Description
The term business cycle (or economic cycle) refers to economy-wide fluctuations in production, trade and economic activity in general over several months or years in an economy organized on free-enterprise principles.
ABSTRACT
Title of dissertation: ESSAYS ON FINANCIAL INTERMEDIARIES,
BUSINESS CYCLES AND
MACROPRUDENTIAL POLICIES
Yasin Mimir, Doctor of Philosophy, 2012
Dissertation directed by: Professor S. Boragan Aruoba
Department of Economics
This study conducts a quantitative analysis of the role of ?nancial shocks and
credit frictions a?ecting the banking sector in driving business cycles as well as the
role of reserve requirements as a macroprudential policy tool. In the ?rst chapter,
I ?rst empirically document three stylized business cycle facts of aggregate ?nan-
cial variables in the U.S. commercial banking sector for the period 1987-2010: (i)
Bank credit, deposits and loan spread are less volatile than output, while net worth
and leverage ratio are more volatile, (ii) bank credit and net worth are procyclical,
while deposits, leverage ratio and loan spread are countercyclical, and (iii) ?nan-
cial variables lead the output ?uctuations by one to three quarters. I then present
an equilibrium business cycle model with a ?nancial sector, featuring a moral haz-
ard problem between banks and its depositors, which leads to endogenous capital
constraints for banks in obtaining funds from households. Credit frictions in bank-
ing sector are modeled as in Gertler and Karadi (2011). The model incorporates
empirically-disciplined shocks to bank net worth (i.e. “?nancial shocks”) that al-
ter the ability of banks to borrow and to extend credit to non-?nancial businesses.
The model is calibrated to U.S. data from 1987 to 2010. I show that the bench-
mark model driven by both standard productivity and ?nancial shocks is able to
deliver most of the stylized facts about real and ?nancial variables simultaneously.
Financial shocks and credit frictions in banking sector are important not only for
explaining the dynamics of aggregate ?nancial variables but also for the dynamics
of standard macroeconomic variables. Financial shocks play a major role in driving
real ?uctuations due to their strong impact on the tightness of bank capital con-
straint and credit spread, which eventually a?ect the saving-investment nexus of the
economy. Finally, the tightness of bank capital constraint given by the Lagrange
multiplier in the theoretical model (which determines the banks’ ability to extend
credit to non-?nancial ?rms) tracks the index of tightening credit standards (which
shows the adverse changes in banks’ lending) constructed by the Federal Reserve
Board quite well.
The second chapter (coauthored with Enes Sunel and Temel Ta¸sk?n) under-
takes a quantitative investigation of the role of reserve requirements as a credit
policy tool. We build a monetary DSGE model with a banking sector in which
(i) an agency problem between households and banks leads to endogenous capital
constraints for banks in obtaining funds from households, (ii) banks are subject to
time-varying reserve requirements that countercyclically respond to expected credit
growth, (iii) households face cash-in-advance constraints, requiring them to hold
real balances, and (iv) standard productivity and money growth shocks are two
sources of aggregate uncertainty. We calibrate the model to the Turkish economy
which is representative of using reserve requirements as a macroprudential policy
tool recently. We also consider the impact of ?nancial shocks that a?ect the net
worth of ?nancial intermediaries. We ?nd that (i) the time-varying required reserve
ratio rule mitigates the negative e?ects of the ?nancial accelerator mechanism trig-
gered by adverse macroeconomic and ?nancial shocks, (ii) in response to TFP and
money growth shocks, countercyclical reserves policy reduces the volatilities of key
real macroeconomic and ?nancial variables compared to ?xed reserves policy over
the business cycle, and (iii) an operational time-varying reserve requirement policy
is welfare superior to a ?xed reserve requirement policy. The credit policy is most
e?ective when the economy is hit by a ?nancial shock. Time-varying required re-
serves policy reduces the intertemporal distortions created by the credit spreads at
expense of generating higher in?ation volatility, indicating an interesting trade-o?
between price stability and ?nancial stability.
ESSAYS ON FINANCIAL INTERMEDIARIES,
BUSINESS CYCLES AND MACROPRUDENTIAL POLICIES
by
Yasin Mimir
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial ful?llment
of the requirements for the degree of
Doctor of Philosophy
2012
Advisory Committee:
Professor S. Boragan Aruoba, Chair/Advisor
Professor Pablo D’Erasmo
Professor Anton Korinek
Professor Enrique G. Mendoza
Professor Phillip L. Swagel
c Copyright by
Yasin Mimir
2012
Dedication
To my love, Meryem.
ii
Acknowledgments
I owe my gratitude to my advisors Professor Boragan Aruoba and Professor
Sanjay Chugh without whom this dissertation could not have been possible.
First and foremost, I would like to thank my committee chair, Boragan Aruoba,
for his encouragement, endless support and guidance from the beginning of my
research journey. Sanjay Chugh pushed me to delve in studying the question at
hand. I cannot overstate my gratitude for his enlightening comments, con?dence
and continual support. They have always made themselves available for numerous
meetings that took their valuable times.
I would also like to thank Professor Enrique Mendoza who honored me by being
in my committee. My warm thanks are to due to my other advisors Professor Pablo
D’Erasmo and Professor Anton Korinek for their guidance and inspiring advice. I am
also grateful to Professor Phillip L. Swagel for agreeing to serve on my dissertation
committee.
I am also thankful to the Board of Governors of the Federal Reserve System for
?nancial support and for hosting me during part of my dissertation. My dissertation
bene?ted greatly from their support.
I am grateful to my colleagues Enes Sunel and Salih Fendoglu who are also
my great friends, for their help and support. Without their cordial companionship,
it would be much more di?cult to complete this dissertation. I am looking forward
to working closely with them in the future research projects. Enes was also a
wonderful roommate with whom I have interesting, enlightening, and entertaining
iii
conversations on numerous subjects. Salih was also a great classmate and roommate
with whom I have the strength to cope with the challenges in my doctoral journey.
I would like to thank the sta? members of the Department of Economics,
Vickie Fletcher, Elizabeth Martinez and Terry Davis for their technical help and
logistical support during my ?ve years at the department.
It is di?cult to overstate my special thanks to my wonderful neighbors Ali
Fuad Selvi, Bengu Caliskan Selvi and Bedrettin Yazan whose friendship has been
an excellent gift. Without their encouragement and enormous support, I cannot
imagine how hard it would be to complete this task. I treasure the moments we all
shared. I also want to thank my dear friends Ferhan Ture and Elif Ture for their
warm friendship.
Finally and most importantly, I owe my deepest thanks to my parents Omer
Mimir and Munevver Mimir as well as my elder sisters Remziye Mimir and Yasemin
Mimir and my elder brother Mustafa Mimir. I would not be able to thank them
enough for always believing in me, helping me pursue my dreams, their unconditional
love and understanding. I would like to show my gratitude to my precious family
for patiently excusing my absence for long years.
My love, Meryem, the re?ection of my soul, I could not imagine my life without
you.
iv
Table of Contents
List of Tables vii
List of Figures viii
List of Abbreviations x
1 Financial Intermediaries, Credit Shocks, and Business Cycles 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Real and Financial Fluctuations in the U.S. economy . . . . . . . . . 8
1.3 A Business Cycle Model with Financial Sector . . . . . . . . . . . . 12
1.3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Financial Intermediaries . . . . . . . . . . . . . . . . . . . . . 15
1.3.2.1 Balance Sheets . . . . . . . . . . . . . . . . . . . . . 15
1.3.2.2 Pro?t Maximization . . . . . . . . . . . . . . . . . . 17
1.3.2.3 Leverage Ratio and Net Worth Evolution . . . . . . 19
1.3.3 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.3.4 Capital Producers . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.3.5 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . 28
1.4 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4.1 Functional Forms, Parametrization and Calibration . . . . . . 31
1.4.2 Long-Run Equilibrium of the Model . . . . . . . . . . . . . . . 35
1.4.3 Intermediary Capital and the Transmission of Shocks . . . . . 38
1.4.3.1 Impulse Responses to TFP Shocks . . . . . . . . . . 38
1.4.3.2 Impulse Responses to Financial Shocks . . . . . . . . 42
1.4.4 Business Cycle Dynamics . . . . . . . . . . . . . . . . . . . . . 43
1.5 Model-Based Simulations of Macro-Financial Shocks vs. U.S. Data . . 46
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2 Required Reserves as a Credit Policy Tool
(joint with Enes Sunel and Temel Ta¸sk?n) 56
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.2.2 Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.2.3 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.2.4 Capital Producers . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.2.5 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.2.6 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . 78
2.3 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.3.1 Functional Forms . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.3.2 Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.3.2.1 Amplifying E?ect of Financial Frictions . . . . . . . 85
2.3.2.2 Impulse Responses to TFP Shocks . . . . . . . . . . 91
v
2.3.2.3 Impulse Responses to Money Growth Shocks . . . . 95
2.3.2.4 Financial Crisis Experiment and Credit Policy . . . . 99
2.3.2.5 E?ects of Time-Varying RRR Policy on Volatilities . 102
2.3.2.6 Credit Policy and Welfare . . . . . . . . . . . . . . . 104
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A 109
A.1 Data Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.2.1 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . 111
A.2.2 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . 113
A.3 Business Cycle Statistics of Aggregate Financial Variables of the
whole U.S. Financial Sector . . . . . . . . . . . . . . . . . . . . . . . 116
A.4 Alternative Measures of Financial Shocks . . . . . . . . . . . . . . . . 122
A.5 Model-Based Simulations of Macro-Financial Shocks using Utilization-
Adjusted TFP series . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
B 139
B.1 Banks’ Pro?t Maximization Problem . . . . . . . . . . . . . . . . . . 139
B.2 Impulse Responses under an Alternative RRR Policy Rule reacting
to Current Credit Growth . . . . . . . . . . . . . . . . . . . . . . . . 143
B.3 Impulse Responses under Zero RRR Policy . . . . . . . . . . . . . . . 153
B.4 Policy Intensity Experiments . . . . . . . . . . . . . . . . . . . . . . . 157
Bibliography 161
vi
List of Tables
1.1 Business Cycle Properties of Real and Financial Variables, Quarterly U.S.
Data, 1987- 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 The Sequence of Events in a Given Time Period . . . . . . . . . . . . 12
1.3 Model Parameterization and Calibration . . . . . . . . . . . . . . . . 32
1.4 Real and Financial Statistics . . . . . . . . . . . . . . . . . . . . . . . 45
2.1 Paremeter Values in the Benchmark Model . . . . . . . . . . . . . . . 83
2.2 Volatilities of Real and Financial Variables . . . . . . . . . . . . . . . 103
A.1 Business Cycle Properties of Real and Financial Variables, Quarterly U.S.
Data, 1987.Q1-2007.Q1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A.2 Business Cycle Statistics, Quarterly U.S. Data, 1952-2009 . . . . . . . 119
A.3 Cross Correlations of Financial Variables with Lags and Leads of GDP120
A.4 Real and Financial Statistics . . . . . . . . . . . . . . . . . . . . . . . 138
vii
List of Figures
1.1 Financial Flows in the U.S. Economy . . . . . . . . . . . . . . . . . . 9
1.2 Time Series of Shocks to Productivity and Credit Conditions . . . . . 34
1.3 Long-run equilibrium as a function of fraction of diverted funds by
bankers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.4 Impulse responses to a negative one-standard-deviation productivity
shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.5 Impulse responses to a negative one-standard-deviation net worth shock 41
1.6 Real Fluctuations: Benchmark vs. RBC model . . . . . . . . . . . . . 47
1.7 Real Fluctuations: Benchmark vs. Only Productivity . . . . . . . . . 49
1.8 Real Fluctuations: RBC vs. Only Productivity . . . . . . . . . . . . . 50
1.9 Financial Fluctuations: Benchmark vs. Only Productivity . . . . . . 52
1.10 Tightness of Credit Conditions in the Benchmark Model . . . . . . . 53
2.1 Evolution of Required Reserve Ratios in Turkey . . . . . . . . . . . . 58
2.2 Negative Productivity Shocks . . . . . . . . . . . . . . . . . . . . . . 86
2.3 Positive Money Growth Shocks . . . . . . . . . . . . . . . . . . . . . 87
2.4 Impulse Responses Led by a 1-? Adverse TFP Shock . . . . . . . . . 90
2.5 Impulse Responses Led by a 1-? Adverse Money Growth Shock . . . 94
2.6 Impulse Responses Led by a 1-? Adverse Financial Shock . . . . . . . 98
A.1 Time Series of Shocks to Productivity and Credit Conditions . . . . . 125
A.2 Real Fluctuations: Benchmark 2 vs. RBC model . . . . . . . . . . . . 126
A.3 Real Fluctuations: Benchmark 2 vs. Only Productivity . . . . . . . . 127
A.4 Real Fluctuations: RBC vs. Only Productivity with Benchmark 2
calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
A.5 Financial Fluctuations: Benchmark 2 vs. Only Productivity . . . . . 129
A.6 Real Fluctuations: Benchmark 4 vs. RBC model . . . . . . . . . . . . 130
A.7 Real Fluctuations: Benchmark 4 vs. Only Productivity . . . . . . . . 131
A.8 Real Fluctuations: RBC vs. Only Productivity with Benchmark 4
calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.9 Financial Fluctuations: Benchmark 4 vs. Only Productivity . . . . . 133
A.10 Real Fluctuations: Benchmark 1 vs. Only Productivity model . . . . 135
A.11 Real Fluctuations: RBC vs. Only Productivity . . . . . . . . . . . . . 136
A.12 Financial Fluctuations: Benchmark 1 vs. Only Productivity . . . . . 137
B.1 The E?ect of Adverse TFP Shocks on Real Variables . . . . . . . . . 144
B.2 The E?ect of Adverse TFP Shocks on Financial Variables . . . . . . . 145
B.3 The E?ect of Adverse TFP Shocks on Monetary Variables . . . . . . 146
B.4 The E?ect of Adverse Money Growth Shocks on Real Variables . . . 147
B.5 The E?ect of Adverse Money Growth Shocks on Financial Variables . 148
B.6 The E?ect of Adverse Money Growth Shocks on Monetary Variables . 149
B.7 The E?ect of Adverse Financial Shocks on Real Variables . . . . . . . 150
B.8 The E?ect of Adverse Financial Shocks on Financial Variables . . . . 151
viii
B.9 The E?ect of Adverse Financial Shocks on Monetary Variables . . . . 152
B.10 Impulse Responses Led by a 1-? Adverse TFP Shock . . . . . . . . . 154
B.11 Impulse Responses Led by a 1-? Adverse Money Growth Shock . . . 155
B.12 Impulse Responses Led by a 1-? Adverse Financial Shock . . . . . . . 156
B.13 Impulse Responses Led by a 1-? Adverse TFP Shock . . . . . . . . . 158
B.14 Impulse Responses Led by a 1-? Adverse Money Growth Shock . . . 159
B.15 Impulse Responses Led by a 1-? Adverse Financial Shock . . . . . . . 160
ix
List of Abbreviations
CBRT Central Bank of the Republic of Turkey
FED Board of Governors of the Federal Reserve System
RRR Required Reserves Ratio
TFP Total Factor Productivity
x
Chapter 1
Financial Intermediaries, Credit Shocks, and Business Cycles
1.1 Introduction
What are the cyclical properties of ?nancial ?ows in the U.S. banking sec-
tor? How important are ?nancial shocks relative to standard productivity shocks in
driving real and ?nancial business cycles in the U.S.? To address these questions,
this study proposes an equilibrium real business cycle model with a ?nancial sector,
that is capable of matching both real and ?nancial ?uctuations observed in the U.S.
data. Although the relevance of ?nancial shocks together with an explicit model-
ing of frictions in ?nancial sector has received attention recently, the behavior of
aggregate ?nancial variables in the U.S. banking sector and how they interact with
real variables over the business cycle have not been fully explored in the literature.
1
Most previous studies have not tried to match ?uctuations in both standard macro
variables and aggregate ?nancial variables simultaneously. In this chapter, I show
that ?nancial shocks to the banking sector contribute signi?cantly to explaining the
observed dynamics of real and ?nancial variables. Financial shocks play a major
role in driving real ?uctuations due to their impact on the tightness of bank capital
constraint and hence credit spread.
1
See Christiano et. al. (2010), Dib (2010), Meh and Moran (2010), Gertler and Kiyotaki
(2010), Gertler and Karadi (2011), Kollman et al. (2011).
1
I ?rst systematically document the business cycle properties of aggregate ?-
nancial variables, using the data on U.S. commercial banks from the Federal Reserve
Board.
2
The following empirical facts emerge from the analysis: (i) Bank credit,
deposits, and loan spread are less volatile than output, while net worth and leverage
ratio are more volatile, (ii) bank assets and net worth are procyclical, while deposits,
leverage ratio, and loan spread are countercyclical, and (iii) ?nancial variables lead
the output ?uctuations by one to three quarters.
I then assess the quantitative performance of a theoretical model by its ability
to match these empirical facts. In particular, there are two main departures from
an otherwise standard real business cycle framework. The ?rst departure is that
I introduce an active banking sector with ?nancial frictions into the model, which
are modeled as in Gertler and Karadi (2011). Financial frictions require that banks
borrow funds from households and their ability to borrow is limited due to a moral
hazard (costly enforcement) problem, leading to an endogenous capital constraint
for banks in obtaining deposits.
3
This departure is needed in order to have balance
sheet ?uctuations of ?nancial sector matter for real ?uctuations. The second depar-
ture is that the model incorporates shocks to bank net worth (i.e.“?nancial shocks”)
that alter the ability of banks to borrow and to extend credit to non-?nancial busi-
nesses.
4
In the context of the theoretical model, this shock can be interpreted as
2
I also document the business cycle properties of aggregate ?nancial variables of the whole U.S.
?nancial sector from 1952 to 2009, using the Flow of Funds data. Interested readers may look at
Appendix A.3.
3
Hellmann, Murdock and Stiglitz (2000) argue that moral hazard in banking sector plays a
crucial role in most of the U.S. economic downturns in the last century. Moreover, the presence
of the agency problem makes the balance sheet structure of ?nancial sector matter for real ?uctu-
ations, invalidating the application of Modigliani-Miller theorem to the model economy presented
below.
4
Hancock, Laing and Wilcox (1995), Peek and Rosengren (1997, 2000) empirically show that
2
a redistribution shock, which transfers some portion of the wealth from ?nancial
intermediaries to households.
5
However, because of the moral hazard problem be-
tween households and bankers, it distorts intermediaries’ role of allocating resources
between households and ?rms, inducing large real e?ects.
I construct the time series of ?nancial shocks as the residuals from the law of
motion for bank net worth, using empirical data for credit spread, leverage ratio,
deposit rate and net worth. This approach is similar to the standard method for
constructing productivity shocks as Solow residuals from the production function
using empirical series for output, capital and labor.
6
The shock series show that U.S.
economy is severely hit by negative ?nancial shocks in the Great Recession. Finally,
in order to elucidate the underlying mechanism as clearly as possible, I abstract
from various real and nominal rigidities that are generally considered in medium
scale DSGE models such as Christiano et. al.(2005) and Smets and Wouters (2007).
adverse shocks to bank capital contributed signi?cantly to the U.S. economic downturns of the
late 1980s and early 1990s. Theoretically, Meh and Moran (2010) consider shocks that originate
within the banking sector and produce sudden shortages in bank capital. They suggest that these
shocks re?ect periods of ?nancial distress and weakness in ?nancial markets. Brunnermeier and
Pedersen (2009) introduce shocks to bank capital and interpret them as independent shocks arising
from other activities like investment banking. Curdia and Woodford (2010) introduce exogenous
increases in the fraction of loans that are not repaid and exogenous increases in real ?nancial inter-
mediation costs, both of which reduce net worth of ?nancial intermediaries exogenously. Mendoza
and Quadrini (2010) study the e?ect of net worth shocks on asset prices and interpret these shocks
as unexpected loan losses due to producers’ default on their debt. A complete model of the deter-
mination of the ?uctuations in net worth of banks is beyond the scope of this study, because my
goal is to analyze the quantitative e?ects of movements in net worth of ?nancial sector on business
cycle ?uctuations of real and ?nancial variables.
5
This interpretation is suggested by Iacoviello (2010). He argues that 1990-91 and 2007-09
recessions can be characterized by situations in which some borrowers pay less than contractually
agreed upon and ?nancial institutions that extend loans to these borrowers su?er from loan losses,
resulting in some sort of a redistribution of wealth between borrowers (households and ?rms) and
lenders (banks).
6
I also consider some alternative measures of ?nancial shocks, including the one constructed
based on loan losses incurred by U.S. commercial banks (using the charge-o? and delinquency rates
data compiled by the Federal Reserve Board). The construction of these alternative measures and
their simulation results can be found in Appendix A.4. The main results of the study do not
change under these alternative measures.
3
The business cycle accounting exercise in this study is important in the sense
that explaining the dynamics of balance sheet ?uctuations in the U.S. banking sec-
tor can help us better understand, capture and predict the dynamics of standard
macroeconomic variables as the ?nancial ?ows in the U.S. banking sector are highly
cyclical and lead the output ?uctuations by one to three quarters. Therefore, the
dynamics of ?nancial variables in the U.S. banking sector may serve as additional
state variables for explaining real ?uctuations. This study is one of the ?rst studies,
which rigorously addressed this issue. It is also the ?rst work that tried to match
?uctuations in both standard macro variables and aggregate ?nancial variables of
U.S. banking sector simultaneously. Finally, in order to start thinking about how
di?erent policy tools can be implemented in an environment in which the ?nancial
sector is crucial for business cycle ?uctuations and what the welfare implications of
these policies are, we need a model capable of matching real and ?nancial ?uctua-
tions simultaneously. It could be asserted that the model proposed in this study is
quite successful in this dimension.
In the theoretical model, there are three main results. First, the benchmark
model driven by both standard productivity and ?nancial shocks is able to deliver
most of the stylized cyclical facts about real and ?nancial variables simultaneously.
Second, ?nancial shocks to banking sector are important not only for explaining the
dynamics of ?nancial variables but also for the dynamics of standard macroeconomic
variables. In particular, the model simulations show that the benchmark model
driven by both shocks has better predictions about investment, hours and output
than the frictionless version of the model (which is standard RBC model with capital
4
adjustment costs) and than the model driven only by productivity shocks. The
benchmark model also performs better than the model with only productivity shocks
in terms of its predictions about aggregate ?nancial variables.
7
Third, the tightness
of bank capital constraint given by the Lagrange multiplier in the theoretical model
(which determines the banks’ ability to extend credit to non-?nancial ?rms) tracks
the index of tightening credit standards (which shows the adverse changes in banks’
lending) constructed by the Federal Reserve Board quite well.
The economic intuition for why ?nancial shocks matter a lot for real ?uctua-
tions in the model lies in the e?ect of these shocks on the tightness of bank capital
constraint and credit spread. When ?nancial shocks move the economy around the
steady state, they lead to large ?uctuations in the tightness of bank capital con-
straint as evidenced by the big swings in the Lagrange multiplier of the constraint.
Since credit spread is a function of this Lagrange multiplier, ?uctuations in the
latter translate into variations in the former. Credit spread appears as a positive
wedge in the intertemporal Euler equation, which determines how households’ de-
posits (savings in the economy) are transformed into bank credit to non-?nancial
?rms. Fluctuations in this wedge move the amount of deposits, therefore the amount
of bank credit that can be extended to ?rms. Since productive ?rms ?nance their
capital expenditures via bank credit, movements in the latter translate into the ?uc-
tuations in capital stock. Because hours worked is complementary to capital stock
in a standard Cobb-Douglas production function, empirically-relevant ?uctuations
7
The RBC model with capital adjustment costs has no predictions about ?nancial variables
since balance sheets of banks in that model are indeterminate.
5
in capital stock lead to empirically-observed ?uctuations in hours, which eventually
generate observed ?uctuations in output.
This study contributes to recently growing empirical and theoretical literature
studying the role of ?nancial sector on business cycle ?uctuations. On the empirical
side, Adrian and Shin (2008, 2009) provide evidence on the time series behavior
of balance sheet items of some ?nancial intermediaries using the Flow of Funds
data.
8
However, they do not present standard business cycle statistics of ?nancial
?ows.
9
On the theoretical side, the current work di?ers from the existing literature
on ?nancial accelerator e?ects on demand for credit, arising from the movements
in the strength of borrowers’ balance sheets.
10
I focus on ?uctuations in supply of
credit driven by movements in the strength of lenders’ balance sheets. Meh and
Moran (2010) investigate the role of bank capital in transmission of technology,
bank capital and monetary policy shocks in a medium-scale New Keynesian, double
moral hazard framework. Jermann and Quadrini (2010) study the importance of
credit shocks in non-?nancial sector in explaining the cyclical properties of equity
and debt payouts of U.S. non-?nancial ?rms in a model without a banking sector.
An independent study that is closely related and complementary to our work is
Iacoviello (2011). In a DSGE framework with households, banks, and entrepreneurs
each facing endogenous borrowing constraints, he studies how repayment shocks
8
They argue that to the extent that balance sheet ?uctuations a?ect the supply of credit, they
have the potential to explain real ?uctuations, and they empirically show that bank equity has a
signi?cant forecasting power for GDP growth.
9
The notion of “procyclical” in their papers is with respect to total assets of ?nancial inter-
mediaries, not with respect to GDP as in the current study. In that sense, this study undertakes
a more standard business cycle accounting exercise.
10
For example, see Kiyotaki and Moore (1997), Carlstrom and Fuerst (1998), Bernanke, Gertler,
and Gilchrist (1999)
6
undermine the ?ow of funds between savers and borrowers in the recent recession.
My work is di?erent from his study in terms of both empirical and theoretical con-
tributions. First, in terms of empirical work, I systemically document the business
cycle properties of aggregate ?nancial variables in the U.S. banking sector from 1987
to 2010, which I then use to judge the quantitative performance of the theoretical
model, while his work particularly focuses on the 2007-09 recession. Second, in the
theoretical model presented below, only the banking sector faces endogenous capital
constraints, which gives me the ability to isolate the role of banks in the transmis-
sion of ?nancial shocks from the role of household and production sectors. Finally,
I employ a di?erent methodology of constructing the series of ?nancial shocks from
the data. In terms of normative policy, Angeloni and Faia (2010) examine the role
of banks in the interaction between monetary policy and macroprudential regula-
tions in a New Keynesian model with bank runs, while Gertler and Kiyotaki (2010),
and Gertler and Karadi (2011) investigate the e?ects of central bank’s credit pol-
icy aimed at troubled banks.
11
Finally, in an open-economy framework, Kollmann
(2011) studies how a bank capital constraint a?ects the international business cycles
driven by productivity and loan default shocks in a two-country RBC model with a
global bank.
The rest of the chapter is structured as follows: In Section 1.2, I document
evidence on the real and ?nancial ?uctuations in U.S. data. Section 1.3 describes the
theoretical model. Section 1.4 presents the model parametrization and calibration
together with the quantitative results of the model. Section 1.5 concludes.
11
The latter also features the interbank market.
