/GDP 0.000 1.324 0.501 0.982 0.664
trade balance/GDP 0.315 0.940 0.355 0.565 0.823
equity price 2.187 0.121 0.046 0.962 0.609
foreign debt-GDP ratio 0.499 37.964 14.358 -0.118 0.994
debt-equity ratio 0.026 2.007 0.759 0.000 0.001
III. NSCG Economy (probability of binding margin constraints = 0.001%)
GDP 7.833 2.644 1.000 1.000 0.683
consumption 5.362 2.052 0.776 0.790 0.724
current account/GDP 0.000 1.487 0.562 0.968 0.660
trade balance/GDP 0.315 1.111 0.420 0.631 0.750
equity price 2.198 0.099 0.037 0.891 0.384
foreign debt/GDP 1.336 41.053 15.526 0.001 0.992
debt-equity ratio 0.071 2.186 0.827 0.000 0.006
IV. SCG Economy (probability of binding margin constraints = 0.001% )
GDP 7.833 2.644 1.000 1.000 0.683
consumption 5.364 2.121 0.802 0.834 0.765
current account/GDP 0.000 1.380 0.522 0.974 0.660
trade balance/GDP 0.315 1.000 0.378 0.599 0.788
equity price 2.188 0.121 0.046 0.903 0.630
foreign debt/GDP 1.114 34.141 12.912 -0.067 0.991
debt-equity ratio 0.059 1.810 0.685 0.000 0.004
Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements,
NSCG is economy with binding margin requirements and non-state-contingent guarantees, and
SCG is economy with binding margin requirements and state-contingent guarantees.
112
Table 2.2: Payo?s of Domestic Agents and Foreign Traders in Baseline Simulations
NFE BMR NSCG SCG
I. Long-run averages
Domestic Agents
Welfare cost 1/ 0.017 0.062 0.057
Foreign Traders
Present value of traders’ returns 17.920 20.519 27.350 25.529
percent change w.r.t. NFE 14.499 52.621 42.460
Returns 0.280 0.321 0.427 0.399
(a) dividend earnings 0.280 0.320 0.427 0.399
(b) trading costs 1.1E-05 2.3E-05 8.8E-05 1.6E-04
II. High leverage Sudden Stop State
Domestic Agents
Welfare cost 1/ 0.367 -1.036 -0.317
(a) short-run cost 2/ 1.376 0.862 0.978
(b) long-run cost 3/ -1.010 -1.899 -1.295
Date-1 rate of time preference 1.58 1.56 1.57 1.57
Foreign Traders
Present value of traders’ returns 10.931 10.940 10.858 10.901
percent change w.r.t. NFE 0.082 -0.670 -0.276
Returns at date 0 -0.192 -3.770 -3.796 -3.791
(a) dividend earnings 0.166 0.166 0.166 0.166
(b) value of trades 0.359 3.927 3.953 3.948
(c) trading costs 1.6E-04 9.8E-03 9.8E-03 9.8E-03
III. Low leverage Sudden Stop State
Domestic Agents
Welfare cost 1/ 0.215 -1.194 -0.393
(a) short-run cost 2/ 0.055 -0.356 -0.293
(b) long-run cost 3/ 0.160 -0.838 -0.100
Date-1 rate of time preference 1.59 1.59 1.59 1.59
Foreign Traders
Present value of traders’ returns 10.931 10.937 10.854 10.901
percent change w.r.t. NFE 0.055 -0.707 -0.272
Returns at date 0 -0.192 -3.056 -3.077 -3.074
(a) dividend earnings 0.166 0.166 0.166 0.166
(b) value of trades 0.359 3.215 3.237 3.234
(c) trading costs 1.6E-04 6.7E-03 6.7E-03 6.7E-03
1/ Compensating variation in date-0 consumption that equates expected lifetime utility obtained
in the BMR, NSCG and SCG economies with that of the NFE.
2/ Compensating variation in date-0 consumption that equates date-0 period utility obtained in
the BMR, NSCG and SCG economies with that of the NFE.
3/ Di?erence of total welfare cost minus short-run cost.
113
Table 2.3: Sensitivity Analysis
Baseline Prod. Shocks Guarantees Trading Costs
(I) (II) (III) (IV) (V) (VI)
? = 0.8 ?
?
= 2.4% 1% above q
f
? = 0.01 a = 2
I. BMR Economy
In. responses in high lev. st.
consumption -1.335 -1.380 -1.404 n.a. -1.453 -3.059
current account/GDP 0.939 0.972 0.997 n.a. 1.023 2.157
equity price -0.413 -0.413 -0.413 n.a. -0.412 -4.324
traders’ return -4.529 -4.526 -4.526 n.a. -4.522 -4.866
Moments of the ergodic dist.
Prob. of bind. mar. cons. (%) 3.973 4.200 2.331 n.a. 16.740 19.444
Averages
consumption 5.365 5.369 5.366 n.a. 5.369 5.378
equity price 2.187 2.187 2.187 n.a. 2.183 2.183
equity holdings 0.883 0.885 0.861 n.a. 0.906 0.907
Standard deviations (%)
consumption 2.186 2.382 2.721 n.a. 2.169 2.454
current account/GDP 1.324 1.325 2.020 n.a. 1.432 1.428
equity price 0.121 0.184 0.100 n.a. 0.114 0.463
Domestic welfare loss1/
high leverage state 0.367 0.361 0.389 n.a. 0.490 4.074
long-run average 0.017 0.013 0.012 n.a. 0.099 0.110
?PDV of traders’ returns1/
high leverage state 0.083 0.082 0.095 n.a. 3.448 0.924
long-run average 14.502 12.163 4.354 n.a. 34.519 27.531
II. NSCG Economy
In. responses in high lev. st.
consumption -0.840 -0.875 -0.901 -0.503 -0.885 -2.205
current account/GDP 0.591 0.616 0.640 0.354 0.623 1.554
equity price 0.259 0.274 0.214 0.718 0.362 -3.256
traders’ return -4.562 -4.560 -4.561 -4.586 -4.561 -4.926
Moments of the ergodic dist.
Prob. of bind. mar. cons. (%) 0.001 0.017 0.024 0.002 0.002 0.000
Prob. of executing guar.(%) 34.290 32.892 15.434 29.650 34.068 28.925
Averages
consumption 5.362 5.365 5.360 5.361 5.362 5.362
equity price 2.198 2.199 2.198 2.208 2.198 2.206
equity holdings 0.844 0.844 0.844 0.842 0.844 0.842
expected PDV of excess prices 0.012 0.013 0.011 0.022 0.015 0.023
Standard deviations (%)
consumption 2.052 2.269 2.615 2.014 2.047 2.191
current account/GDP 1.487 1.473 2.035 1.567 1.490 1.584
equity price 0.099 0.149 0.104 0.091 0.100 0.429
expected PDV of excess prices 2.083 3.913 4.235 1.375 1.368 1.466
Domestic welfare loss1/
high leverage state -1.036 -1.137 -1.033 -2.359 -1.025 1.506
long-run average 0.062 0.063 0.132 0.086 0.286 0.332
?PDV of traders’ returns1/
high leverage state -0.670 -0.732 -0.660 -1.372 2.501 -0.459
long-run average 52.621 51.867 17.567 54.696 122.862 116.646
114
Table 2.3: Sensitivity Analysis (Continued)
Baseline Prod. Shocks Guarantees Trading Costs
(I) (II) (III) (IV) (V) (VI)
? = 0.8 ?
?
= 2.4% 1% above q
f
? = 0.01 a = 2
III. SCG Economy
In. responses in high lev. st.
consumption -0.952 -0.878 -0.988 -0.626 -0.920 -2.182
current account/GDP 0.670 0.618 0.702 0.440 0.648 1.538
equity price 0.107 0.270 0.105 0.550 0.313 -3.227
traders’ return -4.555 -4.560 -4.555 -4.586 -4.558 -4.928
Moments of the ergodic dist.
Prob. of bind. mar. cons. (%) 0.001 0.014 0.042 0.009 0.013 0.000
Prob. of executing guar.(%) 0.035 0.261 0.391 0.502 6.063 3.245
Averages
consumption 5.364 5.369 5.363 5.363 5.358 5.355
equity price 2.188 2.188 2.189 2.190 2.190 2.191
equity holdings 0.855 0.855 0.855 0.850 0.879 0.874
expected PDV of excess prices 0.002 0.002 0.011 0.003 0.007 0.009
Standard deviations (%)
consumption 2.121 2.317 2.709 2.095 2.061 2.298
current account/GDP 1.380 1.369 2.028 1.420 1.466 1.536
equity price 0.121 0.187 0.120 0.137 0.154 0.469
expected PDV of excess prices 42.186 62.894 4.235 52.202 37.543 51.111
Domestic welfare loss1/
high leverage state -0.317 -0.481 -0.297 -0.869 -0.385 2.596
long-run average 0.057 0.053 0.033 0.054 0.086 0.121
?PDV of traders’ returns1/
high leverage state -0.276 -0.359 -0.246 -0.567 2.985 0.167
long-run average 42.460 41.196 9.446 47.217 72.049 73.680
Note: The guaranteed price is 0.5 percent (1 percent for column (IV)) above the fundamentals
price in the low productivity state of the baseline simulation. Welfare costs are compensating
variations in initial consumption that equalize lifetime utility in each simulation with that of the
corresponding NFE. Initial responses are in percent of the corresponding NFE and detrended as
described in the text (except the response for traders’ returns which is in percent of the capital
stock and the response for the current account-output ratio which is the di?erence in percentage
points relative to the corresponding NFE).
1/Percentage change relative to NFE
115
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doc_429715240.pdf
A sudden stop in capital flows is defined as a sudden slowdown in private capital inflows into emerging market economies, and a corresponding sharp reversal from large current account deficits into smaller deficits or small surpluses.
ABSTRACT
Title of dissertation: ESSAYS ON PREVENTING SUDDEN STOPS
Ceyhun Bora Durdu, Doctor of Philosophy, 2006
Dissertation directed by: Professor Enrique G. Mendoza
Department of Economics
Capital markets have witnessed a rash of ‘Sudden Stops’ during the last decade.
Policy proposals to prevent these crises include creating indexed bond markets and
providing price guarantees for emerging market assets. Chapter 1 explores the
macroeconomic implications of indexed bonds with a return indexed to the key
variables driving emerging market economies such as terms of trade or productivity.
We employ a quantitative model of a small open economy in which Sudden Stops are
driven by the ?nancial frictions inherent to world capital markets. While indexed
bonds provide a hedge to income ?uctuations and can undo the e?ects of ?nancial
frictions, they lead to interest rate ?uctuations. Due to this tradeo?, there exists a
non-monotonic relation between the “degree of indexation” (i.e., the percentage of
the shock re?ected in the return) and the overall e?ects of these bonds on macroe-
conomic ?uctuations. Therefore, indexation can improve macroeconomic conditions
only if the degree of indexation is less than a critical value. When the degree of
indexation is higher than this threshold, it strengthens the precautionary savings
motive, increases consumption volatility and impact e?ect of Sudden Stops. The
threshold degree of indexation depends on the volatility and persistence of income
shocks as well as the relative openness of the economy.
Chapter 2 explores the implications of asset price guarantees provided by an
international ?nancial organization on the emerging market assets. This policy is
motivated by the globalization hazard hypothesis, which suggest that Sudden Stops
caused by global ?nancial frictions could be prevented by o?ering foreign investors
price guarantees on emerging markets assets. These guarantees create a trade-
o?, however, because they weaken globalization hazard while creating international
moral hazard. We study this tradeo? using a quantitative, equilibrium asset-pricing
model. Without guarantees, margin calls and trading costs cause Sudden Stops
driven by a Fisherian de?ation. Price guarantees prevent this de?ation by propping
up foreign demand for assets. The e?ectiveness of price guarantees, their distor-
tions on asset markets, and their welfare implications depend critically on whether
the guarantees are contingent on debt levels and on the price elasticity of foreign
demand for domestic assets.
ESSAYS ON PREVENTING SUDDEN STOPS
by
Ceyhun Bora Durdu
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
2006
Advisory Commmittee:
Professor Enrique G. Mendoza, Chair/Advisor
Professor Bora?gan Aruoba
Professor Gurdip Bakshi
Professor Guillermo A. Calvo
Professor John Rust
Professor Carlos Vegh
c Copyright by
Ceyhun Bora Durdu
2006
DEDICATION
To my wife, Emine, my parents and my brother.
ii
ACKNOWLEDGMENTS
I am greatly indebted to all the people who have made this thesis possible.
First and foremost, I’d like to thank my advisor, Enrique Mendoza for his
patience and his continuous support throughout my graduate studies. Right from
the beginning, I learnt a lot from him; how to broaden my view and approach to
economic problems, how to get myself out from technicality into applicability and
intuition. His guidance shaped my ideas, helped me mature. He read every single
detail of my drafts and provided invaluable technical and editorial comments. He
always made himself available for help and advice. Every time I stumbled, I felt
his strong support that helped me stand up and “keep my eyes on the ball.” I am
greatly indebted for all this and his ever lasting friendship.
My special thanks also go to the other members of my core committee, Bora?gan
Aruoba, Guillermo Calvo, and John Rust. Their critiques and insightful comments
improved this thesis drastically. They raised excellent and thoughtful questions that
made me think harder and understand my work better. They also made themselves
available for help and advice anytime I needed. Having the opportunity to work
with such a special group of people has been invaluable.
I also thank Carlos Vegh for his help and support during this process, and join-
ing my committee. Gurdip Bakshi also kindly accepted to serve on my committee,
I owe my gratitude to him.
iii
I owe my deepest thanks to my beloved wife, my colleague, my companion
in this hard work, Emine. She shared every single happiness and disappointment
throughout my studies. She made important contributions to this thesis with our
productive conversations, with her comments on my drafts. She patiently listened
to my presentations over and over again. She stood beside me every time I faced an
obstacle.
I also thank my parents and my brother. They sacri?ced a lot during these
studies. But they never complained, and they have always supported me to pursue
what I have been passionate for and to produce an outcome that they can be proud
of.
Part of this thesis was completed while I visited the International Finance
Division of the Federal Reserve Board as a Dissertation Intern. I thank for their
hospitality and friendship, and my special thanks go to John Rogers, and Felipe
Zana.
This thesis has also bene?ted from the comments of several other people in-
cluding David Bowman, Christian Daude, Jon Faust, Dale Henderson, Ayhan K¨ose,
Marcelo Oviedo, the participants of the Inter University Conference at Princeton
University, Emerging Markets and Macroeconomic Volatility Conference at the Fed-
eral Reserve Bank of San Francisco, 2005 Midwest Macroeconomic Meetings, and
seminars participants at the Federal Reserve Board, the University of Maryland, the
Bank of England, the Bank of Hungary, Ko¸c University, Sabanc?University, Bilkent
University, TOBB ETU University, the Central Bank of Turkey, the Federal Reserve
Bank of Dallas and the Congressional Budget O?ce. I thank them here.
iv
TABLE OF CONTENTS
List of Tables vi
List of Figures vii
1 Are Indexed Bonds a Remedy for Sudden Stops? 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.3 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
1.3.1 The frictionless one-sector model . . . . . . . . . . . . . . . . 14
1.3.2 Two Sector Model with Financial Frictions . . . . . . . . . . . 22
1.3.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 31
1.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2 Are Asset Price Guarantees Useful for Preventing Sudden Stops?: A Quan-
titative Investigation of the Globalization Hazard-Moral Hazard Tradeo?
(coauthored with Enrique G. Mendoza) 52
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.2 A Model of Globalization Hazard and Price Guarantees . . . . . . . . 57
2.2.1 The Emerging Economy . . . . . . . . . . . . . . . . . . . . . 58
2.2.2 The Foreign Securities Firm, the IFO & the Price Guarantees 61
2.2.3 Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
2.3 Characterizing the Globalization Hazard-Moral Hazard Tradeo? . . . 63
2.4 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
2.4.1 Recursive Equilibrium and Solution Method . . . . . . . . . . 69
2.4.2 Deterministic Steady State and Calibration to Mexican Data . 71
2.4.3 Stochastic Simulation Framework . . . . . . . . . . . . . . . . 78
2.4.4 Baseline Results: Globalization Hazard and Sudden Stops
without Price Guarantees . . . . . . . . . . . . . . . . . . . . 80
2.4.5 Baseline Results: State-Contingent and Non-State-Contingent
Price Guarantees . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.5 Normative Implications and Sensitivity Analysis . . . . . . . . . . . . 88
2.5.1 Normative Implications of the Baseline Simulations . . . . . . 88
2.5.2 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . 97
2.6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
Bibliography 116
v
LIST OF TABLES
1.1 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
1.2 Parameter Values . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
1.3 Previous Attempts of Indexed Bonds . . . . . . . . . . . . . . . . . . 38
1.4 Business Cycle Facts for Emerging Countries . . . . . . . . . . . . . . 39
1.5 Long Run Business Cycle Statistics of the One-Sector Model . . . . . 40
1.6 Returns and Natural Debt Limits . . . . . . . . . . . . . . . . . . . . 40
1.7 Variance Decomposition Analysis for Consumption . . . . . . . . . . 40
1.8 Long Run Business Cycle Statistics of the Two-Sector Model . . . . . 41
1.9 Initial Responses to a One-Standard-Deviation Endowment Shock . . 41
1.10 Sensitivity Analysis of the One-Sector Model . . . . . . . . . . . . . . 42
1.11 Sensitivity Analysis of the Two-Sector Model: Higher Share of Non-
tradable Output . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
2.1 Long Run Business Cycle Moments . . . . . . . . . . . . . . . . . . . 112
2.2 Payo?s of Domestic Agents and Foreign Traders in Baseline Simulations113
2.3 Sensitivity Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
2.3 Sensitivity Analysis (Continued) . . . . . . . . . . . . . . . . . . . . . 115
vi
LIST OF FIGURES
1.1 Sudden Stops in Emerging Markets . . . . . . . . . . . . . . . . . . . 44
1.2 Deviations from Trend in Consumption and Ouput . . . . . . . . . . 45
1.3 Long Run Distributions of Bond Holdings in Non-Indexed Economies 46
1.4 Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock . . . . . . . . . . . . . . . . . 47
1.5 Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock . . . . . . . . . . . . . . . . . 48
1.6 Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock . . . . . . . . . . . . . . . . . 49
1.7 Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock . . . . . . . . . . . . . . . . . 50
1.8 Time Series Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 51
2.1 Equilibrium in the Date t Equity Market . . . . . . . . . . . . . . . . 106
2.2 Ergodic Distributions of Domestic Equity and Bond Holdings . . . . 107
2.3 Ergodic Distributions of Domestic Equity and Bond Holdings . . . . 108
2.4 Consumption & Current Account-GDP Ratio Impact E?ects of a
Negative Productivity Shock in the Sudden Stop Region of Equity
& Bonds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
2.5 Conditional Responses to a Negative, One-Standard-Deviation Pro-
ductivity Shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
2.6 Equity Pricing Function in the Low Productivity State . . . . . . . . 111
vii
Chapter 1
Are Indexed Bonds a Remedy for Sudden Stops?
1.1 Introduction
Liability dollarization
1
and frictions in world capital markets have played a key
role in the emerging market crises or Sudden Stops of the last decade. Typically,
these crises are triggered by sudden reversals of capital in?ows that result in sharp
real exchange rate depreciations and collapses in consumption. Figures 1, 2, and
Table 4 document the Sudden Stops observed in Argentina, Chile, Mexico, and
Turkey in the last decade. For example in 1994, Turkey experienced a Sudden Stop
characterized by: 10% current account-GDP reversal, 10% consumption and GDP
drops relative to their trends, and 31% real exchange rate depreciation.
2
In an e?ort to remedy Sudden Stops, Caballero (2002, 2003) and Borensztein
and Mauro (2004) propose the issuance of state contingent debt instruments by
emerging market economies. Caballero’s proposal relies on the premise that crises in
some emerging economies are driven by external shocks (e.g., terms of trade shocks),
and that contrary to their developed counterparts, these economies have di?culty
absorbing these shocks due to imperfections in world capital markets. Most emerging
1
Liability dollarization refers to the denomination of debt in units of tradables (i.e., hard cur-
rencies). Liability dollarization is common in emerging markets, where debt is denominated in
units of tradables but partially leveraged on large non-tradables sectors.
2
See Figures 1 and 2, Table 4 for further documentation of these empirical regularities (see
Calvo et al. (2003) and Calvo and Reinhart (1999) for a more detailed empirical analysis).
1
countries could reduce aggregate volatility in their economies and cut precautionary
savings if they possessed debt instruments for which returns are contingent on the
external shocks that trigger crises.
3
He suggests creating an indexed bonds market
in which bonds’ returns are contingent on terms of trade shocks or commodity
prices.
4
Borensztein and Mauro (2004) argue that GDP-indexed bonds could reduce
the aggregate volatility and the likelihood of unsustainable debt-to-GDP levels in
emerging economies. Hence, they argue that these bonds can help these countries
avoid pro-cyclical ?scal policies.
This chapter introduces indexed bonds into a quantitative general equilibrium
model of a small open economy with ?nancial frictions in order to analyze the
implications of these bonds for macroeconomic ?uctuations and Sudden Stops. The
model incorporates ?nancial frictions proposed in the Sudden Stops literature (Calvo
(1998), Mendoza (2002), Mendoza and Smith (2005), Caballero and Krishnamurthy
(2001), among others). In particular, the economy su?ers from liability dollarization,
international debt markets impose a borrowing constraint in the small open economy.
This constraint limits debt to a fraction of the economy’s total income valued at
tradable goods prices. As established in Mendoza (2002), when the only available
instruments are non-indexed bonds, an exogenous shock to productivity or to the
terms of trade that renders the borrowing constraint binding triggers a Fisherian
debt-de?ation mechanism.
5
A binding borrowing constraint leads to a decline in
3
Precautionary savings refers to extra savings caused by ?nancial markets being incomplete.
Caballero (2002) points out that precautionary savings in emerging countries arise as excessive
accumulation of foreign reserves.
4
Caballero (2002) argues, for example, that Chile could index to copper prices, and that Mexico
and Venezuela could index to oil prices.
5
See Mendoza and Smith (2005), and Mendoza (2005) for further analysis on Fisherian debt-
2
tradables consumption relative to non-tradables consumption, inducing a fall in the
relative price of non-tradables as well as a depreciation of the real exchange rate
(RER). The decline in RER makes the constraint even more binding, creating a
feedback mechanism that induces collapses in consumption and the RER, as well as
a reversal in capital in?ows.
Our analysis consists of two steps. The ?rst step is to consider a one-sector
economy in which agents receive persistent endowment shocks, credit markets are
perfect but insurance markets are incomplete (henceforth frictionless one-sector
model). Second, we analyze a two sector model with ?nancial frictions that can
produce Sudden Stops endogenously through the mechanism explained in the previ-
ous paragraph. The motivation for the ?rst step is to simplify the model as much as
possible in order to understand how the dynamics of the model with indexed bonds
di?er from those of the one with non-indexed bonds.