7
1.2 Real and Financial Fluctuations in the U.S. economy
This section documents some key empirical features of ?nancial cycles in the
U.S. economy. The upper left panel of Figure 1 displays quarterly time series for
loan losses of U.S. commercial banks from 1987 to 2010. The loan loss rates are
expressed as annualized percentages of GDP. The ?gure shows that loan loss rates
increased in last three recessions of the U.S. economy. The loss rates peaked in both
1990-91 and 2007-09 recessions, reaching its highest level of 5% in the latter. The
upper right panel of Figure 1 plots daily time series for Dow Jones Bank Index from
1992 to 2010. The ?gure suggests that the market value of banks’ shares declined
substantially in the recent recession. Finally, the middle left panel of Figure 1
displays real net worth growth of U.S. commercial banks (year-on-year). The ?gure
suggests that banks’ net worth shrank in last three recessions of the U.S. economy,
with a reduction of 40% in the 2007-09 recession. These three plots convey a common
message: substantial loan losses incurred by banks together with the fall in their
equity prices typically cause large declines in banks’ net worth, which might lead to
persistent and mounting pressures on bank balance sheets, worsening the aggregate
credit conditions, and thus causing the observed decline in real economic activity,
which is much more pronounced in the Great Recession.
The middle left panel of Figure 1 plots commercial and industrial loan spreads
over federal funds rate (annualized). The ?gure shows that bank lending spreads
sky-rocketed in the recent crisis, reaching a 3.2% per annum towards the end of
the recession and they keep rising although the recession was o?cially announced
8
0
1
2
3
4
5
88 90 92 94 96 98 00 02 04 06 08 10
Loan losses to GDP ratio
0
100
200
300
400
500
600
92 94 96 98 00 02 04 06 08 10
Dow Jones bank index
-60
-40
-20
0
20
40
60
88 90 92 94 96 98 00 02 04 06 08 10
Net worth growth
1.5
2.0
2.5
3.0
3.5
88 90 92 94 96 98 00 02 04 06 08 10
Interest rate spreads
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Bank credit
-2
0
2
4
6
8
10
88 90 92 94 96 98 00 02 04 06 08 10
Deposit growth
Figure 1.1: Financial Flows in the U.S. Economy
9
to be over. The bottom left panel displays real bank credit growth rates (year-on-
year). The ?gure indicates that bank credit growth fell signi?cantly in the recent
economic downturn. Taken together, these ?gures suggest that the U.S. economy
has experienced a signi?cant deterioration in aggregate credit conditions as total
bank lending to non-?nancial sector declined sharply and the cost of funds for non-
?nancial ?rms increased substantially. Finally, the bottom right panel of Figure 1
plots real deposit growth rates (year-on-year). The ?gure shows that growth rate of
deposits began to fall substantially right after the recent recession.
Table 1.1: Business Cycle Properties of Real and Financial Variables, Quarterly U.S.
Data, 1987- 2010
Standard
Deviation x
t?4
x
t?3
x
t?2
x
t?1
xt x
t+1
x
t+2
x
t+3
x
t+4
Real Variables
Output 1.80 0.15 0.39 0.66 0.87 1.00 0.87 0.66 0.39 0.15
Consumption 0.45 -0.20 0.06 0.37 0.66 0.82 0.80 0.67 0.46 0.25
Investment 2.73 0.27 0.49 0.71 0.87 0.97 0.82 0.59 0.33 0.09
Hours 0.91 -0.01 0.19 0.43 0.65 0.83 0.89 0.83 0.68 0.44
Financial Variables
Bank credit 0.93 -0.20 -0.11 0.02 0.14 0.30 0.47 0.63 0.68 0.63
Deposits 0.69 -0.02 -0.08 -0.18 -0.30 -0.39 -0.42 -0.34 -0.22 -0.07
Net Worth 5.17 -0.15 -0.03 0.14 0.32 0.52 0.70 0.80 0.76 0.63
Leverage Ratio 5.61 0.16 0.05 -0.12 -0.30 -0.49 -0.66 -0.74 -0.70 -0.55
Loan Spread 0.08 0.05 0.04 -0.08 -0.21 -0.39 -0.42 -0.43 -0.32 -0.18
a
Business cycle statistics in the table are based on HP-?ltered cyclical components of quarterly empirical time
series (smoothing parameter:1600).
b
The standard deviation of output is expressed in percent; standard deviations of the remaining variables are
normalized by the standard deviation of output (std(x)/std(GDP)).
c
The correlation coe?cients in bold font are the maximum ones in their respective rows.
d
Data sources are provided in Appendix A.1.
I will assess the performance of the model below by its ability to match empiri-
cal cyclical properties of real and ?nancial variables in the U.S data. Table 1 presents
10
the business cycle properties of aggregate ?nancial variables in U.S. commercial
banking sector together with standard macro aggregates for the period 1987-2010.
12
The standard deviations of real and ?nancial variables except GDP are relative to
the standard deviation of GDP. The correlation coe?cients in bold font are the
maximum ones in their respective rows, which indicate the lead-lag relationship of
variables with output. The aggregate ?nancial variables I consider are U.S. commer-
cial banks’ assets (bank credit), liabilities (deposits), net worth, leverage ratio and
loan spread.
13
Quarterly seasonally-adjusted ?nancial data are taken from the Fed-
eral Reserve Board. Quarterly real data are taken from Federal Reserve Economic
Data (FRED) of St. Louis FED. Financial data at the FED Board is nominal. GDP
de?ator from NIPA accounts is used to de?ate the ?nancial time series. See the data
appendix for a more detailed description.
Table 1.1 gives us the following empirical facts about real and ?nancial vari-
ables. Consumption and hours are less volatile than output, while investment is
more volatile; and consumption, investment, and hours are all strongly procyclical
with respect to output. These are standard business-cycle facts; for example, see
King and Rebelo (1999). Bank credit, deposits, and loan spread are less volatile than
output, while net worth and leverage ratio are nearly 5 times more volatile. Bank
12
I focus on the period that begins in 1987 for two reasons. First, U.S. banking sector witnessed
a signi?cant transformation starting from 1987 such as deregulation of deposit rates, increases in
?nancial ?exibility. Second, it also corresponds to a structural break in the volatility of many
standard macro variables, which is so-called Great Moderation.
13
I also conducted the same empirical exercise for total assets and total liabilities in addition
to the narrow de?nitions of these items here. The business cycle statistics are qualitatively very
similar although there are some negligible quantitative di?erences. The reason might be the fact
that bank credit constitutes a substantial part of total assets of a typical commercial bank and
deposits constitute a big portion of its total liabilities.
11
assets and net worth are procyclical, while deposits, leverage ratio, and loan spread
are countercyclical. Finally, all ?nancial variables lead the output ?uctuations by
one to three quarters.
14
Table 1.2: The Sequence of Events in a Given Time Period
1. Productivity zt and recovery rate ?t are realized.
2. Firms hire labor Ht and use capital Kt they purchased in period t ? 1, which are used for production, Yt.
3. Firms make their wage payments wtHt and dividend payments to shareholders (banks) from period t-1.
4. Banks make their interest payments on deposits of households from period t-1 and bankers exit with prob. (1-?).
5. Households make their consumption and saving decisions and deposit their resources at banks.
6. Firms sell their depreciated capital to capital producers who make investment and produce new capital K
t+1
.
7. Firms issue shares [st = K
t+1
] and sell these shares to banks to ?nance their capital expenditures.
8. Banks purchase ?rms’ shares and their incentive constraints bind.
9. Firms purchase capital K
t+1
from capital producers at the price of qt with borrowed funds.
1.3 A Business Cycle Model with Financial Sector
The model is an otherwise standard real business cycle model with a ?nancial
sector. Market segmentation ensures that households cannot directly lend to ?nal
good ?rms, which makes the ?nancial sector essential for transferring funds from
households to non-?nancial ?rms. Credit frictions in ?nancial sector are modeled as
in Gertler and Karadi (2011). I introduce shocks to bank net worth on top of the
standard productivity shocks. The model economy consists of four types of agents:
households, ?nancial intermediaries, ?rms, and capital producers. The ability of
?nancial intermediaries to borrow from households is limited due to a moral hazard
(costly enforcement) problem, which will be described below. Firms acquire capital
in each period by selling shares to ?nancial intermediaries. Finally, capital producers
14
I also reproduce Table 1.1 for the period 1987:Q1-2007:Q1 in order to see whether the empirical
results are driven or at least substantially a?ected by the recent economic events starting at 2007:Q3
or not. The results show that the key stylized facts about real and ?nancial variables described
above are robust to the sample period taken. The reproduced table can be found in Appendix A.1.
12
are incorporated into the model in order to introduce capital adjustment costs in a
tractable way. Table 1.2 shows the sequence of events in a given time period in the
theoretical model described below. The section below will clarify this timeline.
1.3.1 Households
There is a continuum of identical households of measure unity. Households are
in?nitely-lived with preferences over consumption (c
t
) and leisure (1 ?L
t
) given by
E
0
?
t=0
?
t
U(c
t
, 1 ? L
t
) (1.1)
Each household consumes and supplies labor to ?rms at the market clearing
real wage w
t
. In addition, they save by holding deposits at a riskless real return r
t
at competitive ?nancial intermediaries.
There are two types of members within each household: workers and bankers.
Workers supply labor and return the wages they earn to the household while each
banker administers a ?nancial intermediary and transfers any earnings back to the
household. Hence, the household owns the ?nancial intermediaries that its bankers
administer. However, the deposits that the household holds are put in ?nancial in-
termediaries that it doesn’t own.
15
Moreover, there is perfect consumption insurance
within each household.
At any point in time the fraction 1 ?? of the household members are workers
15
This assumption ensures independent decision-making. Depositors are not the owners of the
bank, so the bankers don’t maximize the depositors’ utility, but the expected terminal net worth
of the banks that they own.
13
and the remaining fraction ? are bankers. An individual household member can
switch randomly between these two jobs over time. A banker this period remains a
banker next period with probability ?, which is independent of the banker’s history.
Therefore, the average survival time for a banker in any given period is 1/(1 ? ?).
The bankers are not in?nitely-lived in order to make sure that they don’t reach
a point where they can ?nance all equity investment from their own net worth.
16
Hence, every period (1 ??)? bankers exit and become workers while the same mass
of workers randomly become bankers, keeping the relative proportion of workers and
bankers constant. Period t bankers learn about survival and exit at the beginning of
period t + 1. Bankers who exit from the ?nancial sector transfer their accumulated
earnings to their respective household. Furthermore, the household provides its new
bankers with some start-up funds.
17
The household budget constraint is given by
c
t
+ b
t+1
= w
t
L
t
+ (1 + r
t
)b
t
+ ?
t
(1.2)
The household’s subjective discount factor is ? ? (0,1), c
t
denotes the house-
hold’s consumption, b
t+1
is the total amount of deposits that the household holds at
the ?nancial intermediary, r
t
is the non-contingent real return on the deposits from
t?1 to t, w
t
is the real wage rate, and ?
t
is the pro?ts to the household from owning
capital producers and banks net of the transfer that it gives to its new bankers plus
16
This assumption ensures that the bankers have to borrow from households to ?nance their
equity purchases.
17
This assumption ensures that banks don’t have zero net worth in any period and is similar to
the one about the entrepreneurial wage in Carlstrom and Fuerst (1998), and Bernanke, Gertler,
and Gilchrist (1999).
14
(minus) the amount of wealth redistributed from banks (households) to households
(banks) induced by the net worth shock.
The household chooses c
t
, L
t
, and b
t+1
to maximize (1.1) subject to the se-
quence of ?ow budget constraints in (1.2). The resulting ?rst order conditions for
labor supply and deposit holdings are given by
U
l
(t)
U
c
(t)
= w
t
(1.3)
U
c
(t) = ?(1 + r
t+1
)E
t
U
c
(t + 1) (1.4)
The condition (1.3) states that the marginal rate of substitution between con-
sumption and leisure is equal to the wage rate. The condition (1.4) is the standard
consumption-savings Euler equation, which equates the marginal cost of not con-
suming and saving today to the expected discounted marginal bene?t of consuming
tomorrow.
1.3.2 Financial Intermediaries
1.3.2.1 Balance Sheets
Financial intermediaries transfer the funds that they obtain from households
to ?rms. They acquire ?rm shares and ?nance these assets with household deposits
and their own equity. At the beginning of period t, before banks collect deposits,
an aggregate net worth shock hits banks’ balance sheets. Let’s denote ?
t
as the
15
time-varying recovery rate of loans as a percentage of bank net worth. Innovations
to ?
t
are shocks to bank net worth. Therefore, ?
t
¯ n
jt
is the e?ective net worth of the
?nancial intermediary. For notational convenience, I denote ?
t
¯ n
jt
by n
jt
. Hence, n
jt
is the net worth of ?nancial ?rm j at the beginning of period t after the net worth
shock hits. The balance sheet identity of ?nancial intermediary j is then given by
q
t
s
jt
= b
jt+1
+ n
jt
(1.5)
where q
t
is the price of a representative ?rm’s shares and s
jt
is the quantity of these
shares owned by bank j, b
jt+1
is the amount of deposits that intermediary j obtains
from the households, n
jt
is the net worth of ?nancial ?rm j at the beginning of
period t after the net worth shock hits.
18
Banks undertake equity investment and
?rms ?nance their capital expenditures by issuing shares. Therefore, the ?nancial
contract between the intermediary and the ?rm is an equity contract (or equivalently
a state-dependent debt contract).
The households put their deposits into the ?nancial intermediary at time t and
obtain the non-contingent real return r
t+1
at t +1. Therefore, b
jt+1
is the liabilities
of the ?nancial intermediary and n
jt
is its equity or capital. The ?nancial inter-
mediaries receive ex-post state-contingent return, r
kt+1
for their equity investment.
The fact that r
kt+1
is potentially greater than r
t+1
creates an incentive for bankers
to engage in ?nancial intermediation.
The ?nancial intermediary’s net worth at the beginning of period t +1 (before
18
In U.S. ?nancial data, household deposits constitute 70% of total liabilities of banks. Boyd
(2007) also suggests that demand (checking) deposits form a substantial portion of bank liabilities.
16
the time t+1 net worth shock hits) is given by the di?erence between the earnings on
equity investment in ?rms (assets of ?nancial intermediary) and interest payments
on deposits obtained from the households (liabilities of ?nancial intermediary). Thus
the law of motion for bank net worth is given by
¯ n
jt+1
= (1 + r
kt+1
)q
t
s
jt
? (1 + r
t+1
)b
jt+1
(1.6)
Using the balance sheet of the ?nancial ?rm given by (1.5), we can re-write (1.6) as
follows:
¯ n
jt+1
= (r
kt+1
? r
t+1
)q
t
s
jt
+ (1 + r
t+1
)n
jt
(1.7)
The ?nancial intermediary’s net worth at time t+1 depends on the premium (r
kt+1
?
r
t+1
) that it earns on shares purchased as well as the total value of these shares,
q
t
s
jt
.
1.3.2.2 Pro?t Maximization
This section describes banks’ pro?t maximization. The ?nancial intermediary
j maximizes its expected discounted terminal net worth, V
jt
, by choosing the amount
of ?rm shares, s
jt
, it purchases, given by
V
jt
= max
s
jt
E
t
?
i=0
(1??)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
?r
t+1+i
)q
t+i
s
jt+i
]+(1+r
t+1+i
)n
jt+i
] (1.8)
17
Since the expected discounted risk premium is positive in any period, the
?nancial intermediary will always have an incentive to buy ?rms’ shares. Obtaining
additional funds (deposits) from the households is the only way to achieve this.
However, an agency problem described below introduces an endogenous borrowing
constraint for banks, thus a limit on the size of the ?nancial intermediaries: At
the end of the period, the ?nancial intermediary may choose to divert ? fraction
of available funds from its shares of ?rms with no legal rami?cation and give them
to the household of which the banker is a member. If the ?nancial intermediary
diverts the funds, the assumed legal structure ensures that depositors are able to
force the intermediary to go bankrupt and they may recover the remaining fraction
1 ? ? of the assets. They are not able to get the remaining fraction ? of the funds
since, by assumption, the cost of recovering these funds is too high.
19
Therefore,
for the banks not to have an incentive to divert the funds, the following incentive
compatibility constraint must be satis?ed at the end of period t:
V
jt
? ?q
t
s
jt
(1.9)
The left-hand side of (1.9) is the value of operating for the bank (or equiva-
lently cost of diverting funds) while the right-hand side is the gain from diverting ?
19
As Christiano (2010) suggests, diverting funds is meant to say that bankers might not manage
funds in the interest of depositors or they might invest funds into risky projects which do not
earn a high return for depositors but a high excess return for bankers themselves (Bankers might
invest ? fraction of funds into very risky projects, which could potentially go bankrupt and reduce
equilibrium return to depositors). Taking this into consideration, depositors put their money at
banks up to a threshold level beyond which if bankers make risky investments, they do this at their
own risk. This threshold level of deposits can be thought as if deposits expand beyond that level,
banks would have an incentive to default. The market discipline prevents deposits from expanding
beyond the default threshold level and interest rate spreads re?ect this fear of default although
defaults are not observed in equilibrium.
18
fraction of assets. The intuition for this constraint is that in order for the ?nancial
intermediary not to divert the funds and for the households to put their deposits
into the bank, the value of operating in ?nancial sector must be greater than or
equal to the gain from diverting assets and going bankrupt.
20
A ?nancial intermediary’s objective is to maximize the expected return to its
portfolio consisting of ?rms’ shares and its capital subject to the incentive compat-
ibility constraint. Then its demand for shares is fully determined by its net worth
position, since as long as the expected return from the portfolio is strictly positive,
it will expand its lending (its size) until the incentive compatibility constraint binds.
1.3.2.3 Leverage Ratio and Net Worth Evolution
Proposition 1 The expected discounted terminal net worth of a bank can be ex-
pressed as the sum of expected discounted total return to its equity investment into
?rms and expected discounted total return to its existing net worth.
Proof : See Appendix A.2.1.
Proposition 1 states that that V
jt
can be expressed as follows:
V
jt
= ?
t
q
t
s
jt
+ ?
t
n
jt
(1.10)
where
20
In equilibrium, given the incentive compatibility constraint binds, the banker is indi?erent
between diverting funds and not diverting them. Here we focus on the equilibrium where banker
chooses to operate in the ?nancial sector rather than diverting money and going bankrupt. There-
fore, we analyze the equilibrium where there are no defaults of banks and the amount of funds
that the bankers can collect from households endogenously depends on bankers’ own net worth.
19
?
t
= E
t
[(1 ? ?)??
t,t+1
(r
kt+1
?r
t+1
) + ??
t,t+1
?
q
t+1
s
jt+1
q
t
s
jt
?
t+1
] (1.11)
?
t
= E
t
[(1 ? ?)??
t,t+1
(1 + r
t+1
) + ??
t,t+1
?
n
jt+1
n
jt
?
t+1
] (1.12)
?
t
can be interpreted as the expected discounted marginal gain to the bank of
buying one more unit of ?rms’ shares, holding its net worth n
jt
constant. The ?rst
term is the discounted value of the net return on shares to the bank if it exits the
?nancial sector tomorrow. The second term is the continuation value of its increased
assets if it survives. Meanwhile, ?
t
can be interpreted as the expected discounted
marginal bene?t of having one more unit of net worth, holding q
t
s
jt
constant. The
?rst term is the discounted value of the return on net worth to the bank if it exits
the ?nancial sector tomorrow. The second term is the continuation value of its
increased net worth if it survives.
Therefore, we can write the incentive compatibility constraint as follows:
?
t
q
t
s
jt
+ ?
t
n
jt
? ?q
t
s
jt
(1.13)
The incentive compatibility constraint above binds as long as 0 < ?
t
< ?. The
intuition is as follows: Assume that ?
t
? ?. Then the left-hand side of (1.13) is
always greater than the right-hand side of (1.13) since ?
t
n
jt
> 0 as can be seen
from (1.12). The franchise value of the bank is always higher than the gain from
diverting funds. Therefore, the constraint is always slack. Moreover, assume that
20
?
t
? 0. Since ?
t
is the expected discounted marginal gain to the bank of increasing
its assets, the intermediary does not have the incentive to expand its assets when
?
t
? 0. In this case, the constraint does not bind because the intermediary does not
collect any deposits from households.
The pro?ts of the ?nancial intermediary will be a?ected by the premium r
kt+1
?
r
t+1
. That is, the banker will not have any incentive to buy ?rms’ shares if the
discounted return on these shares is less than the discounted cost of deposits. Thus
the ?nancial ?rm will continue to operate in period t + i if the following inequality
is satis?ed:
E
t+i
??
t,t+1+i
(r
kt+1+i
?r
t+1+i
) ? 0 ?i ? 0 (1.14)
where ??
t,t+1+i
is the stochastic discount factor that the ?nancial ?rm applies to
its earnings at t +1 +i. The moral hazard problem between households and banks
described above limits banks’ ability to obtain deposits from the households, leading
to a positive premium. The following proposition establishes this fact.
Proposition 2 Risk premium is positive as long as the incentive compatibility con-
straint binds.
Proof : See Appendix A.2.2.
When this constraint binds, the ?nancial intermediary’s assets are limited by
its net worth. That is, if this constraint binds, the funds that the intermediary can
obtain from households will depend positively on its equity capital:
21
q
t
s
jt
=
?
t
? ??
t
n
jt
(1.15)
The constraint (1.15) limits the leverage of the ?nancial intermediary to the
point where its incentive to divert funds is exactly balanced by its loss from doing so.
Thus, the costly enforcement problem leads to an endogenous borrowing constraint
on the bank’s ability to acquire assets. When bank’s leverage ratio and/or bank
equity is high, it can extend more credit to non-?nancial ?rms. Conversely, de-
leveraging or the deterioration in net worth in bad times will limit the bank’s ability
to extend credit. Note that by manipulating this expression using the balance sheet,
I can obtain the bank’s leverage ratio as follows:
b
jt+1
n
jt
=
?
t
? ? ?
t
? 1 (1.16)
The leverage ratio increases in the expected marginal bene?t of buying one
more unit of ?rm share, and in the expected marginal gain of having one more unit
of net worth. Intuitively, increases in ?
t
or ?
t
mean that ?nancial intermediation is
expected to be more lucrative going forward, which makes it less attractive to divert
funds today and thus increases the amount of funds depositors are willing to entrust
to the ?nancial intermediary.
21
21
The amount of deposits at banks does directly depend on banks’ net worth. In good times
banks’ net worth is relatively high and depositors believe that bankers do not misbehave in terms
of managing their funds properly. In these times, credit spreads can be fully explained by observed
bankruptcies and intermediation costs. However, in bad times, banks experience substantial de-
clines in their net worth and depositors are hesitant about putting their money in banks. In these
times, the ?nancial sector operates at a less e?cient level and a smaller number of investment
projects are funded. Large credit spread observed in these times can be explained by the above
factors plus the ine?ciency in the banking system.
22
Using (1.15), I can re-write the law of motion for the banker’s net worth as
follows:
¯ n
jt+1
= [(r
kt+1
?r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)]n
jt
(1.17)
The sensitivity of net worth of the ?nancial intermediary j at t + 1 to the
ex-post realization of the premium r
kt+1
? r
t+1
increases in the leverage ratio.
Proposition 3 Banks have an identical leverage ratio as none of its components
depends on bank-speci?c factors.
Proof : From (1.17), one can obtain the following:
¯ n
jt+1
n
jt
= [(r
kt+1
?r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)] (1.18)
q
t+1
s
jt+1
q
t
s
jt
=
?
t+1
???
t+1
?t
???t
¯ n
jt+1
n
jt
(1.19)
The expressions above show that banks have identical expected growth rates
of assets and net worth, thus have identical leverage ratios.
22
By using Proposition 4, we can sum demand for assets across j to obtain the
total intermediary demand for assets:
q
t
s
t
=
?
t
? ??
t
n
t
(1.20)
22
This immediately implies that ?
t
and ?
t
are independent of j. In Appendix A.2.1, I use this
result in explicit derivation of ?
t
and ?
t
.
23
where s
t
is the aggregate amount of assets held by ?nancial intermediaries and n
t
is the aggregate intermediary net worth. In the equilibrium of the model, move-
ments in the leverage ratio of ?nancial ?rms and/or in their net worth will generate
?uctuations in total intermediary assets.
The aggregate intermediary net worth at the beginning of period t +1 (before
the net worth shock hits but after exit and entry), ¯ n
t+1
, is the sum of the net worth
of surviving ?nancial intermediaries from the previous period, ¯ n
et+1
, and the net
worth of entering ?nancial intermediaries, ¯ n
nt+1
. Thus, we have
¯ n
t+1
= ¯ n
et+1
+ ¯ n
nt+1
(1.21)
Since the fraction ? of the ?nancial intermediaries at time t will survive until
time t + 1, their net worth, ¯ n
et+1
, is given by
¯ n
et+1
= ?[(r
kt+1
? r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)]n
t
(1.22)
Newly entering ?nancial intermediaries receive start-up funds from their re-
spective households. The start-up funds are assumed to be a transfer equal to a
fraction of the net worth of exiting bankers.
23
The total ?nal period net worth of
exiting bankers at time t is equal to (1??)n
t
. The household is assumed to transfer
the fraction
?
(1??)
of the total ?nal period net worth to its newly entering ?nancial
intermediaries. Therefore, we have
23
This assumption is slightly di?erent from that in Gertler&Karadi (2011). They assume that
the net worth of newly entering bankers is a fraction of banks’ total assets rather than its net
worth. Since the fraction is small, it does not change the main results of the study signi?cantly.
24
¯ n
nt+1
= ?n
t
(1.23)
Using (1.21), (1.22), and (1.23), we obtain the following law of motion for ¯ n
t+1
:
¯ n
t+1
= ?[(r
kt+1
? r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)]n
t
+ ?n
t
(1.24)
1.3.3 Firms
There is a continuum of unit mass of ?rms that produce the ?nal output in the
economy. The production technology at time t is described by a constant returns
to scale Cobb-Douglas production function:
Y
t
= z
t
F(K
t
, H
t
) = z
t
K
?
t
H
1??
t
(1.25)
where K
t
is the ?rm’s capital stock, H
t
is the ?rm’s hiring of labor and z
t
is an
aggregate TFP realization.
Firms acquire capital K
t+1
at the end of period t to produce the ?nal output
in the next period. After producing at time t + 1, the ?rm can sell the capital on
the open market.
Firms ?nance their capital expenditures in each period by issuing equities and
selling them to ?nancial intermediaries. Firms issue s
t
units of state-contingent
claims (equity), which is equal to the number of units of capital acquired K
t+1
. The
?nancial contract between a ?nancial intermediary and a ?rm is an equity contract
(or equivalently, a state contingent debt contract). The ?rm pays a state-contingent
25
interest rate equal to the ex-post return on capital r
kt+1
to the ?nancial intermedi-
ary. The ?rms set their capital demand K
t+1
taking this stochastic repayment into
consideration. At the beginning of period t + 1 (after shocks are realized), when
output becomes available, ?rms obtain resources Y
t+1
and use them to make repay-
ments to shareholders (or ?nancial intermediaries). The ?rm prices each ?nancial
claim at the price of a unit of capital, q
t
. Thus, we have
q
t
s
t
= q
t
K
t+1
(1.26)
There are no frictions for ?rms in obtaining funds from ?nancial intermediaries.
The bank has perfect information about the ?rm and there is perfect enforcement.
Therefore, in the current model, only banks face endogenous borrowing constraints
in obtaining funds. These constraints directly a?ect the supply of funds to the ?rms.
Firms choose the labor demand at time t as follows:
w
t
= z
t
F
H
(K
t
, H
t
) (1.27)
Then ?rms pay out the ex-post return to capital to the banks given that they
earn zero pro?t state by state. Therefore, ex-post return to capital is given by
r
kt+1
=
z
t+1
F
K
(K
t+1
, H
t+1
) + q
t+1
(1 ? ?)
q
t
?1 (1.28)
Labor demand condition (1.27) simply states that the wage rate is equal to
the marginal product of labor. Moreover, condition (1.28) states that the ex-post
26
real rate of return on capital is equal to the marginal product of capital plus the
capital gain from changed asset prices.
1.3.4 Capital Producers
Following the literature on ?nancial accelerator, I incorporate capital produc-
ers into the model in order to introduce capital adjustment costs in a tractable way.
Capital adjustment costs are needed to introduce variation in the price of capital;
otherwise the price of capital will not respond to the changes in capital stock and
will always be equal to 1.
24
I assume that households own capital producers and receive any pro?ts. At
the end of period t, competitive capital producers buy capital from ?rms to repair
the depreciated capital and to build new capital. Then they sell both the new and
repaired capital. The cost of replacing the depreciated capital is unity; thus the
price of a unit of new capital or repaired capital is q
t
. The pro?t maximization
problem of the capital producers is given by:
max
It
q
t
K
t+1
?q
t
(1 ? ?)K
t
? I
t
(1.29)
s.t. K
t+1
= (1 ??)K
t
+ ?
_
I
t
K
t
_
K
t
(1.30)
where I
t
) is the total investment by capital producing ?rms and ?
_
It
Kt
_
is the capital
24
There will be no ?nancial accelerator between households and banks if there is no variation
in the price of capital.
27
adjustment cost function. The resulting optimality condition gives the following “Q”
relation for investment:
q
t
=
_
?
?
_
I
t
K
t
__
?1
(1.31)
where ?
?
_
It
Kt
_
is the partial derivative of the capital adjustment cost function with
respect to investment-capital ratio at time t. The ?uctuations in investment expen-
ditures will create variation in the price of capital. A fall in investment at time t
(ceteris paribus) will reduce the price of capital in the same period.
1.3.5 Competitive Equilibrium
A competitive equilibrium of this model economy consists of sequences of allo-
cations {c
t
, L
t
, K
t+1
, s
t
, n
t
, ¯ n
t
, I
t
, ?
t
, ?
t
, H
t
}
?
t=0
, of prices {w
t
, r
kt+1
, r
t+1
, q
t
}
?
t=0
and of
exogenous processes {z
t
, ?
t
}
?
t=0
such that (i) the allocations solve the household’s,
the ?nancial intermediary’s, the ?rm’s and the capital producer’s problems at the
equilibrium prices and (ii) markets for factor inputs clear. The following equilibrium
conditions must be satis?ed:
U
l
(t)
U
c
(t)
= w
t
(1.32)
U
c
(t) = ?(1 + r
t+1
)E
t
U
c
(t + 1) (1.33)
28
r
kt+1
=
z
t+1
F
K
(K
t+1
, H
t+1
) + q
t+1
(1 ? ?)
q
t
?1 (1.34)
w
t
= z
t
F
H
(K
t
, H
t
) (1.35)
n
t
= ?
t
¯ n
t
(1.36)
q
t
s
t
=
?
t
? ??
t
n
t
(1.37)
?
t
= E
t
[(1 ? ?)??
t,t+1
(r
kt+1
?r
t+1
) + ??
t,t+1
?
q
t+1
s
t+1
q
t
s
t
?
t+1
] (1.38)
?
t
= E
t
[(1 ? ?)??
t,t+1
(1 + r
t+1
) + ??
t,t+1
?
n
t+1
n
t
?
t+1
] (1.39)
¯ n
t+1
= ?[(r
kt+1
? r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)]n
t
+ ?n
t
(1.40)
q
t
s
t
= q
t
K
t+1
(1.41)
K
t+1
= (1 ? ?)K
t
+ ?
_
I
t
K
t
_
K
t
(1.42)
29
q
t
=
_
?
?
_
I
t
K
t
__
?1
(1.43)
L
t
= H
t
(1.44)
C
t
+ I
t
= z
t
F(K
t
, H
t
) (1.45)
log(z
t+1
) = ?
z
log(z
t
) + ?
z
t+1
(1.46)
log(?
t+1
) = ?
?
log(?
t
) + ?
?
t+1
(1.47)
1.4 Quantitative Analysis
This section studies the quantitative predictions of the model by examining
the results of numerical simulations of an economy calibrated to quarterly U.S.
data. In order to investigate the dynamics of the model, I compute a second-order
approximation to the equilibrium conditions using Dynare.
30
1.4.1 Functional Forms, Parametrization and Calibration
The quantitative analysis uses the following functional forms for preferences,
production technology and capital adjustment costs:
25
U(c, 1 ? L) = log(c) + ?log(1 ? L) (1.48)
F(K, H) = K
?
H
1??
(1.49)
?
_
I
K
_
=
I
K
?
?
2
_
I
K
??
_
2
(1.50)
Table 1.3 lists the parameter values for the model economy. The preference
and production parameters are standard in business cycle literature. I take the
quarterly discount factor, ? as 0.9942 to match the 2.37% average annualized real
deposit rate in the U.S. for the period 1987.Q1-2010.Q4. I pick the relative utility
weight of labor ? as 1.72 to ?x hours worked in steady state, L, at one third of
the available time. The share of capital in the production function is set to 0.36
to match the labor share of income in the U.S. data. The capital adjustment cost
parameter is taken so as to match the relative volatility of price of investment goods
with respect to output in the U.S. data.
26
The quarterly depreciation rate of capital
is set to 2.25% to match the average annual investment to capital ratio.
25
I choose the functional form of the capital adjustment cost following Bernanke, Gertler and
Gilchrist (1999), Gertler, Gilchrist, and Natalucci (2007).
26
The volatility of price of investment goods is taken from Gomme et al. (2011).
31
Table 1.3: Model Parameterization and Calibration
Description Parameter Value Target Data
Preferences
Quarterly discount factor ? 0.9942 Annualized real deposit rate 2.37%
Relative utility weight of leisure ? 1.7167 Hours worked 0.3333
Production Technology
Share of capital in output ? 0.36 Labor share of output 0.64
Capital adjustment cost parameter ? 3.6 Relative volatility of price of investment 0.37
Depreciation rate of capital ? 0.025 Average annual ratio of investment to capital 10%
Steady-state total factor productivity z 1 Normalization N/A
Financial Intermediaries
Steady-state fraction of assets that can be diverted ? 0.1548 Commercial and industrial loan spread 0.46%
Proportional transfer to the entering bankers ? 0.001 0.1% of aggregate net worth N/A
Survival probability of the bankers ? 0.9685 Leverage ratio of commercial banks 4.62
Steady-state level of net worth shock ? 1 Normalization N/A
Shock Processes
Persistence of TFP process ?z 0.9315 Quarterly persistence of TFP process 0.9315
Standard deviation of productivity shock ?z 0.006424 Quarterly standard dev. of TFP shock 0.0064
Persistence of ? process ?? 0.3744 Quarterly persistence of ? process 0.3744
Standard deviation of net worth shock ?? 0.0512 Quarterly standard dev. of net worth shock 0.0512
The non-standard parameters in our model are the ?nancial sector parame-
ters: the fraction of the revenues that can be diverted, ?, the proportional transfer
to newly entering bankers, ?, and the survival probability of bankers, ?. I set ? to
0.001 so that the proportional transfer to newly entering bankers is 0.1% of aggre-
gate net worth.
27
I pick other two parameters simultaneously to match the following
two targets: an average interest rate spread of 46 basis points, which is the histor-
ical average of the di?erence between the quarterly commercial and industrial loan
spread and the quarterly deposit rate from 1987.Q1 to 2010.Q4, and an average
leverage ratio of 4.61, which is the historical average of U.S. commercial banks’
leverage ratio for the same period. The resulting values for ? and ? are 0.155 and
0.968, respectively.
Finally, turning to the shock processes, I follow the standard Solow residuals
approach to construct the series for productivity shocks.
28
Using the production
27
I keep the proportional transfer to newly entering bankers small, so that it does not have
signi?cant impact on the results.
28
I also perform model-based simulations of macro-?nancial shocks using utilization-adjusted
TFP series constructed by Fernald (2009). The results can be found in Appendix A.5.
32
function, I obtain
z
t
=
y
t
K
?
t
H
1??
t
(1.51)
Using the empirical series for output, y
t
, capital, K
t
, and labor, H
t
, I use equation
(1.51) to obtain the z
t
series. Then I construct the log-deviation of TFP series by
linearly detrending the log of the z
t
series over the period 1987.Q1-2010.Q4.
Similar to the construction of productivity shocks, ?
t
series are constructed
from the law of motion for bank net worth, which is given by
?
t
=
1
?[(r
kt+1
? r
t+1
)
?t
???t
+ (1 + r
t+1
)] + ?
¯ n
t+1
¯ n
t
(1.52)
Using the empirical series for net worth, n
t
, credit spread, r
kt+1
? r
t+1
, leverage,
?t
???t
, and gross deposit rate 1 + r
t+1
, I use equation (1.52) obtain the ?
t
series.
29
Then I construct the log-deviation of ?
t
series by linearly detrending the log of these
series over the period 1987.Q1-2010.Q4. The innovations to ?
t
are net worth shocks.
After constructing the z
t
and ?
t
series over the period 1987.Q1-2010.Q4, I
estimate two independent AR(1) processes for both series:
30
log(z
t+1
) = ?
z
log(z
t
) + ?
z
t+1
(1.53)
29
I constructed two ?
t
series by using the realized and the expected values of credit spread. I
obtain the expected value of credit spread by regressing actual spread on real and ?nancial variables
(such as GDP, consumption, investment, hours, bank credit, deposits, net worth) and getting the
predicted value of it. Both series of ? are very similar to each other (the correlation between the
two series is 0.9934).
30
For the stochastic processes, I also tried ?tting a VAR(1), however, the cross-terms in VAR(1)
are statistically insigni?cant at 5% signi?cance level. I included the main results of the analysis
under the VAR(1) representation into the Appendix A.4. The results are qualitatively very similar
although there are some negligible quantitative di?erences.
33
-.06
-.04
-.02
.00
.02
.04
88 90 92 94 96 98 00 02 04 06 08 10
Level of productivity
-.2
-.1
.0
.1
.2
.3
88 90 92 94 96 98 00 02 04 06 08 10
Level of omega
-.03
-.02
-.01
.00
.01
.02
88 90 92 94 96 98 00 02 04 06 08 10
Innovations to productivity
-.2
-.1
.0
.1
.2
.3
88 90 92 94 96 98 00 02 04 06 08 10
Innovations to omega
Figure 1.2: Time Series of Shocks to Productivity and Credit Conditions
log(?
t+1
) = ?
?
log(?
t
) + ?
?
t+1
(1.54)
where ?
z,t+1
and ?
?,t+1
are i.i.d. with standard deviations ?
z
and ?
?
, respectively.
The resulting parameters are ?
z
= 0.93, ?
?
= 0.37, ?
z
= 0.0064, and ?
?
= 0.05.
The ?rst two panels of Figure 1.2 plot the variables z
t
and ?
t
constructed using
the procedures described above. The ?gures show that the levels of productivity
and credit conditions fell sharply in the recent recession.
31
The bottom panels
31
The level of ?
t
started to decline before the recession o?cially began. However, we see a
sharp increase in the level of ?
t
in the middle of the recession period due to the fact that there
are huge capital transfers from bank holding companies to their commercial banks and injection
of capital from the FED with the capital purchase program. If we remove this spike due to the
capital transfers, we see a decline in the level of ?
t
before the recession starts.
34
plot the innovations ?
z,t
and ?
?,t
. These innovations are unexpected changes in the
levels of productivity and ?nancial conditions. The plots suggest that the U.S.
economy is severely hit by both negative productivity and ?nancial shocks in the
Great Recession.
1.4.2 Long-Run Equilibrium of the Model
This section presents the deterministic steady-state properties of the model
economy. First, I will formally show how the tightness of bank capital constraint
a?ects output. Imposing the steady-state on the competitive equilibrium conditions
of the model economy yields the following analytical expression for output:
y =
_
_
?
(1???)µ?
(1??)?(1+µ)
+
(1??)
?
+ ?
_
_
1
(1??)
L
2??
(1.55)
where µ is the Lagrange multiplier of bank capital constraint. Taking the partial
derivative of output w.r.t. µ, I obtain
?y
?µ
= ?
?
(1 ? ?)
_
_
?
(1???)µ?
(1??)?(1+µ)
+
(1??)
?
+ ?
_
_
?
(1??)
L
2??
_
(1 ? ?)?(1 ? ??)?
[(1 ??)?(1 + µ)]
2
_
?2
< 0
(1.56)
which unambiguously shows that the output will be lower the larger µ. The reason is
simple. As the bank capital constraint gets tighter, the credit spread will be larger,
35
as can be seen from the following expression.
(r
k
? r) =
(1 ???)µ?
(1 ??)?(1 + µ)
(1.57)
The term at the right-hand side of equation (1.57) appears as a positive wedge
in the intertemporal Euler equation, which determines how deposits (savings) are
transformed into credit to ?rms in the economy. This positive wedge reduces the
amount of savings that can be extended as credit to non-?nancial ?rms, lowering
their physical capital accumulation, and thus leading to a lower steady-state output.
The same mechanism is also at work when shocks move the economy around the
steady-state as they tighten or relax the bank capital constraint.
0 0.1 0.2 0.3 0.4
0.8
1
1.2
1.4
1.6
Output
0 0.1 0.2 0.3 0.4
0.7
0.8
0.9
1
Consumption
0 0.1 0.2 0.3 0.4
0.1
0.2
0.3
0.4
0.5
Investment
0 0.1 0.2 0.3 0.4
0.3
0.32
0.34
0.36
Hours
0 0.1 0.2 0.3 0.4
0
5
10
15
Deposits
0 0.1 0.2 0.3 0.4
0
1
2
3
Net Worth
0 0.1 0.2 0.3 0.4
0
5
10
15
20
Leverage Ratio
0 0.1 0.2 0.3 0.4
0
0.5
1
1.5
Credit Spread (%)
0 0.1 0.2 0.3 0.4
5
10
15
20
Total Credit
Figure 1.3: Long-run equilibrium as a function of fraction of diverted funds by
bankers
36
Second, I analytically show how output is a?ected by the severity of credit
frictions in banking sector, which is governed by the fraction of diverted funds by
bankers, ?. Taking the partial derivative of output w.r.t. ?, I get
?y
??
= ?
?L
2??
(1 ? ?)
_
¸
¸
_
?
_
(1???)[(1??)???]
(1??)?(1??)?
_
(1??)
?
(1???)[(1??)???]?
(1??)?(1??)?
+
(1??)+??
?
_
¸
¸
_
?
(1??)
_
(1 ? ??)[(1 ? ?)? ? ?]?
(1 ??)?(1 ? ?)?
+
(1 ? ?) + ??
?
_
?2
< 0
(1.58)
which implies that the steady-state output will be lower the higher the intensity
of ?nancial frictions in banking sector. In order to get the intuition behind this
result, I display long-run equilibria of real and ?nancial variables as a function of
the intensity of the credit friction in the ?nancial sector given by fraction of diverted
funds by bankers, ?. All other parameter values are set to those shown in Table 1.3.
Figure 1.3 shows that the long-run dynamics of the model economy to changes in ?
is monotonic and non-linear. As ? increases, households’ incentive to make deposits
into banks falls since the bankers’ gain from diverting funds rises. Banks have to
?nance their equity investment by internal ?nancing rather than external ?nancing.
Thus, deposits go down and net worth rises, leading to a fall in banks’ leverage ratio.
The decline in leverage ratio is sharper than the rise in net worth, inducing a drop
in total credit to non-?nancial ?rms. Credit conditions tighten for ?rms and their
cost of funds given by credit spread goes up. This leads to a reduction in investment
and output falls.
37
1.4.3 Intermediary Capital and the Transmission of Shocks
I present the dynamics of the model in response to productivity and net worth
shocks. In the ?gures below, credit spread, return to capital, and deposit rate are
expressed in percentage points per annum. The responses of all other variables are
expressed in percentage deviations from their respective steady state values.
1.4.3.1 Impulse Responses to TFP Shocks
Figure 1.4 presents the impulse responses to a one-time, one-standard devi-
ation negative shock to TFP. The negative technology shock reduces the price of
investment goods produced by capital producers by 0.3% on impact, lowering the
value of ?rms’ shares. This makes purchase of their shares less pro?table for banks,
which can also be observed from the 1.2% fall in the return to capital. Thus, banks
have di?culty in obtaining deposits from households since their equity investment
becomes less attractive. This reduces the return to deposits by 0.2%, inducing a
countercyclical credit spread. The spread rises by 0.3% on impact. In order to
compensate the fall in their external ?nancing, banks need to ?nance a larger share
of their purchases of equities from their net worth. However, bank net worth also
falls by 4% due to lower asset prices. Since the decline in net worth is sharper
than the fall in deposits on impact, banks’ leverage ratio rises. Hence, the model
with productivity shocks generates a countercyclical leverage ratio. Because banks
cannot adjust their net worth immediately and the lower price of capital reduces
the value of their net worth, their ?nancing conditions tighten and bank lending in
38
the form of equity purchases falls dramatically (by about 4.6%), inducing aggregate
investment to shrink by 0.9%. Finally, hours fall by 0.15%, and output declines by
1.2%.
39
0 5 10 15 20
?1.2
?1
?0.8
?0.6
?0.4
?0.2
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Output
0 5 10 15 20
?0.4
?0.35
?0.3
?0.25
?0.2
Consumption
0 5 10 15 20
?1
?0.8
?0.6
?0.4
?0.2
0
Investment
0 5 10 15 20
?0.2
?0.15
?0.1
?0.05
0
Hours Worked
0 5 10 15 20
?5.4
?5.2
?5
?4.8
?4.6
?4.4
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Bank Credit
0 5 10 15 20
?5
?4
?3
?2
?1
0
Deposits
0 5 10 15 20
?4
?3
?2
?1
0
Bank Net Worth
0 5 10 15 20
?0.1
0
0.1
0.2
0.3
0.4
Credit Spread (Rk?R)
0 5 10 15 20
?0.3
?0.2
?0.1
0
0.1
Quarters
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Price of Capital
0 5 10 15 20
?1.5
?1
?0.5
0
0.5
Quarters
Return to Capital
0 5 10 15 20
?0.2
?0.15
?0.1
?0.05
0
0.05
Quarters
Deposit Rate
0 5 10 15 20
?0.3
?0.2
?0.1
0
0.1
Quarters
Bank Capital to Asset Ratio
Figure 1.4: Impulse responses to a negative one-standard-deviation productivity shock
4
0
0 5 10 15 20
?1
?0.8
?0.6
?0.4
?0.2
0
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Output
0 5 10 15 20
?0.5
0
0.5
1
Consumption
0 5 10 15 20
?2
?1.5
?1
?0.5
0
0.5
Investment
0 5 10 15 20
?0.4
?0.3
?0.2
?0.1
0
0.1
Hours Worked
0 5 10 15 20
?9
?8
?7
?6
?5
?4
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Bank Credit
0 5 10 15 20
?5
0
5
10
Household Deposits (Bank Liabilities)
0 5 10 15 20
?20
?15
?10
?5
0
Bank Net Worth
0 5 10 15 20
0
0.5
1
1.5
Credit Spread (Rk?R)
0 5 10 15 20
?0.6
?0.4
?0.2
0
0.2
Quarters
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Price of Capital
0 5 10 15 20
?2
?1.5
?1
?0.5
0
0.5
Quarters
Return to Capital
0 5 10 15 20
?1
?0.5
0
0.5
Quarters
Deposit rate
0 5 10 15 20
?1.5
?1
?0.5
0
Quarters
Bank Capital to Asset Ratio
Figure 1.5: Impulse responses to a negative one-standard-deviation net worth shock
4
1
1.4.3.2 Impulse Responses to Financial Shocks
Figure 1.5 presents the impulse responses to a one-time, one-standard devia-
tion negative shock to net worth. The negative net worth shock immediately reduces
net worth of banks. Bank net worth falls roughly by 15% on impact. In order to
compensate the decline in their internal ?nancing, they need to ?nance a larger share
of their purchases of equities from deposits. This induces a rise in their leverage
ratio. Hence, the model driven by net worth shocks also generates a countercycli-
cal leverage ratio. Although they have to ?nance a greater fraction of their equity
investment from deposits, their ability to do so is impaired by the fall in their net
worth, leading deposits to decline after ?ve quarters. Moreover, the fall in their
net worth translates into a reduction in bank credit to ?rms. Bank credit shrinks
by roughly 8% on impact. Since ?rms ?nance their capital expenditures via bank
credit, they cut back their investment severely (by about 2%). The drop in invest-
ment reduces the price of capital by 0.4%, which lowers banks’ net worth further.
Hours fall by 0.4% and output drops by 0.9% on impact. Finally, consumption rises
on impact after the shock hits, which is what was observed at the beginning of the
recent ?nancial crisis. In the context of the model, this seemingly unappealing re-
sult can be explained as follows: On the intratemporal margin, the fall in aggregate
demand caused by lower investment expenditures translates into a reduction in the
demand for labor, which eventually leads to a drop in hours worked. Since wages
are ?exible, the reduction in labor demand also lowers wages, leading to a fall in
households’ wage bill. However, the rise in credit spread on impact raises banks’
42
pro?ts. Since households own banks, the rise in their pro?ts helps households sus-
tain their consumption after the ?nancial shock hits. On impact, the rise in bank
pro?ts dominates the reduction in wage bill, pushing consumption up.
32
1.4.4 Business Cycle Dynamics
This section presents numerical results from stochastic simulations of the
benchmark economy with productivity and net worth shocks. First, I simulate the
model economy 1000 times for 1096 periods each and discard the ?rst 1000 periods
in each simulation so that each simulation has the same length as the data sample.
I then compute the standard business cycle statistics using the cyclical components
of the HP-?ltered series. I also conduct the same quantitative exercise for the fric-
tionless version of the benchmark economy, which is essentially the standard RBC
model with capital adjustment costs, in order to compare the real ?uctuations in
both models. Finally, I simulate the model economy only driven by productivity
shocks to see the contribution of net worth shocks to the observed dynamics of real
and ?nancial variables.
Table 1.4 presents quarterly real and ?nancial statistics in the data and in
the model economies. In particular, it displays the relative standard deviations
of real and ?nancial variables with respect to output and their cross-correlations
with output. Column 3 of the table shows that the standard RBC model with
capital adjustment costs driven by standard productivity shocks is able produce
32
Barro and King (1984) argue that any shock that reduces the quantity of hours worked on
impact has to lead a fall in consumption due to consumption-leisure optimality condition. Ajello
(2010) shows that sticky wages are the key factor in generating a positive comovement between
consumption and investment after a ?nancial shock.
43
the key business cycle facts in the U.S. data as expected: consumption and hours
less volatile than output, while investment is more volatile, all real variables are
highly procyclical. However, this model can only explain 80% of the ?uctuations in
output and less than half of the relative volatility in hours. It also generates roughly
perfect positive correlation between real variables and output, contrary to the data.
Moreover, this model has no predictions about ?nancial variables.
Column 4 of the table shows the business cycle statistics of our model economy
with only productivity shocks. This model is much closer to the data in terms of
real ?uctuations, compared to the RBC model. It now accounts for 85% of the
?uctuations in output and roughly half of the relative volatility in hours. The
model is also able to replicate most of the stylized facts about ?nancial variables:
bank assets, deposits and loan spread is less volatile than output, while net worth
and leverage ratio are more volatile; bank assets and net worth are procyclical, while
leverage ratio and loan spread are countercyclical. However, it generates procyclical
deposits, contrary to the data. Although the model does a good job in terms of key
facts of ?nancial variables, it predicts lower ?uctuations. For example, it can explain
less than half of the relative volatility in bank assets, roughly half of the relative
volatility in deposits, less than one third of the relative volatility in net worth and
leverage ratio. The model virtually matches the relative volatility of credit spread.
44
Table 1.4: Real and Financial Statistics
Statistic Data RBC Only Productivity Benchmark
?
Y
1.80 1.44 1.53 1.81
?
C
0.45 0.41 0.39 0.75
?
I
2.73 2.45 2.98 4.64
?
L
0.91 0.40 0.46 0.84
?
Y,I
0.97 1.00 0.98 0.87
?
Y,C
0.82 0.97 0.85 -0.03
?
Y,L
0.83 0.99 0.96 0.81
?
Assets
0.93 – 0.40 0.58
?
Deposits
0.69 – 0.39 0.87
?
NetWorth
5.17 – 1.36 5.90
?
LeverageR.
5.61 – 1.40 6.40
?
Spread
0.08 – 0.07 0.23
?
Y,Assets
0.30 – 0.90 0.88
?
Y,Deposits
-0.39 – 0.46 -0.23
?
Y,NetWorth
0.52 – 0.87 0.68
?
Y,LeverageR.
-0.49 – -0.71 -0.59
?
Y,Spread
-0.39 – -0.86 -0.67
a
Business cycle statistics in the table are based on HP-?ltered cyclical components of quarterly simulated time
series (smoothing parameter:1600).
b
The standard deviation of output is expressed in percent; standard deviations of the remaining variables are
normalized by the standard deviation of output (std(x)/std(GDP)).
c
In all model economies, capital adjustment cost parameter is set to 3.3, which is calibrated in benchmark model
to match the relative volatility of price of investment.
Column 5 of the table shows the real and ?nancial statistics in the benchmark
economy driven by both shocks. This model is even closer to the data than the
previous model in terms of business cycle properties of real variables. It predicts all
of the ?uctuations in output, almost all of the relative volatility in hours. The cross
correlations of investment and hours with output are quite inline with the data.
45
However, the model generates acyclical consumption due to the reasons explained
in the previous section. This model has better predictions about ?nancial variables.
It is able to reproduce the key facts about aggregate ?nancial variables. Moreover, it
now explains more than half of the relative volatility in bank assets, and somewhat
overpredicts the relative volatility in other ?nancial variables. The last column of
Table 1 establishes the ?rst main result of the ?rst chapter: the benchmark model
driven by both shocks is able to deliver most of the key stylized facts about real and
?nancial variables simultaneously.
1.5 Model-Based Simulations of Macro-Financial Shocks vs. U.S.
Data
I also study the dynamics of the model in response to the actual sequence
of shocks to see whether the model is able to generate the real and ?nancial cycles
observed in the U.S. data.