6
In this frictionless one-sector
model, when the available instruments are only non-indexed bonds with a constant
exogenous return, agents try to insure away income ?uctuations with trade balance
adjustments. Since insurance markets are incomplete, agents are not able to attain
full-consumption smoothing, consumption is volatile, and correlation of consump-
tion with income is positive. Furthermore, agents try to self-insure by engaging in
precautionary savings. If the returns of the bonds are indexed to the exogenous
income shock only, the insurance markets are only “partially complete.” In order
to have complete markets, either full set of state contingent assets such as Arrow
de?ation.
6
This case can also be used to examine the role of indexed bonds in small open developed
economies such as Australia and Sweden, which have relatively large tradables sectors and better
access to international capital markets than most emerging market economies.
3
securities should be available (i.e., there are as many assets as the states of nature)
or the returns should be state contingent (i.e., contingent on both the exogenous
shock and the debt levels, see Section 1.3.1 for further discussion). Although in-
dexed bonds partially complete the market, the hedge provided by these bonds are
imperfect because they introduce interest rate ?uctuations. Assessing whether the
bene?ts (due to hedging) o?set the costs (due to interest rate ?uctuations) induced
by indexed bonds requires quantitative analysis.
Our quantitative analysis of the frictionless one-sector model establishes that
there exists a non-monotonic relation between the “degree of indexation” of the
bonds (i.e., the percentage of the shock that is passed on to the bonds’ return) and
the overall e?ects of these bonds on macroeconomic variables. Therefore, indexed
bonds can reduce precautionary savings, volatility of consumption and correlation
of consumption with income only if the degree of indexation is lower than a critical
value. If it is higher than this threshold (as with full indexation), indexed bonds
worsen these macroeconomic variables.
The changes in precautionary savings are driven by the changes in “catas-
trophic level of income.” Risk averse agents have strong incentives to avoid attain-
ing levels of debt that the economy cannot support when the income is at catas-
trophic level.
7
Because, otherwise agents would attain non-positive consumption
levels which in turn leads to in?nitely negative utility if such income levels realize.
The degree of indexation has a signi?cant e?ect on determining the state of nature
7
The largest debt that the economy can support to guarantee non-negative consumption in the
event that income is almost surely at its catastrophic level is referred as natural debt limit.
4
that de?nes catastrophic levels of income and whether these income levels are higher
or lower than what they would be without indexation. With higher degrees of in-
dexation, these income levels can be determined at a positive shock, because, for
example, if agents receive positive income shocks forever, they will receive higher
endowment income but will also pay higher interest rates. Our analysis shows that
for higher values of the degree of indexation, the latter e?ect is stronger, leading to
lower catastrophic income levels. This in turn creates stronger incentives for agents
to build up bu?er stock savings.
The e?ect of indexation on consumption volatility can be analyzed by de-
composing the variance of consumption. (Consider the budget constraint of such
an economy c
t
= (1 + ?
t
)y ? b
t+1
+ (1 + r + ?
t
)b
t
.
8
Using this budget constraint,
var(c
t
) = var(y
t
) + var(tb
t
) ? 2cov(tb
t
, y
t
)). On one hand, for a given income
volatility, indexation increases the covariance of trade balance with income (since
in good (bad) times indexation commands higher (lower) repayments to the rest of
the world), which lowers the volatility of consumption. On the other hand, index-
ation increases the volatility of trade balance (due to introduction of interest rate
?uctuations), which increases the volatility of consumption. Our analysis suggests
that at high levels of indexation, increase in the variance of trade balance dominates
the increase in the covariance of trade balance with income, which in turn increases
consumption volatility.
This tradeo? is also preserved in the two sector model with ?nancial frictions.
8
Here, b is bond holdings, r is risk free net interest rate, y is endowment income, ?
t
is the
income shock, and c is consumption.
5
In addition, in this model, the interaction of the indexed bonds with the ?nancial
frictions leads to additional bene?ts and costs. Speci?cally, when indexed bonds are
in place, negative shocks can result in a relatively small decline in tradable consump-
tion; as a result, the initial capital out?ow is milder and the RER depreciation is
weaker compared to a case with non-indexed bonds. The cushioning in the RER can
help to contain the Fisherian debt-de?ation process. While these bonds help relax
the borrowing constraint in case of negative shocks, this time, an increase in debt
repayment following a positive shock can lead to a larger need for borrowing, which
can make the borrowing constraint suddenly binding, triggering a debt-de?ation.
Quantitative analysis of this model suggests, once again, that the degree of indexa-
tion needs to be lower than a critical value in order to smooth Sudden Stops. With
indexation higher than this critical value, the latter e?ect dominates the former,
hence lead to more detrimental e?ects of Sudden Stops. We also ?nd that the
degree of indexation that minimizes macroeconomic ?uctuations and impact e?ect
of Sudden Stops depends on the persistence and volatility of the exogenous shock
triggering Sudden Stops, as well as the size of the non-tradables sector relative to
its tradables sector; suggesting that the indexation level that maximizes bene?t of
indexed bonds needs to be country speci?c. Because an indexation level that is
appropriate for one country in terms of its e?ectiveness at preventing Sudden Stops
may not be e?ective for another and may even expose to higher risk of facing Sudden
Stops.
Debt instruments indexed to real variables (i.e., GDP, commodity prices, etc.)
6
have not been widely employed in international capital markets.
9
As Table 1.3
shows, only a few countries issued these types of instruments in the past. In the early
1990s, Bosnia and Herzegovina, Bulgaria, and Costa Rica issued bonds containing
an element of indexation to GDP; at the same time, Mexico and Venezuela issued
bonds indexed to oil. Since the late 1990s, Bulgaria has already swapped a portion
of its debt with non-indexed bonds. France issued gold-indexed bonds in the early
1970s, but due to depreciation of the French Franc in subsequent years, the French
government bore signi?cant losses and halted issuance.
10
Although problems on the
demand side have been emphasized in the literature as the primary reason for the
limited issuance of indexed bonds, the supply of such bonds has always been thin,
as countries have exhibited little interest in issuing them. Our results may also help
to understand why it has been the case: countries may have been reluctant due to
the imperfect hedge that these bonds provide.
Several studies have explored the costs and bene?ts of indexed debt instru-
ments in the context of public ?nance and optimal debt management.
11
As men-
tioned above, Borensztein and Mauro (2004) and Caballero (2003) drew attention
to these instruments as possible vehicles to provide insurance bene?ts to emerging
countries. Moreover, Caballero and Panageas (2003) quanti?ed the potential wel-
fare e?ects of credit lines o?ered to emerging countries. They modelled a one-sector
model with collateral constraints where Sudden Stops are exogenous. They used
9
In terms of hedging perspective CPI-indexed bonds may not provide a hedge against income
risks, since in?ation is pro-cyclical.
10
The French government paid 393 francs in interest payments for each bond issued, far more
than the 70 francs originally planned (Atta-Mensah (2004)).
11
See, for instance, Barro (1995), Calvo(1988), Fischer (1975), Magil and Quinzii (1005), among
others
7
this setup to explore the bene?ts of these credit lines in terms of smoothing Sudden
Stops, interpreting them as akin to indexed bonds. This chapter contributes to
this literature by modelling indexed bonds explicitly in a dynamic stochastic gen-
eral equilibrium model where Sudden Stops are endogenous. Endogenizing Sudden
Stops reveals that the e?cacy of indexed bonds in terms of preventing these crises
depends on whether the bene?ts due to hedging outweigh the imperfections intro-
duced by these bonds. Depending on the structure of indexation, we show that they
can potentially amplify the e?ects of Sudden Stops.
12
This chapter is related to studies in several strands of macro and international
?nance literature. The model has several features common to the literature on
precautionary saving and macroeconomic ?uctuations (e.g., Aiyagari (1994), Hugget
(1993)). The chapter is also related to studies exploring business cycle ?uctuations
in small open economies (e.g., Mendoza (1991), Neumeyer and Perri (2005), Kose
(2002), Oviedo (2005), Uribe and Yue (2005)) from the perspective of analyzing how
interest rate ?uctuations a?ect macroeconomic variables. In addition to the papers
in the Sudden Stops literature, this chapter is also related to follow up studies to this
literature, including Calvo (2002), Durdu and Mendoza (2005), and Caballero and
Panageas (2003), which investigate the role of relevant policies in terms of preventing
Sudden Stops. Durdu and Mendoza (2005) explore the quantitative implications of
price guarantees o?ered by international ?nancial organizations on emerging market
assets. They ?nd that these guarantees may induce moral hazard among global
12
Krugman (1998) and Froot et al. (1989) emphasize moral hazard problems that GDP indexa-
tion can introduce. Here, we point out other adverse e?ects that indexation can cause even in the
absence of moral hazard.
8
investors, and conclude that the e?ectiveness of price guarantees depends on the
elasticity of investors’ demand as well as whether the guarantees are contingent on
debt levels. Similarly, in this chapter, we explore the potential imperfections that
can be introduced by the issuance of indexed bonds, and derive the conditions under
which such a policy could be e?ective in preventing Sudden Stops.
Our ?ndings are closely related to those of Magill and Quinzii (1995). They
compare the welfare e?ects of introduction of in?ation indexed bonds and point out
that while these bonds can eliminate the ?uctuations in purchasing power, they
introduce another risk that arise from relative price ?uctuations; suggesting that
economies might actually be worse o? with introduction of in?ation indexed bonds.
Earlier seminal studies that in ?nancial innovation literature such as Shiller
(1993) and Allen and Gale (1994) analyze how creation of new class of “macro
markets” can help to manage economic risks such as real estate bubbles, in?ation,
recessions, etc. and discusses what sorts of frictions can prevent the creation of
these markets. This chapter emphasizes possible imperfections in global markets,
and points out under which conditions issuance of indexed bonds may not improve
macroeconomic conditions for a given emerging market.
The rest of the chapter proceeds as follows. The next section describes the full
model environment. Section 1.3 presents the quantitative results of the frictionless
one-sector model, and the two-sector model with ?nancial frictions. We conclude
and o?er extensions in Section 1.4.
9
1.2 Model
In this section, we describe the general setup of the two sector model with
?nancial frictions. The model with non-indexed bonds is similar to Mendoza (2002).
Foreign debt is denominated in units of tradables and imperfect credit markets
impose a borrowing constraint that limits external debt to a share of the value of
total income in units of tradables (which therefore re?ects changes in the relative
price of non-tradables that is the model’s RER).
Representative households receive a stochastic endowment of tradables and
non-stochastic endowment of non-tradables, which are denoted (1 + ?
t
)y
T
and y
N
,
respectively. ?
t
is a shock to the world value of the mean tradables endowment
that could represent a productivity shock or a terms-of-trade shock. In our model,
? ? E = [?
1
< ... < ?
m
] (where ?
1
= ??
m
) evolves according to an m-state symmetric
Markov chain with transition matrix P. Households derive utility from aggregate
consumption (c), and maximize Epstein’s (1983) stationary cardinal utility function:
U = E
0
_
?
t=0
exp
_
?
t?1
?=0
? log(1 + c
t
)
_
u(c
t
)
_
. (1.1)
Functional forms are given by:
u(c
t
) =
c
1??
t
?1
1 ??
, (1.2)
c
t
(c
T
t
, c
N
t
) =
_
?(c
T
t
)
?µ
+ (1 ??)(c
N
t
)
?µ
¸
?
1
µ
. (1.3)
10
The instantaneous utility function (1.2) is in constant relative risk aversion
(CRRA) form with an inter-temporal elasticity of substitution 1/?. The consump-
tion aggregator is represented in constant elasticity of substitution (CES) form,
where 1/(1+µ) is the elasticity of substitution between consumption of tradables and
non-tradables and where ? is the CES weighing factor. exp
_
?
t?1
?=0
? log(1 + c
t
)
¸
is
an endogenous discount factor that is introduced to induce stationarity in consump-
tion and asset dynamics. ? is the elasticity of the subjective discount factor with
respect to consumption. Mendoza (1991) introduced preferences with endogenous
discounting to quantitative small open economy models, and such preferences have
since been widely used.
13
The households’ budget constraint is:
c
T
t
+p
N
t
c
N
t
= (1 +?
t
)y
T
+p
N
t
y
N
?b
t+1
+ (1 +r +??
t
)b
t
(1.4)
where b
t
is current bond holdings, (1 + r + ??
t
) is the gross return on bonds, and
p
N
t
is relative price of non-tradables. The indexation of the debt works as follows.
Consider a case in which there are high and low states for tradables income. The
return on the indexed bonds is low in the bad state and high in the good one, but
the mean of the return remains unchanged and equal to R.
14
When households’
13
As explained in Schmitt-Groh´e and Uribe (2003), preferences with constant discounting, where
rate of time preference is equal to real interest rate, introduces non-stationarity in consumption
and asset holdings. Schmitt-Groh´e and Uribe (2003) compares the quantitative implications of the
speci?cations used in the literature to resolve this problem. Kim and Kose (2003) also compares
quantitative implications of endogenous discounting with that of constant discounting.
14
Although return is indexed to terms of trade shock, our modeling approach potentially sheds
light on the implications of RER indexation, as well. In our model, the aggregate price index (i.e.,
the RER) is an increasing function of the relative price of non-tradables (p
N
), which is determined
at equilibrium in response to endowment shocks.
11
current bond holdings are negative, (i.e., when households are debtors) they pay
less (more) in the event of a negative (positive) endowment shock. The standard
assumption on modelling bonds’ return is to assume that indexation is one-to-one;
i.e., the return of indexed bonds is 1+r+?
t
(see for example Borensztein and Mauro
(2004)). Here, we consider a more ?exible setup by assuming a ?exible degree of
indexation by introducing a parameter ? ? [0, 1], which measures the degree of
indexation of the bonds. In particular, the limiting case ? = 0 yields the benchmark
case with non-indexed bonds, while ? = 1 is the full-indexation case. Notice that
? a?ects the variance of the bonds’ return (since var(1 + r + ??
t
) = ?
2
var(?
t
)).
As ? increases, the bonds provide a better hedge against negative income shocks,
but at the same time it introduces additional volatility by increasing the return’s
variance. As explained below, there is a critical degree of indexation beyond which
the distortions due to the increased volatility of returns outweigh the bene?ts that
indexed bonds introduce. In our quantitative experiments, we will characterize the
value of ?; at which, the bonds’ bene?ts are maximized.
To simplify notation, we denote bond holdings as b
t
regardless of whether
bonds are non-indexed or indexed. As mentioned above, when ? is equal to zero,
the bond boils down to a non-indexed bond with a ?xed gross return R = 1 + r.
This return is exogenous and equal to the world interest rate. When ? is greater
than zero, it is an indexed bond with a state contingent return; i.e., it (imperfectly)
hedges income ?uctuations.
In addition to the budget constraint, foreign creditors impose the following
borrowing constraint, which limits debt issuance as a share of total income at period
12
t not to exceed ?:
b
t+1
? ??
_
(1 +?
t
)y
T
+p
N
t
y
N
¸
. (1.5)
The borrowing constraint takes a similar form as those used in the Sudden Stops lit-
erature in order to mimic the tightening of the available credit to emerging countries
(see for example, Caballero and Krishnamurthy (2001), Mendoza (2002), Mendoza
and Smith (2005), Caballero and Panageas (2003)). As Mendoza and Smith (2005)
explain, although these types of borrowing constraints are not based upon a con-
tracting problem between lenders and borrowers, they are realistic in the sense that
they resemble the risk management tools used in international capital markets, such
as Value-at-Risk models employed by investment banks.
The optimality conditions of the problem facing households are standard and
can be reduced to the following equations:
U
c
(t)
_
1 ?
?
t
?
t
_
= exp [?? log(1 + c
t
)] E
t
_
(1 + r +??
t
)p
c
t
p
c
t+1
U
c
(t + 1)
_
(1.6)
1 ??
?
_
c
T
t
c
N
t
_
1+µ
= p
N
t
(1.7)
along with the budget constraint (1.4), the borrowing constraint (1.5), and the
standard Kuhn-Tucker conditions. ? and ? are the Lagrange multipliers of the
borrowing constraint and the budget constraint, respectively. U
c
is the deriva-
tive of lifetime utility with respect to aggregate consumption. p
c
t
is the CES price
index of aggregate consumption in units of tradable consumption, which equals
_
?
1
µ+1
+ (1 ??)
1
µ+1
(p
N
)
µ
µ+1
_
1+µ
µ
. Equation (1.6) is the standard Euler Equation
13
equating marginal utility at date t to that of date t +1. Equation (1.7) equates the
marginal rate of substitution between tradabales consumption and non-tradables
consumption to the relative price of non-tradables.
1.3 Quantitative Analysis
We explore the model’s dynamics in two steps. First, we examine the role
that indexed bonds play in a standard one-sector model in which the problem of
liability dollarization is excluded and there is no borrowing constraint. Then we
introduce the two frictions back as in the complete model described above in order
to examine the role that indexed bonds can play in reducing the adverse e?ects of
liability dollarization and preventing Sudden Stops.
1.3.1 The frictionless one-sector model
In the frictionless one-sector version of the model, indexed bonds with returns
indexed to the exogenous shock are not able to complete the market but just partially
completes it by providing the agents with the means to hedge against ?uctuations
in endowment income. If we call (1 + r + ??)b
t
?nancial income, the underlying
goal to complete the market would be to keep the sum of endowment and ?nancial
incomes constant and equal to the mean endowment income, i.e., (1+?
t
)y
T
+(1+r+
??)b
t
= y
T
. Clearly, we can keep this sum constant only if the bonds’ return is state
contingent (i.e., contingent on both the exogenous shock and the debt stock, which
requires R
t
(b, ?) = ?
?
t
y
T
b
t
or agents can trade Arrow securities (i.e., there are as many
14
assets as the number of state of nature). Hence, indexed bonds introduce a tradeo?:
on one hand it hedges income ?uctuations but on the other hand it introduces
interest rate ?uctuations. In order to analyze the overall e?ect of indexed bonds,
we solve the model numerically. The dynamic programming representation (DPP)
of the household’s problem in this case reduces to:
V (b, ?) = max
b
_
u(c) + (1 + c)
??
E [V (b
, ?
)]
_
s.t.
c
T
= (1 + ?)y
T
?b
+ (1 +r +??)b.
(1.8)
Here, the endogenous state space is given by B = {b
1
< ... < b
NB
}, which is
constructed using NB = 1, 000 equidistant grid points. The exogenous Markov
process is assumed to have two states for simplicity: E = {?
L
< ?
H
}. Optimal
decision rules, b
(b, ?) : E × B ? R, are obtained by solving the above DPP via a
value function iteration algorithm.
Calibration
The parameter values used to calibrate the model are summarized in Table 1.1.
The CRRA parameter ? is set to 2, the mean endowment y
T
is normalized to one,
and the gross interest rate is set to the quarterly equivalent of 6.5%, following the
values used in small open economy RBC literature (see for example Mendoza (1991)).
The steady state debt-to-GDP ratio is set to 35%, which is inline with the estimate
for the net asset position of Turkey (see Lane and Milesi-Ferretti (1999)). The
elasticity of the subjective discount factor follow from euler equation for consumption
15
evaluated at steady-state:
(1 + c)
??
(1 + r) = 1 ?? = log(1 + r)/ log(1 + ¯ c). (1.9)
The standard deviation of the endowment shock is set to 3.51% and the autocorre-
lation is set to 0.524, which are the standard deviation and the autocorrelation of
tradable output for Turkey given in Table 1.4.
Table 1.1: Parameter Values
? 2 relative risk aversion RBC parametrization
y
T
1 tradable endowment normalization
?
?
0.0351 tradable output volatility Turkish data
?
?
0.524 tradable output autocorrelation Turkish data
R 1.0159 gross interest rate RBC parametrization
? 0.0228 elasticity of discount factor steady state condition
Using the “simple persistence” rule, we construct a Markovian representation
of the time series process of output. The transition probability matrix P of the
shocks follows:
P(i, j) = (1 ??
?
)?
i
+?
?
I
i,j
(1.10)
where i, j = 1, 2; ?
i
is the long-run probability of state i; and I
i,j
is an indica-
tor function, which equals 1 if i = j and 0 otherwise, ?
?
is the ?rst order serial
autocorrelation of the shocks.
16
Simulation Results
We report long run values of the key macroeconomic variables, such as mean
bond holdings that is a measure of precautionary savings, volatility of consumption,
correlation of consumption with income, which measures to what extend income ?uc-
tuations a?ect consumption ?uctuations, and serial autocorrelation of consumption
which measures the persistence of consumption, of the model to highlight the e?ect
of indexation on consumption smoothing in Table 1.5. Without indexation (? = 0),
mean bond holdings are higher than the case with perfect foresight (?0.35) (which
is an implication of precautionary savings), volatility of consumption is positive,
and consumption is correlated with income.
Now we analyze how the results change when we index debt repayments to
endowment shocks. As Table 1.5 reveals, when the degree of indexation is in the
[0.015, 0.25) range, households engage in less precautionary savings (as measured
by the long run average of b) and the standard deviation of consumption declines
relative to the case in which there is no indexation. Moreover, in this range, correla-
tion of consumption with GDP falls slightly and its serial autocorrelation increases
slightly. These results suggests that when the degree of indexation is in this range,
indexation improves these macroeconomic variables from the consumption smooth-
ing perspective. However, when the degree of indexation is greater than 0.25, these
improvements reverse. In the full-indexation (? = 1) case, for example, the stan-
dard deviation of consumption is 4.8%, four times the standard deviation in the
no-indexation case. The persistence of consumption also declines at higher degrees
17
of indexation. The autocorrelation of consumption in the full indexation case is
0.886, compared to 0.978 in the no-indexation case and the high of 0.984 in the case
where ? = 0.10. Not surprisingly, the ranking of welfare is in line with the ranking
of consumption volatility, as the last row of Table 1.5 reveals. However, the absolute
values of the di?erences in welfare are quite small.
15
The above changes are driven by the changes in the ability to hedge income
?uctuations with indexed bonds. This hedging ability is a?ected by the degree of
indexation because the degree of indexation alter the incentives for precautionary
savings. In particular, it has a signi?cant e?ect on determining the state of nature
that de?nes the “catastrophic” level of income at which household reach their natural
debt limits. The natural debt limit (?) is the largest debt that the economy can
support to guarantee non-negative consumption in the event that income remain at
its catastrophic level almost surely, i.e.,
? = ?
(1 ??)y
T
r
. (1.11)
With non-indexed bonds, catastrophic level of income is realized at state of nature
with the negative endowment shock. When the debt approaches to the natural
debt limit, consumption approaches zero, which leads to in?nitely negative utility.
Hence, agents have strong incentives to avoid holding debt levels lower than natural
debt limit. In order to guarantee positive consumption almost surely in the event
that income remains at its catastrophic level, agents engage in strong precaution-
15
As pointed out by Lucas (1987), welfare implications of altering consumption ?uctuations in
these type of models are quite low.
18
ary savings. An increase (decrease) in this debt limit strengthens (weakens) the
incentives to save, since the level of debt that agents would try to avoid would be
higher (lower). With indexation, the natural debt limit can be determined at either
negative or positive realization of the endowment shock, depending on which yields
the lower income (determines the catastrophic level of income). To see this, notice
that using the budget constraint, when the shock is negative, we derive:
c
t
? 0 ?(1 ??)y ?b
t+1
+b
t
(1 +r ???) ? 0 ??
L
? ?
(1 ??)y
r ???
, if r ??? > 0.
(1.12)
Notice that for the ranges of values of ? where r ? ?? < 0, Equation 1.12 yields
an upper bound for the bond holdings; i.e., ?
L
? ?
(1??)y
r???
). Hence, in this range,
negative shock will not play any role in determining the natural debt limit. Again
using the budget constraint, positive endowment shock implies the following natural
debt limit:
c
t
? 0 ?(1 +?)y ?b
t+1
+b
t
(1 +r +??) ? 0 ??
H
? ?
(1 + ?)y
r +??
.
(1.13)
Combining these two equations, we get:
? =
_
¸
¸
_
¸
¸
_
max {?
(1??)y
r???
, ?
(1+?)y
r+??
}, if ? < r/?
?
(1+?)y
r+??
, if ? > r/?.
(1.14)
Further algebra suggest that when
1??
1+?
<
r???
r+??
or ? < r, natural debt limit is
19
determined at state of nature with a negative endowment shock and in this case,
??/?? < 0, i.e., increasing the degree of indexation decreases the natural debt limit
or weakens the precautionary savings incentive. However if
1??
1+?
>
r???
r+??
or ? > r,
??/?? > 0, i.e., increasing the degree of indexation increases the natural debt limit
or strengthens the precautionary savings incentive.
In Table 1.6, we numerically calculate these natural debt limits as functions
of the degrees of indexation, along with the corresponding returns in both states
(R
i
t
= 1 + r + ??
t
) and con?rm the analytical results derived above. When the
degree of indexation is less than 0.0159, the natural debt limit is determined by the
negative shock and decreases (i.e., the debt limit becomes looser) as we increase ?.
When ? is greater than 0.0159, it is determined by the positive shock and increases
(i.e., the debt limit becomes tighter) as we increase ? (we print the corresponding
limits darker in the table). In the full-indexation case, for example, this debt limit
is -20.09, whereas the corresponding value is -61.49 in the non-indexed case. In
other words, in the full-indexation case, positive endowment shocks decrease the
catastrophic level of income to one third of the value in the non-indexed case. This
in turn sharply strengthen precautionary savings motive.
In order to understand the role of indexation on volatility of consumption,
we perform a variance decomposition analysis. Higher indexation provides a better
hedge to income ?uctuations by increasing the covariance of the trade balance (tb
=b
? R
i
t
b) with income (since in good (bad) times agents pay more (less) to the
rest of the world). However, higher indexation also increases the volatility of the
trade balance. In order to pin down the e?ect of indexation on these variables, we
20
perform a variance decomposition using the following identity:
var(c
T
) = var(y
T
) + var(tb) ?2cov(tb, y
T
).
In Table 1.7, we present the corresponding values for the last two terms in the above
equation for each of the indexation levels.
16
Clearly, both the variance of the trade
balance and the covariance of the trade balance with income monotonically increase
with the level of indexation. However, the term var(tb) ?2cov(tb, y
T
) ?uctuates in
the same direction as the volatility of consumption, suggesting that at high levels
of indexation the rise in the variance of the trade balance o?sets the improvement
in the co-movement of the trade balance with income, i.e., the e?ect of increased
?uctuation in interest rate dominates the e?ect of hedging provided by indexation.
Hence, consumption becomes more volatile for higher degrees of indexation.
To sum up, when the degree of indexation is higher than a critical value (as
with full-indexation), the precautionary savings motive is stronger and the volatil-
ity of consumption is higher than in the non-indexed case. These results arise
because the natural debt limit is lower at higher levels of indexation and because
the increased volatility in the trade balance far outweighs the improvement in the
co-movement of the trade balance with income.
These results suggest that in order to improve macroeconomic variables, the
indexation level should be low. When ? is lower than 0.25, agents can better hedge
against ?uctuations in endowment income than when ? is at higher levels. In this
16
Since the endowment is not a?ected by changes in the indexation level, its variance is constant.
21
case, the precautionary savings motive is weaker, the volatility of consumption is
smaller, and consumption is more persistent. When ? is in the [0.10, 0.25] range, the
correlation of consumption with income approaches zero and the autocorrelation of
consumption nears unity. These values resemble the results that could be attained
in the full-insurance scenario, and suggest that partial indexation is optimal.
The results using a frictionless one-sector model shed light on the debate about
the indexation of public debt. Our ?ndings in this section suggest that the hedge
indexed bonds provide is imperfect and that indexation of the debt in a one-to-
one fashion may not improve macroeconomic variables. However, partial indexation
could prove bene?cial by mimicking outcomes that would arise under full insurance.
1.3.2 Two Sector Model with Financial Frictions
When we introduce liability dollarization and a borrowing constraint, the DPP
of the household’s problem becomes:
V (b, ?) = max
b
_
u(c) + (1 + c)
??
E [V (b
, ?
)]
_
s.t.
c
T
= (1 + ?)y
T
?b
+ (1 + ??)Rb
c
N
= y
N
b
? ??
_
(1 + ?)y
T
+p
N
y
N
¸
.
(1.15)
As in the previous one-sector model, the endogenous state space is given by
B = {b
1
< ... < b
NB
}, and the exogenous Markov process is assumed to have two
states: E = {?
L
< ?
H
}. Optimal decision rules, b
(b, ?) : E × B ? R, are obtained
22
by solving the above DPP.
Solving the Model
We solve the stochastic simulations using value function iteration over a dis-
crete state space in the [-2.5, 5.5] interval with 1,000 evenly spaced grid points. We
derive this interval by solving the model repeatedly until the solution captures the
ergodic distribution of bond holdings. The endowment shock has the same Markov
properties described in the previous section. The solution procedure is similar to
that in Mendoza (2002). We start with an initial conjecture for the value function
and solve the model without imposing the borrowing constraint for each coordinate
(b, ?) in the state space, and check whether the implied b
satis?es the borrowing
constraint. If so, the solution is found and we calculate the implied value function
that is then used as a conjecture for the next iteration. If not, we impose the bor-
rowing constraint with equality and solve a system of non-linear equations de?ned
by the three constraints given in the DPP (1.15) as well as the optimality condition
given in Equation (1.7). Then, we calculate the implied value function using the
optimal b
, and iterate to convergence.
Calibration
We calibrate the model such that aggregates in the non-binding case match
the certain aggregates of Turkish data. In addition to the parameters used in the
frictionless one-sector model, we introduce the following parameters, the values of
23
which we summarize in Table 1.2.: y
N
is set to 1.3418, which implies a share of
non-tradables output in line with the average ratio of the non-tradable output to
tradable output in between 1987-2004 for Turkey; µ is set to 0.316, which is the
value Ostry and Reinhart (1992) estimate for emerging countries; the steady state
relative price of non-tradables is normalized to unity, which implies a value of 0.4027
for the CES share of tradable consumption (?), calculated by using the condition
that equates the marginal rate of substitution between tradables and non-tradables
consumption to the relative price of non-tradables (Equation (1.7)). The elasticity
of the subjective discount factor (?) is recalculated including these new variables
in the solution of the non-linear system of equations implied by the steady-state
equilibrium conditions of the model given in Equation (1.9). ? is set to 0.3 (i.e.
households can borrow up to 30% of their current income), which is found by solving
the model repeatedly until the model matches the empirical regularities of a typical
Sudden Stop episode at a state where the borrowing constraint binds with a positive
probability in the long run.
Table 1.2: Parameter Values
µ 0.316 elasticity of substitution Ostry and Reinhart (1992)
y
N
/y
T
1.3418 share of NT output Turkish data
p
N
1 relative price of NT normalization
? 0.3 constraint coe?cient set to match SS dynamics
? 0.4027 CES weight calibration
? 0.0201 elasticity of discount factor calibration
24
Simulation Results
The stochastic simulation results are divided into three sets. In the ?rst set,
which we refer to as the frictionless economy, the borrowing constraint never binds.
In the second set of results, which we refer to as the constrained economy, the
borrowing constraint occasionally binds and households can issue only non-indexed
bonds. In the last set, which we refer to as the indexed economy, borrowing con-
straint occasionally binds but households can issue indexed bonds.
Our results that compare the frictionless and constrained economies are anal-
ogous of those presented by Mendoza (2002). Hence, here we just emphasize the
results that are speci?c and crucial to the analysis of indexed bonds and refer the
interested reader to Mendoza (2002) for further details. Since at equilibrium, the
relative price of non-tradables is a convex function of the ratio of tradables consump-
tion to non-tradables consumption, a decline in tradables consumption relative to
non-tradables consumption due to a binding borrowing constraint leads to a decline
in the relative price of non-tradables, which makes the constraint more binding and
leads to a further decline in tradables consumption.
Figure 1.3 shows the ergodic distributions of bond holdings. The distribution
in the frictionless economy is close to normal and symmetric around its mean. Mean
bond holdings are -0.299, higher than the steady state bond holdings of -0.35; this
re?ects the precautionary savings motive that arises as a result of uncertainty and
the incompleteness of ?nancial markets. The distribution of bond holdings in the
constrained economy is shifted right relative to that of the frictionless economy.
25
Mean bond holdings in the constrained economy are 0.244, which re?ects a sharp
strengthening in the precautionary savings motive due to the borrowing constraint.
Table 1.8 presents the long-run business cycle statistics for the simulations.
Relative to the frictionless economy, the correlation of consumption with the trad-
ables endowment is higher in the constrained economy. In line with this stronger
co-movement, the persistence (autocorrelation) of consumption is lower in the con-
strained economy.
Behavior of the model can be divided into three ranges. In the ?rst range,
debt is su?ciently low that the constraint is not binding. In this case, the response
of the constrained economy to a negative endowment shock is similar to that of the
frictionless economy, and a negative endowment shock is smoothed by a widening
in the current account de?cit as a share of GDP. There is also a range of bond
holdings in which debt levels are too high. In this range, the constraint always
binds regardless of the endowment shock. However, at more realistic debt levels
where the constraint only binds when the economy su?ers a negative shock, the
model with non-indexed bonds roughly matches the empirical regularities of Sudden
Stops. This range, which we call the “Sudden Stop region” following Mendoza and
Smith (2005), corresponds to the 218-230th grid points.
In Figure 1.4, we plot the conditional forecasting functions of the frictionless
and constrained economies for tradables consumption, aggregate consumption, the
relative prices of non-tradables, and the current account-GDP ratios, in response to
a one-standard deviation endowment shock. These forecasting functions are condi-
tional on the 229th bond grid, which is one of the Sudden Stop states and has a
26
long-run probability of 0.47%, and they are calculated as responses of these variables
as percentage deviations from the long-run means of their frictionless counterparts.
17
As these graphs suggest, the response of the constrained economy is dramatic.
The endowment shock results in a 4.1% decline in tradable consumption. That
compares to a decline of only 0.9% in the frictionless economy. In line with the larger
collapse in the tradables consumption, the responses of aggregate consumption and
the relative price of non-tradables are more dramatic in the constrained economy
than in the frictionless economy. While households in the frictionless economy are
able to absorb the shock via adjustments in the current account (the current account
de?cit slips to 1.4% of GDP), households in the constrained economy cannot due to
the binding borrowing constraint (the current account shows a surplus of 0.02% of
GDP). These ?gures also suggest that the e?ects of Sudden Stops are persistent. It
takes more than 40 quarters for these variables to converge back to their long-run
means.
Figures 1.5, 1.6, and 1.7 compare the detrended conditional forecasting func-
tions of the constrained economy with that of the indexed economy to illustrate how
indexed bonds can help smooth Sudden Stop dynamics (the degrees of indexation
are provided on the graphs).
18
As Figure 1.5 suggests, when the degree of index-
ation is 0.05, indexed bonds provide little improvement over the constrained case;
indeed, the di?erence in the forecasting functions is not visible. When indexation
reaches 0.10, however, the improvements are minor yet noticeable. At this degree of
17
Bond holdings on this grid point are equal to -0.674, which implies a debt-to-GDP ratio of
30%.
18
These forecasting functions are detrended by taking the di?erences relative to the frictionless
case.
27
indexation, aggregate consumption rises 0.11%, tradables consumption rises 0.24%,
the relative price of non-tradables increases 0.30%.
With increases in the degree of indexation to 0.25 and 0.45, the initial ef-
fects are relatively small. Figure 1.6 suggests that the improvements in tradables
consumption are close to 1% and 1.8% when the degrees of indexation are 0.25
and 0.45, respectively. Figure 1.7 suggests that when the degree of indexation gets
higher, 0.7 and 1.0 for example, tradables consumption and aggregate consumption
fall below the constrained case after the fourth quarter and stay below for more
than 30 quarters despite the initially small e?ects of a negative endowment shock.
In other words, degrees of indexation higher than 0.45 in an indexed economy imply
more pronounced detrimental Sudden Stop e?ects than in a constrained economy.
Table 1.9 summarizes the initial e?ects of both a negative and a positive
shock conditional on the same grid points used in the forecasting functions. When
indexed bonds are in place, our results suggest that if the degree of indexation is
within [0.05, 0.25], indexed bonds help to smooth the e?ects of Sudden Stops. As
Table 1.9 suggests, when the degree of indexation is 0.05, indexed bonds provide
little improvement. As we increase the degree of indexation, the initial impact of
a negative endowment shock on key variables gets smaller. In this case, debt relief
accompanies a negative endowment shock, and this relief helps to reduce the initial
impact of a binding borrowing constraint. Hence, the depreciation in the relative
price of non-tradables is milder, which in turn prevents the Fisherian debt-de?ation.
Table 1.9 also suggests that although the smallest initial impact of a negative
endowment shock occurs when the degree of indexation is unity (full-indexation),
28
this level of indexation has signi?cant adverse e?ects if a positive shock realizes. In
this case, households must pay a signi?cantly higher interest rate over and above
the risk-free rate. Although the constrained economy is not vulnerable to a Sudden
Stop when there is a positive endowment shock, agents in such an economy face a
Sudden Stop due to a sudden jump in debt servicing costs.
Hence, our analysis suggests that household face a tradeo? when they engage
in debt contracts with high degrees of indexation. If the households are hit by
a negative endowment shock, highly indexed bonds can allow them to absorb the
shock without su?ering severely in terms of consumption. Such a shock might
trigger a Sudden Stop if households were to borrow instead via non-indexed bonds
(the initial e?ects are closest to the frictionless case when the degree of indexation
is one). However, if they receive a positive endowment shock, the initial e?ects
are larger in the indexed economy (where the degree of indexation equals 1) than
in the constrained economy (e.g., the impact on tradable consumption jumps from
-1.1% to -6.7%). Analyzing the results in columns 3-9, we conclude that degrees
of indexation in the [0.45, 1.0] interval lead to stronger Sudden Stop e?ects. If we
take the average of initial responses across the high and the low states in this range
of values, we ?nd that the minimum of these averages is attained when the degree
of indexation is 0.25, which suggests that households with concave utility functions
would attain a higher utility with this consumption pro?le than ones achieved with
indexation levels higher than 0.25.
In Figure 1.8, we plot the time series simulations of the frictionless, con-
strained, and indexed economies. These simulations are derived ?rst by generating
29
a random exogenous endowment shock process using the transition matrix, P, and
then by feeding these series into each of the respective economies. On the top left
graph, the dotted line is the tradable consumption series for the frictionless econ-
omy. The solid line is the series for the constrained economy. As the graphs reveal,
although patterns of consumption in each economy mostly move together, there are
cases (around periods 2000, 3600, 6500, 8800), where we observe sharp declines in
constrained economy. These declines correspond to Sudden Stop episodes. In these
cases, a consecutive series of negative endowment shocks make the constraint bind-
ing, which in turn triggers a debt-de?ation that ultimately leads to a collapse in
consumption.
When the return is indexed and the degree of indexation is 0.05 (top right
graph), the volatility of consumption is noticeably lower than in the constrained
case, and collapses in consumption during Sudden Stop episodes are milder. When
we increase the degree of indexation to 0.45, however, there is a signi?cant increase
in the volatility of consumption, and there are more frequent collapses. When the de-
gree of indexation is 1.0 (due to space limitations, we leave out the ?gures associated
with other degrees of indexation), we observe a spike in volatility and much more
frequent and sizeable collapses in consumption. These simulations illustrate that
when indexation is full, the e?ect on consumption can be signi?cantly negative, fur-
thermore that indexation can yield bene?ts in terms of consumption volatility only
if the degree of indexation is quite low.
Table 1.8 suggests that in addition to the tradeo? of gains in the low state
versus losses in the high state, there is also a short run versus long run tradeo?
30
with respect to issuing indexed bonds with high degrees of indexation. With higher
indexation levels, indexed bonds can generate substantial short-run bene?ts, but also
introduce more severe adverse e?ects in the long run; i.e., consumption volatility and
its co-movement with income increase with greater degrees of indexation. Consistent
with our ?ndings in the frictionless one-sector model, the value of indexation that
minimizes the co-movement of consumption with GDP and yields more persistent
consumption is low (in the range of [0.05, 0.1] for this calibration). These results
also suggest that, depending on the objectives, the optimal degree of indexation level
may vary. As we illustrated before, the level of indexation that would minimize the
e?ect of Sudden Stops is in the [0.25, 0.45] interval, whereas the one that minimizes
long-run ?uctuations is in the [0.05, 0.1] range. However, regardless of whether
we would like to smooth Sudden Stops or long-run ?uctuations, full-indexation is
undesirable.
1.3.3 Sensitivity Analysis
This section presents the results of analysis aimed at evaluating the robustness
of our results to several variations in model parameterization. Due to space limita-
tions, for the ?rst three sensitivity analysis we present result of the the frictionless
one-sector model. These results are summarized in Table 1.10.
We ?rst analyze the robustness of the results to changes in the number of
exogenous state variables. For this analysis, we use a seven-state Markov chain
that maintains the same autocorrelation and standard deviation of the shock as in
31
the previous setup. Note that the simple persistence rule can be employed only if
the number of exogenous state variables is two. In order to create the transition
matrix with seven exogenous states, we employ the method described in Tauchen
and Hussey (1991). The ?rst block in Table 1.10 presents key long-run statistics,
which are nearly identical to the ones presented in Table 1.5; in fact, for a given
indexation level, the statistics are the same out to two decimal points. Hence, we
conclude that our results are robust to the number of state variables used in the
Markov process.
Second, we increase the standard deviation of the exogenous endowment shock
to 4.5%. As Table 1.10 suggests, when bonds are not indexed, the precautionary
savings motive is stronger, consumption is more volatile, and consumption displays
greater correlation with income when we increase variation in the magnitude of
the exogenous endowment shock. Comparing Table 1.10 with Table 1.5 for the
indexed case, we conclude that the optimal indexation level that minimizes long-run
macroeconomic ?uctuations is in the [0.05, 0.1] interval in the former case, whereas
it is in the [0.1, 0.25] interval in the latter one. In other words, the optimal degree
of indexation decreases with increases in the volatility of the exogenous endowment
shock.
Next, we evaluate the changes in results that arise when we lower the autocor-
relation of the endowment shock. Compared to the baseline results given in Table
1.5, with an endowment shock autocorrelation of 0.4, agents engage in less pre-
cautionary savings. Furthermore, consumption volatility and its co-movement with
income are lower. When indexed bonds are in place, the lower the persistence of the
32
shock, the higher the degree of indexation that would minimize the co-movement of
consumption with income. For instance, when the indexation is 0.1, the correlation
of consumption with income is 0.07 when the autocorrelation of the shock is 0.4.
By comparison, at the same indexation level, the correlation of consumption with
income is 0.017 when the autocorrelation is 0.524.
As a ?nal robustness check, we examine the e?ect of having a larger non-
tradables sector. The results are summarized in Table 1.11. We set the y
N
/y
T
ratio
to 1.6, which implies that the degree of openness of the country is lower than in
the baseline case. Not surprisingly, the model in this case captures the empirical
regularities of an economy with less ?nancial integration. In particular, consump-
tion is more volatile than in the baseline case (for instance, the volatility of the
tradables consumption in the frictionless economy increases to 1.6%, compared to
the baseline value of 1.5%), and the co-movement of consumption with income is
stronger (the correlation of tradables consumption with income in the frictionless
economy increases to 0.75 from the baseline value of 0.69). When we compare the
initial responses of each of these economies to a one-standard-deviation endowment
shock, the response of the constrained economy with a higher share of non-tradable
output is stronger than that of the one with baseline parameters, which suggests
that the debt-de?ation process is more severe in the former economy. This result
is consistent with the empirical evidence on the relationship between the degree of
openness and the severity of Sudden Stops (see Calvo et al. (2003)). In order to
compare the optimal indexation levels across di?erent parameterizations, we com-
pare the average responses of these economies in the high and the low states to a
33
one-standard-deviation endowment shock. These results suggest that the minimum
average response is attained when the degree of indexation is 0.25, which is the
same degree of indexation in the baseline results. However, this result depends on
the coarseness of the indexation intervals with which we are solving the problem.
Economic intuition suggests that lower ?nancial integration would require higher
indexation levels to smooth exogenous shocks better.
The sensitivity analysis presented in this section suggests that the optimal
indexation level depends on the properties of the exogenous shock, including its
persistence and its volatility. Hence, the optimal degree of indexation needs to
be country speci?c, since it is highly likely that each emerging country receives
shocks with di?erent statistical properties.The ?ndings of this chapter suggest that
while indexed bonds might aid many countries in averting or at least mitigating the
e?ects of Sudden Stops in emerging markets, an indexation level appropriate for one
country might not be optimal for another.
1.4 Conclusion
Recent policy proposals argue that indexing the debt of emerging markets
could help prevent the sudden reversals of capital in?ows accompanied by real ex-
change rate devaluations that were typical of the emerging market crises of the
last decade. This chapter explores the quantitative implications of this policy in a
DSGE model. Debt is denominated in units of tradables, and international lenders
impose a borrowing constraint that limits debt to a fraction of national income. The
34
benchmark model with non-indexed bonds and credit constraints features Sudden
Stops as an equilibrium outcome that results from a debt-de?ation process, the feed-
back mechanism between liability dollarization and the borrowing constraint that
operates through the relative price of non-tradables.
We conducted our quantitative experiments to evaluate the e?ects of indexed
bonds in two steps. First, we studied the e?ects of bonds indexed to output in a
canonical one-sector small open economy model with varying degrees of indexation.
We found that the introduction of indexed bonds partially completes the insurance
market in such an economy, and whether they help to reduce precautionary savings,
the volatility of consumption, and the correlation of consumption with income de-
pends on the degree of indexation of the bond. When this degree is higher than a
critical threshold (as with the full indexation for example), indexation can, in fact,
make agents worse o?. Because increase in the variance of trade balance (due to
higher interest rate ?uctuations) outweighed the improvement in the covariance of
trade balance with income, which then led to higher volatility of consumption; and
natural debt limits became tighter, which then led to an increase in precautionary
savings.