33
I feed the actual innovations to z
t
and ?
t
into the model
and compute the responses of real and ?nancial variables over the period 1987 to
2010.
Figure 1.6 displays the quarterly time series of output, investment and hours
in the data, in the standard RBC model with capital adjustment costs, and in the
benchmark economy. The RBC model is driven by standard productivity shocks,
while the benchmark model is driven by both shocks. Both the quarterly times se-
33
Although I feed the actual series of shocks into the model, they are not perfectly anticipated
by the agents in the economy as they predict future values of z
t
and ?
t
using the AR(1) processes
given by (1.53) and (1.54).
46
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 1
GDP
corr(data, rbc) = 0.69
corr(data, benchmark 1) = 0.80
-50
-40
-30
-20
-10
0
10
20
30
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 1
Investment
corr(data, rbc) = 0.72
corr(data, benchmark 1) = 0.79
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 1
Hours
corr(data, rbc) = 0.39
corr(data, benchmark 1) = 0.60
Figure 1.6: Real Fluctuations: Benchmark vs. RBC model
47
ries of the variables and their model counterparts are log-linearly detrended over the
period 1987.Q1 - 2010.Q4, and plotted in percentage deviations from their trends.
The correlations between the actual and the model-simulated series are also reported
in the graphs. The ?gure suggests that both the RBC model and the benchmark
economy generate series of real variables that closely follow their empirical coun-
terparts. However, the RBC model predicts lower ?uctuations in all real variables.
In particular, the RBC model predicts a smaller decline in output in the 1990-91
recession. Moreover, it generates declines in investment and hours that are smaller
than the actual declines in the 1990-91 and 2007-09 recessions. On the other hand,
the benchmark model generates larger ?uctuations in real variables, consistent with
the data. Since this model has one additional shock compared to the RBC model,
higher volatility can be expected. However, the benchmark model also improves
upon the RBC model in the sense that for output, investment and hours, the cross-
correlations between the data and the benchmark model is much higher than those
between the data and the RBC model. Moreover, the model’s success in generating
empirically-relevant ?uctuations in hours hinges on the fact that it is able to produce
quantitatively reasonable ?uctuations in capital. Since labor is complementary to
capital stock in a standard Cobb-Douglas production function, empirically-relevant
changes in capital stock lead to observed ?uctuations in hours. The second dimen-
sion that the benchmark model improves upon the RBC model is that the latter has
no predictions about ?nancial variables by construction while the former generates
movements in ?nancial variables consistent with the U.S. ?nancial data.
Figure 1.7 displays the quarterly time series of output, investment and hours
48
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
GDP
corr(data, only prod.) = 0.68
corr(data, benchmark 1) = 0.80
-50
-40
-30
-20
-10
0
10
20
30
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Investment
corr(data, only prod.) = 0.68
corr(data, benchmark 1) = 0.79
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Hours
corr(data, only prod.) = 0.33
corr(data, benchmark 1) = 0.60
Figure 1.7: Real Fluctuations: Benchmark vs. Only Productivity
49
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
GDP
corr(data, rbc) = 0.69
corr(data, only prod.) = 0.68
-40
-30
-20
-10
0
10
20
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Investment
corr(data, rbc) = 0.72
corr(data, only prod.) = 0.68
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Hours
corr(data, rbc) = 0.39
corr(data, only prod.) = 0.33
Figure 1.8: Real Fluctuations: RBC vs. Only Productivity
in the data, in the model driven only by productivity shocks, and in the benchmark
economy. The ?gure suggests that the benchmark economy performs better than
the model with only productivity shocks in terms of both volatilities of real variables
and cross-correlations of those variables with the data. For all the real variables,
the cross-correlations with the data in the benchmark model is higher than those
with the data in the model with only productivity shocks.
Figure 1.8 displays the quarterly time series of output, investment and hours
in the data, in the RBC model, and in the model driven only by productivity
shocks. This ?gure suggests that the model with only productivity shocks is not
50
very di?erent from the RBC model in terms of its quantitative performance in real
variables. Actually, the series of real variables generated by these two models are
almost the same. Therefore, we can say that credit frictions in banking sector
by themselves are not enough to improve upon the RBC model and to produce
real ?uctuations consistent with the data. Financial shocks are quite important in
explaining the observed dynamics of real variables.
Figure 1.9 shows the quarterly time series of bank credit, deposits, net worth,
leverage ratio, and credit spread both in the data, in the model driven only by
productivity shocks and in the benchmark model. Both the quarterly time series of
?nancial variables and their model counterparts are log-linearly detrended over the
period 1987.Q1 - 2010.Q4, and plotted in percentage deviations from their trends.
Credit spread is plotted in annualized percentages. The correlations between the
actual and the model-simulated series are also reported in the graphs. For all the
?nancial variables, the cross-correlations with the data in the benchmark model is
signi?cantly higher than those with the data in the model with only productivity
shocks. Speci?cally, for net worth, leverage ratio and credit spread, the benchmark
model produces highly positively correlated series with the data, while the model
with only productivity shocks predicts negative correlations. Thus, ?gures 1.7 and
1.9 establish the second main result of the chapter that ?nancial shocks contribute
signi?cantly to explaining the observed dynamics of ?nancial variables.
Figure 1.10 plots the ?uctuations in the Lagrange multiplier of bank capital
constraint in the benchmark model and those in the index of credit tightness con-
structed by Federal Reserve Board using the Senior Loan O?cer Opinion Survey
51
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Bank credit
corr(data, only prod.) = 0.66
corr(data, benchmark 1) = 0.75
-10
-8
-6
-4
-2
0
2
4
6
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Deposits
corr(data, only prod.) = 0.48
corr(data, benchmark 1) = 0.50
-80
-60
-40
-20
0
20
40
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Net worth
corr(data, only prod.) = -0.17
corr(data, benchmark 1) = 0.74
-40
-20
0
20
40
60
80
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Leverage ratio
corr(data, only prod.) = -0.07
corr(data, benchmark 1) = 0.72
-2
0
2
4
6
8
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Credit spread
corr(data, only prod.) = -0.09
corr(data, benchmark 1) = 0.45
Figure 1.9: Financial Fluctuations: Benchmark vs. Only Productivity
52
-60
-40
-20
0
20
40
60
80
100
88 90 92 94 96 98 00 02 04 06 08 10
Survey of senior officers
Lagrange multiplier
Index of tightening credit standards
Figure 1.10: Tightness of Credit Conditions in the Benchmark Model
on Bank Lending Practices. Starting with the second quarter of 1990, this sur-
vey basically asks senior loan o?cers whether they have recently tighten the credit
standards for commercial and industrial loans, and the collected responses are used
to create an index of credit tightness as the percentage of respondents, reporting
tightening standards. Increases in both the multiplier and the index show the ad-
verse changes in bank lending to non-?nancial businesses. The ?gure shows that
the multiplier tracks the index well. The multiplier also explains the severity of
credit conditions experienced by the U.S. economy in the last three recessions by
capturing most of the ?uctuations in the index. However, there seems to be a phase
shift between these two series.
34
There might be two reasons behind this. The ?rst
one is the inability of standard RBC models to match the lead-lag relationships of
macro variables. The second one is using lagging ?nancial variables from H.8 tables
34
If I use loan losses data to construct the ?nancial shock series, there is no phase shift in the
tightness of credit conditions.
53
while constructing ?nancial shocks rather than using leading ?nancial variables from
Consolidated Reports of Condition and Income (Call) Reports. Bearing this caveat
in mind, we can say that ?gure 1.10 establishes the third main result of this chapter:
U.S. banks experienced a signi?cant deterioration in their lending ability in the last
recessions, especially in 1990-91 and 2007-09 recessions.
1.6 Conclusion
This study quantitatively investigates the joint role of ?nancial shocks and
credit frictions a?ecting banking sector in driving the real and ?nancial ?uctuations
in the U.S. data. To this end, I ?rst characterize the empirical cyclical behavior of
aggregate ?nancial variables of U.S. banking sector. I then use an otherwise standard
real business cycle model with a ?nancial sector, which features an agency problem
between banks and their depositors, leading to endogenous borrowing constraints
for banks in obtaining funds from households. I incorporate empirically-disciplined
shocks to bank net worth (i.e. “?nancial shocks”) which a?ect the ability of banks
to obtain funds from households and to extend credit to non-?nancial sector.The
time series of ?nancial shocks are constructed from the data. The resulting shock
series show that credit conditions in the U.S. economy deteriorated signi?cantly in
the recent recession.
Several key ?ndings emerge from the quantitative analysis. First, the bench-
mark model driven by both productivity and ?nancial shocks is able to explain
most of the empirical facts about real and ?nancial variables simultaneously. Sec-
54
ond, ?nancial shocks to banking sector contribute signi?cantly not only to the ob-
served dynamics of aggregate ?nancial variables but also to the observed dynam-
ics of standard macroeconomic variables. In particular, the benchmark model has
better predictions about real and ?nancial variables than the model driven only
by productivity shocks. Third, the simulation of the benchmark model points a
signi?cant worsening in banks’ lending ability in 1990-91 and 2007-09 recessions.
The main transmission mechanism of ?nancial shocks is through bank capital chan-
nel. In particular, ?nancial shocks are transmitted to the real economy through
tightening bank capital constraint, which eventually leads to rising credit spread.
Non-?nancial ?rms perceive this rise in credit spread as an increase in their cost of
borrowing from banks, leading to a decline in their external ?nance for investment
expenditures. Falling aggregate demand caused by lower investment reduces the
demand for labor, which brings a drop in hours worked, and hence output.
For further research, one can investigate the normative implications of the
model in the light of the recent ?nancial crisis, as U.S. government has assisted
many ?nancial ?rms in order to raise their franchise value, and hence to support
real economic activity. In order to start thinking about how di?erent policy tools
can be implemented in an environment in which the ?nancial sector is crucial for
business cycle ?uctuations and what the welfare implications of these policies are,
we need a model capable of matching real and ?nancial ?uctuations simultaneously.
We think that the model proposed in this study is quite successful in this dimension.
55
Chapter 2
Required Reserves as a Credit Policy Tool
(joint with Enes Sunel and Temel Ta¸sk?n)
2.1 Introduction
Policymakers in both advanced and emerging countries have been exercising
a variety of measures to mitigate the transmission of ?nancial disruptions to the
real sector. To that end, frictions in the ?nancial sector and macroprudential policy
instruments have been the focal point of the recent literature on macroeconomic
dynamics and policy. Among many, reserve requirements have been used extensively
as a macroprudential policy tool in several emerging countries, recently. China,
Brazil, Malaysia, Peru, Colombia and Turkey are some of the countries among others
who have used this tool mostly to curb excessive credit growth in upturns along with
other reasons.
1
In terms of their main objectives, they employ reserve requirements
either as a monetary policy tool to achieve price stability or as a macroprudential
policy tool to foster ?nancial stability, or both. For example, the Central Bank
of the Republic of Turkey (CBRT, hereafter) regards the interest rate as the main
policy tool for price stability, with a secondary role for ?nancial stability, and reserve
requirements as the main policy tool for ?nancial stability, with a secondary role
1
See Montoro and Moreno (2011), Montoro (2011), Gray (2011), Glocker and Towbin (2012)
for the discussion of country experiences.
56
for price stability.
2
The main idea behind using reserve requirements as the main
instrument for ?nancial stability and interest rate as the main instrument for price
stability might be to separate tasks, which increases transparency and facilitates
communication of these policies. In this regard, this study explicitly focuses on the
?nancial stability of reserve requirements.
Central banks could use reserve requirements to achieve ?nancial stability in
the following manner as Montoro and Moreno (2011) noted: they can raise reserve
requirements to contain credit growth in the boom part of the business cycle in
order to counteract ?nancial imbalances in the economy or in an economic downturn,
they can lower reserve requirements to utilize reserve bu?ers accumulated during the
boom part, having the banking sector extend more credit to non-?nancial businesses.
Therefore, reserve requirements can be used as a cyclical policy instrument to ease
credit ?uctuations in the ?nancial sector, and hence to stabilize the real economy.
The goal of this study is to investigate the e?ectiveness of reserve requirements
that respond to expected credit growth in moderating the real and ?nancial cycles of
an economy. We do so in a model where real and ?nancial ?uctuations are ampli?ed
by a ?nancial accelerator mechanism. Speci?cally, we explore the stabilizing role
of reserve requirements as a credit policy tool, on the transmission mechanism of
productivity, monetary and ?nancial shocks. The results suggest that a time-varying
reserve requirement policy mitigates the ?uctuations in key macroeconomic variables
and improves welfare vis-a-vis a ?xed reserve requirement policy.
3
2
Basci (2010).
3
At this point, we acknowledge that cancelling reserve requirements altogether might improve
aggregate welfare of the economy. However, mostly due to precautionary reasons, positive reserve
requirements do exist in practice and since it is beyond the scope of this paper, we do not bring
57
Figure 2.1: Evolution of Required Reserve Ratios in Turkey
We extend the basic ?nancial intermediation framework to one in which “money”
is explicitly modelled via a cash-in-advance constraint. Consequently, we introduce
required reserves into the model in a very tractable way, since we have the concept
of a monetary base.
After the mid of 2010, the CBRT has determined two policy targets in order to
mitigate macro-?nancial imbalances in Turkish economy as Basci and Kara (2011)
elaborated. The ?rst one is to reduce short-term capital in?ows to lower current
account de?cit, and the second one is to curb excessive credit growth in banking
any micro-foundation to this institutional framework in what follows.
58
sector. In this regard, it was decided that in addition to short-term interest rate,
reserve requirements and interest rate corridor are used to foster ?nancial stability
without compromising price stability. Moreover, in order to increase the e?ectiveness
of reserve requirements as a policy tool, the CBRT let the interest rate ?uctuate in
a controlled manner at overnight market to use interest rate corridor as an active
policy instrument and terminated paying interest on required reserves by September
2010. It also di?erentiated required reserves at di?erent maturities (having a higher
required reserve ratio for short-term liabilities) and hence extended the maturity of
banking sector’s liabilities in order to strengthen ?nancial stability.
We calibrate the model to the Turkish economy which exempli?es the use of
reserve requirements as a macroprudential tool since the end of 2010 (see ?gure 2.1).
In particular, the CBRT has increased weighted average of required reserves ratio –
henceforth, RRR – from 5% to 13% between the period October 2010 and April 2011,
in a stepwise manner. This period also coincides with the aftermath of the second
phase of quantitative easing implemented by monetary authorities in a number of
advanced economies. Evidently, this period is characterized by an increase in the
risk appetite of global investors and excessive credit growth in emerging economies
such as Turkey. On the other hand, same measure of RRR has been reduced to
about 10% around November 2011 by the CBRT following the debt crisis of the
Euro area.
Our quantitative exercise involves comparing a “?xed RRR economy” in which
the RRR is calibrated to its “long-run” value preceding the interventions of the
CBRT and the “time-varying RRR economy” in which the RRR is countercycli-
59
cal with respect to expected credit growth.
4
We approximate the required reserves
policy implemented by the CBRT with this countercyclical rule since the CBRT of-
?cials and economists stated that it used the reserve requirements to curb excessive
credit growth in the banking sector after the second phase of quantitative easing
conducted by many advanced economies’ central banks and to ease credit condi-
tions in the banking sector after the Eurozone debt crisis.
5
Moreover, we model
the rule as the one which reacts to expected credit growth in order to re?ect the
CBRT’s incentive to use this policy tool proactively and in a macroprudential and
forward-looking manner.
6
We also simulate the model under moderate and aggres-
sive required reserve policies in order to understand the e?ectiveness of the policy
as a macroprudential policy tool.
There are three main results of this study: First, the time-varying required
reserve ratio rule mitigates the negative e?ects of adverse macroeconomic and ?nan-
cial shocks and the ?nancial accelerator mechanism on real and ?nancial variables.
As a result, we conclude that RRRs might be used as a macroprudential policy
tool in an economy that exhibits ?nancial frictions. Second, in response to TFP
and money growth shocks, countercyclical reserves policy reduces the volatilities of
key variables such as output, consumption, investment, bank credit, credit spreads
and asset prices in comparison with ?xed reserves policy. This happens because
the ampli?cation e?ect of the ?nancial sector is mitigated by time-varying reserve
4
We also conduct the analysis of a model economy with zero required reserves policy. The
dynamics of this case strongly resemble those of the ?xed RRR economy.
5
Basci and Kara (2011) and Kara (2012).
6
The results seem quite similar if the rule responds to current credit growth. The main idea
behind this rule is to reduce the procyclicality of the banking sector in the face of adverse macro
shocks and hence to stabilize the real economy.
60
requirements. Third, a time-varying reserve requirement policy is welfare superior
to a ?xed reserve requirement policy.
The workings of the model might be elaborated in greater detail as follows:
An adverse TFP shock reduces the demand of ?nancial intermediaries for equity
and drives down its price. The collapse in asset prices feeds back into the endoge-
nous capital constraints of intermediaries and causes banks’ net worth to decline.
Accordingly, the shortage in loanable funds, which manifests itself as a rise in credit
spreads, combined with the collapse in asset prices causes investment to decline
substantially. When the RRR is ?xed, the dynamics of reserves resembles that of
deposits.
When the countercyclical RRR policy is in place, the fall in bank credit led
by the adverse TFP shock calls for a reduction in the RRR. This induces banks to
substitute loans for reserves on the assets side of the balance sheet, because the cost
of raising external ?nance is lower with a smaller RRR. Accordingly, larger supply
of funds extended by banks mitigates the collapse in investment and asset prices,
countervailing the ?nancial accelerator mechanism. This also limits the rise in credit
spreads, which is an intertemporal distortion created by ?nancial frictions in the
consumption-savings margin of workers. The downward response of RRR reduces
the demand for monetary base and shoots up in?ation on impact. Therefore, the
credit policy mitigates the ?nancial accelerator at the expense of higher in?ation.
However, since this immediate surge is transitory and driven by the reserves policy,
the model implies an undershooting of in?ation in the following periods. This implies
a substitution of consumption for leisure on the part of forward looking households
61
and labor supply increases in contrast with the ?xed RRR economy. Increased
labor supply combined with a stronger trajectory for capital mitigates the collapse
in output signi?cantly.
A positive money growth shock increases in?ation and crowds out deposits
and consumption for leisure in our cash-in-advance speci?cation. Therefore, a posi-
tive money growth produces similar dynamics to that of TFP shocks in the model.
Consequently, the counter-cyclical RRR policy rule stabilizes key ?nancial and real
variables in response to money growth shocks again at the expense of higher in?a-
tion.
Lastly, we run a ?nancial crisis experiment in which we consider an exoge-
nous decline in the net worth of ?nancial intermediaries as in Hancock, Laing and
Wilcox (1995), Meh and Moran (2010), Brunnermeier and Pedersen (2009), Curdia
and Woodford (2010), Mendoza and Quadrini (2010), Iacoviello (2010), and Mimir
(2011). This shock crudely captures loan losses, asset write-downs or asset revalu-
ations that we observe in the recent ?nancial crisis. Most importantly, it might be
interpreted as an exogenous variation in the risk appetite of international investors,
that may have destabilizing e?ects on the ?nancial system of an economy such as
Turkey.
Although the initial decline in banks’ net worth led by the ?nancial shock is
exogenous, there will be second round e?ects that amplify the collapse in internal
?nance of banks. This would create a shortage of bank credit and would drive a
drop in investment, and in the price of capital. Banks then increase their demand
for external ?nancing (i.e. increase their deposit demand) to compensate for the
62
decline in bank net worth. This causes reserves to increase and drives down in?ation,
pointing out a di?erence from the case of TFP and money growth shocks on part
of the nominal dynamics. Yet, since the shock is transitory, in?ation overshoots in
the period that follows the shock and workers’ expectations regarding the hike in
future in?ation causes hours to decline substantially on impact. Therefore, output
collapses together with investment.
Credit policy in response to ?nancial shock calls for a reduction in the RRR
and is again in?ationary in the sense that the reduction in in?ation on impact
becomes substantially lower. Accordingly, overshooting in in?ation becomes less as
well, limiting the collapse in hours. In this manner, the analysis shows that the
counter-cyclical RRR policy has a stabilizing e?ect in response to ?nancial shocks
in addition to TFP and money growth shocks and might be used by the central
bank as a macroprudential policy tool.
Related Literature
Our work is mostly related to the studies by Glocker and Towbin (2012) and Mon-
toro (2011) who analyze the role of reserve requirements as a macroprudential policy
tool. Glocker and Towbin (2012) augment required reserves as an additional policy
instrument and variations in loans as an additional target into an open-economy
model with nominal rigidities and ?nancial frictions. Their results imply that re-
quirements are in favor of price stability objective only if ?nancial frictions are non-
trivial and are more e?ective if there is a ?nancial stability objective and debt is
denominated in foreign currency. In their work, due to the endogeneity of monetary
63
base, an increase in the RRR increases loan-deposit spreads only if the remuneration
of reserves is below the market rate. Since they obtain impact of policy change on
consumption and investment, the overall e?ect on aggregate demand and in?ation
is ambiguous.
Montoro (2011) introduces counter-cyclical RRR policy tools in an otherwise
standard New-Keynesian setting that introduce collateral and liquidity constraints
as in Kiyotaki and Moore (2008) and maturity mismatch frictions as in Benes and
Lees (2010). He ?nds that RRRs contain the procyclicality of the ?nancial system
in response to demand shocks but not under supply shocks. The main di?erences
of our work with these papers is that we model ?nancial frictions a-la’ Gertler and
Karadi (2011) that introduces an agency problem between depositors and bankers
and that involves equity ?nancing of non-?nancial ?rms. An important deviation
from the former study is that we also explore the role of RRRs in response to ?nancial
shocks and from the latter study is that we ?nd that RRRs might be stabilizing even
under supply shocks. From an alternative perspective, our ?nding that credit policy
implemented by RRRs is the most e?ective in response to ?nancial shocks is in line
with the ?nding of Glocker and Towbin (2012) that RRRs are mostly e?ective when
?nancial frictions are relevant.
Another closely related work to the current study is that of Christensen et al.
(2011) which explores the role of countercyclical bank capital regulations as a macro-
prudential policy tool. Similar to our experiment, they compare time-varying and
constant bank capital regulations and ?nd that the former regime reduces volatili-
ties of real variables and bank lending. However, as they state in their paper, the
64
type of ?nancial friction that they introduce di?ers from that of Gertler and Karadi
(2011) in that it is driven by asymmetric information between bankers and their
creditors a la’ Holmstrom and Tirole (1997), instead of limited commitment. While
the macroprudential regulation in their work is focused on the “size” of the balance
sheet, in our work it is focused on the “composition of the assets side” of the balance
sheet.
Our work also has linkages to closed economy frameworks of Kashyap and Stein
(2012) and Curdia and Woodford (2011) in which the remuneration of reserves has
been studied. Yet, it is obvious that reserves policy studied in these papers are more
related to the central bank balance sheet considerations of the Federal Reserve at
the onset of the sub-prime ?nancial crisis and do not have the focus of containing
excessive credit growth in contrast with the focus of our work. From another per-
spective, the descriptive work of Gray (2011) on recent reserve requirement policy
experiences and the work of Reinhart and Reinhart (1999) on the use of required
reserves for stability of international capital ?ows relates to the current study.
The rest of the paper is organized as follows. Section 2.2 describes the model
economy and characterizes equilibrium. Section 2.3 undertakes the quantitative
analysis regarding the dynamics introduced by macroeconomic and ?nancial shocks
and section 2.4 concludes.
65
2.2 The Model
The model economy is inhabited by households, banks, ?nal goods producers,
capital producers, and a government. Time is discrete. Two ?nancial frictions
characterize the economy. First, market segmentation ensures that households who
are the ultimate savers in the economy cannot directly lend to non-?nancial ?rms.
This assumption makes the banking sector essential for transferring funds from
ultimate savers (households) to ultimate borrowers (?nal goods producers). Second,
banking sector is characterized by credit frictions that are modelled a la Gertler
and Karadi (2011). Households face a cash-in-advance constraint, which makes
them hold real balances, leading to the existence of monetary equilibria. Finally,
banks are subject to time-varying reserve requirements imposed by the central bank,
which reacts countercyclically to expected credit expansion in the economy. Below
is a detailed description of economic agents that reside in this model economy.
2.2.1 Households
The population consists of a continuum of in?nitely-lived identical households.
We assume that each household is composed of a worker and a banker who perfectly
insure each other. Workers supply labor to the ?nal goods producers and assumed
to deposit their savings in the banks owned by the banker member of “other” house-
holds.
7
A representative household maximizes the discounted lifetime utility ?ow earned
7
This assumption is useful in making the agency problem that we introduce in section 2.2.2
more realistic.
66
from consumption, c
t
and leisure, l
t
,
E
0
?
t=0
?
t
u
_
c
t
, l
t
_
(2.1)
where 0 < ? < 1 the subjective discount factor and E is the expectation operator.
Households face the following ?ow budget constraint,
c
t
+ b
t+1
+
M
t+1
P
t
= w
t
(1 ? l
t
) + R
t
b
t
+
M
t
P
t
+ ?
t
+
T
t
P
t
(2.2)
where b
t
is the beginning of period t balance of deposits held at commercial banks, P
t
is the general nominal price level, w
t
is the real wage earned per labor hour, R
t
is the
gross risk free deposits rate, ?
t
is the pro?ts remitted from the ownership of banks
and capital producers and T
t
is lump-sum transfers remitted by the government.
Households face a cash-in-advance constraint which re?ects the timing assump-
tion that asset markets open ?rst as in Cooley and Hansen (1989):
c
t
?
M
t
P
t
+
T
t
P
t
+ R
t
b
t
?b
t+1
(2.3)
Solution of the utility maximization problem of households yield the optimality
conditions below,
67
u
c
(t) = ?R
t+1
E
t
u
c
(t + 1) (2.4)
u
l
(t)
P
t
w
t
= ?E
t
_
u
c
(t + 1)
P
t+1
_
(2.5)
Condition (2.4) is a standard consumption-savings optimality condition, which equates
marginal bene?t of current consumption to the expected discounted bene?t of sav-
ing in deposits. Equation (2.5) on the other hand is a non-standard consumption-
leisure optimality condition due to the existence of cash-in-advance friction which
transforms the trade-o? between the two into an inter-temporal one. Speci?cally,
increasing leisure demand by 1 unit today reduces savings in cash by
P
P
?
=
1
1+?
?
future units because the yield of cash balances is de?ated by in?ation. Therefore,
the utility cost of leisure is measured only in terms of future utility foregone by
facing a tighter cash-in-advance constraint in the next period.
2.2.2 Banks
The modelling of ?nancial sector closely follows that in Gertler and Karadi
(2011). To summarize the key ingredients, we denote the period t balance sheet of
a bank j as,
q
t
s
jt
= (1 ?rr
t
)b
jt+1
+ n
jt
(2.6)
68
The right hand side of the balance sheet denotes the resources of bank j,
namely, net worth, n
jt
and deposits, b
t+1
needed to ?nance its credit extension to
non-?nancial ?rms, q
t
s
jt
. The loans to ?rms serve as state-contingent claims s
jt
towards the ownership of ?rms and are traded at the market price q
t
. Note that
the bank can only loan (1 ? rr
t
) fraction of deposits to the ?rms where rr
t
is the
required reserve ratio set by the central bank as we describe below. The balance
sheet of banks described in equation (2.6) imply an evolution equation for net worth
as follows:
n
jt+1
=
_
R
kt+1
?