In the second step, we analyzed the role of indexed bonds in smoothing Sud-
den Stops and RER ?uctuations. We found that indexed bonds can reduce the
initial capital out?ow in the event of an exogenous shock that otherwise trigger a
Sudden Stop in an economy with only non-indexed bonds. Indexed bonds can in
turn reduce the depreciation in the RER and break the Fisherian debt-de?ation
mechanism. However, once again, the bene?t of these bonds depends critically on
35
the degree of indexation. When the level of indexation is lower than a critical value,
indexed bonds weaken Sudden Stops. If indexation is higher than this critical value,
although indexed bonds can provide some temporary relief in the event of a negative
shock, the initial improvement is short lived. Moreover, in the event of a positive
shock, the economy is vulnerable to a Sudden Stop even though such a shock would
never trigger a Sudden Stop in an economy in which household facing borrowing
constraints can only issue non-indexed bonds. Because in this case, positive shock
commands higher repayment, which increases the need for larger borrowing, this in
turn can make the borrowing constraint suddenly binding, and triggering a debt-
de?ation.
To conclude, bonds on which the return is indexed in a one-to-one fashion (i.e.,
full-indexation) will not necessarily provide bene?ts to emerging countries. However,
indexed bonds with optimal degree of indexation can help these countries smooth
Sudden Stops. This optimal value depends on the persistence and the volatility
of the exogenous shocks a given country experiences, as well as the size of the
country’s non-tradables sector relative to the its tradables sector (i.e., the openness
of the country). Hence, in terms of policy implications, our analysis reveals that the
degree of indexation is a key variable that should optimally be chosen in order to
smooth Sudden Stops, and furthermore that this value should be country speci?c.
In our analysis, we assumed that investors are risk-neutral and that indexing
debt repayments would not require them to obtain more country speci?c informa-
tion. It may be the case that indexed returns may a?ect investors’ incentives to col-
lect more country speci?c information. The implications of introducing risk-averse
36
investors or informational costs in a dynamic setup are left for future research. The
model can also be used to explore the implications of indexation to relative price of
non-tradables, or to CPI, but it is left for further research. Analyzing if trading in
option or futures markets can help emerging countries for mitigating Sudden Stops
is an avenue of research. This would require a richer model, and it is left for further
research, as well. Another avenue for future research could be analyzing the im-
plications of indexed bonds on default probabilities. In order to carry out such an
analysis, indexed bonds could be introduced into “willingness to pay” models such
as those of Eaton and Gersovitz (1980) and Arellano (2004).
37
Table 1.3: Previous Attempts of Indexed Bonds
Date Issued Indexation Clause Note
Argentina 1972-1989 CPI
Australia 1985-1988 CPI
Bosnia and
1990s GDP Issued as part of Brady Plan, VRRs
Herzegovina
Brazil 1964- CPI
Bulgaria 1990s GDP Issued as part of Brady Plan, VRRs
Colombia 1967- CPI
Costa Rica 1990s GDP Issued as part of Brady Plan, VRRs
Chile 1956- CPI
Israel 1955- CPI
France 1973 Gold
Debt servicing cost increased signi?cantly
due to depreciation of French Franc against gold
Mexico
1970s Oil Petro-bonos
1990s Oil Issued as part of Brady Plan, VRRs
1989- CPI
Turkey 1994- CPI
UK 1975- CPI
Venezuela 1990s Oil Issued as part of Brady Plan, VRRs
Sources: Borensztein and Mauro (2004), Campell and Shiller (1996), Kopcke and Kimball(1999),
Atta-Mensah (2004).
38
Table 1.4: Business Cycle Facts for Emerging Countries
Variable:x ?(x) ?(x)/?(Y ) ?(x) ?(x, Y ) Sudden Stop
Sudden Stop
relative to std.
Argentina 2002:1-2
GDP (Y) 4.022 1.000 0.865 1.000 -12.952 3.220
tradables GDP 4.560 1.134 0.667 0.923 -15.100 3.311
nontradables GDP 3.977 0.989 0.894 0.990 -12.169 3.060
consumption 4.475 1.113 0.830 0.975 -17.063 3.813
real exchange rate 15.189 3.777 0.754 0.454 -48.177 3.172
CA/Y 0.916 0.228 0.837 -0.802 1.353 1.476
Chile 1998:4-1999:1
GDP (Y) 2.093 1.000 0.731 1.000 -4.492 2.147
tradables GDP 1.833 0.876 0.473 0.762 -5.068 2.764
nontradables GDP 2.520 1.204 0.796 0.961 -4.840 1.921
consumption 4.184 1.999 0.748 0.898 -8.410 2.010
real exchange rate 0.007 0.003 0.649 0.372 -0.019 2.578
CA/Y 3.302 1.578 0.352 -0.512 10.932 3.311
Mexico 1994:4-1995:1
GDP (Y) 2.261 1.000 0.799 1.000 -7.440 3.290
tradables GDP 2.682 1.186 0.712 0.921 -8.976 3.347
nontradables GDP 2.189 0.968 0.832 0.978 -6.178 2.822
consumption 4.222 1.867 0.841 0.973 -11.200 2.653
real exchange rate 8.627 3.816 0.726 0.599 -32.844 3.807
CA/Y 0.698 0.309 0.831 -0.475 2.220 3.180
Turkey 1994:1-2
GDP (Y) 3.695 1.000 0.667 1.000 -10.383 2.001
tradables GDP 3.511 0.950 0.524 0.962 -10.925 3.112
nontradables GDP 4.021 1.088 0.680 0.982 -10.007 2.489
consumption 4.134 1.119 0.746 0.919 -10.098 2.443
real exchange rate 9.110 2.465 0.675 0.602 -31.630 3.472
CA/Y 2.744 0.743 0.633 -0.591 9.704 3.375
Source: Argentinean Ministry of Finance (MECON), Bank of Chile, Bank of Mexico, Central
Bank of Turkey, International Financial Statistics. The data cover periods 1993:Q1-2004:Q4 for
Argentina, 1986:Q1-2001:Q3 for Chile, 1987:Q1-2004:Q4 for Mexico, 1987:Q1-2004:Q4 for Turkey.
Data are quarterly seasonally adjusted real series. GDP and consumption data are logged and
?ltered using an HP ?lter with a smoothing parameter 1600. Real exchange rates are calculated
using the IMF de?nition (RER
i
= NER
i
×CPI
i
/CPI
US
for country i).
39
Table 1.5: Long Run Business Cycle Statistics of the One-Sector Model
Degree of Indexation (?)
0.00 0.015 0.02 0.05 0.10 0.25 0.45 0.70 1.0
E(b) -0.328 -0.349 -0.355 -0.385 -0.428 -0.042 0.522 1.458 2.026
?(cons) 1.243 1.242 1.240 1.236 1.209 1.474 2.119 3.291 4.731
?(tb/y) 3.486 3.516 3.527 3.590 3.674 4.211 4.820 5.724 6.755
?(cons, y) 0.186 0.160 0.151 0.097 0.017 -0.311 -0.409 -0.381 -0.304
?(tb/y, y) 0.936 0.937 0.937 0.939 0.945 0.943 0.916 0.849 0.752
?(cons) 0.978 0.980 0.980 0.981 0.984 0.909 0.870 0.876 0.886
?(tb/y) 0.549 0.549 0.548 0.546 0.541 0.542 0.562 0.601 0.646
welfare n.a. 0.0025 0.0034 0.0090 0.0146 -0.0032 -0.0092 -0.0120 -0.0136
Note: Standard deviations are in percent of the mean. Welfare gains are in percent and relative
to the non-indexed model.
Table 1.6: Returns and Natural Debt Limits
Degree of Indexation (?)
0.00 0.01 0.015 0.05 0.10 0.25 0.45 0.70 1.0
R
i
(L) 1.016 1.016 1.015 1.014 1.012 1.007 1.000 0.991 0.981
R
i
(H) 1.016 1.016 1.016 1.018 1.019 1.025 1.032 1.040 1.051
NDL(L) -61.487 -62.182 -62.894 -68.503 -78.431 -138.754 5440.508 106.131 48.760
NDL(H) -64.517 -63.819 -63.136 -58.642 -53.262 -41.767 -32.434 -25.353 -20.089
Note: First two rows are the corresponding gross returns in each states. In the last two rows, the
implied natural debt limits are printed bolder.
Table 1.7: Variance Decomposition Analysis for Consumption
Degree of Indexation (?)
0.00 0.015 0.02 0.05 0.10 0.25 0.45 0.70 1.0
?(cons) 1.243 1.242 1.240 1.236 1.209 1.474 2.119 3.291 4.731
var(tb) 12.241 12.463 12.540 13.008 13.638 17.707 22.903 31.959 44.788
cov(tb, y) 11.508 11.620 11.660 11.897 12.248 13.929 15.365 16.724 17.364
var(tb)
-10.775 -10.777 -10.781 -10.792 -10.857 -10.147 -7.827 -1.488 10.061
?2cov(tb, y)
40
Table 1.8: Long Run Business Cycle Statistics of the Two-Sector Model
Degree of Indexation (?)
F C 0.05 0.10 0.25 0.45 0.70 1.0
E(b) -0.299 0.244 0.122 0.276 0.594 1.599 2.328 2.516
?(c
T
) 1.530 1.268 1.251 1.389 1.851 2.835 3.914 5.266
?(c) 0.775 0.638 0.631 0.697 0.923 1.392 1.889 2.508
?(p
N
) 2.026 1.682 1.660 1.845 2.467 3.804 5.291 7.162
?(tb/y) 1.534 1.467 1.491 1.610 1.799 2.113 2.398 2.755
?(c
T
, y) 0.687 0.663 0.636 0.567 0.609 0.773 0.875 0.930
?(c, y) 0.687 0.664 0.637 0.567 0.608 0.770 0.870 0.924
?(p
N
, y) 0.687 0.663 0.636 0.567 0.609 0.774 0.877 0.933
?(tb/y, y) 0.512 0.648 0.646 0.548 0.290 -0.141 -0.404 -0.580
?(c
T
) 0.986 0.971 0.976 0.967 0.953 0.926 0.911 0.907
?(c) 0.986 0.971 0.976 0.967 0.953 0.925 0.909 0.903
?(p
N
) 0.986 0.971 0.976 0.967 0.953 0.927 0.912 0.909
?(tb/y) 0.581 0.546 0.540 0.546 0.572 0.609 0.631 0.661
Note: The ?rst column is the frictionless economy, the second column is the constrained economy,
and the rest of the columns are for the economy with borrowing constraint and indexed bonds
(with given degrees of indexation). Standard Deviations are in percent.
Table 1.9: Initial Responses to a One-Standard-Deviation Endowment Shock
Non-Indexed Degree of Indexation (?)
F C 0.05 0.10 0.25 0.45 0.70 1.0
A) Negative Shock
tradable consumption -0.907 -4.126 -4.007 -3.888 -3.531 -3.056 -1.657 -1.748
aggregate consumption -0.384 -1.780 -1.728 -1.676 -1.520 -1.312 -0.706 -0.745
relative price of non-tradables -1.197 -5.398 -5.244 -5.090 -4.626 -4.007 -2.179 -2.299
B) Positive Shock
tradable consumption -0.291 -1.095 -2.019 -2.138 -2.494 -2.970 -4.369 -6.691
aggregate consumption -0.120 -0.464 -0.862 -0.913 -1.068 -1.275 -1.887 -2.919
relative price of non-tradables -0.387 -1.444 -2.653 -2.808 -3.274 -3.895 -5.714 -8.716
Note: The ?rst column is the frictionless economy, the second column is the constrained economy,
and the rest of the columns are for the economy with borrowing constraint and indexed bonds (with
given degrees of indexation). Initial responses are calculated as percentage deviations relative to
the long-run mean of the frictionless economy.
41
Table 1.10: Sensitivity Analysis of the One-Sector Model
Degree of Indexation (?)
0.00 0.015 0.02 0.05 0.10 0.25 0.45 0.70 1.0
I. seven-state markov chain
E(b) -0.320 -0.345 -0.351 -0.369 -0.371 -0.083 0.548 1.459 1.968
?(cons) 1.246 1.245 1.244 1.243 1.258 1.487 2.147 3.319 4.776
?(cons, y) 0.182 0.154 0.144 0.079 0.031 -0.301 -0.410 -0.378 -0.293
?(cons) 0.970 0.971 0.971 0.974 0.982 0.906 0.869 0.870 0.869
II. ?
?
=0.045
E(b) -0.315 -0.335 -0.343 -0.359 -0.295 -0.017 0.908 1.741 2.064
?(cons) 1.567 1.566 1.566 1.560 1.576 1.919 2.899 4.372 6.226
?(cons, y) 0.208 0.173 0.160 0.085 -0.046 -0.270 -0.357 -0.307 -0.230
?(cons) 0.983 0.987 0.988 0.991 0.974 0.927 0.892 0.893 0.898
III. ?
?
=0.4
E(b) -0.335 -0.357 -0.361 -0.398 -0.477 -0.300 0.180 0.918 1.637
?(cons) 1.074 1.069 1.068 1.060 1.034 1.202 1.462 2.229 3.351
?(cons, y) 0.178 0.157 0.152 0.112 0.070 -0.167 -0.361 -0.367 -0.301
?(cons) 0.966 0.968 0.969 0.970 0.975 0.944 0.865 0.865 0.885
Note: Resulting transition matrix for seven-state markov chain is approximated using the method
described in Tauchen and Hussey (1991). Standard deviations are in percent.
42
Table 1.11: Sensitivity Analysis of the Two-Sector Model: Higher Share of Non-
tradable Output
Degree of Indexation (?)
F C 0.05 0.10 0.25 0.45 0.70 1.0
I. Long run statistics
E(b) -0.290 0.258 0.084 0.682 0.667 1.739 2.399 2.551
?(c
T
) 1.590 1.306 1.261 1.639 1.957 2.919 3.956 5.300
?(c) 0.822 0.671 0.649 0.836 0.994 1.457 1.941 2.565
?(p
N
) 2.105 1.734 1.672 2.182 2.609 3.920 5.351 7.211
?(c
T
, y) 0.749 0.716 0.691 0.664 0.714 0.844 0.913 0.951
?(c, y) 0.750 0.718 0.692 0.664 0.713 0.841 0.908 0.945
?(p
N
, y) 0.749 0.716 0.691 0.664 0.714 0.845 0.915 0.953
?(c
T
) 0.987 0.975 0.975 0.973 0.956 0.931 0.914 0.909
?(c) 0.987 0.976 0.976 0.974 0.956 0.930 0.911 0.905
?(p
N
) 0.987 0.975 0.975 0.973 0.957 0.932 0.915 0.911
II. Initial Responses
A)Negative Shock
tradable consumption -1.036 -4.254 -4.122 -3.991 -3.596 -3.070 -1.608 -1.623
aggregate consumption -0.395 -1.655 -1.603 -1.551 -1.395 -1.187 -0.616 -0.622
relative price of non-tradables -1.366 -5.565 -5.395 -5.224 -4.711 -4.025 -2.115 -2.135
B)Positive Shock
tradable consumption -0.420 -2.029 -2.156 -2.292 -2.686 -3.213 -4.675 -7.074
aggregate consumption -0.157 -0.780 -0.818 -0.883 -1.037 -1.244 -1.823 -2.788
relative price of non-tradables -0.557 -2.666 -2.985 -3.010 -3.525 -4.211 -6.111 -9.208
Notes: y
N
/y
T
ratio is set to 1.6 in this analysis. Standard deviations are in percent of the mean.
The ?rst column is the frictionless economy, the second column is the constrained economy, and
the rest of the columns are for the economy with borrowing constraint and indexed bonds (with
given degrees of indexation).
43
Figure 1.1: Sudden Stops in Emerging Markets
a. Current Account-GDP Ratio
b. Real Exchange Rate
-2
-1
0
1
2
3
93 94 95 96 97 98 99 00 01 02
Argentina
-12
-10
-8
-6
-4
-2
0
2
4
90 91 92 93 94 95 96 97 98 99 00 01
Chile
-3
-2
-1
0
1
2
88 90 92 94 96 98 00 02 04
Mexico
-8
-6
-4
-2
0
2
4
6
88 90 92 94 96 98 00 02 04
Turkey
20
40
60
80
100
120
93 94 95 96 97 98 99 00 01 02
Argentina
90
100
110
120
130
140
150
93 94 95 96 97 98 99 00 01 02
Chile
100
120
140
160
180
200
93 94 95 96 97 98 99 00 01 02
Mexico
80
90
100
110
120
130
140
93 94 95 96 97 98 99 00 01 02
Turkey
44
Figure 1.2: Deviations from Trend in Consumption and Ouput
a. Consumption
b. Output
-0.20
-0.15
-0.10
-0.05
0.00
0.05
0.10
93 94 95 96 97 98 99 00 01 02
Argentina
-0.10
-0.05
0.00
0.05
0.10
0.15
86 88 90 92 94 96 98 00
Chile
-0.15
-0.10
-0.05
0.00
0.05
0.10
88 90 92 94 96 98 00 02 04
Mexico
-0.15
-0.10
-0.05
0.00
0.05
0.10
88 90 92 94 96 98 00 02 04
Turkey
-0.15
-0.10
-0.05
0.00
0.05
0.10
93 94 95 96 97 98 99 00 01 02
Argentina
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
86 88 90 92 94 96 98 00
Chile
-0.08
-0.06
-0.04
-0.02
0.00
0.02
0.04
0.06
88 90 92 94 96 98 00 02 04
Mexico
-0.15
-0.10
-0.05
0.00
0.05
0.10
88 90 92 94 96 98 00 02 04
Turkey
45
Figure 1.3: Long Run Distributions of Bond Holdings in Non-Indexed Economies
?2 ?1 0 1 2 3 4
0
1
2
3
4
5
6
7
x 10
?3
Bond Holdings
Frictionless Economy
Costrained Economy
46
Figure 1.4: Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock
0 5 10 15 20 25 30 35 40
?1.8
?1.6
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
Aggregate Consumption
frictionless
constrained
0 5 10 15 20 25 30 35 40
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
Tradable Consumption
frictionless
constrained
0 5 10 15 20 25 30 35 40
?1.5
?1
?0.5
0
0.5
1
CAY Ratio
frictionless
constrained
0 5 10 15 20 25 30 35 40
?5.5
?5
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
Relative Price of NT
frictionless
constrained
Note: Forecasting functions are conditional on the 229th grid point of the bond holdings, which
implies a debt-to-GDP ratio of 30%. Solid and dashed lines are forecasting functions of the
frictionless, and constrained economies, respectively.
47
Figure 1.5: Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock
0 5 10 15 20 25 30 35 40
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
Aggregate Consumption
constrained
indexed, 0.05
indexed, 0.10
0 5 10 15 20 25 30 35 40
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Tradable Consumption
constrained
indexed, 0.05
indexed, 0.10
0 5 10 15 20 25 30 35 40
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
CAY Ratio
constrained
indexed, 0.05
indexed, 0.10
0 5 10 15 20 25 30 35 40
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Relative Price of NT
constrained
indexed, 0.05
indexed, 0.10
Note: Forecasting functions are conditional on the 229th grid point of the bond holdings, which
implies a debt-to-GDP ratio of 30%.
48
Figure 1.6: Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock
0 5 10 15 20 25 30 35 40
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
Aggregate Consumption
constrained
indexed, 0.25
indexed, 0.45
0 5 10 15 20 25 30 35 40
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Tradable Consumption
constrained
indexed, 0.25
indexed, 0.45
0 5 10 15 20 25 30 35 40
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
CAY Ratio
constrained
indexed, 0.25
indexed, 0.45
0 5 10 15 20 25 30 35 40
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Relative Price of NT
constrained
indexed, 0.25
indexed, 0.45
Note: Forecasting functions are conditional on the 229th grid point of the bond holdings, which
implies a debt-to-GDP ratio of 30%.
49
Figure 1.7: Conditional Forecasting Functions in Response to a One-Standard-
Deviation Negative Endowment Shock
0 5 10 15 20 25 30 35 40
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
Aggregate Consumption
constrained
indexed, 0.7
indexed, 1.0
0 5 10 15 20 25 30 35 40
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Tradable Consumption
constrained
indexed, 0.7
indexed, 1.0
0 5 10 15 20 25 30 35 40
1
1.2
1.4
1.6
1.8
2
2.2
2.4
2.6
2.8
3
CAY Ratio
constrained
indexed, 0.7
indexed, 1.0
0 5 10 15 20 25 30 35 40
?4.5
?4
?3.5
?3
?2.5
?2
?1.5
?1
?0.5
0
0.5
Relative Price of NT
constrained
indexed, 0.7
indexed, 1.0
Note: Forecasting functions are conditional on the 229th grid point of the bond holdings, which
implies a debt-to-GDP ratio of 30%.
50
Figure 1.8: Time Series Simulation
1000 2000 3000 4000 5000 6000 7000 8000 9000
?10
?8
?6
?4
?2
0
2
4
6
8
10
Tradable consumption
frictionless
constrained
1000 2000 3000 4000 5000 6000 7000 8000 9000
?10
?8
?6
?4
?2
0
2
4
6
8
10
Tradable consumption
constrained
indexed,0.05
1000 2000 3000 4000 5000 6000 7000 8000 9000
?10
?8
?6
?4
?2
0
2
4
6
8
10
Tradable consumption
constrained
indexed,0.45
1000 2000 3000 4000 5000 6000 7000 8000 9000
?10
?8
?6
?4
?2
0
2
4
6
8
10
Tradable consumption
constrained
indexed,1.0
Note: Consumptions are in percentage deviations from their corresponding means. The ?rst
1,000 periods have been excluded from these graphs to focus on the data which are independent
of initial conditions.
51
Chapter 2
Are Asset Price Guarantees Useful for Preventing Sudden Stops?: A
Quantitative Investigation of the Globalization Hazard-Moral
Hazard Tradeo? (coauthored with Enrique G. Mendoza)
2.1 Introduction
The Sudden Stop phenomenon of emerging markets crises is characterized by
three stylized facts: sudden reversals of capital in?ows and current account de?cits,
collapses in output and private absorption, and large relative price corrections in
domestic goods prices and asset prices. A large fraction of the literature on this
subject is based on a hypothesis that Calvo (2002) labeled ”globalization hazard.”
According to this hypothesis, world capital markets are inherently imperfect, and
hence prone to display contagion and overreaction in asset positions and prices rel-
ative to levels consistent with ”fundamentals” (see Arellano and Mendoza (2003)
for a short survey of this literature). This argument suggests that an international
?nancial organization (IFO) could help prevent Sudden Stops by o?ering global
investors ex-ante price guarantees on the emerging-markets asset class. Calvo pro-
posed an arrangement for implementing this policy and compared it with other
arrangements that favor ex-post guarantees (including the IMF’s Contingent Credit
Line and Lerrick and Meltzer’s (2003) proposal).
Ex-ante price guarantees aim to create an environment in which asset prices
can be credibly expected to remain above the crash levels that trigger Sudden Stops
52
driven by globalization hazard. Calvo views this facility as akin to an open-markets
operation facility: it would exchange a liquid, riskless asset (e.g., U.S. T-bills) for an
index of emerging markets assets whenever the value of the index falls by a certain
amount, and would re-purchase the riskless asset when the index recovers. Market
participants would consider in their expectations that these guarantees would be
executed if a systemic ?re sale makes asset prices crash, and hence the guarantees
could rule out rational expectations equilibria in which Sudden Stops occur. If
globalization hazard is the only cause of Sudden Stops, and if the support of the
probability distribution of the shocks that causes them is known (i.e., if there are
no truly “unexpected” shocks), the facility would rarely trade.
A potentially important drawback of ex-ante price guarantees is that they in-
troduce moral hazard incentives for global investors. Everything else the same, the
introduction of the guarantees increases the foreign investors’ demand for emerg-
ing markets assets, since the downside risk of holding these assets is transferred
to the IFO providing the guarantees. This can be a serious drawback because a
similar international moral hazard argument has been forcefully put forward as an
alternative explanation of Sudden Stops (see the Meltzer Commission report and
Lerrick and Meltzer (2003)).
1
Proponents of this view argue that Sudden Stops are
induced by excessive indebtedness of emerging economies driven by the expectation
of global investors that IFOs will bail out countries in ?nancial di?culties. Based
1
Part of the literature on Sudden Stops focuses on domestic moral hazard problems caused
by government guarantees o?ered to domestic agents (see, for example, Krugman (2000)). This
chapter focuses instead on Sudden Stops triggered by globalization hazard, and on the tradeo?
between this hazard and the international moral hazard created by o?ering price guarantees to
global investors.
53
on this premise, Lerrick and Meltzer proposed the use of ex-post price guarantees to
be o?ered by an IFO to anchor the orderly resolution of a default once it has been
announced and agreed to with the IFO. The IFO would determine the crash price
of the asset in default and would require the country to commit to re-purchase the
asset at its crash price (making the arrangement credible by committing the IFO
to buy the asset at a negligible discount below the crash price if the country were
unable to buy it).
The tensions between the globalization hazard and moral hazard hypothe-
ses, and their alternative proposals for using price guarantees, re?ect an important
tradeo? that ex-ante price guarantees create. On one hand, ex-ante price guaran-
tees could endow IFOs with an e?ective tool to prevent and manage Sudden Stops
driven by globalization hazard. On the other hand, ex-ante guarantees could end up
making matters worse by strengthening international moral hazard (even if it were
true that globalization hazard was the only cause of Sudden Stops in the past).
The goal of this chapter is to study the globalization hazard-moral hazard
tradeo? from the perspective of the quantitative predictions of a dynamic, stochastic
general equilibrium model of asset pricing and current account dynamics. The model
is based on the globalization hazard setup of Mendoza and Smith (2004). This
chapter adds to their framework an IFO that o?ers ex-ante guarantees to foreign
investors on the asset prices of an emerging economy. We are interested in particular
in studying how the guarantees a?ect asset positions, asset price volatility, business
cycle dynamics, and the magnitude of Sudden Stops.
Asset price guarantees have not received much attention in quantitative equi-
54
librium asset pricing theory, with the notable exception of the work by Ljungqvist
(2000), and these guarantees have yet to be introduced into the research program
dealing with quantitative models of Sudden Stops. The theoretical literature and
several policy documents on Sudden Stops have examined various aspects of the
globalization hazard and international moral hazard hypotheses separately. From
this perspective, one contribution of this chapter is that it studies the interaction
between these two hypotheses in a uni?ed dynamic equilibrium framework.
The two ?nancial frictions that we borrow from Mendoza and Smith (2004)
to construct a model in which globalization hazard causes Sudden Stops are: (a) a
margin constraint on foreign borrowing faced by the agents of an emerging economy,
and (b) asset trading costs incurred by foreign securities ?rms specialized in trading
the equity of the emerging economy.
2
These frictions are intended to represent the
collateral constraints and informational frictions that have been widely studied in
the Sudden Stops literature (see, for example, Calvo (1998), Izquierdo (2000), Calvo
and Mendoza (2000a, 2000b), Caballero and Krishnamurty (2001), and Mendoza
(2004)).
The model introduces asset price guarantees in the form of ex-ante guarantees
o?ered to foreign investors on the liquidation price (or equivalently, on the return)
of the emerging economy’s assets. Thus, these guarantees are akin to a ”put option”
with minimum return. An IFO o?ers these guarantees and ?nances them with a
lump-sum tax on foreign investors’ pro?ts. Hence, forward-looking equity prices
2
These two frictions are modeled following the closed-economy analysis of Aiyagari and Gertler
(1999).
55
re?ect the e?ects of margin constraints, trading costs and ex-ante price guarantees.
The setup of the price guarantees is similar to the one proposed in Ljungqvist’s
(2000) closed-economy, representative-agent analysis, but framed in the context of
what is e?ectively a two-agent equilibrium asset-pricing model with frictions.
Price guarantees have di?erent implications depending on the level at which
they are set. If they are set so low that they are never executed, globalization
hazard dominates and the model yields the same Sudden Stop outcomes of the
Mendoza-Smith model. If they are set so high that they are always executed, the
model yields equilibria highly distorted by international moral hazard. Hence, the
interesting range for studying the globalization hazard-moral hazard tradeo? lies
between these two extremes. The quantitative analysis shows that guarantees set
slightly above the model’s “fundamentals” price (by 1/2 to 1 percent) contain the
Sudden Stop e?ects of globalization hazard and virtually eliminate the probability of
margin calls in the stochastic steady state. If the guarantee is non-state-contingent,
however, the guarantee is executed often (with a long-run probability of about 1/3)
and the model predicts persistent overvaluation of asset prices above the prices
obtained in a frictionless environment. A guaranteed price set at the same level but
o?ered only at high levels of external debt is executed much less often (with a long
run probability below 1/100) and it is equally e?ective at containing Sudden Stops
without inducing persistent asset overvaluation.
Analysis of the normative implications of the model shows that, when the
elasticity of foreign demand for domestic assets is high, the guarantees improve
domestic welfare measured from initial conditions at a Sudden Stop state, with
56
negligible changes in long-run welfare levels. At the same time, the value of foreign
traders’ ?rms measured in a Sudden Stop state falls slightly, while their long-run
average rises sharply. In this case the balance tilts in favor of using price guarantees
to contain globalization hazard. On the other hand, when the elasticity of foreign
demand for domestic assets is low, higher price guarantees are needed to prevent
Sudden Stops, and as a result large moral hazard distortions reduce domestic welfare
gains at Sudden Stop states and enlarge average welfare losses in the stochastic
steady state. In this case, price guarantees can be a misleading policy instrument
that yields a short-term improvement in macroeconomic indicators and welfare at
the expense of a long-term welfare loss.
The chapter is organized as follows. Section 2.2 presents the model and char-
acterizes the competitive equilibrium in the presence of margin constraints, trading
costs and ex-ante price guarantees. Section 2.3 studies key properties of this equi-
librium that illustrate the nature of the globalization hazard-moral hazard tradeo?.
Section 2.4 represents the model’s competitive equilibrium in a recursive form suit-
able for quantitative analysis and examines a set of baseline results. Section 2.5
conducts normative and sensitivity analyses. Section 2.6 concludes.
2.2 A Model of Globalization Hazard and Price Guarantees
Consider a small open economy (SOE) inhabited by a representative household
that rents out labor and a time-invariant stock of capital to a representative ?rm.
Households can trade the equity of this ?rm with a representative foreign securities
57
?rm specialized in trading the economy’s equity, and can also access a global credit
market of one-period bonds. In addition, an IFO operates a facility that guarantees
a minimum sale price to foreign traders on their sales of the emerging economy’s
equity. Dividend payments on the emerging economy’s equity are stochastic and
vary in response to exogenous productivity shocks. Markets of contingent claims are
incomplete because trading equity and bonds does not allow domestic households to
fully hedge domestic income uncertainty, and the credit market is imperfect because
of margin constraints and trading costs.
2.2.1 The Emerging Economy
The representative ?rm inside the SOE produces a tradable commodity by
combining labor
and a time-invariant stock of physical capital (k) using a Cobb-Douglas technology: exp(?
t
)F(k, n), where ?
t
is a Markov productivity shock. This
?rm participates in competitive factor and goods markets taking the real wage (w)
as given. Thus, the choice of labor input consistent with pro?t maximization yields
standard marginal productivity conditions for labor demand and the rate of dividend
payments (d):
w
t
= exp(?
t
)F
n
(k, n
t
) (2.1)
d
t
= exp(?
t
)F
k
(k, n
t
) (2.2)
Households choose stochastic sequences of consumption (c), labor supply
, equityholdings (?), and foreign bond holdings (b) so as to maximize the following utility
58
function:
U(c, n) = E
0
_
?
t=0
exp
_
?
t?1
?=0
?(c
?
?h(n
?
))
_
u(c
t
?h(n
t
))
_
(2.3)
This utility function is a time-recursive, intertemporal utility index with an endoge-
nous rate of time preference that introduces an “impatience e?ect” on the marginal
utility of consumption (i.e., changes in ct alter the subjective discount rate applied
to future utility ?ows). Utility functions with this feature are commonly used in
small open economy models to obtain well-de?ned long-run equilibria for holdings of
foreign assets.
3
As Section 2.3 shows, in models with credit constraints these prefer-
ences are also critical for supporting long-run equilibria in which credit constraints
can bind.
The period utility function u(·) is a standard, concave, twice-continuously
di?erentiable utility function. The function ?(·) is the time preference function,
which is also concave and twice-continuously di?erentiable. The argument of both
functions is a composite good de?ned by consumption minus the disutility of labor
c ? h
, where h(·) is an increasing, convex, continuously-di?erentiable function.Greenwood, Hercowitz and Hu?man (1988), GHH, introduced this composite good
as a way to eliminate the wealth e?ect on labor supply. As in Mendoza and Smith
(2004), this property of preferences, together with conditions (2.1) and (2.2), sepa-
rates the determination of equilibrium wages, dividends, labor and output from the
equilibrium allocations of consumption, saving and portfolio choice.
3
See Arellano and Mendoza (2003) for further details on this issue.
59
The household maximizes lifetime utility subject to the following budget con-
straint:
c
t
= ?
t
kd
t
+w
t
n
t
+q
t
(?
t
??
t+1
)k ?b
t+1
+b
t
R (2.4)
where ?
t
and ?
t+1
are beginning- and end-of-period shares of capital owned
by households, q
t
is the price of equity, and R is the world real interest rate (which
is kept constant for simplicity).
Foreign debt contracts feature a collateral constraint in the form of a margin
clause that limits the debt not to exceed the fraction ? of the market value of the
SOE’s equity holdings:
b
t+1
? ??q
t
?
t+1
k, 0 ? ? ? 1 (2.5)
Margin clauses of this form are widely used in international capital markets. In
some instances they are imposed by regulators with the aim of limiting the exposure
of ?nancial intermediaries to idiosyncratic risk in lending portfolios, but they are
also widely used by investment banks and other lenders to manage default risk
(either in the form of explicit margin clauses attached to speci?c securities o?ered
as collateral, or as implicit margin requirements linked to the volatility of returns of
an asset class like those implied by value-at-risk collateralization). Margin clauses
are a particularly e?ective collateral constraint (compared to the classic constraint
of Kiyotaki and Moore (1997) that limits debt to the discounted liquidation value of
assets one period ahead) because: (a) custody of the securities o?ered as collateral
60
is surrendered at the time the credit contract is entered and (b) margin calls to
make up for shortfalls in the market value of the collateral are automatic once the
value of the securities falls below the contracted value.
Households in the small open economy also face a short-selling constraint in
the equity market: ?
t+1
? ? with ??< ? < 1 for all t. This constraint is necessary
in order to make the margin constraint non-trivial. Otherwise, any borrowing limit
in the bond market implied by a binding margin constraint could always be undone
by taking a su?ciently short equity position.
2.2.2 The Foreign Securities Firm, the IFO & the Price Guarantees
The representative foreign securities ?rm obtains funds from international in-
vestors and specializes in investing them in the SOE’s equity. This ?rm maximizes
its net present value discounted at the discount factor of its international clients
(i.e., the world interest rate). Thus, the foreign traders’ problem is to choose ?
?
t+1
,
for t = 1, ..., ?, so as to maximize:
D = E
0
_
?
t=0
R
?t
?
t
_
,
?
t
? k
_
?
?
t
d
t
?
_
q
t
?
?
t+1
?max(q
t
, ˜ q
t
)?
?
t
_
?q
t
_
a
2
_
_
?
?
t+1
??
?
t
+?
_
2
?T
?
t
_
.
(2.6)
The total net return of the foreign securities ?rm (?
t
) is the sum of: (a)
dividend earnings on current equity holdings (k?
?
t
d
t
), minus (b) the value of equity
trades, which is the di?erence between equity purchases q
t
k?
?
t+1
and equity sales
max(q
t
, ˜ q
t
)k?
?
t
executed at either the market price q
t
or the guaranteed price ˜ q
t
,
61
whichever is greater, minus (c) trading costs, which include a term that depends on
the size of trades (?
?
t+1
??
?
t
) and a recurrent trading cost (theta), minus (d) lump
sum taxes paid to the IFO (kT
?
t
). Trading costs are speci?ed in quadratic form, so
a is a standard adjustment-cost coe?cient.
The IFO buys equity from the foreign traders at the guaranteed price and sells
it at the equilibrium price. Thus, the IFO’s budget constraint is:
T
?
t
= max(0, (˜ q
t
?q
t
)?
?
t
) (2.7)
If the guarantee is not executed, the tax is zero. If the guarantee is executed, the
IFO sets the lump-sum tax to match the value of the executed guarantee (i.e., the
extra income that foreign traders earn by selling equity to the IFO instead of selling
it in the equity market). Since the return on equity is R
q
t
? [d
t
+q
t
] /q
t
? 1, the
IFO’s o?er to guarantee the date-t price implies a guaranteed return on the emerging
economy’s equity
˜
R
q
T
= [˜ q +d
t
]/q
t?1
.
2.2.3 Equilibrium
A competitive equilibrium is given by stochastic sequences of prices and allo-
cations such that: (a) households maximize the utility function (2.3) subject to the
constraints (2.4) and (2.5) and the short-selling constraint, taking prices, wages and
dividends as given, (b) domestic ?rms maximize pro?ts so that equations (2.1) and
(2.2) hold, taking wages and dividends as given, (c) foreign traders maximize (2.6)
taking the price of equity, the price guarantees and lump-sum taxes as given, (d)
62
the budget constraint of the IFO in equation (2.7), holds and (e) the equity market
clears (i.e., ?
t
+?
?
t
= 1 for all t).
2.3 Characterizing the Globalization Hazard-Moral Hazard Tradeo?
The tradeo? between the globalization hazard introduced by the distortions
that margin constraints and trading costs create and the moral hazard introduced by
distortions due to price guarantees can be illustrated with the optimality conditions
of the competitive equilibrium. Consider the ?rst-order conditions of the domestic
household’s maximization problem:
U
c
(c, n) = ?
t
(2.8)
h
(n
t
) = w
t
(2.9)
q
t
(?
t
??
t
?) = E
t
[?t + 1(d
t+1
+q
t+1
)] + ?
t
(2.10)
?
t
??
t
= E
t
[?
t+1
R] (2.11)
U
c
(c, n) is the derivative of the SCU function with respect to c
t
(which includes the
impatience e?ect), and ?
t
, ?
t
and ?
t
are the Lagrange multipliers on the budget
constraint, the margin constraint, and the short-selling constraint respectively.
Condition (2.8) has the standard interpretation: at equilibrium, the marginal
utility of wealth equals the lifetime marginal utility of consumption. Condition
(2.9) equates the marginal disutility of labor with the real wage. This is the case
because the GHH composite good implies that the marginal rate of substitution
63
between c
t
and n
t
is equal to the marginal disutility of labor h
(n
t
), and thus is
independent of c
t
. It follows from this result that condition (2.9) together with (2.1)
and (2.2) determine the equilibrium values of n
t
, w
t
and d
t
as well as the equilibrium
level of output. These “supply-side” solutions are independent of the dynamics of
consumption, saving, portfolio choices and equity prices, and are therefore also
independent of the distortions induced by ?nancial frictions and price guarantees.
This result simpli?es signi?cantly the numerical solution of the model. Mendoza
(2004) studies the implications of margin constraints in a small-open-economy model
with endogenous investment in which ?nancial frictions a?ect dividends, investment
and the Tobin Q, but abstracting from international equity trading.
Conditions (2.10) and (2.11) are Euler equations for the accumulation of equity
and bonds respectively. As in Mendoza and Smith (2004), these conditions can be
combined to derive expressions for the forward solution of equity prices and the
excess return on equity from the perspective of the emerging economy. The forward
solution for equity prices is:
q
t
= E
t
_
?
i=0
_
i
j=0
_
1 ?
?
j+1
?
j+1
?
_
?1
_
M
t+1+i
d
t+1+i
_
(2.12)
where M
t+1+i
? ?
t+1+i
/?
t
, for i = 0, ..., ?, is the marginal rate of substitution
between c
t+1+i
and c
t
. The excess return on domestic equity is:
E
t
_
R
q
t+1
¸
?R =
?
t
(1 ??) ?
?
t
q
t
?COV
t
(?
t+1
, R
q
t+1
)
E
t
[?
t+1
]
(2.13)
64
Given these results, the forward solution for equity prices can also be expressed as:
q
t
= E
t
_
?
i=0
_
i
j=0
_
R
q
t+1+j
_
?1
_
d
t+1+i
_
(2.14)
Expressions (2.12)-(3.14) show the direct and indirect e?ects of margin calls on
domestic demand for equity and excess returns. The direct e?ect of a date-t margin
call is represented by the term ?
t
(1??) in (2.13), or the term ?
t
? in (2.12): When a
margin call occurs, domestic agents “?re sale” equity in order to meet the call and
satisfy the borrowing constraint. Everything else the same, this e?ect lowers the
date-t equity price and increases the expected excess return for t+1. The indirect
e?ect of the margin call is re?ected in the fact that a binding borrowing limit makes
“more negative” the co-variance between the marginal utility of consumption and
the rate of return on equity (since a binding borrowing limit hampers the households’
ability to smooth consumption). These direct and indirect e?ects increase the rate
at which future dividends are discounted in the domestic agents’ valuation of asset
prices, and thus reduce their demand for equity. Interestingly, the date-t equity
price along the domestic agents’ demand curve is reduced by a margin constraint
that is binding at date t or by any expected binding margin constraint in the future.
As a result, equity prices and the domestic demand for equity can be distorted by
the margin requirements even in periods in which the constraint does not bind.
In a world with frictionless asset markets, domestic agents facing margin calls
could sell assets in a perfectly-competitive market in which the world demand for
the emerging economy’s assets is in?nitely elastic at the level of the fundamentals
65
price. Margin calls would trigger portfolio reallocation e?ects without any price
movements. However, in the presence of frictions that make the world demand for
the emerging economy’s assets less than in?nitely elastic, the equilibrium asset price
falls. Since households were already facing margin calls at the initial price, this price
decline tightens further the margin constraint triggering a new round of margin calls.
This downward spiral in equity prices is a variant of Fisher’s (1933) debt-de?ation
mechanism, which magni?es the direct and indirect e?ects of the margin constraint.
The foreign demand for the emerging economy’s assets is less than in?nitely
elastic because of the trading costs that foreign traders pay. De?ne the fundamentals
price as the conditional expected value of dividends discounted at the world interest
rate q
f
t
? E
t
_
?
i=0
R
?(t+1+i)
d
t+1+i
_
. The ?rst-order condition for the optimization
problem of foreign traders implies then:
_
?
?
t+1
??
?
t
_
=
1
a
_
q
f
t
q
t
?1 +
E
t
_
?
i=1
R
?(t+i)
(max(q
t+i
, ˜ q
t+i
) ?q
t+i
)
¸
q
t
_
?? (2.15)
The foreign traders’ demand for the emerging economy’s assets is an increas-
ing function of: (a) the percent deviation of qt f relative to qt (with an elasticity
equal to 1/a) and (b) the expected present discounted value of the “excess prices”
induced by the price guarantees in percent of today’s equity price. The ?rst e?ect
re?ects the in?uence of the per-trade trading costs. If a = 0 and there are no price
guarantees, the foreign traders’ demand function is in?nitely elastic at q
f
. The
second e?ect is the international moral hazard e?ect of the guarantees, which acts
as a demand shifter on the foreign traders’ demand function. Foreign traders that
66
expect price guarantees to be executed at any time in the future have a higher de-
mand for domestic assets at date t than they would in a market without guarantees.
The recurrent trading costs are also a demand shifter (the foreign traders’ demand
function is lower the higher is ? ).
In light of the previous results, the tradeo? between globalization hazard and
international moral hazard can be summarized as follows. Suppose the date-t as-
set price in a market without margin constraints and without price guarantees is
determined at the intersection of the domestic agents’ and foreign traders’ demand
curves (HH and FF respectively) at point A in Figure 2.1.
The demand function of foreign traders is simply equation (2.15), shown in
Figure 2.1 as a linear function for simplicity and as an upward sloping curve because
the horizontal axis measures ?, which is the complement of ?
?
. This FF curve is
relatively ?at to approximate a situation with low per-trade costs. There is no
closed-form solution for HH, so the curve depicted is intended only to facilitate
intuition. HH is shown as a downward-slopping curve but, since domestic agents
respond to wealth, intertemporal-substitution and portfolio-composition e?ects in
choosing their equity holdings, HH can be downward or upward slopping depending
on which e?ect dominates.
Suppose that a margin call hits domestic agents because an adverse shock
hits the economy when their debt is su?ciently high relative to the value of their
assets. As a result, HH shifts to HH
. In Figure 2.1, HH
represents the “?nal”
demand function, including the magni?cation e?ect of the Fisherian debt-de?ation
mechanism. Without price guarantees, the date-t equilibrium price would fall to
67
point B. This is the “Sudden Stop scenario,” in which margin calls result in lower
asset prices and reversals in consumption and the current account. Enter now an
IFO that sets a price guarantee higher than the market price at B. The international
moral hazard e?ect shifts the foreign traders’ demand curve to FF
and the new
date-t market price is determined at point C, which yields the fundamentals price.
The scenario depicted here is an ideal one in which the IFO is assumed to know
exactly at what level to set the guaranteed price so as to stabilize the market price
at the fundamentals level. In contrast, if the guarantee is set below the price at
B, it would have no e?ect on the Sudden Stop equilibrium price, and thus price
guarantees would be irrelevant. If the guarantee is set too high, it can lead to a
price higher than the fundamentals price (with the overpricing even larger than the
underpricing that occurs at B). Hence, ex-ante price guarantees do not necessarily
reduce the volatility of asset prices (as Ljungqvist’s (2000) ?ndings showed).
From the perspective of the dynamic stochastic general equilibrium model,
Figure 2.1 is a partial equilibrium snapshot of the date-t asset market. The forward-
looking behavior of domestic households and foreign traders implies that changes
that a?ect the date-t asset market spillover into the market outcomes at other dates
and vice versa. For example, the price guarantee may not be in force at t but the
expectation of executing future price guarantees will shift upward the FF curve at
t. Similarly, the margin constraint may not bind at t, but the expectation of future
margin calls is enough to shift the date-t HH curve. Given the lack of closed-form
solutions for equilibrium allocations and prices, the only way to study the e?ects
of price guarantees on the dynamics of consumption, the current account, asset
68
holdings, and asset prices is by exploring the model’s quantitative implications via
numerical simulation.