_
R
t+1
?rr
t
1 ? rr
t
__
q
t
s
jt
+
_
R
t+1
? rr
t
1 ?rr
t
_
n
jt
(2.7)
It is evident in equation (2.7) that an increase in the required reserve ratio
rr
t
decreases the returns to assets and increases the returns to equity all else equal.
That induces banks to substitute internal ?nancing (n
t
) for external ?nancing (b
t+1
).
Bankers have a ?nite life and survive to the next period with probability ?. At
the end of each period 1 ?? number of new bankers are born and are remitted
?
1??
of the net worth owned by the exiting bankers. Bankers’ objective is to maximize
the present discounted value of the terminal net worth of their ?nancial ?rm, V
jt
,
by choosing the amount of claims against the ?rm ownership, s
jt
. That is,
69
V
jt
= max
s
jt
E
t
?
i=0
(1??)?
i
?
i+1
?
t,t+1+i
__
R
kt+1+i
?
_
R
t+1+i
? rr
t+i
1 ? rr
t+i
__
q
t+i
s
jt+i
+
_
R
t+1+i
? rr
t+i
1 ? rr
t+i
_
n
jt+i
_
(2.8)
The ?nite life of bankers, ? < 1, ensures that bankers never accumulate enough net
worth to ?nance all their equity purchases of non-?nancial ?rms via internal funds
so that they have to borrow from households in the form of deposits.
The key feature of the ?nancial sector unfolds around a moral hazard problem
between banks and households: In this model of banking, households believe that
banks might divert ? fraction of their total assets for their own bene?t. This might
be thought of as investing part of q
t
s
jt
in excessively risky projects that go bankrupt
eventually and not paying back the corresponding liability to the depositor. In this
case, depositors shall cause a bank run and lead to the liquidation of the bank
altogether. Therefore, bankers’ optimal plan regarding the choice of s
jt
at any date
t should satisfy an incentive compatibility constraint,
V
jt
? ?q
t
s
jt
(2.9)
This inequality suggests that the loss of bankers, V
jt
, from diverting the funds
and investing them in risky projects that would likely fail should be greater than or
equal to the diverted portion of the assets, ?q
t
s
jt
.
By using an envelope condition and algebraic manipulation, one can write the
70
optimal value of banks as
V
?
jt
= ?
t
q
t
s
?
jt
+ ?
t
n
?
jt
(2.10)
where the recursive objects,
8
?
t
= E
t
_
(1 ??)??
t,t+1
_
R
kt+1
?
_
R
t+1
? rr
t
1 ?rr
t
__
+ ???
t,t+1
?
t
?
t+1
_
(2.11)
and
?
t
= E
t
_
(1 ??)??
t,t+1
_
R
t+1
? rr
t
1 ?rr
t
_
+ ???
t,t+1
?
t
?
t+1
_
(2.12)
represent the marginal values of relaxing credit and accumulating net worth for the
bank respectively. The growth rates of assets and net worth of banks are denoted
with ?
t
=
q
t+1
s
jt+1
qts
jt
and ?
t
=
n
jt+1
n
jt
.
One can obtain the following by combining equations (2.9) and (2.10):
?
t
q
t
s
jt
+ ?
t
n
jt
? ?q
t
s
jt
(2.13)
The above constraint binds only if 0 < ?
t
< ?. This happens because ?
t
n
jt
is
greater than zero. If ?
t
? ?, then left hand side would be strictly greater than right
8
Proofs of equations (2.10), (2.11), and (2.12) are available in technical appendix upon request.
71
hand side in equation (2.13). Under plausible values of parameters, this constraint
always binds in equilibrium, which in turn produces the endogenous borrowing con-
straint for the bank as follows:
q
t
s
jt
=
?
t
? ??
t
n
jt
= ?
t
n
jt
. (2.14)
This endogenous constraint which emerges from the costly enforcement prob-
lem described above ensures that banks’ leverage might always be equal to
?t
???t
and
is decreasing with the fraction of funds (?) that depositors believe that banks will
divert.
Due to the fact that ?
t
does not depend on j, one can aggregate equation
(2.14) and obtain the following aggregate relationship:
q
t
s
t
= ?
t
n
t
(2.15)
where s
t
and n
t
represent aggregate levels of banks’ assets and net worth, respec-
tively.
The evolution of aggregate net worth depends on that of the surviving bankers
(n
et+1
) and the start-up funds of the new entrants (n
nt+1
):
n
t+1
= n
et+1
+ n
nt+1
. (2.16)
72
The net worth of new entrants is de?ned as an ? fraction of banks’ aggregate
net worth, that is:
9
n
nt+1
= ?n
t
(2.17)
The fact that ? fraction of banks survive over next period equates the net
worth of surviving banks to the following:
n
et+1
= ?
__
R
kt+1
?
_
R
t+1
? rr
t
1 ? rr
t
__
?
t
+
_
R
t+1
?rr
t
1 ? rr
t
__
n
t
(2.18)
One can sum up equations (2.17) and (2.18) to obtain the evolution of net
worth for the entire set of banks:
n
t+1
=
_
?
__
R
kt+1
?
_
R
t+1
? rr
t
1 ?rr
t
__
?
t
+
_
R
t+1
? rr
t
1 ? rr
t
__
+ ?
_
n
t
(2.19)
Equation (2.19) shows that the evolution of net worth depends on e?ective
spread and leverage ratio of banks.
9
This assumption is slightly di?erent from that in Gertler&Karadi (2011). They assume that
the net worth of newly entering bankers is a fraction of banks’ total assets rather than its net
worth. Since the fraction is small, it does not change the main results of the study signi?cantly.
73
2.2.3 Firms
Firms produce the consumption good by using physical capital and labor as
production factors. They operate with a constant returns to scale technology F(., .)
that is subject to total factor productivity shocks, z
t
y
t
= exp(z
t
)F(k
t
, h
t
) (2.20)
where
z
t+1
= ?
z
z
t
+ ?
zt+1
(2.21)
with zero mean and constant variance innovations, ?
zt+1
.
Firms ?nance capital at date t by issuing claims s
t
to ?nancial intermediaries
and acquire capital k
t+1
from capital producers. Therefore,
q
t
s
t
= q
t
k
t+1
(2.22)
with q
t
is the market price of the ?rms’ equity and capital.
Banks’ claim against the ownership of the ?rm pays out its dividend via the
marginal product of capital in the next period. Hence, the cost of credit to the ?rm
is state-contingent. As a result, the cost of credit to the ?rm must satisfy
R
kt
=
z
t
F
k
(k
t
, h
t
) + q
t
(1 ??)
q
t?1
(2.23)
74
Finally, the optimal labor demand of the ?rm must satisfy the usual static
condition,
w
t
= exp(z
t
)F
h
(k
t
, h
t
) (2.24)
which equates marginal product of labor to the marginal cost of it.
2.2.4 Capital Producers
Capital producers are introduced in order to obtain variation in the price
of capital which is necessary for the ?nancial accelerator mechanism to operate.
To that end, capital producers provide physical capital to the ?rms and repair the
depreciated capital and incur the cost of investment. Consequently, the optimization
problem of capital producers reads,
max
it
q
t
k
t+1
? q
t
(1 ??)k
t
?i
t
(2.25)
subject to the capital accumulation technology,
k
t+1
= (1 ??)k
t
+ ?
_
i
t
k
t
_
k
t
(2.26)
where the function ?(·) represents the capital adjustment cost. The optimality
condition that emerges from the solution to this problem is the well-known “q”
relation that pins down the price of capital,
75
q
t
=
_
?
?
_
i
t
k
t
__
?1
(2.27)
2.2.5 Government
The government is essentially responsible for coordinating monetary policy.
To that end, it controls the supply of money M
0t+1
and determines the required
reserve ratio rr
t
. Any growth of the monetary base is remitted to households in the
form of lump-sum transfers, T
t
. The monetary base grows at the rate µ
t
,
M
0t+1
= exp(µ
t
)M
0t
(2.28)
where the growth rate of money supply is subject to zero mean, constant variance
normally distributed innovations so that,
µ
t+1
= (1 ? ?
µ
)¯ µ + ?
µ
µ
t
+ ?
µt+1
(2.29)
In order to contain the ?nancial accelerator mechanism, the government uses
required reserves as a macroprudential rule. Speci?cally, the required reserves ratio
is assumed to follow a rule that reacts to the expected growth rate of bank credit
at date t + 1 compared to its level in the current period.
10
rr
t
= ¯ rr + ?E
t
[log(q
t+1
s
t+1
) ? log(q
t
s
t
)] (2.30)
10
We also consider a rule which reacts to current credit growth rather than expected future
credit growth. The main results of the study remain unchanged as can be seen from Appendix
B.2.
76
where, ¯ rr is the steady-state value of the required reserves ratio and ? > 0. Con-
sequently, the central bank increases the e?ective pro?t to banks of extending new
loans when credit in the aggregate economy is shrinking, and vice versa. The gov-
ernment budget constraint is given by
T
t
= M
t+1
? M
t
+ P
t
rr
t
b
t+1
? P
t
rr
t?1
b
t
(2.31)
The government uses the seignorage revenue plus the increases in its reserves to
?nance the lump-sum transfer payments to households, which include both workers
and bankers.
11
Within this framework, the money market equilibrium turns out as
the following condition:
M
0t+1
= M
t+1
+ P
t
rr
t
b
t+1
(2.32)
where P
t
is the general price level of the consumption good. The money supply
equals to the currency demand by workers plus the reserve demand by bankers. Since
the left hand side is exogenously determined by the central bank, equilibrium in the
money market might call for adjustments in price level in response to ?uctuations
in reserves. That being said, we also want to emphasize the fact that ?exible-price
models are not good models in explaining the dynamics of in?ation. The only reason
to talk about in?ation dynamics here is to show that using reserve requirements leads
to a possibly interesting trade-o? between price stability and ?nancial stability faced
11
The lump-sum transfer payments to the households equals to the change in money demand
by workers plus the change in reserves demand by bankers.
77
by many emerging market central banks recently. To be precise, this trade-o? is to
reduce the intertemporal distortions created by the credit spread at the expense of
generating higher in?ation volatility.
2.2.6 Competitive Equilibrium
Notice that nominal monetary base and prices grow constantly in this model,
which renders the equations listed above non-stationary. Therefore, following Coo-
ley and Hansen (1989), we make the model stationary by applying the following
normalizations:
´
P
t
= P
t
/M
0t+1
and ˆ m
t
= M
t+1
/(
´
P
t
M
0t+1
) and solve the model
locally around a deterministic steady state.
A competitive equilibrium of this model economy is de?ned by sequences of al-
locations {c
t
, k
t+1
, i
t
, l
t
, h
t
, s
t
, n
t
, n
e
t, n
n
t, b
t+1
, ?
t,t+1
, ?
t
, ?
t
, ?
t
, ?
t,t+1
, ?
t,t+1
, ˆ m
t+1
, ?
t
}
?
t=0
,
prices {q
t
, R
kt+1
, R
t+1
, w
t
,
´
P
t
}
?
t=0
, shock processes {z
t
, µ
t
}
?
t=0
and the government pol-
icy {rr
t
}
?
t=0
that satisfy the following optimality and market clearing conditions:
?
t,t+1
=
u
c
(t + 1)
u
c
(t)
(2.33)
1 = ?E
t
R
t+1
?
t,t+1
(2.34)
c
t
=
exp(µ
t
) ? 1 + ˆ m
t
ˆ
P
t
ˆ
P
t
exp(µ
t
)
+ R
t
b
t
?b
t+1
(2.35)
78
u
l
(t)
w
t
ˆ
P
t
= ?E
t
_
u
c
(t + 1)
ˆ
P
t+1
exp(µ
t+1
)
_
(2.36)
?
t
=
?
t
? ? ?
t
(2.37)
q
t
s
t
= ?
t
n
t
(2.38)
q
t
s
t
= (1 ?rr
t
)b
t+1
+ n
t
(2.39)
?
t,t+1
=
_
R
kt+1
?
R
t+1
?rr
t
1 ? rr
t
_
?
t
+
R
t+1
? rr
t
1 ? rr
t
(2.40)
?
t,t+1
= ?
t,t+1
?
t+1
?
t
(2.41)
n
et
= ??
t?1,t
n
t?1
(2.42)
n
nt
= ?n
t?1
(2.43)
n
t
= n
et
+ n
nt
(2.44)
79
?
t
= E
t
_
(1 ??)??
t,t+1
_
R
kt+1
?
R
t+1
?rr
t
1 ? rr
t
_
+ ??
t,t+1
??
t,t+1
?
t+1
_
(2.45)
?
t
= E
t
_
(1 ? ?)??
t,t+1
_
R
t+1
?rr
t
1 ? rr
t
_
+ ??
t,t+1
??
t,t+1
?
t+1
_
(2.46)
w
t
= exp(z
t
)F
h
(k
t
, h
t
) (2.47)
R
kt
=
exp(z
t
)F
k
(k
t
, h
t
) + q
t
(1 ? ?)
q
t?1
(2.48)
k
t+1
= (1 ??)k
t
+ ?
_
i
t
k
t
_
k
t
(2.49)
q
t
=
_
?
?
_
i
t
k
t
__
?1
(2.50)
exp(z
t
)F(k
t
, h
t
) = c
t
+ i
t
(2.51)
s
t
= k
t+1
(2.52)
1 = l
t
+ h
t
(2.53)
80
exp(?
t
) = exp(µ
t
)
´
P
t
¯
P
t?1
(2.54)
z
t+1
= ?
z
z
t
+ ?
zt+1
(2.55)
µ
t+1
= (1 ? ?
µ
)¯ µ + ?
µ
µ
t
+ ?
µt+1
(2.56)
rr
t
= ¯ rr + ?E
t
[log(q
t+1
s
t+1
) ? log(q
t
s
t
)] (2.57)
1
´
P
t
= ˆ m
t+1
+ rr
t
b
t+1
(2.58)
2.3 Quantitative Analysis
2.3.1 Functional Forms
Preferences: We use a standard CRRA utility function and separable utility
for leisure:
u(c
t
, l
t
) =
c
1??
t
1 ? ?
??
h
1+?
t
1 + ?
(2.59)
with ? > 1, ?, ? > 0.
Production: Firms produce according to a constant returns to scale Cobb-Douglas
81
production function:
exp(z
t
)F(k
t
, h
t
) = exp(z
t
)k
?
t
h
1??
t
(2.60)
with 0 < ? < 1.
Capital Producers: Capital producers are subject to a convex adjustment cost
function:
?
_
i
t
k
t
_
=
?
2
_
i
t
k
t
??
_
2
(2.61)
The parameter values used in the quantitative analysis are reported in Table
2.1. The preference and production parameters are standard in business cycle liter-
ature. The share of capital in the production function is set to 0.4, and the capital
adjustment cost parameter is 2.75. We borrow the standard values of ? and v from
literature as 2 and 2, respectively. We take the quarterly discount factor, ? as 0.9885
to match the 2006-2011 average annualized real deposit rate, 4.73%, in Turkey. We
pick the relative utility weight of labor ? to ?x hours worked in steady state, L, at
one third of the available time. The quarterly depreciation rate of capital is set to
3.7% to match the 1987-2011 average annual investment to capital ratio of 14.8% in
Turkey.
Parameters related to the ?nancial sector are calibrated to match ?nancial
statistics of the Turkish economy in the period 2006-2011. We set ? to 0.001 so
that the proportional transfer to newly entering bankers is 5.71% of aggregate net
82
Table 2.1: Paremeter Values in the Benchmark Model
Description Value Target
Preferences
Quarterly discount factor (?) 0.9885 Annualized real deposit rate (4.73%)
Relative utility weight of consumption (?) 2
CRRA parameter in the utility (v) 2 Literature
Relative utility weight of leisure (?) 15.182 Hours worked (0.33)
Production Technology
Share of capital in output (?) 0.4 Labor share of output (0.64)
Capital adjustment cost parameter (?) 2.75 Relative volatility of investment = 2.25
Depreciation rate of capital (?) 0.037 Average annual ratio of investment to capital (14.8%)
Government
Steady-state value of RRR ( ¯ rr) 0.05 Pre macroprudential policy period
Adjustment parameter in the RRR rule (?) 5.15 Standard deviation of di?erences in RRR for 2009:4-
2012:2 (1.73%)
Financial Intermediaries
Fraction of diverted loans (?) 0.5 Annual commercial & industrial loan spread (1.96%)
Prop. transfer to the entering bankers (?) 0.001 5.71% of aggregate net worth
Survival probability of the bankers (?) 0.962 Capital adequacy ratio of 16% for commercial banks
Shock Processes
Persistence of TFP process (?z) 0.9821 Estimated from detrended log TFPt = ?z log TFP
t?1
+ ?zt
Std. deviation of productivity shocks (?z) 0.0183
Persistence of money growth process (?µ) 0.5702 Estimated from log ?M1t = ?µ log ?M1
t?1
+ ?µt
Std. deviation of money growth shocks (?µ)0.0275
worth. We pick the fraction of diverted funds, ?, and the survival probability, ?,
simultaneously to match the following two targets: an average interest rate spread of
48 basis points, which is the historical average of the di?erence between the quarterly
commercial and industrial loan rates and the quarterly deposit rate from 2006:Q1
to 2011:Q4, and an average capital adequacy ratio of 16%, which is the historical
average of Turkish commercial banks’ capital adequacy ratio for the same period.
12
12
The legal target of risk-weighted capital adequacy ratio set by the Banking Regulation and
Supervision Agency in Turkey is 8%, however, commercial banks in Turkey maintain 16% for this
83
The resulting values for ? and ? are 0.5 and 0.962, respectively. The benchmark
model involves the macroprudential policy rule illustrated in equation (2.30) which
does not alter the steady state of the model but a?ects the dynamics around it. We
calibrate the response parameter of the RRR rule ? to 5.15 in order to match the
standard deviation of the di?erences in RRR of 1.73% for the Turkish economy in
the period 2009:4-2012:2.
We estimate an AR(1) process for the log of TFP for the period 1988:Q2-
2011:Q2 and ?nd a persistence of, ?
z
= 0.9821, and a standard deviation of in-
novations to TFP, ?
z
= 0.0183. The money growth process on the other hand is
estimated for the period 2003:Q1-2011:Q4 using M1 series, following Cooley and
Hansen (1989).
13
Estimation results implied a persistence of, ?
z
= 0.5702, and a
standard deviation of innovations to money growth shocks, ?
µ
= 0.0275.
With the parameterized economy, we ?rst illustrate the role of ?nancial accel-
erator driven by credit frictions in the banking sector. We then study the dynamics
of the model by focusing on impulse responses to one standard deviation nega-
tive productivity and positive money growth shocks in environments that involve
alternative required reserves policies. We also document implications of using a
time-varying required reserves ratio in terms of its e?ect on the volatilities of real
and ?nancial variables in order to understand its e?ectiveness as a macroprudential
policy tool. Finally, we analyze the welfare implications of alternative RRR policies.
ratio in practice.
13
The choice of estimation period re?ects the structural disin?ation that the Turkish economy
has experienced, see Sunel (2011). Moreover, we also estimated an AR(1) for the money growth
process using M0 series. The parameters of the process are quite similar.
84
2.3.2 Findings
In the following subsections, we ?rst display the role of ?nancial accelerator by
comparing the usual cash-in-advance model with the model described in section 2.2.
We then compare the dynamics of negative TFP and positive money growth shocks
under two model economies with time-varying and ?xed RRR policies. Lastly, we
run a ?nancial crisis experiment, in which the net worth of banks are hit by a one-
time exogenous shock, and compare the implications of the two reserve requirement
regimes.
14
2.3.2.1 Amplifying E?ect of Financial Frictions
The dashed plots in ?gures 2.2 and 2.3 represent the monetary economy that
exhibits ?nancial accelerator mechanism and the straight plots represent the cash-
in-advance model with no ?nancial frictions. Required reserves ratio in the former
economy is set to zero to isolate the impact of ?nancial frictions.
Figure 2.2 below illustrates that the collapse in output, investment, price of
capital and loan-deposit spreads is ampli?ed when ?nancial frictions are in place.
We especially want to highlight the almost tripling increase in the reduction of
investment and asset prices and 250 basis points of increase in the credit spreads in
annualized terms. The last one is even more striking because in the economy with
no ?nancial frictions, there is no-arbitrage between return to capital and return
to deposits. The evident ampli?cation owes to the reduced demand of banks for
14
We also analyzed the case with zero reserve requirements policy. Since the dynamics are quite
similar to a ?xed RRR regime, we do not report those results, which are available upon request.
85
0 10 20 30 40
?1.8
?1.6
?1.4
?1.2
?1
Output
%
?
f
r
o
m
S
.
S
.
FA
DSGE
0 10 20 30 40
?4
?3.5
?3
?2.5
?2
?1.5
Investment
0 10 20 30 40
?0.4
?0.3
?0.2
?0.1
0
0.1
Price of Equity
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?50
0
50
100
150
200
250
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
Figure 2.2: Negative Productivity Shocks
86
0 10 20 30 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
FA
DSGE
0 10 20 30 40
?0.8
?0.6
?0.4
?0.2
0
Investment
0 10 20 30 40
?0.06
?0.04
?0.02
0
0.02
Price of Equity
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
0
5
10
15
20
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
Figure 2.3: Positive Money Growth Shocks
87
deposits in case of lower productivity. This stems from the decline in the return to
state-contingent equity issued by ?rms when productivity is lower. This depresses
the price of equity issued by ?rms and results in a collapse in the value of funds
provided to them. As a result, ?rms acquire less capital and investment declines
more.
Figure 2.3 illustrates the dynamics in response to a positive money growth
shock. An important feature of this cash-in-advance economy is that as equa-
tions (2.3) (with equality) and (2.5) illustrate, investment and leisure are cash and
credit goods, respectively. Therefore, when in?ation rises following a positive money
growth shock, labor supply and investment decreases causing a decline in output.
We again obtain ampli?ed responses of investment, asset prices, output and credit
spreads on impact following the shock. Yet, the trajectory of all variables except the
last appears to be similar to the economy with no ?nancial frictions. The ampli?ed
response of investment is coupled with larger degree of declines in asset prices and
credit spreads as in the case of TFP shocks. We also note that the quantitative
impact of monetary shocks are much smaller compared to TFP shocks.
We now analyze the implications of the RRR policy on the dynamics of real,
?nancial, and monetary variables. In ?gures 2.4 and 2.5, we compare the dynamics
of these variables in response to one standard deviation negative TFP and positive
money growth shocks. In ?gure 2.6 we explore the implications of RRR policy
on the dynamics model variables in a ?nancial crisis scenario. The speci?c ?nancial
disruption is a balance sheet shock that bankers face as in mostly recent literature.
15
15
Hancock, Laing and Wilcox (1995), Meh and Moran (2010), Brunnermeier and Pedersen
88
In ?gures 2.4 to 2.6, the dashed plots correspond to the benchmark econ-
omy with the countercyclical RRR rule and the straight plots correspond to an
economy with ?xed RRR. The dynamics of the economy with no reserves closely
resemble those with a ?xed RRR. Therefore for space considerations, we do not
discuss them here and only present the comparison of ?xed RRR economy with
the benchmark economy that displays a countercyclical RRR.
16
Unless otherwise is
stated, the numbers in the y-axes correspond to percentage deviations of variables
from their long-run values. For the case of in?ation and RRR, we plot percentage
“point changes” and for the case of credit spreads we plot “basis point changes” in
annualized terms. In addition, we explore the impact of implementing aggressive
credit policy rules by increasing the response parameter ?. In these experiments, as
anticipated, the impact of the time-varying RRR rule is enhanced when ? is larger.
17
(2009), Curdia and Woodford (2010), Mendoza and Quadrini (2010), Iacoviello (2010), and Mimir
(2011).
16
The dynamics of the economy with no reserves can be found in Appendix B.3.
17
Charts regarding policy intensity experiments can be found in Appendix B.4.
89
0 20 40
?2
?1.5
?1
?0.5
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy Fixed RR Ratio
0 20 40
?4
?3
?2
?1
0
1
Investment
0 20 40
0
0.5
1
1.5
2
2.5
Hours
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?6
?4
?2
0
2
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?2
0
2
4
Leverage
0 20 40
?2
?1.5
?1
?0.5
0
Bank Credit
0 20 40
?100
0
100
200
300
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?1.5
?1
?0.5
0
0.5
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
0
5
10
15
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
1.5
Inflation
Quarters
0 20 40
?25
?20
?15
?10
?5
0
Reserves
Quarters
Figure 2.4: Impulse Responses Led by a 1-? Adverse TFP Shock
9
0
2.3.2.2 Impulse Responses to TFP Shocks
The general observation that emerges from ?gure 2.4 is that the time-varying
RRR policy dampens the impact of the ?nancial accelerator on key macroeconomic
real and ?nancial variables at the expense of higher in?ation in response to TFP
shocks.
In the economy with ?xed RRR, as expected, households reduce their demand
for consumption and supply of deposits in response to the adverse TFP shock since
output and the pro?ts that accrue from the ownership of banks and capital producers
are lower. On the banks’ side, the reduced TFP highlights the reduction in the
pro?tability of equity loans to ?rms, inducing them to reduce their demand for
deposits.
Under ?xed RRR economy, as ?gure 2.4 shows, the net worth of banks collapse
by 4% re?ecting the feedback e?ect of a 0.6% decline in asset prices through the
endogenous capital constraint of banks, represented by equation (2.15). The decline
in net worth in accordance with the decline in deposits downsizes the total ?nancing
for non-?nancial ?rms (see ?gure 2.4). However, since the decline in bank capital
is larger than that of the value of bank assets, the model implies a countercyclical
bank leverage, which increases by 3.5%. On the other hand, the scarcity of funds
for ?rms shoots up loan-deposits spreads by about 250 basis points in annualized
terms (see the middle panel of ?gure 2.4). The reduction in the quantity of equities
traded and the collapse in asset prices trigger a downsizing in bank credit of about
0.75%. As a combined outcome of these dynamics, investment falls by 3.75% and
91
output declines by about 1.75%.
The nominal price level increases (the bottom panel of ?gure 2.4) because the
economy is now less productive in generating output. Hence, in?ation increases by
0.2 percentage points causing the real balances demand to decline and consumption
velocity of monetary base to increase by about 1%.
Now, we explain how the credit policy de?ned by a countercyclical RRR rule
mitigates the impact of the ?nancial accelerator on key macroeconomic real and
?nancial variables (see the dashed plots in ?gure 2.4). Since bank credit declines in
response to the adverse TFP shock, the policy rule implies a reduction in the RRR
by about 1 percentage point, which can be seen in the bottom panel of the ?gure.