2.4 Quantitative Analysis
2.4.1 Recursive Equilibrium and Solution Method
In the recursive representation of the equilibrium, the state variables are the
current holdings of assets and bonds in the emerging economy, ? and b, and the
realization of the productivity shock e. The state space of asset positions spans
the discrete grid of NA nodes A = ?
1
< ?
2
< < ?
NA
with ?
1
= ?, and the state
space of bonds spans the discrete grid of NB nodes B = b
1
< b
2
< < b
NB
. The
endogenous state space is de?ned by the discrete set Z = A × B of NA × NB
elements. Productivity shocks follow a stationary, two-point Markov chain with
realizations E = ?
L
< ?
H
. Equilibrium wages, dividends, labor and output are
determined by solving the supply-side system given by equations (2.1), (2.2), (2.9)
and the production function. The solutions are given by functions that depend only
on ?: w(?), d(?), n(?) and F(?).
The numerical solution of the recursive equilibrium is obtained using a modi-
?ed version of Mendoza and Smith’s (2004) quasi-planning problem algorithm. The
algorithm starts with a conjecture for the function
ˆ
G(?, b, ?) : E×Z ?R
+
, which re-
turns the expected present discounted value of “excess prices” for any triple (?, b, ?)
in the state space. Given this conjecture, the optimal decision rules for equity and
bond holdings of domestic agents, are obtained by solving the following dynamic
69
programming problem:
V (?, b, ?) = max
?
,b
?A×B
{u(c ?h(n(?))) + exp(??(c ?h(n(?))))E[V (?
, b
, ?
)]}
(2.16)
subject to:
c = ?kd(?) +w(?)n(?) +
q
f
(?) +
ˆ
G(?, b, ?)
1 + a? +a(? ??
)
k(? ??
) ?b
+bR (2.17)
b
? ??
q
f
(?) +
ˆ
G(?, b, ?)
1 + a? +a(? ??
)
?
k (2.18)
Note that equity prices in (2.19) and (2.20) were replaced with the prices along the
demand curve of foreign traders by imposing equity market clearing and solving for
equity prices using (2.15).
The decision rule for equity holdings is plugged into equation (2.15) to derive
an “actual” asset pricing function (for the given conjecture
ˆ
G(?, b, ?)). The decision
rules for bonds and equity, the guaranteed prices, and this “actual” pricing function
are then used to solve for the “actual” function. The conjectured and actual G func-
tions are then combined to create a new conjecture using a Gauss-Siedel rule, and the
procedure starts again with the Bellman equation (2.18). The process is repeated
until
ˆ
G(·) and G(·) converge, so that the function
ˆ
G(?, b, ?) that is taken as given in
the dynamic programming problem is consistent with the function G(?, b, ?) implied
by the asset pricing function and decision rules that are endogenous outcomes of
that problem.
70
The drawback of this method is that it assumes that the emerging economy
internalizes the demand function of foreign traders. As a result, the equilibrium of
problem (2.18) is equivalent to a competitive equilibrium for a variant of the model
with a proportional tax or subsidy on asset returns, with tax revenues rebated as a
lump-sum transfer. In the simulations we discuss below, however, the implied taxes
are negligible: The maximum taxes in absolute values range between 0.08 (0.4) and
0.2 (0.8) percent when a = 0.2(2). The average tax in absolute value is 0.03 (0.3)
percent in the simulations with a = 0.2(2).
2.4.2 Deterministic Steady State and Calibration to Mexican Data
The functional forms that represent preferences and technology are the follow-
ing:
F(k, n
t
) = k
(1??)
n
?
t
, 0 ? ? ? 1 (2.19)
u(c
t
?h(n
t
)) =
[c
t
?h(n
t
)]
1??
?1
1 ??
, ? > 1 (2.20)
?(c
t
?h(n
t
)) = ?[Ln(1 + c
t
?h(n
t
))], 0 < ? ? ? (2.21)
h(n
t
) =
n
?
t
?
, ? > 1 (2.22)
? is the labor income share, ? is the coe?cient of relative risk aversion, ? is the
elasticity of the rate of time preference with respect to 1 + c
t
? h(n
t
), and ? sets
the wage elasticity of labor supply (which is equal to 1/(? ? 1)). The condition
0 < ? ? ? is required to limit impatience e?ects and obtain a well-de?ned limiting
distribution of foreign bonds (see Arellano and Mendoza (2003) for details).
71
The calibration strategy di?ers markedly from the one in Mendoza and Smith
(2004). They normalize the capital stock to k=1 and let the steady-state equity price
adjust to the value implied by the asset pricing condition, given a set of parameter
values taken directly from the data or set to enable the model to match ratios of
national accounts statistics. Here, we normalize instead the steady-state equity
price so that the capital stock matches the deterministic, steady-state capital stock
of a typical RBC-SOE model calibrated to Mexican data (see Mendoza (2004)).
The steady state of this RBC-SOE model is a frictionless, neoclassical stationary
equilibrium. Calibrating to this frictionless equilibrium helps focus the analysis
on the use of price guarantees to prevent Sudden Stops triggered by margin calls
that hit the economy only when it is highly leveraged (and hence o? the long-run
equilibrium).
The risk aversion parameter is set at ? = 2 in line with values often used in
RBC-SOE studies. The parameter values that enter into the supply-side system are
determined as follows. The labor share is set at ? = 0.65, in line with international
evidence on labor income shares. The Mexican average share of labor income in
value added in an annual sample for 1988-2001 is 0.34, but values around 0.65 are
the norm in several countries and there is concern that the Mexican data may mea-
sure inaccurately proprietors income and other forms of labor income (see Mendoza
(2004) for details). The real interest rate is set at 6.5 percent, which is also a value
widely used in the RBC literature. Since the model is set to a quarterly frequency,
this implies R = 1.065
1/4
. The labor disutility coe?cient is set to the same value
as in Mendoza and Smith (2004), ? = 2, which implies a unitary wage elasticity of
72
labor supply.
As in a typical RBC calibration exercise, the calibration is designed to yield
a set of parameter values such that the model’s deterministic steady state matches
actual averages of the GDP shares of consumption (sc), investment (si), govern-
ment purchases (sg) and net exports (snx). In the Mexican data, these shares are
sc = 0.684, si = 0.19, sg = 0.092, and snx = 0.034. Since the model does not
have investment or government purchases, their combined share (0.282) is treated
as exogenous absorption of output equivalent to 28.2 percent of steady-state GDP.
In the stochastic simulations we keep the corresponding level of these expenditures
constant at 28.2 percent of the value obtained for steady-state output in the cali-
bration.
The typical RBC-SOE model features a standard steady-state optimality con-
dition that equates the marginal product of capital net of depreciation with the
world interest rate, and a standard law of motion of the capital stock that relates
the steady-state investment rate to the steady-state capital-output ratio. Given
the values of si, ?, ? and R, these two steady-state conditions yield values of the
depreciation rate (dep) and the capital-output ratio (sk). On an annual basis, the
resulting depreciation rate is 7.75 percent and sk is about 2.5.
In a deterministic steady state of the model of Section 2 in which the credit
constraint does not bind and there are no price guarantees, the equity price is
q = q
f
= d/(R?1). Given the RBC-SOE calibration criterion that the steady-state
marginal product of capital net of depreciation equals the net world interest rate, q
f
can be re-written as F
k
(k, n)/(F
k
(k, n) ?dep). With the Cobb-Douglas production
73
function this reduces to q
f
= (1 ??)/(1 ?? ?si). Thus, the requirement that the
model’s dividend rate must match a typical RBC-SOE calibration implies that the
steady-state equity price is determined by si and g. With the parameter values set
above we obtain q
f
= 2.19.
Given the values of ?, ?, R, and q
f
the steady-state solutions for n, w, k, and
F(k, n) follow from solving the supply-side system conformed by (2.1), (2.2), (2.9)
and (2.21). The resulting steady-state capital stock is k = 79. By construction, this
capital stock is also consistent with the estimated capital-output ratio of 2.5 and
the observed Mexican investment rate of 0.19.
The parameters that remain to be calibrated are the time-preference elasticity
coe?cient b and the ?nancial frictions parameters a, ? and k. The value of ? is
derived from the consumption Euler equation as follows. In the deterministic sta-
tionary state of the model there are no credit constraints and hence the endogenous
rate of time preference equals the real interest rate:
_
1 + scF(k, n) ?
n
?
?
_
?
= R (2.23)
Given the values of R, ?, n, F(k, n) and sc, this condition can be solved for the
required value of ?. The solution yields ? = 0.0118. The total stock of do-
mestic savings at steady state follows then from the resource constraint as s =
[c ?F(k, n)(si +sg) ?wn]/(R ?1) = ?q
f
k +b.
Up to this point the calibration followed the typical RBC-SOE deterministic
calibration exercise. A problem emerges, however, when we try to determine the
74
composition of the savings portfolio because the allocation of savings across bonds
and equity is undetermined. Any portfolio (?, b) ? A × B is consistent with the
RBC-SOE deterministic steady state as long as it supports the unique steady-state
level of savings (i.e., ?q
f
k + b = s) and the margin and short-selling constraints
do not bind (b > ?k?q
f
k and ? > ?). Moreover, given the values of s, q
f
and k
implied by the calibration, it follows from the de?nition of savings that there is only
a small subset of portfolios in which the economy borrows in the bond market (i.e.,
portfolios with b < 0) in the set of multiple steady-state portfolios. Debt portfolios
require ? > 0.9. If domestic agents own less than 90 percent of k, their steady-state
bond position is positive and grows larger the smaller is a. This also implies that it
will take low values of ? to make the margin constraint bind. In particular, setting
the upper bound of ? at 100 percent, it takes ? ? 0.10 for the margin constraint to
bind for at least some of the multiple steady-state pairs of (?, b). These low values of
? can be justi?ed by considering that the margin constraint represents the fraction
of domestic capital that is useful collateral for external debt. Several studies in the
Sudden Stops literature provide arguments to suggest that this fraction is small (see,
for example, Caballero and Krishnamurty (2001)).
The stochastic RBC-SOE without credit constraints has the additional un-
appealing feature that it can lead to degenerate long-run distributions of equity
and bonds in which domestic agents hold the smallest equity position (?) and use
bonds to engage in consumption smoothing and precautionary saving. The reason is
that, without credit constraints and zero recurrent trading costs, risk-averse domes-
tic agents demand a risk premium to hold equity while risk-neutral foreign traders
75
do not.
4
Hence, domestic agents end up selling all the equity they can to foreign
traders, although the process takes time because of the trading costs that foreign
traders pay.
To circumvent the problems of portfolio determination in the deterministic and
stochastic RBC-SOE steady states, we calibrate the values of the ?nancial frictions
parameters (?, q and k) so that the allocations and prices obtained with the deter-
ministic RBC-SOE steady state can be closely approximated as the deterministic
steady state of an economy with negligible (but positive) recurrent trading costs
and a margin constraint that is just slightly binding. This calibration scenario is
labeled the “nearly frictionless economy”(NFE).
The deterministic steady state of the NFE has well-de?ned, unique solutions
for bond and equity positions. In particular, foreign traders hold a stationary equity
position at the price q = q
f
/(1 + a?). Since this price is less than q
f
, which is
the price at which the return on domestic equity equals R, it follows that at this
lower price R
q
> R. Thus, foreign traders now require an equity premium to
hold a stationary equity position. The ratio of the Lagrange multipliers of the
domestic agent’s margin constraint and budget constraint can then be found to be
?/? = (R
q
? R)/(R
q
? R?). In addition, since the margin constraint binds, bond
holdings must satisfy b = ???qk, and hence a unique stationary domestic equity
position can be obtained from the steady-state consumption Euler equation. This
4
With ? = 0 and no price guarantees, equation (2.15) implies that foreign traders attain a
stationary equity position when the equity price equals the fundamentals price, and the latter
implies a stationary asset return equal to R. Thus, at this steady state foreign traders hold equity
at zero equity premium.
76
is the value of a that solves the following expression:
_
1 + ?kd +wn ??q?k(R ?1) ?
n
?
?
_
?
=
R
1 ?(?/?)
(2.24)
Equation (26) illustrates the key role of the endogenous rate of time preference in
supporting deterministic stationary equilibria with binding credit limits: it allows
the rate of time preference to adjust so as to make the higher long-run consumption
level, implied by the fact that the credit constraint prevents domestic agents from
borrowing as they desire in the transition to steady state, to be consistent with the
higher e?ective long-run real interest rate also implied by the credit constraint. The
recurrent trading cost is also critical. With ? = 0, a stationary equity position for
foreign traders requires a price equal to q
f
and a return on equity equal to R, but
the latter implies that ?/? = 0, so the borrowing constraint could not bind.
In the NFE steady state, the values of a, ? and kappa are set to support a
deterministic steady state with a binding borrowing constraint that satis?es the
following conditions: (1) the debt-GDP ratio is in line with Mexican data, (2)
the allocations, factor payment rates and the equity price are nearly identical to
those obtained for the frictionless RBC-SOE deterministic steady state, and (3) the
elasticity of the foreign trader’s demand curve is relatively high. The values of the
?nancial frictions parameters are: a = 0.2, ? = 0.001 and ? = 0.03. With these
parameter values, and the values set earlier for ?, ?, ?, and R, the NFE steady
state yields values of c, s, n, w, d, q, and R
q
nearly identical to those of the RBC-
SOE deterministic steady state, but the NFE also has unique portfolio allocations
77
of ? = 0.931 and b = ?4.825 (which implies a debt-GDP ratio of about 0.62).
2.4.3 Stochastic Simulation Framework
The stochastic simulations are solved over a discrete state space with 78 evenly-
spaced nodes in the equity grid and 120 evenly-spaced nodes in the bonds grid. The
lower bound for equity is set at c=0.84, so the equity grid spans the interval [0.84,1].
These equity bounds, together with the maximum equity price de?ned in (2.17) and
the margin constraint, set the lower bound for bonds as ??q
max
k = ?5.2. This
is the largest debt that the SOE could leverage by holding the largest possible
equity position at the highest possible price. The upper bound of bonds is found
by solving the model repeatedly starting with an upper bound that supports steady
state savings with the equity position at its lowest, and then increasing the upper
bound until the grid captures the support of the ergodic distribution of bonds. The
resulting grid spans the interval [-5.2,25.7]. The segment of debt positions inside
this interval is relatively small, re?ecting the fact that, despite the frictions induced
by asset trading costs, domestic agents still have a preference for riskless bonds as
a vehicle to smooth consumption and build a bu?er stock of savings.
A lower bound on domestic equity holdings of 84 percent seems much higher
than the conventional short-selling limit set at 0 but it is consistent with the national
aggregates targeted in the calibration. In Mexico, the 1988-2000 average ratio of
stock market capitalization to GDP was 27.6 percent. Since the calibration produced
an estimate of the capital-output ratio of about 2.5, the shares of publicly traded
78
?rms constitute just 11 percent of the capital stock. A large fraction of Mexico’s
capital is owned by non-publicly-traded ?rms and by owners of residential property,
and thus does not have a liquid market in which shares are traded with foreign
residents. In general, it is hard to argue that a large fraction of the physical capital
of most emerging economies has a liquid international market. Moreover, the result
from the calibration showing that bond positions become positive and unrealistically
large for ? < 0.9 also argues for a high value of ?.
Productivity shocks are modeled as a two-point, symmetric Markov process
that follows the “simple persistence” rule. The two points of the Markov chain and
the transition probability matrix are set so that the model mimics the standard
deviation and ?rst-order autocorrelation of the quarterly cyclical components of
Mexico’s GDP reported in Mendoza (2004) – 2.64 percent and 0.683 respectively.
This requires a Markov process of productivity shocks with a standard deviation
(?
?
) of 1.79 percent and a ?rst-order autocorrelation coe?cient (?
?
) of 0.683. The
simple persistence rule implies then that the two points of the Markov chain are
-?
L
= ?
H
= 0.0179 and these two states a long-run probability of . The transition
probability of remaining in either state is given by (1 ? ?
?
) + ?
?
= 0.8415 and the
transition probability of shifting across states is (1 ??
?
) = 0.1585.
79
2.4.4 Baseline Results: Globalization Hazard and Sudden Stops with-
out Price Guarantees
The baseline results include four simulations: (1) the NFE case, (2) the econ-
omy with binding margin requirements (BMR), which uses a margin coe?cient set
at ? = 0.005, (3) a simple price-guarantees policy that sets a single, non-state-
contingent guaranteed price (NSCG) for all dates and states, and (4) an economy
with the same guaranteed price but as a state-contingent guarantee (SCG) that
applies only in a subset of the state space.
The key result that emerges from comparing the NFE and BMR economies is
that the ?nancial frictions representing globalization hazard in the model do cause
Sudden Stops when the ratio of debt to the market value of equity is high and the
equity market has enough liquidity (i.e., domestic agents are not at their short-
selling limit). Since this result echoes ?ndings from Mendoza and Smith (2004), we
keep the presentation short and refer the reader to their article for details.
Figures 2 shows the long run distributions of equity and bonds for the four
simulations. Comparing the bond distributions of the NFE and BMR simulations,
the e?ect of the margin constraint is evident. The distribution is biased to the
left in the two economies but it shifts markedly to the right in the BMR case.
The opposite occurs with the distribution of equity. The bias to the left in the
distribution of equity re?ects the incentive that risk-averse domestic agents have
to sell equity to risk-neutral foreign traders. Binding margin constraints shift the
equity distribution further to the left because of the equity ?re sales triggered by
80
margin calls. These shifts in the distributions of equity and bonds also re?ect the
outcome of precautionary saving. Domestic agents, aware of the imperfections of
?nancial markets, have an incentive to build up a bu?er stock of savings so as to
minimize the risk of large declines in consumption, and in doing so they also lower
the risk of facing states in which margin constraints bind in the long run (Figure 2
shows that the long run distribution of bonds of the BMR economy rules out states
with very large debt positions). Still, Table 1 shows that the long-run probability
of binding margin constraints is about 4 percent. Sudden Stops are therefore rare
but non-zero probability events in the stochastic steady state (although many of the
states in which margin constraints bind in the long run do not trigger Sudden Stops,
as explained below). Note also that margin constraints cause a portfolio reallocation
of savings from equity into bonds. Table 1 shows that the long-run average of the
bonds-output ratio increases from 18 percent in the NFE to 50 percent in the BMR
economy.
Financial frictions have negligible e?ects on business cycle moments (see Table
2.1). Hence, as in Mendoza and Smith (2004), we study Sudden Stops by examining
the model’s dynamics in the high-debt region of the state space in which the margin
constraint binds (i.e., the “Sudden Stop region”). Figure 2.3 shows the date-0
responses (or impact e?ects) of consumption, and the current account-GDP ratio
(ca/y) to a negative, one-standard-deviation productivity shock for (?, b) pairs in
the Sudden Stop region, measured in percent of the long-run mean of each variable.
The Sudden Stop region includes the ?rst 25 nodes of the B grid and all 72 nodes
of the A grid.
81
Figure 3 suggests that there are two key factors driving impact e?ects in the
Sudden Stop region: (1) The leverage ratio, de?ned as the ratio of debt to the
market value of equity, and (2) The liquidity of the equity market, de?ned as the
di?erence between ? and ?. Sudden Stops with large reversals in c and ca/y occur
when the leverage ratio is high, but given high leverage the impact on asset prices
is di?erent depending on asset market liquidity. If the asset market is illiquid, the
Sudden Stop can feature negligible asset price declines because domestic agents are
close to ? and hence have little equity to sell (see Figure 2.5a), but if there is some
liquidity in the asset market, the Sudden Stop in c and ca/y is accompanied by a
fall in q. In contrast, when the leverage ratio is su?ciently low and the asset market
is su?ciently liquid, the drop in consumption and the current account reversal are
small (nearly as small as in the NFE case) but the drop in asset prices is larger.
In this case, domestic agents liquidate more equity and trigger larger asset price
collapses, but they do so in order to swap their limited borrowing ability via bonds
for equity sales so as to minimize the drop in consumption. This pattern of larger
current account corrections coinciding with smaller asset price collapses ?ts the
observations of some emerging markets crises. The current account reversal in the
?rst quarter of 1995 in Mexico was 5.2 percent of GDP but the drop in real equity
prices was nearly 29 percent. In contrast, in Korea the current account reversal in
the ?rst quarter of 1998 was twice as large but the asset price drop was just 10
percent.
Figure 2.4 illustrates Sudden Stop dynamics using the conditional forecasting
functions of c, q and ca/y. The ?rst two are shown as percentages of their long-run
82
averages in the NFE and the last is shown as the percentage points di?erence relative
to the long-run average in the NFE. These forecasting functions represent non-linear
impulse response functions to a negative, one-standard-deviation productivity shock
conditional on initial positions of equity and bonds inside the Sudden Stop region.
The Figures plot two sets of forecasting functions, one for a high leverage initial
state, at which ? = 0.938 and b = ?4.68 (with debt ratio of 60 percent of GDP
and a leverage ratio of 3 percent of GDP), and one for a low leverage state with the
same a but b = ?3.38 (with a debt ratio of 43 percent of GDP and a leverage ratio
of 2 percent of GDP). Since these initial states are distant from the corresponding
long-run averages, the data in the Figures were adjusted to remove low-frequency
transitional dynamics driven by the convergence of bonds and equity to their long-
run means. Given that c, q and ca/y have nearly identical long-run averages in the
four baseline experiments (except for the mean of q in the NSCG economy, which
is higher), the forecasting functions were detrended by taking di?erences relative to
the NFE forecasting functions.
The impact e?ects in the initial date of the forecasting functions of the BMR
economy di?er sharply across the high and low leverage states, and those of the high
leverage state deviate signi?cantly from those of the NFE (or from zero in terms
of Figure 2.4, since the data are plotted as di?erences relative to the NFE). In the
high leverage state of the BMR economy, the negative shock triggers a Sudden Stop
driven by the mechanisms described in Section 2.3: Domestic agents sell equity to
meet margin calls and trigger a Fisherian de?ation that reduces further their ability
to borrow. The net result is that, on impact, a one-standard-deviation shock to
83
productivity causes c and q to drop by 1.5 and 0.4 percent more than in the NFE
respectively and ca/y to rise by about 1 percentage point of GDP. In the low leverage
state, domestic agents are better positioned to smooth consumption by substituting
debt for equity to ?nance a current account de?cit. As a result, the responses of c
and ca/y in the BMR economy are nearly identical to those in the NFE, so their
detrended forecasting functions hover around zero. This occurs even though the
sales of equity still make q fall by about the same amount as in the high leverage
scenario. Notice also that the drop in asset prices is small relative to observed
Sudden Stops, but very large relative to the standard deviation of asset prices in
the NFE.
One caveat about the plots in Figure 2.4: The initial bond and equity positions
used to generate them yield outcomes consistent with Sudden Stops, but the set of
impact e?ects that the model predicts for all initial conditions inside the Sudden
Stop region are shown in Figures 2.3. As these Figures show, the Sudden Stop re-
gion includes scenarios with much larger consumption and current-account reversals
than those shown in Figure 2.4, as well as scenarios in which there is little di?erence
between the BMR and NFE because the asset market is su?ciently liquid to main-
tain a similar current account de?cit by selling equity when the margin constraint
binds. Precautionary saving implies, however, that all the scenarios with very large
reversals in consumption have zero probability in the long run. Notice also that,
since the Sudden Stop region includes instances in which the margin constraint binds
but ?re sales of assets prevent a sharp current account reversal, the probability of
binding margin constraints is not identical to the probability of Sudden Stops.