This reduces the cost of extending credit for banks and induces a substitution from
reserves balances to loans in the asset side of their balance sheet. Consequently,
the stronger demand for ?rm equity stabilizes the price of it on impact, and the
peak of decline in equity price is about 0.2% less than how much it is in the ?xed
RRR economy. The substitution in the balance sheet of banks combined with the
better outlook of asset prices reduce the collapse in bank credit from 0.8% to 0.2%.
Accordingly, output and investment decline by 1.3% and 3.5% less than how much
they decline in the ?xed RRR economy.
The support of the central bank via lower reserve requirements cause credit
spreads to rise by about 150 basis points less compared to the ?xed RRR econ-
omy over 5 quarters. We emphasize this ?nding because credit spreads introduce
an intertemporal wedge to the savings decision of the aggregate economy and are
created by ?nancial frictions. The relatively muted response of spreads stems from
92
the reduced decline in return to ?rm equity. The stronger outlook of the economy
re?ects into the balance sheet of banks and bank capital declines by 4% less com-
pared to the ?xed RRR economy and even increases above its long-run level for 20
quarters, since RRR is lower than its long-run value for about 30 quarters. The
immediate implication of stronger trajectory of net worth is a rise of virtually zero
in bank leverage on impact (against a 3.25% hike with ?xed RRR) and even implies
a decline of it up to 2% caused by the increase in bank capital.
The substantial collapse in reserves demand (about 20%) drives down the price
of money and ampli?es the upwards response of in?ation obtained in the ?xed RRR
economy (see bottom panel of ?gure 2.4). However, since this immediate surge is
transitory and driven by the reserves policy, the model implies an undershooting of
in?ation in the coming 7 quarters. This implies a substitution of consumption for
leisure on the part of forward looking households and labor supply increases by 2%
more compared to the ?xed RRR economy. Hence, we obtain the stabilizing impact
of the countercyclical RRR rule on the dynamics of output displayed in the top
panel of ?gure 2.4. Consistent with these ?ndings, real balances demand collapses
on impact but outweighs its steady state level along the transition and consumption
velocity increases by 11% more than the ?xed RRR economy.
To sum up, we obtain the interesting result that the countercyclical RRR
policy mitigates the impact of ?nancial accelerator triggered by TFP shocks on
real and ?nancial variables at the expense of higher in?ation. Now, we explore the
dynamics driven by money growth shocks.
93
0 20 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy Fixed RR Ratio
0 20 40
?0.6
?0.4
?0.2
0
0.2
Investment
0 20 40
?0.3
?0.2
?0.1
0
0.1
Hours
0 20 40
?0.08
?0.06
?0.04
?0.02
0
0.02
Price of Equity
0 20 40
?0.6
?0.4
?0.2
0
0.2
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?0.1
0
0.1
0.2
0.3
0.4
Leverage
0 20 40
?0.1
?0.08
?0.06
?0.04
?0.02
0
Bank Credit
0 20 40
?5
0
5
10
15
20
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.06
?0.04
?0.02
0
0.02
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.5
0
0.5
1
1.5
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.1
0
0.1
0.2
0.3
Inflation
Quarters
0 20 40
?1.5
?1
?0.5
0
0.5
Reserves
Quarters
Figure 2.5: Impulse Responses Led by a 1-? Adverse Money Growth Shock
9
4
2.3.2.3 Impulse Responses to Money Growth Shocks
In this section, we analyze the dynamics of model economies in response to
a one-standard deviation positive money growth shock. Figure 2.5 displays the
impulse responses of key real, ?nancial and monetary variables. Although the impact
of a money growth shock on those variables is an order of magnitude smaller than
that of a productivity shock, these ?gures deliver the same message as in the previous
section that the time-varying RRR policy mitigates the adverse e?ects of money
growth shocks on real and ?nancial variables driven by the ?nancial accelerator
mechanism while creating higher in?ation rates compared to ?xed RRR policy.
We should ?rstly note that the dynamics of the model with ?xed required
reserves ratio policy strongly resemble the properties of a standard stochastic cash-
in-advance economy by Stockman (1981) and Cooley and Hansen (1989), which is
modi?ed to cover bank deposits in the cash-in-advance constraint. In this sense, we
follow the timing assumption of Cooley and Hansen (1989) that asset markets open
?rst for workers, but with the di?erence that b
t+1
is not necessarily (and actually
never) equal to zero, and higher rates of in?ation discourage household savings in
the form of deposits. In the end, the general mechanism in this basic model is
broadly summarized by the idea that an expansionary shock to the growth rate
of money supply raises in?ation rate and induces households to substitute credit
goods for cash goods. The re?ection of that mechanism to the current model is that
consumption and deposit savings decline and leisure demand increases as implied by
equations (2.3) and (2.5). Since deposit savings are intermediated to non-?nancial
95
?rms’ equity ?nancing, investment declines in response to a positive money growth
shock. Lower investment and the decline in labor supply then reduce output and
consumption.
In the ?xed RRR economy, in?ation rate increases by about 0.2% percentage
points on impact. This reduces hours worked by 0.25% since consumption and
deposits are the cash goods and leisure is the credit good. The fall in household
deposits leads to a reduction in bank credit in the form of equity purchases. As the
demand for non-?nancial ?rms’ shares decline, the price of equity falls by 0.07%.
The decline in equity prices causes bank net worth to shrink by 0.4% on impact,
leading to a rise in credit spreads by about 20 annualized basis points. Since the cost
of ?nancing capital expenditures is now higher for non-?nancial ?rms, investment
and output drop by 0.4% and 0.15%, respectively. In terms of monetary variables,
as in?ation rate rises, real money balances decrease and consumption velocity surges
by 0.4%.
When the central bank puts the credit policy to work, RRR declines about
0.06 percentage points as bank credit falls in response to a positive money growth
shock. There is an immediate decline of 1.25% in the reserves, and deposit demand
by banks. The reduced cost of extending credit induces banks to substitute away
their assets from reserves to ?rm equity, and accordingly the initial decline in bank
credit is 0.07% smaller. As equity purchases by banks are larger, the decline in
the price of equity on impact is totally eliminated in comparison to the ?xed RRR
policy. This is re?ected into the balance sheet of banks and intermediary capital
does not decline at all compared to a reduction of 0.45% in the ?xed RRR economy.
96
Furthermore, the rise in credit spreads are about 15 annualized basis points lower
and the stronger trajectory of bank net worth causes leverage to decline by 0.05%
over 5 quarters instead of an increase of about 0.4%. Since credit spreads are the
main source of intertemporal distortion caused by the credit frictions in ?nancial
sector, the central bank e?ectively mitigates the adverse impact of this distortion
on the economy via implementing a lower reserve requirement policy. As another
favorable result of these dynamics, investment falls by 0.3% less in the case of time-
varying reserve requirements.
The initial fall in reserves by 1.2% creates an excess supply of monetary base
in the economy and raises the in?ation rate by 0.25% percentage points to restore
equilibrium in the money market (see ?gure 2.5). Therefore the trade-o? between
price and ?nancial stability is still evident under money growth shocks. This causes
the real money demand to decline and consumption velocity of monetary base to
rise by 0.6% more. Lastly, we again obtain the undershooting of in?ation following
the ?rst period as opposed to the case with ?xed RRR. This feeds back into the
consumption-leisure margin of workers and hours decline by about 0.2% less com-
pared to the ?xed RRR economy. This results in stabilizing output on impact and
obtaining 0.1% less decline in it over 5 quarters when the rule is in place.
97
0 20 40
?2
?1.5
?1
?0.5
0
0.5
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy Fixed RR Ratio
0 20 40
?6
?4
?2
0
Investment
0 20 40
?3
?2
?1
0
1
Hours
0 20 40
?1
?0.5
0
0.5
Price of Equity
0 20 40
?15
?10
?5
0
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
0
2
4
6
8
10
Leverage
0 20 40
?1.5
?1
?0.5
0
Bank Credit
0 20 40
0
100
200
300
400
500
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?8
?6
?4
?2
0
2
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
Inflation
Quarters
0 20 40
?15
?10
?5
0
5
Reserves
Quarters
Figure 2.6: Impulse Responses Led by a 1-? Adverse Financial Shock
9
8
2.3.2.4 Financial Crisis Experiment and Credit Policy
The previous two sections illustrated that the macroprudential reserves policy
stabilizes key macroeconomic and ?nancial variables in response to conventional
shocks along the business cycle. In this section, we explore how countercyclical
reserve requirements perform during a ?nancial crisis. The speci?c experiment is
to consider an exogenous decline in the net worth of ?nancial intermediaries. This
shock crudely captures loan losses, asset write-downs or asset revaluations that we
observe in the recent ?nancial crisis. As stated in the Introduction, it might be
though of as a sharp reversal in the risk appetite of international investors, which
is an exogenous factor that threatens the ?nancial stability of a country such as
Turkey.
Although the initial decline in banks’ net worth that we introduce is exogenous,
there will be second round e?ects that endogenously trigger an adverse ?nancial
accelerator mechanism. The initial fall in the net worth reduces the amount of
bank credit that can be extended to non-?nancial ?rms as banks are not able to
compensate the decline in their internal ?nancing with households’ deposits. Since
non-?nancial ?rms ?nance their capital expenditures via bank credit, there will be
a drop in investment, and hence in the price of capital. The value of intermediary
capital depends on asset prices. The endogenous decline in asset prices leads to a
further deterioration in banks’ net worth, creating an adverse feedback loop of falling
aggregate demand, declining asset prices, and deteriorating intermediary balance
sheets.
99
Speci?cally, we consider an initiating disturbance of a 5% decline in the net
worth of ?nancial intermediaries. This disturbance will be a one-time shock and we
want to think of it as a rare event. We analyze the e?ects of this shock in the model
economy with ?xed RRR policy and then illustrate the mitigating e?ects of time-
varying RRR policy on real, ?nancial and monetary variables. Figure 2.6 shows the
impulse responses of real, ?nancial and monetary variables under di?erent policy
regimes.
In the economy with ?xed RRR, the negative net worth shock immediately
reduces bank capital by 11% on impact (see the middle panel of ?gure 2.6). Although
deposits rise due to banks’ increased demand for deposits to compensate the decline
in their internal ?nancing, the deterioration of bank capital causes total ?nancing by
?nancial intermediaries to shrink. This translates into a reduction in bank credit in
the form of equity purchases to ?rms by 1.2% on impact. As the demand for ?rms’
shares is lower, the price of equity falls by 1%. This ampli?es the exogenous impact
of the ?nancial shock via endogenous capital constraint of banks and explains the
substantial decline of 11% in the net worth. The decline in bank capital rises their
leverage by 10% on impact. Induced by the shortage in credit and collapse in asset
prices, credit spreads rise by 450 basis points in annualized terms. This in turn
causes ?rms to cut back their investment severely (by about 6%) due to lower bank
credit and higher cost of ?nancing.
The increase in bank deposits driven by banks’ e?ort to compensate for the
net worth loss increases reserves balances by 1% in the ?xed RRR economy. This
creates an excess demand for monetary base and in?ation declines on impact by 0.6
100
percentage points (see the bottom panel of ?gure 2.6). However, since the shock is
transitory, in?ation overshoots by 0.7 percentage points in the period that follows the
shock and workers’ expectations regarding the hike in future in?ation causes hours
to decline by 2.75% on impact. Therefore, output shrinks by 1.6% as shown in the
top panel of the ?gure. The dynamics of real balances demand and consumption
velocity of monetary base resemble the expected implication of the dynamics of
in?ation.
In the model economy with credit policy, the time-varying rule induces a fall
in the RRR of about 0.6 percentage points since bank credit declines in response to
the negative ?nancial shock. Reserves immediately drop by 11% and eliminate the
collapse in in?ation almost completely. Most importantly, the dynamics of reserves
moves in?ation in such a way to induce hours and accordingly output to increase
on impact (see the bottom and top panels of ?gure 2.6).
Following the reduced cost of making equity loans to ?rms, banks substitute
away their assets from reserves to ?rm equity, therefore the initial decline in bank
credit is 1% smaller. As the demand for ?rm equity is higher in the model with credit
policy, the 1% reduction in the price of equity is in the model economy with ?xed
RRR policy is almost totally eliminated. This reinforces the intermediary capital
via the leverage constraint and reduces the collapse in bank net worth by 5%. We
emphasize this ?nding that the macroprudential policy reduces the ampli?ed impact
of the ?nancial shock on bank capital by 50%. Accordingly, the rise in credit spreads
are 200 basis points lower in annualized terms and bank leverage increases by 5%
instead of 10%. As another favorable outcome, investment falls by 5% less than how
101
much it declines in the ?xed RRR economy over 5 quarters. To sum up, we obtain
the result that a macroprudential reserve requirements policy that has a ?rst order
impact on the balance sheet of ?nancial intermediaries is the most e?ective in the
event of a ?nancial turmoil.
For all shocks, the higher the intensity of required reserves policy, which is
measured by a larger ? parameter, the lower is the contraction in real macroeco-
nomic and ?nancial variables. Most importantly, the adverse hike in credit spreads,
which is the indicator of ?nancial frictions in this model economy are eliminated
to substantial degrees as the credit policy is implemented more aggressively. Ad-
ditionally, as expected, the in?ationary cost of macroprudential intervention is also
magni?ed as the policy becomes more intense.
Now we proceed to the next section in which we report the impact of coun-
tercyclical reserve requirement policy on the volatilities of key macroeconomic real
and ?nancial variables.
2.3.2.5 E?ects of Time-Varying RRR Policy on Volatilities
Table 2.2 below displays the volatilities of real and ?nancial variables when
TFP and money growth shocks are realized over su?ciently long simulations of
the model economy with three di?erent regimes: (i) ?xed RRR, (ii) a moderate
required reserve policy (? = 5.15), and (iii) an aggressive required reserve policy
(? = 10). As indicated in the table, the economy with a moderate credit policy
features lower volatilities in real variables such as output, consumption, investment
102
as well as in ?nancial variables such as bank credit, loan-deposit spread, and asset
prices, compared to the economy with a ?xed RRR policy. Column 4 of the table
shows that as the required reserve policy gets more aggressive, the volatilities of
output, consumption, investment, bank credit, loan-deposit spread, and asset prices
are even lower. We especially want to highlight the 50% decline in the volatilities of
credit spreads and leverage ratio, the 22% decline in the volatilities of investment
and asset prices, and 77% decline in the volatility of bank net worth when the
moderate credit policy is in place. Since volatilities over the business cycle are lower
under credit policy, we consider exploring welfare implications of it worthwhile.
Accordingly, in the following section, we carry out welfare comparisons of di?erent
reserve requirement policies. Finally, we emphasize that as the time-varying RRR
policy gets aggressive, in?ation volatility gets higher.
Table 2.2: Volatilities of Real and Financial Variables
Variable Fixed Reserves Credit Policy (? = 5.15) Credit Policy (? = 10)
Real Variables
Output 2.77 2.26 2.07
Consumption 1.59 1.47 1.41
Investment 6.01 4.70 4.22
Hours 0.35 2.44 2.62
Financial Variables
Credit 1.08 0.89 0.82
Deposits 1.22 1.76 2.57
Net Worth 4.35 1.24 1.31
Leverage Ratio 4.04 2.01 2.04
Credit Spread 0.28 0.14 0.12
Asset Prices 0.62 0.48 0.43
Monetary Variables
In?ation 0.18 0.27 0.37
103
2.3.2.6 Credit Policy and Welfare
Consider the time-varying reserve requirement policy, denoted by trp, and the
?xed reserve requirement policy, denoted by frp. We de?ne the welfare associated
with the time-invariant equilibrium given by the countercyclical reserve requirement
policy conditional on a particular state of the economy in period 0 as
V
trp
0
= E
0
?
t=0
?
t
U(c
trp
t
, l
trp
t
) (2.62)
where E
0
denotes conditional expectation over the initial state, and c
trp
t
and l
trp
t
stand for the contingent plans for consumption and leisure under the time-varying
reserve requirement policy. Similarly, the welfare associated with the time-invariant
equilibrium given by the ?xed reserve requirement policy conditional on a particular
state of the economy in period 0 as
V
frp
0
= E
0
?
t=0
?
t
U(c
frp
t
, l
frp
t
), (2.63)
where c
frp
t
and l
frp
t
stand for the contingent plans for consumption and leisure under
the ?xed reserve requirement policy.
We then compute consumption-based welfare gains for each alternative time-
varying reserve requirement policy (moderate or aggressive). Let ?
c
stand for the
welfare gain of adopting time-varying reserve requirement policy instead of the ?xed
one conditional on a particular state in period 0. We de?ne ?
c
as the proportional
increase of regime frp’s consumption plan that a household must demand to be as
104
well o? under policy regime trp. Therefore, ?
c
is implicitly de?ned by
V
trp
0
= E
0
?
t=0
?
t
U
_
(1 + ?
c
)c
frp
t
, l
frp
t
_
(2.64)
Hence, a positive value for ?
c
implies that the time-varying reserve requirement
policy is welfare superior to the ?xed reserve requirement policy.
In order to obtain accurate welfare rankings, we perform a second-order ap-
proximation to the policy functions and the welfare given by V
0
. It is very well-known
that welfare levels would be equal to each other under alternative policy regimes if
we conduct a ?rst-order approximation to the policy functions since the expected
value of endogenous variables would be equal to their non-stochastic steady state
levels across all alternative reserve policies. We then de?ne welfare in the following
recursive form to conduct a second-order approximation to V
0
:
V
0,t
= U(c
t
, l
t
) + ?E
t
V
0,t+1
. (2.65)
Schmitt-Grohe and Uribe (2006) show that V
0
can also be represented as
V
0,t
= V
0
+
1
2
?(V
0
) (2.66)
where V
0
is the level of welfare evaluated at the non-stochastic steady-state, and
?(V
0
) is the constant correction term, denoting the second-order derivative of the
policy function for V
0,t
with respect to the variance of shock processes. Therefore,
equation (2.66) is an approximation to the welfare V
0,t
, capturing the ?uctuations
105
of endogenous variables at the stochastic steady state.
We compare three di?erent policy regimes in terms of their welfare gains:
(i) a ?xed reserve requirement policy, frp, (ii) a moderate time-varying reserve
requirement policy (? = 5.15), mtrp and (iii) an aggressive time-varying reserve
requirement policy (? = 10), atrp. We ?nd that the welfare gain of the central
bank following mtrp rather than frp is 0.05% in consumption-equivalent welfare
terms. Moreover, the welfare gain of the central bank following atrp rather than
frp is 0.13% in consumption-equivalent welfare terms. These results indicate that
following an operational time-varying reserve requirement policy is always welfare
improving compared to an inactive reserve policy. Additionally, on quantitative
grounds, these welfare gains are non-trivial as far as closed economy models are
concerned.
2.4 Conclusion
There are certain advantages and drawbacks of using reserve requirements to
achieve ?nancial stability. The main advantages are (i) it is one of the two main
policy tools that most central banks can use, (ii) the central bank does not directly
face any costs since reserve requirements e?ectively alter the ?nancial sector’s own
balance sheet in order to provide liquidity to the system, and (iii) the central bank
can employ reserve requirements without requiring banks to have low-risk assets as
collateral, which is unlike the re-discount window. On the other hand, there are
some drawbacks of using reserve requirements, including (i) their role as a tax on
106
the banking sector, putting depository institutions at a competitive disadvantage
compared to unregulated ?nancial institutions, and (ii) they may lead to rise in the
credit spreads as they put additional costs on ?nancial intermediation. One can
assess the e?ectiveness of reserve requirements as a ?nancial stability tool through
their e?ects on credit spreads and bank credit to non-?nancial sector. Other things
being equal, we expect countercyclical implementation of reserve requirement ratios
to mitigate the decline in credit growth and accordingly moderate the rise in credit
spreads in economic downturns, and curb excessive credit growth in boom periods.
To that purpose, we build a quantitative monetary DSGE model with a bank-
ing sector that is subject to time-varying reserve requirements imposed by the central
bank and endogenous capital constraints due to an agency problem. We model re-
serve requirements as an exogenous policy rule that countercyclically responds to
credit growth in the ?nancial sector in a forward looking sense. We consider the
e?ects of three di?erent types of shocks: productivity, money growth and ?nancial
shocks. For each type of shock, we ?nd that the time-varying required reserve ra-
tio rule mitigates the negative e?ects of adverse shocks ampli?ed by the ?nancial
accelerator mechanism on real and ?nancial variables. In each case, it reduces the
intertemporal distortions created by the credit spread at the expense of generating
higher in?ation, pointing out the clear trade-o? between price stability and ?nancial
stability faced by many central banks nowadays. It also reduces the volatilities of
key variables such as output, consumption, investment, bank credit, loan spread
and asset prices, indicating the role of reserve requirements as a macroprudential
policy instrument. Finally, we ?nd that a time-varying reserve requirement policy
107
achieves a higher welfare than a ?xed reserve requirement policy.
This study illustrates that when ?nancial frictions are important, monetary
policy that adopts macroprudential reserve requirement ratios as an instrument
might have real e?ects even if there are no nominal or real rigidities. Our work is
also timely in the sense that academicians and policy makers are expressing their
doubts about in?ation targeting contemporaneously, and accordingly, quantity of
money has emerged as an explicit policy instrument.
There are several further research avenues: one can introduce liquidity shocks
in order to bring a microfoundation to holding reserves in order to rationalize the
optimality of positive reserve requirements. It might also be interesting to focus on
the tradeo? between price stability and ?nancial stability in a framework in which an
interest rate feedback rule is introduced under nominal rigidities such as Christiano
et al. (2005) and Smets and Wouters (2007). Lastly, it might also be worthwhile
to study an open economy model to explicitly consider the e?ects of international
capital ?ows in the design of required reserves policies.
108
Appendix A
A.1 Data Appendix
Quarterly seasonally-adjusted data on standard macroeconomic variables ex-
cept Hours are taken from the Federal Reserve Economic Data (FRED) of St. Louis
FED. Hours data are taken from Current Employment Statistics survey published
by the Bureau of Labor Statistics. GDP de?ator from NIPA accounts is used to
de?ate the time series of the nominal macro aggregates. Consumption is the sum of
“Personal consumption expenditures on nondurables” (PCND) and “Personal con-
sumption expenditures on services”. Investment is the sum of “Personal consump-
tion expenditures on durables” (PCDG) and “Gross private domestic investment”
(GPDI). GDP is the sum of Consumption and Investment. Hours is computed as
the multiplication of “average weekly hours in private sector” with “average number
of workers in private sector”. Quarterly time series of capital stock to obtain z
t
se-
ries are constructed using the approach described in the online appendix of Jermann
and Quadrini (2010).
Quarterly ?nancial time series of Bank assets and Bank liabilities are con-
structed using the monthly data on Assets and Liabilities of Commercial Banks in
the U.S. from Data Download Program of Statistical & Historical Database of the
Federal Reserve Board. Financial data at the FED board are seasonally-adjusted
but nominal. GDP de?ator from NIPA accounts is used to de?ate the ?nancial time
109
series. Bank assets are bank credit at the asset side of the balance sheet of the U.S.
commercial banks. Bank liabilities are deposits held at the U.S. commercial banks.
Quarterly time series of Loan spread are taken from Survey of Terms of Business
Lending from Statistical & Historical Database of the FED Board. Loan spread is
commercial and industrial loan spread over intended federal funds rate. Quarterly
deposit rates are constructed using monthly data on 3-month certi?cate of deposit
secondary market rate from FRED. The in?ation rate computed from GDP de?ator
is used to make nominal deposit rate data real.
Table A.1: Business Cycle Properties of Real and Financial Variables, Quarterly U.S.
Data, 1987.Q1-2007.Q1
Standard
Deviation x
t?4
x
t?3
x
t?2
x
t?1
xt x
t+1
x
t+2
x
t+3
x
t+4
Real Variables
Output 1.48 0.15 0.39 0.66 0.88 1.00 0.87 0.66 0.39 0.15
Consumption 0.44 -0.20 0.07 0.37 0.66 0.82 0.80 0.67 0.46 0.25
Investment 2.68 0.27 0.49 0.71 0.87 0.97 0.82 0.59 0.33 0.09
Hours 0.96 -0.01 0.19 0.43 0.65 0.83 0.89 0.83 0.68 0.44
Financial Variables
Bank credit 0.82 0.07 0.21 0.34 0.45 0.54 0.56 0.57 0.50 0.39
Deposits 0.83 0.09 0.00 -0.09 -0.19 -0.29 -0.37 -0.36 -0.31 -0.24
Net Worth 5.29 0.03 0.20 0.38 0.55 0.70 0.76 0.74 0.63 0.47
Leverage Ratio 5.99 0.00 -0.16 -0.34 -0.51 -0.65 -0.70 -0.68 -0.56 -0.39
Loan Spread 0.09 -0.18 -0.23 -0.32 -0.34 -0.35 -0.22 -0.17 -0.09 -0.03
a
Business cycle statistics in the table are based on HP-?ltered cyclical components of quarterly empirical time
series (smoothing parameter:1600).
b
The standard deviation of output is expressed in percent; standard deviations of the remaining variables are
normalized by the standard deviation of output (std(x)/std(GDP)).
c
The correlation coe?cients in bold font are the maximum ones in their respective rows.
110
A.2 Proofs
A.2.1 Proof of Proposition 1
Let’s conjecture that the bank’s franchise value is given by
V
jt
= ?
t
q
t
s
jt
+ ?
t
n
t
(A.1)
Comparing the conjectured solution for V
jt
to the expected discounted terminal net
worth yields the following expressions,
?
t
q
t
s
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
? r
t+1+i
)q
t+i
s
jt+i
] (A.2)
?
t
n
jt
= E
t
?
i=0
(1 ??)?
i
?
i+1
?
t,t+1+i
(1 + r
t+1+i
)n
jt+i
(A.3)
I write ?
t
and ?
t
recursively using the expression above. Let’s begin with ?
t
. To
ease the notation, let’s drop expectations for now.
?
t
=
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
? r
t+1+i
)x
t,t+i
] (A.4)
where x
t,t+i
=
q
t+i
s
jt+i
qts
jt
.
?
t
= (1 ? ?)??
t,t+1
(r
kt+1
?r
t+1
) +
?
i=1
(1 ??)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
? r
t+1+i
)x
t,t+i
]
(A.5)
111
?
t
= (1??)??
t,t+1
(r
kt+1
?r
t+1
)+??
t,t+1
?x
t,t+1
?
i=0
(1??)?
i+1
?
i+1
?
t+1,t+2+i
[(r
kt+2+i
? r
t+2+i
)x
t+1,t+1+i
]
(A.6)
The in?nite sum at the right-hand side of equation (A.6) is one period updated
version of equation (A.4), given by
?
t+1
=
?
i=0
(1 ? ?)?
i+1
?
i+1
?
t+1,t+2+i
[(r
kt+2+i
? r
t+2+i
)x
t+1,t+1+i
] (A.7)
where x
t+1,t+1+i
=
q
t+1+i
s
jt+1+i
q
t+1
s
jt+1
.
Hence, we can re-write (A.6) with the expectations as follows:
?
t
= E
t
[(1 ??)??
t,t+1
(r
kt+1
? r
t+1
) + ??
t,t+1
?x
t,t+1
?
t+1
] (A.8)
Let’s continue with ?
t
. To ease the notation, let’s drop expectations for now.
?
t
=
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
(1 + r
t+1+i
)z
t,t+i
(A.9)
where z
t,t+i
=
n
jt+i
n
jt
?
t
= (1 ? ?)??
t,t+1
(1 + r
t+1
) +
?
i=1
(1 ??)?
i
?
i+1
?
t,t+1+i
(1 + r
t+1+i
)z
t,t+i
(A.10)
112
?
t
= (1??)??
t,t+1
(1+r
t+1
)+??
t,t+1
?z
t,t+1
?
i=0
(1??)?
i+1
?
i+1
?
t+1,t+2+i
(1+r
t+2+i
)z
t+1,t+1+i
(A.11)
The in?nite sum at the right-hand size of equation (A.11) is one period updated
version of equation (A.9), given by
?
t+1
=
?
i=1
(1 ? ?)?
i+1
?
i+1
?
t+1,t+2+i
(1 + r
t+2+i
)z
t+1,t+1+i
(A.12)
where z
t+1,t+1+i
=
n
jt+1+i
n
jt+1
Hence, we can re-write equation (A.11) with the expectations as follows:
?
t
= E
t
[(1 ? ?)??
t,t+1
(1 + r
t+1
) + ??
t,t+1
?z
t,t+1
?
t+1
] (A.13)
A.2.2 Proof of Proposition 2
The pro?t maximization problem by a representative bank is given by
V
jt
= max
s
jt
E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
?r
t+1+i
)q
t+i
s
jt+i
+ (1 + r
t+1+i
)n
jt+i
]
(A.14)
s.t. V
jt
? ?q
t
s
jt
(µ
t
) (A.15)
where µ
t
is the Lagrange multiplier associated with the incentive compatibility con-
113
straint. Using the solution for V
jt
in Proposition 2, I can re-write the intermediary’s
maximization problem using the Lagrangian,
L = ?
t
q
t
s
jt
+ ?
t
n
jt
+ µ
t
[?
t
q
t
s
jt
+ ?
t
n
jt
??q
t
s
jt
] (A.16)
The ?rst order conditions w.r.t. s
jt
and µ
t
are given respectively by
(1 + µ
t
)?
t
q
t
= µ
t
?q
t
(A.17)
V
jt
??q
t
s
jt
= 0 (A.18)
Rearranging (A.17) gives us the following expression,
?
t
=
µ
t
?
(1 + µ
t
)
(A.19)
Therefore, we establish that the incentive compatibility constraint binds (µ
t
> 0)
as long as expected discounted marginal gain of increasing bank assets is positive.
Replacing the de?nition of ?
t
, we obtain
E
t
[(1 ??)??
t,t+1
(r
kt+1
? r
t+1
) + ??
t,t+1
?
q
t+1
s
jt+1
q
t
s
jt
?
t+1
] =
µ
t
?
(1 + µ
t
)
(A.20)
Imposing the steady-state, we get the following expression,
114
(1 ? ?)?(r
k
?r)
(1 ? ??)
=
µ?
(1 + µ)
(A.21)
Rearranging gives us
(r
k
? r) =
(1 ???)µ?
(1 ??)?(1 + µ)
(A.22)
As long as µ is positive, i.e. the incentive compatibility constraint binds, risk pre-
mium is positive. Since I solve the model using linear approximation around the
steady-state and the shocks are su?ciently small, the premium is always positive in
numerical simulations.
115
A.3 Business Cycle Statistics of Aggregate Financial Variables of the
whole U.S. Financial Sector
For interested readers, this section documents empirical cyclical properties of
aggregate measures of the leverage ratio, debt and equity of U.S. ?nancial ?rms and
of the credit spread using quarterly data for the period 1952-2009. In particular, I
compute standard business cycle statistics of the aggregate ?nancial variables, such
as their standard deviations, cross-correlations with output.
I use quarterly balance sheet data from the Flow of Funds Accounts of the
Federal Reserve Board.
1
The theoretical model described below treats the entire
?nancial intermediary sector as a group of identical institutions although there is
a considerable amount of heterogeneity among ?nancial institutions in terms of
both their functions and balance sheet structures. For example, some ?nancial
intermediaries such as private pension funds, mutual funds, retirement funds, are
?nanced only by equity while some others such as banks, security-brokers and dealers
use leverage extensively. In order to be consistent with the model, I only select
?nancial institutions that always carry some leverage.
I focus on both depository and non-depository ?nancial institutions. The de-
pository institutions are U.S. chartered commercial banks, savings institutions, and
credit unions. The non-depository institutions are issuers of asset-backed securities,
bank holding companies, security brokers and dealers, ?nance companies, insurance
1
Total ?nancial assets and total liabilities in the Flow of Funds Accounts are partly measured
at book values and may be di?erent from market values. The di?erences between book values
and market values are more likely to disappear when the balance sheet of a particular ?nancial
institution is marked to market and/or when total ?nancial assets or liabilities are short-term.
116
companies, funding corporations, and real estate investment trusts. These institu-
tions perform the majority of activity in the U.S. ?nancial sector as measured by
their total assets.
2
Liabilities are de?ned as the sum of “Total liabilities” of each
of the aforementioned depository and non-depository ?nancial institutions in the
U.S. ?nancial system, while Net Worth is de?ned as the sum of “Total ?nancial
assets” minus the sum of “Total liabilities” of the same institutions. Leverage ratio
is the ratio of Liabilities to Net Worth. Credit spread measure I use is the di?erence
between quarterly real return to capital and quarterly real deposit rate. Quarterly
real return to capital data are taken from Gomme et.al. (2011). Quarterly deposit
rate data is taken from Federal Reserve Economic Data (FRED) of St. Louis FED.
I use quarterly in?ation rate computed using GDP de?ator to make nominal deposit
rates real.
Quarterly ?nancial data are taken from the Flow of Funds Accounts (FFA)
of the Federal Reserve Board. Quarterly real data except Hours and deposit rate
data are taken from Federal Reserve Economic Data (FRED) of St. Louis FED.
Hours data are taken from Current Employment Statistics survey published by the
Bureau of Labor Statistics. The return to capital data are taken from Gomme et
al. (2011). This paper constructs an empirical measure of the return to capital
for the U.S., which directly corresponds to the de?nition of the return to capital
in this paper. The balance sheet data in the level tables of FFA are nominal and
2
The total assets of these institutions is 90% of the total assets of the U.S. ?nancial sector.
Moreover, our de?nition of U.S. ?nancial sector includes important marked based ?nancial insti-
tutions such as security broker&dealers, ?nance companies, asset backed security (ABS) issuers,
and commercial banks as Adrian and Shin (2009) suggest. They argue that the balance sheet
?uctuations of these institutions are important determinants of real ?uctuations.
117
are not seasonally adjusted. All ?nancial data are seasonally adjusted using Census
X12 and are de?ated using GDP de?ator. I use FFA coded level tables released on
March 10, 2011 when I refer to the balance sheet items of ?nancial sector. Financial
and real data sources for ?gures 1 and 2, and tables 1 and 2 are given below.
Liabilities are the sum of “Total liabilities” of each of the following ?nancial
institutions: U.S. chartered commercial banks (Table L.110, Line 23), savings in-
stitutions (Table L.114, Line 23), credit unions (Table L.115, Line 16), issuers of
asset-backed securities (Table L.126, Line 11), bank holding companies (Table L.112,
Line 11), security brokers and dealers (Table L.129, Line 13), ?nance companies (Ta-
ble L.127, Line 10), property-casualty insurance companies (Table L.116, Line 16),
life insurance companies (Table L.117, Line 16), funding corporations (Table L.130,
Line 12), and real estate investment trusts (Table L.128, Line 11).
Net Worth is the sum of “Total ?nancial assets” minus the sum of “Total
liabilities” of each of the following ?nancial institutions: U.S. chartered commercial
banks (Table L.110, Line 1 minus Line 23), savings institutions (Table L.114, Line 1
minus Line 23), credit unions (Table L.115, Line 1 minus Line 16), issuers of asset-
backed securities (Table L.126, Line 1 minus Line 11), bank holding companies
(Table L.112, Line 1 minus Line 11), security brokers and dealers (Table L.129, Line
1 minus Line 13), ?nance companies (Table L.127, Line 1 minus Line 10), property-
casualty insurance companies (Table L.116, Line 1 minus Line 16), life insurance
companies (Table L.117, Line 1 minus Line 16), funding corporations (Table L.130,
Line 1 minus Line 12), and real estate investment trusts (Table L.128, Line 1 minus
Line 11).
118
Leverage Ratio is is the ratio of Liabilities to Net Worth. Finally, Credit
Spread is computed as the di?erence between the quarterly return to capital and
the quarterly deposit rate.
Consumption is the sum of “Personal consumption expenditures on nondurables”
(PCND) and “Personal consumption expenditures on services”. Investment is the
sum of “Personal consumption expenditures on durables” (PCDG) and “Gross pri-
vate domestic investment” (GPDI). GDP is the sum of Consumption and Invest-
ment. Hours is computed as the multiplication of “average weekly hours in private
sector” with “average number of workers in private sector”.
Table A.2: Business Cycle Statistics, Quarterly U.S. Data, 1952-2009
GDP C I Leverage R. Liabilities Net Worth Credit Spread
Standard deviation (%) 1.97 0.89 5.56 5.33 2.16 5.76 0.22
Quarterly autocorrelation 0.83 0.86 0.82 0.74 0.92 0.79 0.75
GDP 1 0.54 0.96 -0.08 0.57 0.28 -0.56
C – 1 0.29 0.10 0.07 -0.08 -0.05
Correlation matrix I – – 1 -0.10 0.63 0.33 -0.62
Leverage R. – – – 1 -0.03 -0.92 0.14
Liabilities – – – – 1 0.40 -0.51
Net Worth – – – – – 1 -0.32
Credit Spread – – – – – 1
a
Business cycle statistics for GDP, consumption and investment are computed using quarterly data from FRED
database. Consumption is the sum of personal consumption expenditures on nondurables and services (PCND +
PCESV). Investment is the sum of personal consumption expenditures on durable goods and gross private domestic
investment (PCDG + GPDI). GDP is the sum of consumption and investment.
b
Business cycle statistics in the table are based on HP-?ltered cyclical components over the period 1952-2009.
c
The correlation coe?cients greater than 0.13 are statistically signi?cant at 5% signi?cance level.
Table A.1 presents business cycle statistics for the aggregate leverage ratio, ag-
gregate liabilities, and aggregate equity of U.S. ?nancial sector together with those
for the credit spread. The volatility of the leverage ratio is nearly 3 times larger
than that of output and is roughly equal to that of investment. Table 1 shows
that the ?nancial leverage ratio is acyclical. The contemporaneous correlation be-
tween the ?nancial leverage ratio and output is -0.08. The volatility of aggregate
119
equity is 3 times larger than that of output, while the volatility of aggregate debt is
roughly equal to that of output.
3
The contemporaneous correlation between aggre-
gate liabilities and output is 0.57 while that between aggregate equity and output
is 0.28, indicating that both series are procyclical.
4
Moreover, the contemporane-
ous correlation with between credit spread and GDP is -0.56, showing that it is
countercyclical.
Table A.3: Cross Correlations of Financial Variables with Lags and Leads of GDP
Variable Y
t?5
Y
t?4
Y
t?3
Y
t?2
Y
t?1
Y
t
Y
t+1
Y
t+2
Y
t+3
Y
t+4
Y
t+5
Liabilities 0.01 0.13 0.27 0.41 0.52 0.57 0.57 0.50 0.39 0.26 0.12
NetWorth 0.00 0.04 0.09 0.14 0.21 0.28 0.34 0.35 0.31 0.20 0.05
LeverageR. 0.00 0.00 0.00 0.00 -0.03 -0.08 -0.14 -0.18 -0.18 -0.10 0.00
Spread 0.28 0.17 0.03 -0.15 -0.34 -0.56 -0.67 -0.60 -0.46 -0.29 -0.11
a
See the footnote (b) in Table 2 for the construction of aggregate ?nancial variables.
b
Business cycle statistics in the table are based on HP-?ltered cyclical components over the period 1952-
2009.
c
The correlation coe?cients greater than 0.13 are statistically signi?cant at 5% signi?cance level.
Table A.2 displays the cross-correlations of ?nancial variables with di?erent
lags and leads of GDP. It shows that aggregate ?nancial variables lead business cy-
cles in the U.S. In particular, the ?nancial leverage ratio, equity and credit spread
lead output by three, two and one quarters, respectively. However, liabilities con-
temporaneously move with output.
The following facts emerge from the empirical analysis above: (1) Financial
3
Using the Flow of Funds database, Jermann and Quadrini (2009) shows that relative volatili-
ties of non-?nancial sector debt and equity to non?nancial business sector GDP are 1.29 and 1.05,
respectively.
4
Jermann and Quadrini (2009) ?nd that debt is countercyclical and equity is procyclical for
non-?nancial ?rms for the same time period. In addition, using Compustat database, Covas and
Den Haan (2006) shows that debt and equity issuance is procyclical for the majority of publicly
listed ?rms.
120
leverage ratio and equity are three times more volatile than output, liabilities are a
little more volatile than output, (2) liabilities and equity are procyclical, ?nancial
leverage ratio is acyclical, and credit spread is countercyclical, and (3) Financial
leverage ratio, equity and credit spread lead output by three, two and one quarters,
respectively, while liabilities contemporaneously move with output.
121
A.4 Alternative Measures of Financial Shocks
This section presents alternative measures of ?nancial shocks and the simula-
tion results of the benchmark models under these alternative measures. I label the
benchmark model presented in the text as Benchmark 1.
The ?rst alternative measure for ?
t
series is constructed using the charge-o?
and delinquency rates of all loans, the level of outstanding loans, and net worth of
U.S. commercial banks from the Federal Reserve Board:
?
t
=
(1 ?Loanlossrates) ? Outstandingloans
Networth
(A.23)
Then I construct the log-deviation of ?
t
series by linearly detrending the log
of these series over the period 1987.Q1-2010.Q4. The ?
t
series can be interpreted
as the level of recovery rates of loans as a percentage of net worth. These recovery
rates determine the level of credit conditions in the economy since banks’ ability to
extend loans to non-?nancial businesses depends on their level of net worth, which
can be seen from equation (1.20). Therefore, the innovations to ?
t
are shocks to
the recovery rates, hence to the level of ?nancial conditions in the economy. First, I
estimate a VAR(1) for both TFP series and this alternative measure of ?. However,
the cross-terms in the VAR coe?cient matrix are not statistically signi?cant at 5%
signi?cance level. Then I estimate two independent AR(1) processes for both series.
The resulting persistence of the ? series is ?
?
= 0.9690 and the standard deviation
of the shock is ?
?
= 0.003111. The levels of z
t
and ?
t
series and the innovations to
those series are plotted in Figure A.1. I label the model driven by both standard
122
productivity shock and this alternative measure of ?nancial shock as Benchmark 2.
The second alternative measure for ?
t
series is constructed by calibrating the
persistence, ?
?
, and the standard deviation of the shock, ?
?
, to match the persistence
and the volatility of net worth in the data. The resulting persistence is ?
?
= 0.55,
and the resulting standard deviation of the shock is ?
?
= 0.04. I label the model
driven by both standard productivity shock and this alternative measure of ?nancial
shock as Benchmark 3.
Finally, the third alternative measure for ?
t
series is constructed as in the main
text. However, this time I estimate a VAR(1) for both TFP and ? series instead of
estimating two independent AR(1) processes as follows:
_
¸
¸
¸
_
´ z
t+1
´ ?
t+1
_
¸
¸
¸
_
=
_
¸
¸
¸
_
?
z
?
z,?
?
?,z
?
?
_
¸
¸
¸
_
_
¸
¸
¸
_
´ z
t
´ ?
t
_
¸
¸
¸
_
+
_
¸
¸
¸
_
?
z,t+1
?
?,t+1
_
¸
¸
¸
_
.
The resulting parameters are ?
z
= 0.9467, ?
z,?
= -0.0142, ?
?,z
= 0.9129, ?
?
=
0.2824, ?
z
= 0.006378, and ?
?
= 0.0489. I assume that the shocks are i.i.d. as the
correlation coe?cient between the innovations is not statistically signi?cant at 5%
signi?cant level. I label the model driven by both standard productivity shock and
this alternative measure of ?nancial shock as Benchmark 4.
Table A.3 presents the business cycle properties of real and ?nancial variables
of four di?erent benchmark models under alternative ?nancial shock measures. The
table suggests that main results of the paper don’t change across under alternative
?nancial shock series: all of the benchmark models are able to reproduce the key
123
business cycle facts about real variables: consumption and hours are less volatile
than output, while investment is more volatile. Investment and hours are highly
procyclical. However, Benchmark 1, 3 and 4 generates a counterfactual negative or
zero correlation between consumption and output. Moreover, Benchmark 4 predicts
higher volatilities in real variables compared to other three models. In terms of
?nancial variables, all of the benchmark models can explain most of the key empirical
regularities about aggregate ?nancial variables: bank assets, deposits, and spread are
less volatile than output, while net worth and leverage ratio are more volatile. Assets
and net worth are procyclical, while leverage ratio and spread are countercyclical.
Benchmark 1 and 3 predict countercyclical deposits, consistent with the data, while
Benchmark 2 and 4 generate procyclical deposits, contrary to the data. Overall,
regardless of which ?nancial shock measure is taken, we can say that ?nancial shocks
help the theoretical model explain ?nancial ?uctuations better, while preserving
most of its predictions about real variables.
For interested readers, I also include the ?gures A.2 to A.9 that display the
quarterly time series of real variables in the data, in the standard RBC model with
capital adjustment costs, and in the benchmark model economies (2 and 4) and
that display the quarterly time series of ?nancial variables in the data, in the model
driven only by productivity shocks, and in the benchmark model economies (2 and
4).
124
-.06
-.04
-.02
.00
.02
.04
88 90 92 94 96 98 00 02 04 06 08 10
Level of productivity
-.03
-.02
-.01
.00
.01
.02
88 90 92 94 96 98 00 02 04 06 08 10
Level of omega
-.03
-.02
-.01
.00
.01
.02
88 90 92 94 96 98 00 02 04 06 08 10
Innovations to productivity
-.020
-.015
-.010
-.005
.000
.005
.010
88 90 92 94 96 98 00 02 04 06 08 10
Innovations to recovery rates
Figure A.1: Time Series of Shocks to Productivity and Credit Conditions
125
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 2
GDP
corr(data, rbc) = 0.65
corr (data, benchmark 2) = 0.86
-50
-40
-30
-20
-10
0
10
20
30
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 2
corr(data, rbc) = 0.72
corr(data, benchmark 2) = 0.83
Investment
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 2
corr(data, rbc) = 0.39
corr(data, benchmark 2) = 0.64
Hours
Figure A.2: Real Fluctuations: Benchmark 2 vs. RBC model
126
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
corr(data, only prod.) = 0.68
corr(data, benchmark 2) = 0.86
GDP
-50
-40
-30
-20
-10
0
10
20
30
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Investment
corr(data, only prod.) = 0.68
corr(data, benchmark 2) = 0.83
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Hours
corr(data, only prod.) = 0.33
corr(data, benchmark 2) = 0.64
Figure A.3: Real Fluctuations: Benchmark 2 vs. Only Productivity
127
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
GDP
corr(data, rbc) = 0.69
corr(data, only prod.) = 0.68
-40
-30
-20
-10
0
10
20
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Investment
corr(data, rbc) = 0.72
corr(data, only prod.) = 0.68
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
corr(data, rbc) = 0.39
corr(data, only prod.) = 0.33
Hours
Figure A.4: Real Fluctuations: RBC vs. Only Productivity with Benchmark 2
calibration
128
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Bank credit
corr(data, only prod.) = 0.60
corr(data, benchmark 2) = 0.31
-10
-8
-6
-4
-2
0
2
4
6
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Deposits
corr(data, only prod.) = 0.46
corr(data, benchmark 2) = 0.46
-80
-60
-40
-20
0
20
40
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
corr(data, only prod.) = 0.12
corr(data, benchmark 2) = 0.51
Net Worth
-60
-40
-20
0
20
40
60
80
100
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Leverage Ratio
corr(data, only prod.) = 0.03
corr(data, benchmark 2) = 0.44
-1
0
1
2
3
4
5
6
7
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Credit spread
corr(data, only prod.) = -0.10
corr(data, benchmark 2) = 0.32
-60
-40
-20
0
20
40
60
80
100
88 90 92 94 96 98 00 02 04 06 08 10
Survey of senior officers
Productivity shocks
Benchmark
Index of tightening credit conditions
corr(survey, prod) = 0.46
corr(survey, benchmark) = 0.53
Figure A.5: Financial Fluctuations: Benchmark 2 vs. Only Productivity
129
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 4
GDP
corr(data, rbc) = 0.69
corr(data, benchmark 4) = 0.77
-100
-80
-60
-40
-20
0
20
40
60
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 4
Investment
corr(data, rbc) = 0.72
corr(data, benchmark 4) = 0.81
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 4
Hours
corr(data, rbc) = 0.40
corr(data, benchmark 4) = 0.53
Figure A.6: Real Fluctuations: Benchmark 4 vs. RBC model
130
-15
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
GDP
corr(data, only prod.) = 0.73
corr(data, benchmark 4) = 0.77
-100
-80
-60
-40
-20
0
20
40
60
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Investment
corr(data, only prod.) = 0.79
corr(data, benchmark 4) = 0.81
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Hours
corr(data, only prod.) = 0.47
corr(data, benchmark 4) = 0.53
Figure A.7: Real Fluctuations: Benchmark 4 vs. Only Productivity
131
-15
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
GDP
corr(data, rbc) = 0.69
corr(data, only prod.) = 0.73
-100
-80
-60
-40
-20
0
20
40
60
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Investment
corr(data, rbc) = 0.72
corr(data, only prod.) = 0.80
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Hours
corr(data, rbc) = 0.40
corr(data, only prod.) = 0.47
Figure A.8: Real Fluctuations: RBC vs. Only Productivity with Benchmark 4
calibration
132
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Bank credit
corr(data, only prod.) = 0.81
corr(data, benchmark 4) = 0.80
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Deposits
corr(data, only prod.) = 0.48
corr(data, benchmark 4) = 0.62
-80
-60
-40
-20
0
20
40
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Net worth
corr(data, only prod.) = -0.01
corr(data, benchmark 4) = 0.69
-40
-20
0
20
40
60
80
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Leverage ratio
corr(data, only prod.) = 0.01
corr(data, benchmark 4) = 0.73
-4
-2
0
2
4
6
8
10
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Credit spread
corr(data, only prod.) = 0.07
corr(data, benchmark 4) = 0.36
Figure A.9: Financial Fluctuations: Benchmark 4 vs. Only Productivity
133
A.5 Model-Based Simulations of Macro-Financial Shocks using Utilization-
Adjusted TFP series
134
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
GDP
corr(data, only prod) = 0.52
corr(data, benchmark) = 0.77
-40
-30
-20
-10
0
10
20
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Investment
corr(data, only prod) = 0.31
corr(data, benchmark) = 0.70
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Hours
corr(data, only prod) = 0.21
corr(data, benchmark) = 0.63
Figure A.10: Real Fluctuations: Benchmark 1 vs. Only Productivity model
135
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
RBC
GDP
corr(data, rbc) = 0.54
corr(data, only prod) = 0.52
-40
-30
-20
-10
0
10
20
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
RBC
Investment
corr(data, rbc) = 0.39
corr(data, only prod) = 0.31
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
RBC
Hours
corr(data, rbc) = 0.29
corr(data, only prod) = 0.21
Figure A.11: Real Fluctuations: RBC vs. Only Productivity
136
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Bank credit
corr(data, only prod) = 0.12
corr(data, benchmark) = 0.49
-10
-8
-6
-4
-2
0
2
4
6
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Deposits
corr(data, only prod) = 0.57
corr(data, benchmark) = 0.57
-80
-60
-40
-20
0
20
40
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Net worth
corr(data, only prod) = 0.09
corr(data, benchmark) = 0.77
-40
-20
0
20
40
60
80
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Leverage Ratio
corr(data, only prod) = -0.07
corr(data, benchmark) = 0.73
-60
-40
-20
0
20
40
60
80
100
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Index of tightening credit standards
corr(data, only prod) = -0.38
corr(data, benchmark) = 0.16
Figure A.12: Financial Fluctuations: Benchmark 1 vs. Only Productivity
137
Table A.4: Real and Financial Statistics
Statistic Data Benchmark 1 Benchmark 2 Benchmark 3 Benchmark 4
?
Y
1.80 1.81 1.65 1.83 2.75
?
C
0.45 0.75 0.52 0.77 0.57
?
I
2.73 4.64 3.77 4.68 5.13
?
L
0.91 0.84 0.64 0.88 0.94
?
Y,I
0.97 0.87 0.92 0.88 0.97
?
Y,C
0.82 -0.03 0.34 -0.09 -0.70
?
Y,L
0.83 0.81 0.86 0.81 0.96
?
Assets
0.93 0.58 0.53 0.57 0.69
?
Deposits
0.69 0.87 0.44 0.74 0.74
?
NetWorth
5.17 5.90 2.10 5.17
?
4.21
?
LeverageR.
5.61 6.40 2.18 5.92 3.68
?
Spread
0.08 0.23 0.11 0.22 0.17
?
Y,Assets
0.30 0.88 0.91 0.87 0.86
?
Y,Deposits
-0.39 -0.23 0.48 -0.21 0.19
?
Y,NetWorth
0.52 0.68 0.82 0.67 0.70
?
Y,LeverageR.
-0.49 -0.71 -0.57 -0.66 -0.60
?
Y,Spread
-0.39 -0.67 -0.78 -0.70 -0.83
a
Business cycle statistics in the table are based on HP-?ltered cyclical components of quarterly simulated time series
(smoothing parameter:1600).
b
The standard deviation of output is expressed in percent; standard deviations of the remaining variables are normalized
by the standard deviation of output (std(x)/std(GDP)).
c ?
denotes calibration target.
138
Appendix B
B.1 Banks’ Pro?t Maximization Problem
Let’s conjecture that the bank’s franchise value is given by
V
jt
= ?
t
q
t
s
jt
+ ?
t
n
t
(B.1)
Comparing the conjectured solution for V
jt
to the expected discounted terminal net
worth yields the following expressions,
?
t
q
t
s
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
_
R
kt+1+i
?
_
R
t+1+i
?rr
t+i
1 ?rr
t+i
__
q
t+i
s
jt+i
(B.2)
?
t
n
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
_
R
t+1+i
? rr
t+i
1 ? rr
t+i
_
n
jt+i
(B.3)
Let’s ESP
t+i
stand for
_
R
kt+1+i
?
_
R
t+1+i
?rr
t+i
1?rr
t+i
__
and let’s RR
t+i
stand for
_
R
t+1+i
?rr
t+i
1?rr
t+i
_
.