84
Figure 2.4 suggests that Sudden Stops in the model are short-lived. The
responses of the BMR economy converge to those of the NFE in about 4 quarters.
Mendoza and Smith (2004) obtained Sudden Stops with more persistence using
higher per-trade costs, which hamper the foreign traders’ ability to adjust equity
holdings.
2.4.5 Baseline Results: State-Contingent and Non-State-Contingent
Price Guarantees
The price guarantees are set above the fundamentals price in the low produc-
tivity state.
5
This is motivated by a theoretical result that holds for stationary
decision rules (i.e., ?
t+1
= a
t
, b
t+1
= b
t
) and equilibrium equity prices in the high
productivity state that exceed a time- and state-invariant guaranteed price. Under
these assumptions, we can show that G(?, b, ?
L
) = z
_
˜ q ?
q
f
(?
L
)
1+a?
_
, where z is a posi-
tive fraction that depends on R, a, ? and the transition probabilities of the shocks.
Hence, ˜ q >
q
f
(?)
1+a?
is a necessary condition for the guarantees to be executed at least
in some states.
The non-state-contingent price guarantee is set of a percentage point above
the fundamentals price in the low productivity state (2.185). Hence, the guaranteed
price is 2.196. This guarantee is o?ered in all states (?, b, ?) in the NSCG economy.
In contrast, the SCG economy provides the same guaranteed price only for (a,b)
pairs inside the Sudden Stop region.
5
Note that incomplete asset markets and the risk-averse nature of domestic agents imply that
equilibrium prices in the NFE di?er from the fundamentals price that discounts dividends at the
risk-free rate.
85
Figure 2.2 shows that, relative to the BMR case, the non-state-contingent
guarantee shifts the distribution of equity (bonds) markedly to the left (right). The
long-run average of the expected present value of excess prices (i.e., the long-run
average of G ) is 0.01, which is about of a percent above the mean equity price
in the stochastic stationary state. Comparing long-run moments across Panels I,
II and III of Table 1, the main change in the NSCG simulation is the reduction
in the probability of binding margin constraints. The probability is almost zero
with price guarantees, compared with 4 percent in the BMR economy. The long-
run moments of the model’s endogenous variables vary slightly with the non-state-
contingent guarantee. Asset-price ?uctuations display less variability, persistence
and co-movement with output in the NSCG economy relative to the NFE and BMR
cases. The mean equity price increases by 0.053 percent, slightly more than the
percent di?erence between the guaranteed price and the fundamentals price of the
low productivity state. The coe?cient of variation of consumption falls by about
1/5 of a percentage point and the variability of the current account and the trade
balance increase slightly. Consumption also becomes less correlated with GDP.
The e?ects of the price guarantee on Sudden Stop dynamics are shown in
Figure 2.4. Price guarantees are an e?ective policy for containing Sudden Stops.
Comparing the NSCG and BMR economies in the high leverage state, the initial
consumption and current account reversals are smaller in the NSCG economy, and
the drop in equity prices turns into an increase of about 1/2 of a percentage point.
In the low leverage state, the increase in equity prices in the NSCG economy is
slightly larger than in the high leverage state, and we now obtain an increase in
86
consumption and a widening of the current account de?cit at date 0. The price
guarantee results in a price of equity at date 0 that is 2/3 of a percentage point
higher in the NSCG than in the BMR economy in both the high and low leverage
states. The price guarantee is executed in both states of the NSCG economy.
Figure 5 plots the levels of equity prices in the low productivity state of the
NFE, BMR and NSCG economies for all equity and bond positions. The plots
show that the non-state-contingent guarantee not only results in higher prices in
the Sudden Stop region, but it actually increases prices in all states. In fact, the
guarantee produces signi?cantly higher asset prices in the NSCG economy than in
either the NFE or BMR economies in states well outside the Sudden Stop region.
This is a potentially important drawback of non-state-contingent price guarantees:
they distort asset prices even when the economy is in states where it is far from
vulnerable to Sudden Stops.
One alternative to remedy the drawbacks of non-state-contingent price guar-
antees is to consider state-contingent guarantees. Figure 2.2 shows that the SCG
economy yields a long-run distribution of equity (bonds) that is less skewed to the
left (right) than in the NSCG economy. Table 1 shows that the changes in the long-
run business cycle moments of the SCG economy relative to the NFE and BMR cases
are qualitatively similar to those noted for the NSCG economy but the magnitude
of the changes is smaller. The SCG economy still features near-zero percent prob-
ability of observing states of nature in which the margin constraint binds. Hence,
the state-contingent guarantee is as e?ective as the non-state-contingent guarantee
at eliminating the possibility of hitting states with binding margin requirements in
87
the long run.
Figure 2.4 shows that, in both the high and low leverage states, the SCG
economy features nearly identical date-0 responses in consumption and the current
account as the NSCG economy and a slightly smaller recovery in asset prices. After
date 0, the SCG economy converges faster to the dynamic paths of the NFE economy.
Finally, a comparison of the middle and bottom plots of Figure 5 shows that the SCG
economy yields higher asset prices mainly in the Sudden Stop region of the state
space. Thus, state contingent guarantees induce smaller distortions on asset demand
and asset prices than the non-state-contingent guarantees, particularly outside the
Sudden Stop region, yet they have similar e?ects in terms of their ability to prevent
Sudden Stops.
2.5 Normative Implications and Sensitivity Analysis
2.5.1 Normative Implications of the Baseline Simulations
We study next the normative implications of the baseline simulations by ex-
amining how domestic welfare and the value of foreign securities ?rms varies across
the NFE, BMR, NSCG and SCG simulations. Welfare costs, W(?, b, ?), are mea-
sured by computing compensating variations in date-0 consumption that equate
expected lifetime utility in the BMR, NSCG and SCG economies with that of the
NFE for any triple (?, b, ?) in the state space. Welfare e?ects are typically com-
puted as compensating variations that apply to consumption at all dates, but in
principle both measures are useful for converting ordinal units of utility into the
88
cardinal units needed for quantitative welfare comparisons. The two measures yield
identical welfare rankings for the four experiments, but the measure based on date-0
consumption highlights better the welfare costs of Sudden Stops and the potential
bene?ts of price guarantees because large deviations from the consumption dynam-
ics of the NFE occur only in Sudden Stop states (in which bond and equity positions
are distant from their long-run averages).
The model belongs to the class of models in which capital markets are used
to smooth consumption over the business cycle. Hence, since it is well-known that
the welfare cost of ”typical” consumption ?uctuations is small in these models, the
mean welfare costs of deviating from the NFE (E[W(?, b, ?)]) computed with the
ergodic distribution) should be small. As Table 2.2 shows, welfare comparisons
based on date-0 consumption preserve this result. Agents in the BMR, NSCG and
SCG economies incur average welfare losses relative to the NFE equivalent to cuts
of less than 0.07 percent in c
0
. This is also in line with Mendoza’s (1991) results
showing trivial welfare costs for giving up access to world capital markets in an
RBC-SOE model.
The situation is very di?erent when comparing welfare conditional on Sudden
Stop states. Since the Bellman equation implies that lifetime utility as of date 0
can be expressed as V (t) = u(t) +exp(?v(t))Et[V (t + 1)], Table 2 decomposes the
total welfare cost into a short-run cost (i.e., the percent change in c
0
that equates
u(0) in the distorted economies with that of the NFE) and a long-run cost (i.e., the
percent change in c0 that equates exp(?v(0))E
0
[V (1)] in the distorted economies
with that of the NFE). The Table also lists the rate of time preference, exp(?v(0)),
89
to show that changes in the endogenous subjective discount are irrelevant for the
welfare analysis.
In the high leverage Sudden Stop state, which is the one that in the BMR
economy produces dynamics closer to those of observed Sudden Stops, the short-run
welfare costs show that domestic agents are worse o? in the BMR, NSCG and SCG
economies than in the NFE. The welfare cost is 1.4 percent for the BMR economy
and 0.9 and 1 percent for the NSCG and SCG economies respectively. This ranking
re?ects the fact that declines in date-0 consumption, and hence u(0), are smallest
in the NFE because it provides the best environment for consumption smoothing,
followed by the economies in which price guarantees help contain Sudden Stops.
The long-run costs are negative (i.e., domestic agents make welfare gains) be-
cause consumption after date 0 increases at least temporarily in the BMR, NSCG
and SCG economies. In the high leverage case of the BMR economy, the binding
credit constraint tilts the consumption pro?le by reducing consumption at date 0
and increasing it later, resulting in a long-run welfare gain of about 1 percent. Con-
sumption tilting is also at work in the NSCG and SCG economies, but in addition
the higher (distorted) asset prices lead to higher consumption relative to both the
BMR and the NFE for three quarters beyond the initial date (see Figure 4). This
expansion of consumption in the economies with price guarantees is driven in turn
by larger current account de?cits, which are ?nanced by equity sales at higher prices.
After date 0, domestic agents set to rebalance their portfolios from equity into bonds
gradually, but in economies with price guarantees the capital in?ows from equity
sales exceed the out?ows from bond purchases in the early periods of transition thus
90
producing larger external de?cits. This leads to long-run welfare gains in the high
leverage NSCG and SCG economies (1.9 and 1.3 percent respectively) that are large
enough to o?set the short-run costs, so that domestic agents obtain total welfare
gains of 1 percent in the NSCG and 0.3 percent in the SCG. These results show that
the asset price changes induced by price guarantees represent non-trivial distortions
relative to the NFE. Moreover, as we show below, the same distortions that increase
domestic welfare in the high leverage Sudden Stop states of the NSCG and SCG
economies reduce the value of foreign traders’ ?rms in those states.
At equilibrium, the foreign traders’ net returns can be written as:
ˆ ?(?, b, ?) ? k{[(1 ??)d(?)] ?[q(?, b, ?)(? ? ˆ ?
(?, b, ?))]?
_
q(?, b, ?)
_
a
2
_
(? ? ˆ ?
(?, b, ?) + ?)
2
_
}
(2.25)
The three terms in square brackets in the right-hand-side of this expression represent
the foreign traders’ dividend earnings, the net value of their trades, and the trading
costs they incur. Notice that, since the budget constraint of the IFO holds, the lump
sum taxes paid by foreign traders cancel with the value of the executed guarantees.
Thus, price guarantees distort the traders’ optimality condition with the moral
hazard e?ect identi?ed in (2.15) without direct income e?ects.
The payo? of foreign traders D is the expected present discounted value of
the stream of net returns. In the recursive representation of the equilibrium, this
present value of returns is a function D(?, b, ?), and hence we can compute long-run
averages of net returns, E[D(?, b, ?)], and values of D(?, b, ?) conditional on Sudden
91
Stop states. Since the model has a well-de?ned stochastic steady state, the long-run
mean of net returns is given by E[D] = kE[ˆ ?]R(R ?1)
?1
.
Table 2.2 shows that, relative to the NFE, E[D] and are 14.5 percent higher
in the BMR economy and 52.6 and 42.5 percent higher in the NSCG and SCG
economies respectively. Thus, from the perspective of the long-run average of the
value of their ?rms, foreign traders are better o? in the BMR economy and signif-
icantly better o? in the economies with price guarantees than in the NFE. Table
2.2 also shows that this is the case mainly because of the increased average equity
holdings of foreign traders in the BMR, NSCG and SCG economies, and the corre-
sponding increase in their average dividend earnings. The contribution of changes
in the value of trades to changes in E[D] and is zero by de?nition (since the un-
conditional means of at and ?
t+1
are identical) and the contribution of changes in
trading costs is negligible. Foreign traders build up a larger equity position in the
BMR economy as a result of the rebalancing of the portfolio of domestic agents
from equity into bonds shown in Figure 2.2, and also because in some states foreign
traders buy assets at crash prices (i.e., when domestic agents ?re sale assets to meet
margin calls). Foreign traders are much better o? when price guarantees are in
place because the price guarantees are equivalent to a guaranteed minimum return,
which reduces sharply the downside risk of holding equity and results in even larger
domestic portfolio reallocations from equity into bonds.
The result that the payo? of foreign traders is signi?cantly higher on average
in the long run with price guarantees hides the fact that, when evaluated conditional
on a Sudden Stop state, the payo? of foreign traders is lower in economies with price
92
guarantees. Table 2.2 shows that the ranking of foreign traders’ payo?s obtained
by comparing D(?, b, ?) across Sudden Stop states with low or high leverage is the
opposite from the one obtained by comparing E[D]. Relative to the NFE, the
present value of pro?ts is nearly unchanged in the BMR economy and it falls in the
high and low leverage states of the economies with price guarantees (by about 0.7
and 0.3 percent in the NSCG and SCG economies respectively). The latter occurs
because in the NSCG and SCG economies the increase in the long-run average of net
returns (E[ˆ ?]) is not su?cient to o?set the short-run decline in returns (ˆ ?(?, b, ?))
that occurs at date 0 when a Sudden Stop hits (see Table 2.2). In turn, this decline
in net returns at date 0 is almost entirely driven by changes in the value of trades.
The value of trades in the high (low) leverage state rises from 0.36 in the NFE to
3.93 (3.22) in the BMR economy and to about 3.95 (3.24) in the NSCG and SCG
economies. In the BMR economy, the increase re?ects the domestic agents’ ?re sales
of equity to meet margin calls. The equity price falls, and when it falls foreign traders
demand more equity and the value of their trades increases. In the economies with
price guarantees, the moral hazard distortion exacerbates this e?ect by increasing
the foreign traders’ equity demand and producing equilibrium prices higher than in
the BMR economy. In line with the increase in trading values, trading costs rise
sharply from the NFE economy to the other economies, but their absolute amounts
remain small. Dividend earnings do not change because date-0 equity holdings are
the same in all four economies and the dividends of domestic ?rms are independent
of ?nancial frictions and price guarantees.
In principle, the present value of foreign traders’ net returns conditional on
93
a Sudden Stop state could be higher or lower with price guarantees than without
depending on whether the short-run e?ect lowering date-0 net returns is weaker or
stronger than the long-run e?ect increasing average net returns. The strength of
these e?ects depends in turn on how much and how fast equilibrium equity positions
and equity prices move, which depends on the parameters driving the demand for
equity of domestic agents and foreign traders. According to Table 2, however, the
substantial increases in the average payo? of foreign traders (E[D]) in the NSCG
and SCG economies exceed by large margins the small reductions in D(?, b, ?) to
which foreign traders are exposed with very low probability in the long run.
To analyze the distributional implications of price guarantees, consider the
“resource constraint” implied by the households’ budget constraint and the traders’
net returns:
c = ?F(k, n) ?[k?
?
d ?b(R ?1)] + [qk (?
?
??
?
) ?(b
?b)] (2.26)
As noted earlier, the long-run averages of consumption in the NFE, BMR,
NSCG and SCG economies are nearly identical (see Table 1). On the other hand,
Table 2.2 shows that the long-run average of the foreign traders’ dividend earnings is
higher in the latter three than in the NFE. Taking the long-run average of equation
(28), it follows from these two observations that domestic agents can sustain similar
long-run average consumption levels because their average savings remain nearly
unchanged: The drop in dividend earnings on equity is nearly o?set by increased
interest income from bonds. Thus, the baseline results suggest that globalization
94
hazard and price guarantees, as modeled in this chapter, do not alter the long-run
average shares of global income and wealth across the small open economy and the
rest of the world. Foreign traders receive a larger share of domestic GDP but GNP
is una?ected because domestic agents increase bond holdings and thus collect more
interest income from abroad. The independence of GDP from ?nancial frictions and
price guarantees is a strong assumption that plays a key role in this result. The
SOE assumption also plays a role because it allows the domestic portfolio swap of
equity for bonds to occur without increasing the price of these bonds, which would
lower the world interest rate.
Short-run distributional e?ects at a Sudden Stop state are di?erent. GNP
and GDP are unchanged across the four simulations, but there is a redistribution of
world income via the current account. Relative to the NFE, foreign traders transfer
income to domestic households in the BMR, NSCG and SCG economies, as the
value of trades in the third term of the right-hand-side of (28) increases because
domestic agents ?re-sale equity to meet margin calls. But whether the domestic
economy receives more or less income from the rest of the world as a whole depends
on whether the ?re sale of assets can prevent the current account reversal, which
in turn depends on the leverage ratio and the liquidity of the asset market. Table
2.2 shows that ˆ ?(?, b, ?) falls at date 0 in the high and low leverage states, but
Figure 2.4 shows that the reversal in ca/y is larger in the former. Thus, the high
leverage state features a redistribution of income from foreign traders to domestic
agents via the equity market, but the larger current account reversal indicates that
this redistribution is more than o?set by the loss of access to the credit market,
95
so that the domestic economy reduces the share of world output that it absorbs.
In contrast, in the low leverage state the current account de?cit remains close to
the level of the NFE and hence the domestic economy maintains its share of world
output. These results hold across the BMR, NSCG and SCG economies compared
to the NFE but the e?ects are stronger in the economies with price guarantees.
The above results show that, comparing long-run averages of the payo?s of
domestic agents and foreign traders, foreign traders are signi?cantly better o? in
the economies with price guarantees than in the NFE or BMR economies, while
domestic agents are nearly indi?erent. This suggests that price guarantees could
be close to a win-win situation, but this result has some caveats. In particular,
domestic agents are nearly indi?erent between the long-run outcomes of the four
economies because of the trivial cost of consumption ?uctuations in models of the
class examined here, and foreign traders make large gains in the BMR, NSCG and
SCG economies because their dividend earnings are una?ected by ?nancial frictions.
Interestingly, in the short run and starting at a Sudden Stop state, the moral hazard
distortion of economies with price guarantees yields persistently higher asset prices
that redistribute income from foreign traders to domestic agents by more than is
needed if the aim were just to recover the outcome of the NFE (hence making
domestic agents better o? and foreign traders worse o?). Still, foreign traders are
much better o? in the long run because the large increase in E[D] in the NSCG and
SCG economies dwarfs the small, near-zero-probability reduction in D(?, b, ?) for
Sudden Stop states.
96
2.5.2 Sensitivity Analysis
Table 2.3 reports the results of a sensitivity analysis that evaluates the ro-
bustness of the baseline results to the following parameter changes: Columns (II)
and (III), larger and more persistent productivity shocks (?
?
=0.024 and ?
?
=0.8),
Column (IV), higher price guarantees (1 percent above q
f
(?
L
)), Column (V), higher
recurrent trading costs (? =0.01), and Column (VI), higher per-trade costs (a =2).
Column (I) reproduces the baseline results. The Table shows panels with results for
the BMR, NSCG and SCG economies for all six scenarios. In each case, three sets
of results are listed: (a) Sudden Stop e?ects as measured by the detrended, date-0
forecasting functions conditional on the high leverage state, (b) key moments of the
ergodic distribution, and (c) changes in the payo?s of domestic agents and foreign
traders, relative to the corresponding NFE simulation, for the high leverage Sudden
Stop state and in the long-run averages.
Consider ?rst the BMR panel. Columns (I)-(VI) show that the results of the
comparison of the baseline NFE and BMR economies are robust to the parameter
changes considered. Increases in se and re result in small changes in Columns (II)
and (III) relative to Column (I). The exceptions are the probability of binding margin
constraints, which rises (falls) to 4.2 (2.3) percent when re (?
?
) increases, and the
long-run average of the value of the foreign traders’ ?rms, which falls to 12.2 and
4.4 percent in Columns (II) and (III) respectively. The changes in the probability
of margin calls result from portfolio rebalancing e?ects. More persistent (variable)
shocks increase (reduce) slightly the long-run average of domestic equity holdings,
97
and have the opposite e?ects on bond holdings. As a result, the economy with more
persistent (variable) shocks is more (less) likely to hit low bond positions (i.e., high
debt positions) in which the margin constraint binds.
Consider ?rst the BMR panel. Columns (I)-(VI) show that the results of the
comparison of the baseline NFE and BMR economies are robust to the parameter
changes considered. Increases in se and re result in small changes in Columns (II)
and (III) relative to Column (I). The exceptions are the probability of binding margin
constraints, which rises (falls) to 4.2 (2.3) percent when ?
?
(?
varepsilon
) increases, and
the long-run average of the value of the foreign traders’ ?rms, which falls to 12.2 and
4.4 percent in Columns (II) and (III) respectively. The changes in the probability
of margin calls result from portfolio rebalancing e?ects. More persistent (variable)
shocks increase (reduce) slightly the long-run average of domestic equity holdings,
and have the opposite e?ects on bond holdings. As a result, the economy with more
persistent (variable) shocks is more (less) likely to hit low bond positions (i.e., high
debt positions) in which the margin constraint binds.
In line with the ?ndings of Mendoza and Smith (2004), Columns (V) and (VI)
show that BMR economies with higher ? or higher a display larger Sudden Stops,
with the latter showing stronger e?ects. The long-run probability of margin calls
is also sharply higher in these economies, reaching 16.7 percent with q = 0.01 and
19.4 percent with a =2. The BMR economy with a =2 is the only scenario in
Table 3 that can account for large consumption and current account reversals and
large drops in asset prices, as in actual Sudden Stops. This scenario also results in
increased long-run variability in consumption and asset prices, and sharply higher
98
domestic welfare costs.
Comparing now Columns (I)-(VI) across the BMR, NSCG and SCG panels,
we ?nd that price guarantees always work to virtually eliminate the long-run prob-
ability of binding margin constraints. On the other hand, the long-run probability
of executing the guarantees is high in the NSCG economy, ranging between 29 and
34 percent in all scenarios except the one with higher sigma
?
, in which it falls to
15 percent. In contrast, the probability of executing the guarantees in the SCG
economy is below 1 percent in all the scenarios except those with ? =0.01 and a
=2, in which it reaches 6 and 3.2 percent respectively. Thus, state-contingent guar-
antees are as e?ective as non-state-contingent guarantees at reducing the long-run
probability of margin calls, with the advantage that in the SCG economy the IFO
would be trading much less frequently.
A comparison of Columns (I) and (IV) shows that rising the guaranteed price
1 percent above q
f
(?
L
), twice as large than in the baseline, the NSCG and SCG
economies dampen the Sudden Stops of the BMR economy even more than in the
baseline. With the higher price guarantee in Column (IV), the fall in c is just 0.5
(0.6) percent in the NSCG (SCG), compared to 0.8 (0.9) percent in the correspond-
ing baseline simulations. Similarly, the reversal in ca/y in the NSCG (SCG) is just
0.3 (0.4) percentage points of GDP in Column (IV), compared to 0.6 (0.7) in Col-
umn (I). On the other hand, the economies with higher guarantees prop up asset
prices in the Sudden Stop state even more than in Column (I), with price increases
of 0.7 (0.6) percent in the NSCG (SCG) economy. The domestic welfare gain in the
high leverage Sudden Stop state increases to 2.4 (0.9) percent in Column (IV) of
99
the NSCG (SCG) economy, compared to 1 (0.3) percent in the corresponding base-
line simulations, while the long-run welfare losses remain nearly unchanged across
Columns (I) and (IV). At the same time as the domestic welfare gains in the Sudden
Stop state grow, the decline in the payo? of the foreign traders in the same state
grows from 0.7 (0.3) percent in the NSCG (SCG) baseline to 1.4 (0.9) percent in
the NSCG (SCG) with higher guarantees. In contrast, the long-run average of the
traders’ payo? increases with the higher guarantees. Thus, the results regarding the
e?ects of price guarantees obtained with the baseline simulations are qualitatively
similar to those obtained with higher guarantees, but quantitatively the higher guar-
antees induce larger moral hazard distortions, which result in weaker Sudden Stops
but larger redistribution e?ects across foreign traders and domestic agents.
Column (VI) shows that, if the baseline level of price guarantees is applied to an
economy with higher per-trade asset trading costs, the price guarantees still work to
weaken the real e?ects of Sudden Stops relative to those in the BMR economy. With
a =2, however, the guarantee set 0.5 percent above q
f
(?
L
) is insu?cient to prevent
marked reversals in c and ca/y and a sharp drop in q. Consequently, domestic agents
su?er a substantial welfare loss of 1.5 (2.6) percent in the high leverage Sudden
Stop state of the NSCG (SCG) economy, instead of the small gains obtained in the
corresponding baseline simulations with a=0.2. Moreover, the long-run average of
welfare costs increases about 5 (2) times in the NSCG (SCG) economy with a=2
relative to the same simulations with a=0.2. Interestingly, the payo? of the foreign
traders in the high leverage Sudden Stop state is larger in the NSCG and SCG
economies with a=2 than in their baseline counterparts with a=0.2. In fact, in the
100
SCG economy with a=2 the value of the foreign traders’ ?rm in the high leverage
state is even higher than that in the corresponding NFE economy.
The above results show that, for a given guaranteed price, there can be a
su?ciently high value of a such that the mix of globalization hazard and international
moral hazard yields outcomes in which domestic agents su?er large welfare losses at
Sudden Stops, but still these losses are smaller than in the BMR economy without
guarantees. Moreover, for given a, higher guarantees dampen Sudden Stops more
and produce welfare gains at Sudden Stop states. These ?ndings suggest that price
guarantees should be higher the higher are trading costs. The results also show,
however, that economies with higher a face higher long-run averages of welfare costs
with price guarantees than without them (the cost is 1/3 of a percent in the NSCG
panel of Column (VI), compared to 1/10 of a percent in the corresponding BMR). In
addition, economies with higher guarantees and the baseline value of a yield larger
long-run welfare losses (see Column IV). Thus, if per-trade trading costs are high,
increasing price guarantees makes domestic agents better o? at Sudden Stop states
by weakening more the e?ects of globalization hazard, but the stronger e?ects of
international moral hazard makes them worse o? on average in the long run.
The ?ndings of the sensitivity analysis suggest that the size of per-trade costs
is crucial for the e?ectiveness of price guarantees and the globalization hazard-
moral hazard tradeo?. Mendoza and Smith (2004) showed that this parameter
is also crucial for the model’s ability to account for asset price collapses of the
magnitude observed in Sudden Stops, and documented empirical evidence of trading
costs roughly in line with the model’s predictions. Nevertheless, the crucial feature
101
is not the magnitude of a per se but the elasticity of world demand for the SOE’s
equity, which can be in?uenced by factors other than trading costs. The ?ndings
of this chapter suggest that, if this elasticity is high, it is relatively easy to set up
state-contingent price guarantees that reduce the probability of margin calls, undo
the Sudden Stop e?ects of globalization hazard, and make domestic agents better
o? at Sudden Stop states with negligible e?ects on foreign traders’ returns in those
states, and with trivial implications for the long-run welfare of domestic agents. On
the other hand, as the elasticity falls, price guarantees still weaken Sudden Stops
but the globalization hazard-moral hazard tradeo? can have negative consequences
for domestic welfare.
2.6 Conclusions
This chapter shows that, in the presence of globalization hazard caused by
world capital market frictions, providing ex-ante price guarantees on emerging mar-
kets assets can be an e?ective means to contain Sudden Stops. The same theory
predicts, however, that these guarantees create a form of international moral hazard
that props up the foreign investors’ demand for emerging markets assets. Hence, ex-
ante price guarantees create a tradeo? between the bene?ts of undoing globalization
hazard and the costs of international moral hazard.
The chapter borrows from Mendoza and Smith (2004) a dynamic, stochastic
equilibrium model of asset prices in which the sources of globalization hazard are
collateral constraints and asset trading costs. Collateral constraints are modeled as
102
margin constraints that limit the ability of domestic agents to leverage foreign debt
on equity holdings. Asset trading costs are incurred by foreign traders and take the
form of per-trade costs and recurrent costs. In this environment, typical realizations
of productivity shocks trigger margin calls when the economy’s debt is su?ciently
large relative to the value of its equity. Margin calls lead to ?re sales of equity and a
Fisherian de?ation of asset prices. If domestic asset markets are relatively illiquid,
the result is a Sudden Stop with reversals in consumption and the current account
and a fall in asset prices.
This chapter introduced into the Mendoza-Smith model an IFO that o?ers
foreign traders ex-ante guarantees to buy the emerging economy’s assets at pre-
announced minimum prices. The resulting international moral hazard distortion in-
creases the foreign traders’ demand for the emerging economy’s assets by an amount
that depends on the traders’ conditional expected present value of the excess of guar-
anteed prices over market prices.
The chapter’s quantitative analysis, based on a calibration to Mexican data,
showed that guaranteed prices set to 1 percent above the fundamentals price in a
low productivity state reduce signi?cantly the Sudden Stop e?ects of globalization
hazard, and eliminate the long-run probability of margin calls. If the guarantee is
non-state-contingent, however, the IFO trades often (with a long-run probability of
executing the guarantee of about 1/3), and there is persistent asset overvaluation
above the prices obtained without globalization hazard. The IFO trades much less
often, with a long run probability below 1/100, if the same guaranteed price is
o?ered as a state-contingent guarantee that applies only at high debt levels. These
103
state-contingent guarantees are just as e?ective at containing Sudden Stops and
they do not cause persistent asset overvaluation.
The e?ectiveness of price guarantees to prevent Sudden Stops and increase
social welfare hinges on the relative magnitudes of globalization hazard and inter-
national moral hazard. The price elasticity of world demand for domestic assets,
which in the model depends on the size of per-trade costs, is the key determinant
of both. The Fisherian de?ation that governs globalization hazard depends on how
much prices have to fall for foreign traders’ to accommodate the ?re sales of domes-
tic assets. The moral hazard distortion increases foreign demand for domestic assets
by an amount proportional to the price elasticity of this demand. With per-trade
costs that yield an elasticity of 5, guaranteed prices set to 1 percent above the low-
productivity fundamentals price result in domestic welfare gains when the economy
hits a Sudden Stop, with negligible changes in long-run welfare. The value of for-
eign traders’ ?rms in a Sudden Stop state falls slightly but its long-run average rises
sharply. Hence, in this case the bene?ts of price guarantees to contain globalization
hazard outweigh the costs of international moral hazard.
These results are reversed when per-trade costs yield an elasticity of world
demand for domestic equity of . In this case, globalization hazard causes larger
Sudden Stops and higher price guarantees are needed to contain them. However,
even with guarantees set at to 1 percent above the low-productivity fundamentals
price, which cannot prevent reversals in consumption and the current account, the
moral hazard distortion is magni?ed signi?cantly. Welfare gains for the emerging
economy at Sudden Stop states are smaller, and the economy su?ers non-trivial
104
welfare losses in the stochastic steady state. In this case, price guarantees yield
a short-term improvement in macroeconomic indicators and welfare because they
weaken globalization hazard, but international moral hazard outweighs this bene?t
and causes a long-run welfare loss. This outcome can be altered increasing guaran-
teed prices (to fully o?set Sudden Stop e?ects) and adjusting their state-contingent
structure (to weaken the moral hazard distortion) at the same time.
The challenge to the IFO is to design ex-ante price guarantees that can yield
better outcomes than those obtained without an instrument to contain Sudden
Stops. The ?ndings of our quantitative analysis illustrate the complexity of this
task. An e?ective system of price guarantees requires a ”useful” quantitative model
of asset prices that can explain the features of Sudden Stops and provide assessments
of the e?ects of the guarantees taking into account how they a?ect the optimal plans
of forward-looking agents. This challenge also applies to ex-post price guarantees.
The Lerrick-Meltzer and IMF proposals assume that a “useful” model sets sus-
tainable levels of external debt and the “normal” and crash prices of an emerging
economy’s assets. This chapter makes some progress towards developing models that
can be used for these purposes, but clearly there is a lot left for further research.
105
Figure 2.1: Equilibrium in the Date t Equity Market
?
t+1
?
t+1
*
q
t
HH
HH’
FF
FF’
A
B
C
D
106
Figure 2.2: Ergodic Distributions of Domestic Equity and Bond Holdings
0.00
0.02
0.04
0.06
0.08
10 20 30 40 50 60 70 80 90 100 110 120
0.00
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50 60 70 80 90 100 110 120
0.00
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50 60 70
NFE BMR
0.00
0.05
0.10
0.15
0.20
0.25
0.30
10 20 30 40 50 60 70
NSCG SCG
Bonds Bonds
Domestic Equity Domestic Equity
Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements,
NSCG is economy with binding margin requirements and non-state-contingent guarantees, and
SCG is economy with binding margin requirements and state-contingent guarantees.
107
Figure 2.3: Ergodic Distributions of Domestic Equity and Bond Holdings
0.00
0.02
0.04
0.06
0.08
10 20 30 40 50 60 70 80 90 100 110 120
0.00
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50 60 70 80 90 100 110 120
0.00
0.01
0.02
0.03
0.04
0.05
0.06
10 20 30 40 50 60 70
NFE BMR
0.00
0.05
0.10
0.15
0.20
0.25
0.30
10 20 30 40 50 60 70
NSCG SCG
Bonds Bonds
Domestic Equity Domestic Equity
Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements,
NSCG is economy with binding margin requirements and non-state-contingent guarantees, and
SCG is economy with binding margin requirements and state-contingent guarantees.
108
Figure 2.4: Consumption & Current Account-GDP Ratio Impact E?ects of a Neg-
ative Productivity Shock in the Sudden Stop Region of Equity & Bonds
5
10
15
20
25
5
10
15
20
25
?80
?60
?40
?20
b (grid position)
NFE
? (grid position)
%
d
e
v
i
a
t
i
o
n
f
r
o
m
m
e
a
n
5
10
15
20
25
5
10
15
20
25
?80
?60
?40
?20
b (grid position)
BMR
? (grid position)
%
d
e
v
i
a
t
i
o
n
f
r
o
m
m
e
a
n
5
10
15
20
25
5
10
15
20
25
0
20
40
b (grid position)
NFE
? (grid position)
%
d
e
v
i
a
t
i
o
n
f
r
o
m
m
e
a
n
5
10
15
20
25
5
10
15
20
25
0
20
40
b (grid position)
BMR
? (grid position)
%
d
e
v
i
a
t
i
o
n
f
r
o
m
m
e
a
n
a. Consumption Impact Effect
b. Current Account?GDP Ratio Impact Effect
Note: The values are in percent deviations from long run average for consumption impact e?ects,
and percentage point di?erence for current account-GDP ratio impact e?ects.
109
Figure 2.5: Conditional Responses to a Negative, One-Standard-Deviation Produc-
tivity Shock
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18
consumption
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18
equity price
-0.8
-0.4
0.0
0.4
0.8
1.2
2 4 6 8 10 12 14 16 18
current account-GDP ratio
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18
consumption
-1.5
-1.0
-0.5
0.0
0.5
1.0
2 4 6 8 10 12 14 16 18
equity price
-0.8
-0.6
-0.4
-0.2
0.0
0.2
0.4
0.6
0.8
1.0
1.2
2 4 6 8 10 12 14 16 18
BMR NSCG SCG
current account-GDP ratio
High Leverage State1/ Low Leverage State2/
1/ Forecasting functions of each variable’s equilibrium Markov process conditional on initial states
?=0.938 and b=-4.68, which imply a leverage ratio of 0.029 and a debt/GDP ratio of 0.597.
2/ Forecasting functions of each variable’s equilibrium Markov process conditional on initial states
?=0.938 and b=-3.38, which imply a leverage ratio of 0.021 and a debt/GDP ratio of 0.43
110
Figure 2.6: Equity Pricing Function in the Low Productivity State
20
40
60
80
100
120
20
40
60
2.175
2.18
2.185
2.19
2.195
b (grid position)
equity price
? (grid position)
20
40
60
80
100
120
20
40
60
2.175
2.18
2.185
2.19
2.195
b (grid position)
equity price
? (grid position)
20
40
60
80
100
120
20
40
60
2.175
2.18
2.185
2.19
2.195
b (grid position)
equity price
? (grid position)
Note: The top graph is the Economy with Binding Margin Requirements. The bottom left graph
is the Economy with Non-State-Contingent Guarantees. The bottom right graph is the Economy
with State-Contingent Guarantees
111
Table 2.1: Long Run Business Cycle Moments
Variable mean std. dev. std. dev. correlation ?rst order
(in %) rel. to GDP with GDP autocorr.
I. NFE
GDP 7.833 2.644 1.000 1.000 0.683
consumption 5.366 2.185 0.826 0.853 0.770
current account/GDP 0.000 1.347 0.509 0.979 0.660
trade balance/GDP 0.315 0.948 0.358 0.564 0.811
equity price 2.187 0.121 0.046 0.961 0.606
foreign debt-GDP ratio 0.177 56.694 21.442 -0.076 0.997
debt-equity ratio 0.010 2.888 1.092 0.000 0.001
II. BMR Economy (probability of binding margin constraints = 3.973%)
GDP 7.833 2.644 1.000 1.000 0.683
consumption 5.365 2.186 0.827 0.856 0.771
current account/GDP 0.000 1.324 0.501 0.982 0.664
trade balance/GDP 0.315 0.940 0.355 0.565 0.823
equity price 2.187 0.121 0.046 0.962 0.609
foreign debt-GDP ratio 0.499 37.964 14.358 -0.118 0.994
debt-equity ratio 0.026 2.007 0.759 0.000 0.001
III. NSCG Economy (probability of binding margin constraints = 0.001%)
GDP 7.833 2.644 1.000 1.000 0.683
consumption 5.362 2.052 0.776 0.790 0.724
current account/GDP 0.000 1.487 0.562 0.968 0.660
trade balance/GDP 0.315 1.111 0.420 0.631 0.750
equity price 2.198 0.099 0.037 0.891 0.384
foreign debt/GDP 1.336 41.053 15.526 0.001 0.992
debt-equity ratio 0.071 2.186 0.827 0.000 0.006
IV. SCG Economy (probability of binding margin constraints = 0.001% )
GDP 7.833 2.644 1.000 1.000 0.683
consumption 5.364 2.121 0.802 0.834 0.765
current account/GDP 0.000 1.380 0.522 0.974 0.660
trade balance/GDP 0.315 1.000 0.378 0.599 0.788
equity price 2.188 0.121 0.046 0.903 0.630
foreign debt/GDP 1.114 34.141 12.912 -0.067 0.991
debt-equity ratio 0.059 1.810 0.685 0.000 0.004
Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements,
NSCG is economy with binding margin requirements and non-state-contingent guarantees, and
SCG is economy with binding margin requirements and state-contingent guarantees.
112
Table 2.2: Payo?s of Domestic Agents and Foreign Traders in Baseline Simulations
NFE BMR NSCG SCG
I. Long-run averages
Domestic Agents
Welfare cost 1/ 0.017 0.062 0.057
Foreign Traders
Present value of traders’ returns 17.920 20.519 27.350 25.529
percent change w.r.t. NFE 14.499 52.621 42.460
Returns 0.280 0.321 0.427 0.399
(a) dividend earnings 0.280 0.320 0.427 0.399
(b) trading costs 1.1E-05 2.3E-05 8.8E-05 1.6E-04
II. High leverage Sudden Stop State
Domestic Agents
Welfare cost 1/ 0.367 -1.036 -0.317
(a) short-run cost 2/ 1.376 0.862 0.978
(b) long-run cost 3/ -1.010 -1.899 -1.295
Date-1 rate of time preference 1.58 1.56 1.57 1.57
Foreign Traders
Present value of traders’ returns 10.931 10.940 10.858 10.901
percent change w.r.t. NFE 0.082 -0.670 -0.276
Returns at date 0 -0.192 -3.770 -3.796 -3.791
(a) dividend earnings 0.166 0.166 0.166 0.166
(b) value of trades 0.359 3.927 3.953 3.948
(c) trading costs 1.6E-04 9.8E-03 9.8E-03 9.8E-03
III. Low leverage Sudden Stop State
Domestic Agents
Welfare cost 1/ 0.215 -1.194 -0.393
(a) short-run cost 2/ 0.055 -0.356 -0.293
(b) long-run cost 3/ 0.160 -0.838 -0.100
Date-1 rate of time preference 1.59 1.59 1.59 1.59
Foreign Traders
Present value of traders’ returns 10.931 10.937 10.854 10.901
percent change w.r.t. NFE 0.055 -0.707 -0.272
Returns at date 0 -0.192 -3.056 -3.077 -3.074
(a) dividend earnings 0.166 0.166 0.166 0.166
(b) value of trades 0.359 3.215 3.237 3.234
(c) trading costs 1.6E-04 6.7E-03 6.7E-03 6.7E-03
1/ Compensating variation in date-0 consumption that equates expected lifetime utility obtained
in the BMR, NSCG and SCG economies with that of the NFE.
2/ Compensating variation in date-0 consumption that equates date-0 period utility obtained in
the BMR, NSCG and SCG economies with that of the NFE.
3/ Di?erence of total welfare cost minus short-run cost.
113
Table 2.3: Sensitivity Analysis
Baseline Prod. Shocks Guarantees Trading Costs
(I) (II) (III) (IV) (V) (VI)
? = 0.8 ?
?
= 2.4% 1% above q
f
? = 0.01 a = 2
I. BMR Economy
In. responses in high lev. st.
consumption -1.335 -1.380 -1.404 n.a. -1.453 -3.059
current account/GDP 0.939 0.972 0.997 n.a. 1.023 2.157
equity price -0.413 -0.413 -0.413 n.a. -0.412 -4.324
traders’ return -4.529 -4.526 -4.526 n.a. -4.522 -4.866
Moments of the ergodic dist.
Prob. of bind. mar. cons. (%) 3.973 4.200 2.331 n.a. 16.740 19.444
Averages
consumption 5.365 5.369 5.366 n.a. 5.369 5.378
equity price 2.187 2.187 2.187 n.a. 2.183 2.183
equity holdings 0.883 0.885 0.861 n.a. 0.906 0.907
Standard deviations (%)
consumption 2.186 2.382 2.721 n.a. 2.169 2.454
current account/GDP 1.324 1.325 2.020 n.a. 1.432 1.428
equity price 0.121 0.184 0.100 n.a. 0.114 0.463
Domestic welfare loss1/
high leverage state 0.367 0.361 0.389 n.a. 0.490 4.074
long-run average 0.017 0.013 0.012 n.a. 0.099 0.110
?PDV of traders’ returns1/
high leverage state 0.083 0.082 0.095 n.a. 3.448 0.924
long-run average 14.502 12.163 4.354 n.a. 34.519 27.531
II. NSCG Economy
In. responses in high lev. st.
consumption -0.840 -0.875 -0.901 -0.503 -0.885 -2.205
current account/GDP 0.591 0.616 0.640 0.354 0.623 1.554
equity price 0.259 0.274 0.214 0.718 0.362 -3.256
traders’ return -4.562 -4.560 -4.561 -4.586 -4.561 -4.926
Moments of the ergodic dist.
Prob. of bind. mar. cons. (%) 0.001 0.017 0.024 0.002 0.002 0.000
Prob. of executing guar.(%) 34.290 32.892 15.434 29.650 34.068 28.925
Averages
consumption 5.362 5.365 5.360 5.361 5.362 5.362
equity price 2.198 2.199 2.198 2.208 2.198 2.206
equity holdings 0.844 0.844 0.844 0.842 0.844 0.842
expected PDV of excess prices 0.012 0.013 0.011 0.022 0.015 0.023
Standard deviations (%)
consumption 2.052 2.269 2.615 2.014 2.047 2.191
current account/GDP 1.487 1.473 2.035 1.567 1.490 1.584
equity price 0.099 0.149 0.104 0.091 0.100 0.429
expected PDV of excess prices 2.083 3.913 4.235 1.375 1.368 1.466
Domestic welfare loss1/
high leverage state -1.036 -1.137 -1.033 -2.359 -1.025 1.506
long-run average 0.062 0.063 0.132 0.086 0.286 0.332
?PDV of traders’ returns1/
high leverage state -0.670 -0.732 -0.660 -1.372 2.501 -0.459
long-run average 52.621 51.867 17.567 54.696 122.862 116.646
114
Table 2.3: Sensitivity Analysis (Continued)
Baseline Prod. Shocks Guarantees Trading Costs
(I) (II) (III) (IV) (V) (VI)
? = 0.8 ?
?
= 2.4% 1% above q
f
? = 0.01 a = 2
III. SCG Economy
In. responses in high lev. st.
consumption -0.952 -0.878 -0.988 -0.626 -0.920 -2.182
current account/GDP 0.670 0.618 0.702 0.440 0.648 1.538
equity price 0.107 0.270 0.105 0.550 0.313 -3.227
traders’ return -4.555 -4.560 -4.555 -4.586 -4.558 -4.928
Moments of the ergodic dist.
Prob. of bind. mar. cons. (%) 0.001 0.014 0.042 0.009 0.013 0.000
Prob. of executing guar.(%) 0.035 0.261 0.391 0.502 6.063 3.245
Averages
consumption 5.364 5.369 5.363 5.363 5.358 5.355
equity price 2.188 2.188 2.189 2.190 2.190 2.191
equity holdings 0.855 0.855 0.855 0.850 0.879 0.874
expected PDV of excess prices 0.002 0.002 0.011 0.003 0.007 0.009
Standard deviations (%)
consumption 2.121 2.317 2.709 2.095 2.061 2.298
current account/GDP 1.380 1.369 2.028 1.420 1.466 1.536
equity price 0.121 0.187 0.120 0.137 0.154 0.469
expected PDV of excess prices 42.186 62.894 4.235 52.202 37.543 51.111
Domestic welfare loss1/
high leverage state -0.317 -0.481 -0.297 -0.869 -0.385 2.596
long-run average 0.057 0.053 0.033 0.054 0.086 0.121
?PDV of traders’ returns1/
high leverage state -0.276 -0.359 -0.246 -0.567 2.985 0.167
long-run average 42.460 41.196 9.446 47.217 72.049 73.680
Note: The guaranteed price is 0.5 percent (1 percent for column (IV)) above the fundamentals
price in the low productivity state of the baseline simulation. Welfare costs are compensating
variations in initial consumption that equalize lifetime utility in each simulation with that of the
corresponding NFE. Initial responses are in percent of the corresponding NFE and detrended as
described in the text (except the response for traders’ returns which is in percent of the capital
stock and the response for the current account-output ratio which is the di?erence in percentage
points relative to the corresponding NFE).
1/Percentage change relative to NFE
115
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