Therefore,
?
t
q
t
s
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
ESP
t+i
q
t+i
s
jt+i
(B.4)
?
t
n
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
RR
t+i
n
jt+i
(B.5)
139
We write ?
t
and ?
t
recursively using the expressions above. Let’s begin with ?
t
. To
ease the notation, let’s drop expectations for now.
?
t
=
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
ESP
t+i
x
t,t+i
(B.6)
where x
t,t+i
=
q
t+i
s
jt+i
qts
jt
. Let’s separate (B.6) into two parts.
?
t
= (1 ? ?)??
t,t+1
ESP
t
+
?
i=1
(1 ? ?)?
i
?
i+1
?
t,t+1+i
ESP
t+i
x
t,t+i
(B.7)
Rearrange the second term at the right-hand size of the expression (B.7),
?
t
= (1??)??
t,t+1
ESP
t
+??
t,t+1
?x
t,t+1
?
i=0
(1??)?
i+1
?
i+1
?
t+1,t+2+i
ESP
t+1+i
x
t+1,t+1+i
(B.8)
The in?nite sum at the right-hand side of equation (B.8) is one period updated
version of equation (B.6), given by
?
t+1
=
?
i=0
(1 ? ?)?
i+1
?
i+1
?
t+1,t+2+i
ESP
t+1+i
x
t+1,t+1+i
(B.9)
where x
t+1,t+1+i
=
q
t+1+i
s
jt+1+i
q
t+1
s
jt+1
.
Hence, we can re-write (B.8) with the expectations as follows:
?
t
= E
t
[(1 ? ?)??
t,t+1
ESP
t
+ ??
t,t+1
?x
t,t+1
?
t+1
] (B.10)
140
Let’s continue with ?
t
. To ease the notation, let’s drop expectations for now.
?
t
=
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
RR
t+i
z
t,t+i
(B.11)
where z
t,t+i
=
n
jt+i
n
jt
. Let’s separate (B.11) into two parts.
?
t
= (1 ? ?)??
t,t+1
RR
t
+
?
i=1
(1 ??)?
i
?
i+1
?
t,t+1+i
RR
t+i
z
t,t+i
(B.12)
Rearrange the second term at the right-hand size of the expression (B.12),
?
t
= (1 ??)??
t,t+1
RR
t
+??
t,t+1
?z
t,t+1
?
i=0
(1 ??)?
i+1
?
i+1
?
t+1,t+2+i
RR
t+1+i
z
t+1,t+1+i
(B.13)
The in?nite sum at the right-hand size of equation (B.12) is one period updated
version of equation (B.10), given by
?
t+1
=
?
i=1
(1 ??)?
i+1
?
i+1
?
t+1,t+2+i
RR
t+1+i
z
t+1,t+1+i
(B.14)
where z
t+1,t+1+i
=
n
jt+1+i
n
jt+1
.
Hence, we can re-write equation (B.12) with the expectations as follows:
?
t
= E
t
[(1 ? ?)??
t,t+1
RR
t
+ ??
t,t+1
?z
t,t+1
?
t+1
] (B.15)
The pro?t maximization problem by a representative bank is given by
141
V
jt
= max
s
jt
E
t
?
i=0
(1 ??)?
i
?
i+1
?
t,t+1+i
ESP
t+i
q
t+i
s
jt+i
+ RR
t+i
n
jt+i
] (B.16)
s.t. V
jt
? ?q
t
s
jt
(µ
t
) (B.17)
where µ
t
is the Lagrange multiplier associated with the incentive compatibility con-
straint. Using the conjectured solution for V
jt
above, we can re-write the interme-
diary’s maximization problem using the Lagrangian,
L = ?
t
q
t
s
jt
+ ?
t
n
jt
+ µ
t
[?
t
q
t
s
jt
+ ?
t
n
jt
??q
t
s
jt
] (B.18)
The ?rst order conditions w.r.t. s
jt
and µ
t
are given respectively by
(1 + µ
t
)?
t
q
t
= µ
t
?q
t
(B.19)
V
jt
??q
t
s
jt
= 0 (B.20)
Rearranging (B.19) gives us the following expression,
?
t
=
µ
t
?
(1 + µ
t
)
(B.21)
Therefore, we establish that the incentive compatibility constraint binds (µ
t
> 0)
as long as expected discounted marginal gain of increasing bank assets is positive.
142
B.2 Impulse Responses under an Alternative RRR Policy Rule reacting to Current Credit Growth
1
4
3
0 10 20 30 40
?1.8
?1.6
?1.4
?1.2
?1
?0.8
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?1.4
?1.2
?1
?0.8
?0.6
Consumption
0 10 20 30 40
?4
?3
?2
?1
0
Investment
0 10 20 30 40
0
0.5
1
1.5
2
Hours
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?2
?1.5
?1
?0.5
0
Equity
0 10 20 30 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 10 20 30 40
?2.6
?2.4
?2.2
?2
?1.8
?1.6
Wage
Quarters
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?3
?2
?1
0
1
Ex?post Return to Capital
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?1
?0.5
0
0.5
Deposit Rate
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.1: The E?ect of Adverse TFP Shocks on Real Variables
1
4
4
0 10 20 30 40
?5
?4
?3
?2
?1
0
1
Net Worth
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?2.5
?2
?1.5
?1
?0.5
0
Deposits
0 10 20 30 40
?2
?1
0
1
2
3
4
Leverage
0 10 20 30 40
?1.8
?1.6
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
Bank Credit
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?50
0
50
100
150
200
250
300
Loan?Deposit Spread
Quarters
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
Figure B.2: The E?ect of Adverse TFP Shocks on Financial Variables
1
4
5
0 10 20 30 40
?8
?6
?4
?2
0
2
4
6
Real Balances
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
0
2
4
6
8
10
12
Velocity
0 10 20 30 40
?0.5
0
0.5
1
1.5
Inflation
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?25
?20
?15
?10
?5
0
Reserves
Quarters
Figure B.3: The E?ect of Adverse TFP Shocks on Monetary Variables
1
4
6
0 10 20 30 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.04
?0.03
?0.02
?0.01
0
Consumption
0 10 20 30 40
?0.5
?0.4
?0.3
?0.2
?0.1
0
Investment
0 10 20 30 40
?0.3
?0.2
?0.1
0
0.1
Hours
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.04
?0.03
?0.02
?0.01
0
Equity
0 10 20 30 40
?0.1
?0.05
0
0.05
0.1
Price of Equity
0 10 20 30 40
?0.05
0
0.05
0.1
0.15
Wage
Quarters
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.4
?0.2
0
0.2
0.4
Ex?post Return to Capital
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.05
0
0.05
0.1
0.15
Deposit Rate
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.4: The E?ect of Adverse Money Growth Shocks on Real Variables
1
4
7
0 10 20 30 40
?0.6
?0.5
?0.4
?0.3
?0.2
?0.1
0
0.1
Net Worth
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.07
?0.06
?0.05
?0.04
?0.03
?0.02
?0.01
0
Deposits
0 10 20 30 40
?0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Leverage
0 10 20 30 40
?0.1
?0.08
?0.06
?0.04
?0.02
0
Bank Credit
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?5
0
5
10
15
20
25
Loan?Deposit Spread
Quarters
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.06
?0.05
?0.04
?0.03
?0.02
?0.01
0
0.01
0.02
Required Reserves Ratio
Quarters
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.5: The E?ect of Adverse Money Growth Shocks on Financial Variables
1
4
8
0 10 20 30 40
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
Real Balances
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.2
0
0.2
0.4
0.6
0.8
1
1.2
Velocity
0 10 20 30 40
?0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Inflation
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
Reserves
Quarters
Figure B.6: The E?ect of Adverse Money Growth Shocks on Monetary Variables
1
4
9
0 10 20 30 40
?2
?1.5
?1
?0.5
0
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.2
?0.1
0
0.1
0.2
0.3
Consumption
0 10 20 30 40
?8
?6
?4
?2
0
Investment
0 10 20 30 40
?4
?3
?2
?1
0
1
Hours
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.5
?0.4
?0.3
?0.2
?0.1
0
Equity
0 10 20 30 40
?1.5
?1
?0.5
0
0.5
Price of Equity
0 10 20 30 40
?0.5
0
0.5
1
1.5
Wage
Quarters
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?6
?4
?2
0
2
4
Ex?post Return to Capital
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?1
0
1
2
3
4
Deposit Rate
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.7: The E?ect of Adverse Financial Shocks on Real Variables
1
5
0
0 10 20 30 40
?14
?12
?10
?8
?6
?4
?2
0
Net Worth
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.4
?0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Deposits
0 10 20 30 40
0
2
4
6
8
10
12
Leverage
0 10 20 30 40
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
Bank Credit
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
0
100
200
300
400
500
600
Loan?Deposit Spread
Quarters
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.6
?0.5
?0.4
?0.3
?0.2
?0.1
0
0.1
Required Reserves Ratio
Quarters
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.8: The E?ect of Adverse Financial Shocks on Financial Variables
1
5
1
0 10 20 30 40
?2
0
2
4
6
8
10
Real Balances
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?8
?6
?4
?2
0
2
Velocity
0 10 20 30 40
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
0.6
0.8
Inflation
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?12
?10
?8
?6
?4
?2
0
2
Reserves
Quarters
Figure B.9: The E?ect of Adverse Financial Shocks on Monetary Variables
1
5
2
B.3 Impulse Responses under Zero RRR Policy
1
5
3
0 20 40
?2
?1.5
?1
?0.5
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy (phi = 5.15) Fixed RR Ratio No Reserves
0 20 40
?4
?3
?2
?1
0
Investment
0 20 40
0
0.5
1
1.5
2
2.5
Hours
0 20 40
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?3
?2
?1
0
1
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?4
?2
0
2
4
Leverage
0 20 40
?2
?1.5
?1
?0.5
0
Bank Credit
0 20 40
?100
0
100
200
300
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?1.5
?1
?0.5
0
0.5
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
0
5
10
15
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
1.5
Inflation
Quarters
0 20 40
?25
?20
?15
?10
?5
0
Reserves
Quarters
Figure B.10: Impulse Responses Led by a 1-? Adverse TFP Shock
1
5
4
0 20 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy (phi = 5.15) Fixed RR Ratio No Reserves
0 20 40
?0.6
?0.4
?0.2
0
0.2
Investment
0 20 40
?0.3
?0.2
?0.1
0
0.1
Hours
0 20 40
?0.06
?0.04
?0.02
0
0.02
Price of Equity
0 20 40
?0.4
?0.3
?0.2
?0.1
0
0.1
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?0.1
0
0.1
0.2
0.3
Leverage
0 20 40
?0.08
?0.06
?0.04
?0.02
0
Bank Credit
0 20 40
?5
0
5
10
15
20
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.06
?0.04
?0.02
0
0.02
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.5
0
0.5
1
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.1
0
0.1
0.2
0.3
Inflation
Quarters
0 20 40
?1.5
?1
?0.5
0
0.5
Reserves
Quarters
Figure B.11: Impulse Responses Led by a 1-? Adverse Money Growth Shock
1
5
5
0 20 40
?3
?2
?1
0
1
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy (phi = 5.15) Fixed RR Ratio No Reserves
0 20 40
?8
?6
?4
?2
0
2
Investment
0 20 40
?4
?3
?2
?1
0
1
Hours
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?10
?8
?6
?4
?2
0
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
0
2
4
6
8
10
Leverage
0 20 40
?1
?0.8
?0.6
?0.4
?0.2
0
Bank Credit
0 20 40
0
100
200
300
400
500
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.6
?0.4
?0.2
0
0.2
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?8
?6
?4
?2
0
2
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
Inflation
Quarters
0 20 40
?15
?10
?5
0
5
Reserves
Quarters
Figure B.12: Impulse Responses Led by a 1-? Adverse Financial Shock
1
5
6
B.4 Policy Intensity Experiments
1
5
7
0 20 40
?2
?1.5
?1
?0.5
Output
%
?
f
r
o
m
S
.
S
.
Moderate Credit Policy (phi = 5.15) Fixed RR Ratio Aggressive Credit Policy (phi=10)
0 20 40
?4
?3
?2
?1
0
Investment
0 20 40
0
0.5
1
1.5
2
2.5
Hours
0 20 40
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?3
?2
?1
0
1
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?3
?2
?1
0
1
2
3
Leverage
0 20 40
?2
?1.5
?1
?0.5
0
Bank Credit
0 20 40
?50
0
50
100
150
200
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?2
?1.5
?1
?0.5
0
0.5
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
0
5
10
15
20
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
1.5
2
Inflation
Quarters
0 20 40
?40
?30
?20
?10
0
Reserves
Quarters
Figure B.13: Impulse Responses Led by a 1-? Adverse TFP Shock
1
5
8
0 20 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
Moderate Credit Policy (phi = 5.15) Fixed RR Ratio Aggressive Credit Policy (phi=10)
0 20 40
?0.6
?0.4
?0.2
0
0.2
Investment
0 20 40
?0.3
?0.2
?0.1
0
0.1
Hours
0 20 40
?0.05
?0.04
?0.03
?0.02
?0.01
0
0.01
Price of Equity
0 20 40
?0.4
?0.3
?0.2
?0.1
0
0.1
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?0.1
0
0.1
0.2
0.3
Leverage
0 20 40
?0.08
?0.06
?0.04
?0.02
0
Bank Credit
0 20 40
?5
0
5
10
15
20
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.08
?0.06
?0.04
?0.02
0
0.02
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.5
0
0.5
1
1.5
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.1
0
0.1
0.2
0.3
Inflation
Quarters
0 20 40
?1.5
?1
?0.5
0
0.5
Reserves
Quarters
Figure B.14: Impulse Responses Led by a 1-? Adverse Money Growth Shock
1
5
9
0 20 40
?2
?1.5
?1
?0.5
0
0.5
Output
%
?
f
r
o
m
S
.
S
.
Moderate Credit Policy (phi = 5.15) Fixed RR Ratio Aggressive Credit Policy (phi=10)
0 20 40
?8
?6
?4
?2
0
2
Investment
0 20 40
?3
?2
?1
0
1
Hours
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?10
?8
?6
?4
?2
0
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
0
2
4
6
8
10
Leverage
0 20 40
?1
?0.8
?0.6
?0.4
?0.2
0
Bank Credit
0 20 40
0
100
200
300
400
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?8
?6
?4
?2
0
2
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
Inflation
Quarters
0 20 40
?15
?10
?5
0
5
Reserves
Quarters
Figure B.15: Impulse Responses Led by a 1-? Adverse Financial Shock
1
6
0
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doc_961185648.pdf
The term business cycle (or economic cycle) refers to economy-wide fluctuations in production, trade and economic activity in general over several months or years in an economy organized on free-enterprise principles.
ABSTRACT
Title of dissertation: ESSAYS ON FINANCIAL INTERMEDIARIES,
BUSINESS CYCLES AND
MACROPRUDENTIAL POLICIES
Yasin Mimir, Doctor of Philosophy, 2012
Dissertation directed by: Professor S. Boragan Aruoba
Department of Economics
This study conducts a quantitative analysis of the role of ?nancial shocks and
credit frictions a?ecting the banking sector in driving business cycles as well as the
role of reserve requirements as a macroprudential policy tool. In the ?rst chapter,
I ?rst empirically document three stylized business cycle facts of aggregate ?nan-
cial variables in the U.S. commercial banking sector for the period 1987-2010: (i)
Bank credit, deposits and loan spread are less volatile than output, while net worth
and leverage ratio are more volatile, (ii) bank credit and net worth are procyclical,
while deposits, leverage ratio and loan spread are countercyclical, and (iii) ?nan-
cial variables lead the output ?uctuations by one to three quarters. I then present
an equilibrium business cycle model with a ?nancial sector, featuring a moral haz-
ard problem between banks and its depositors, which leads to endogenous capital
constraints for banks in obtaining funds from households. Credit frictions in bank-
ing sector are modeled as in Gertler and Karadi (2011). The model incorporates
empirically-disciplined shocks to bank net worth (i.e. “?nancial shocks”) that al-
ter the ability of banks to borrow and to extend credit to non-?nancial businesses.
The model is calibrated to U.S. data from 1987 to 2010. I show that the bench-
mark model driven by both standard productivity and ?nancial shocks is able to
deliver most of the stylized facts about real and ?nancial variables simultaneously.
Financial shocks and credit frictions in banking sector are important not only for
explaining the dynamics of aggregate ?nancial variables but also for the dynamics
of standard macroeconomic variables. Financial shocks play a major role in driving
real ?uctuations due to their strong impact on the tightness of bank capital con-
straint and credit spread, which eventually a?ect the saving-investment nexus of the
economy. Finally, the tightness of bank capital constraint given by the Lagrange
multiplier in the theoretical model (which determines the banks’ ability to extend
credit to non-?nancial ?rms) tracks the index of tightening credit standards (which
shows the adverse changes in banks’ lending) constructed by the Federal Reserve
Board quite well.
The second chapter (coauthored with Enes Sunel and Temel Ta¸sk?n) under-
takes a quantitative investigation of the role of reserve requirements as a credit
policy tool. We build a monetary DSGE model with a banking sector in which
(i) an agency problem between households and banks leads to endogenous capital
constraints for banks in obtaining funds from households, (ii) banks are subject to
time-varying reserve requirements that countercyclically respond to expected credit
growth, (iii) households face cash-in-advance constraints, requiring them to hold
real balances, and (iv) standard productivity and money growth shocks are two
sources of aggregate uncertainty. We calibrate the model to the Turkish economy
which is representative of using reserve requirements as a macroprudential policy
tool recently. We also consider the impact of ?nancial shocks that a?ect the net
worth of ?nancial intermediaries. We ?nd that (i) the time-varying required reserve
ratio rule mitigates the negative e?ects of the ?nancial accelerator mechanism trig-
gered by adverse macroeconomic and ?nancial shocks, (ii) in response to TFP and
money growth shocks, countercyclical reserves policy reduces the volatilities of key
real macroeconomic and ?nancial variables compared to ?xed reserves policy over
the business cycle, and (iii) an operational time-varying reserve requirement policy
is welfare superior to a ?xed reserve requirement policy. The credit policy is most
e?ective when the economy is hit by a ?nancial shock. Time-varying required re-
serves policy reduces the intertemporal distortions created by the credit spreads at
expense of generating higher in?ation volatility, indicating an interesting trade-o?
between price stability and ?nancial stability.
ESSAYS ON FINANCIAL INTERMEDIARIES,
BUSINESS CYCLES AND MACROPRUDENTIAL POLICIES
by
Yasin Mimir
Dissertation submitted to the Faculty of the Graduate School of the
University of Maryland, College Park in partial ful?llment
of the requirements for the degree of
Doctor of Philosophy
2012
Advisory Committee:
Professor S. Boragan Aruoba, Chair/Advisor
Professor Pablo D’Erasmo
Professor Anton Korinek
Professor Enrique G. Mendoza
Professor Phillip L. Swagel
c Copyright by
Yasin Mimir
2012
Dedication
To my love, Meryem.
ii
Acknowledgments
I owe my gratitude to my advisors Professor Boragan Aruoba and Professor
Sanjay Chugh without whom this dissertation could not have been possible.
First and foremost, I would like to thank my committee chair, Boragan Aruoba,
for his encouragement, endless support and guidance from the beginning of my
research journey. Sanjay Chugh pushed me to delve in studying the question at
hand. I cannot overstate my gratitude for his enlightening comments, con?dence
and continual support. They have always made themselves available for numerous
meetings that took their valuable times.
I would also like to thank Professor Enrique Mendoza who honored me by being
in my committee. My warm thanks are to due to my other advisors Professor Pablo
D’Erasmo and Professor Anton Korinek for their guidance and inspiring advice. I am
also grateful to Professor Phillip L. Swagel for agreeing to serve on my dissertation
committee.
I am also thankful to the Board of Governors of the Federal Reserve System for
?nancial support and for hosting me during part of my dissertation. My dissertation
bene?ted greatly from their support.
I am grateful to my colleagues Enes Sunel and Salih Fendoglu who are also
my great friends, for their help and support. Without their cordial companionship,
it would be much more di?cult to complete this dissertation. I am looking forward
to working closely with them in the future research projects. Enes was also a
wonderful roommate with whom I have interesting, enlightening, and entertaining
iii
conversations on numerous subjects. Salih was also a great classmate and roommate
with whom I have the strength to cope with the challenges in my doctoral journey.
I would like to thank the sta? members of the Department of Economics,
Vickie Fletcher, Elizabeth Martinez and Terry Davis for their technical help and
logistical support during my ?ve years at the department.
It is di?cult to overstate my special thanks to my wonderful neighbors Ali
Fuad Selvi, Bengu Caliskan Selvi and Bedrettin Yazan whose friendship has been
an excellent gift. Without their encouragement and enormous support, I cannot
imagine how hard it would be to complete this task. I treasure the moments we all
shared. I also want to thank my dear friends Ferhan Ture and Elif Ture for their
warm friendship.
Finally and most importantly, I owe my deepest thanks to my parents Omer
Mimir and Munevver Mimir as well as my elder sisters Remziye Mimir and Yasemin
Mimir and my elder brother Mustafa Mimir. I would not be able to thank them
enough for always believing in me, helping me pursue my dreams, their unconditional
love and understanding. I would like to show my gratitude to my precious family
for patiently excusing my absence for long years.
My love, Meryem, the re?ection of my soul, I could not imagine my life without
you.
iv
Table of Contents
List of Tables vii
List of Figures viii
List of Abbreviations x
1 Financial Intermediaries, Credit Shocks, and Business Cycles 1
1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Real and Financial Fluctuations in the U.S. economy . . . . . . . . . 8
1.3 A Business Cycle Model with Financial Sector . . . . . . . . . . . . 12
1.3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
1.3.2 Financial Intermediaries . . . . . . . . . . . . . . . . . . . . . 15
1.3.2.1 Balance Sheets . . . . . . . . . . . . . . . . . . . . . 15
1.3.2.2 Pro?t Maximization . . . . . . . . . . . . . . . . . . 17
1.3.2.3 Leverage Ratio and Net Worth Evolution . . . . . . 19
1.3.3 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
1.3.4 Capital Producers . . . . . . . . . . . . . . . . . . . . . . . . . 27
1.3.5 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . 28
1.4 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
1.4.1 Functional Forms, Parametrization and Calibration . . . . . . 31
1.4.2 Long-Run Equilibrium of the Model . . . . . . . . . . . . . . . 35
1.4.3 Intermediary Capital and the Transmission of Shocks . . . . . 38
1.4.3.1 Impulse Responses to TFP Shocks . . . . . . . . . . 38
1.4.3.2 Impulse Responses to Financial Shocks . . . . . . . . 42
1.4.4 Business Cycle Dynamics . . . . . . . . . . . . . . . . . . . . . 43
1.5 Model-Based Simulations of Macro-Financial Shocks vs. U.S. Data . . 46
1.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
2 Required Reserves as a Credit Policy Tool
(joint with Enes Sunel and Temel Ta¸sk?n) 56
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
2.2 The Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.2.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
2.2.2 Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
2.2.3 Firms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
2.2.4 Capital Producers . . . . . . . . . . . . . . . . . . . . . . . . . 75
2.2.5 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
2.2.6 Competitive Equilibrium . . . . . . . . . . . . . . . . . . . . . 78
2.3 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.3.1 Functional Forms . . . . . . . . . . . . . . . . . . . . . . . . . 81
2.3.2 Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
2.3.2.1 Amplifying E?ect of Financial Frictions . . . . . . . 85
2.3.2.2 Impulse Responses to TFP Shocks . . . . . . . . . . 91
v
2.3.2.3 Impulse Responses to Money Growth Shocks . . . . 95
2.3.2.4 Financial Crisis Experiment and Credit Policy . . . . 99
2.3.2.5 E?ects of Time-Varying RRR Policy on Volatilities . 102
2.3.2.6 Credit Policy and Welfare . . . . . . . . . . . . . . . 104
2.4 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
A 109
A.1 Data Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
A.2 Proofs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 111
A.2.1 Proof of Proposition 1 . . . . . . . . . . . . . . . . . . . . . . 111
A.2.2 Proof of Proposition 2 . . . . . . . . . . . . . . . . . . . . . . 113
A.3 Business Cycle Statistics of Aggregate Financial Variables of the
whole U.S. Financial Sector . . . . . . . . . . . . . . . . . . . . . . . 116
A.4 Alternative Measures of Financial Shocks . . . . . . . . . . . . . . . . 122
A.5 Model-Based Simulations of Macro-Financial Shocks using Utilization-
Adjusted TFP series . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
B 139
B.1 Banks’ Pro?t Maximization Problem . . . . . . . . . . . . . . . . . . 139
B.2 Impulse Responses under an Alternative RRR Policy Rule reacting
to Current Credit Growth . . . . . . . . . . . . . . . . . . . . . . . . 143
B.3 Impulse Responses under Zero RRR Policy . . . . . . . . . . . . . . . 153
B.4 Policy Intensity Experiments . . . . . . . . . . . . . . . . . . . . . . . 157
Bibliography 161
vi
List of Tables
1.1 Business Cycle Properties of Real and Financial Variables, Quarterly U.S.
Data, 1987- 2010 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
1.2 The Sequence of Events in a Given Time Period . . . . . . . . . . . . 12
1.3 Model Parameterization and Calibration . . . . . . . . . . . . . . . . 32
1.4 Real and Financial Statistics . . . . . . . . . . . . . . . . . . . . . . . 45
2.1 Paremeter Values in the Benchmark Model . . . . . . . . . . . . . . . 83
2.2 Volatilities of Real and Financial Variables . . . . . . . . . . . . . . . 103
A.1 Business Cycle Properties of Real and Financial Variables, Quarterly U.S.
Data, 1987.Q1-2007.Q1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 110
A.2 Business Cycle Statistics, Quarterly U.S. Data, 1952-2009 . . . . . . . 119
A.3 Cross Correlations of Financial Variables with Lags and Leads of GDP120
A.4 Real and Financial Statistics . . . . . . . . . . . . . . . . . . . . . . . 138
vii
List of Figures
1.1 Financial Flows in the U.S. Economy . . . . . . . . . . . . . . . . . . 9
1.2 Time Series of Shocks to Productivity and Credit Conditions . . . . . 34
1.3 Long-run equilibrium as a function of fraction of diverted funds by
bankers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
1.4 Impulse responses to a negative one-standard-deviation productivity
shock . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
1.5 Impulse responses to a negative one-standard-deviation net worth shock 41
1.6 Real Fluctuations: Benchmark vs. RBC model . . . . . . . . . . . . . 47
1.7 Real Fluctuations: Benchmark vs. Only Productivity . . . . . . . . . 49
1.8 Real Fluctuations: RBC vs. Only Productivity . . . . . . . . . . . . . 50
1.9 Financial Fluctuations: Benchmark vs. Only Productivity . . . . . . 52
1.10 Tightness of Credit Conditions in the Benchmark Model . . . . . . . 53
2.1 Evolution of Required Reserve Ratios in Turkey . . . . . . . . . . . . 58
2.2 Negative Productivity Shocks . . . . . . . . . . . . . . . . . . . . . . 86
2.3 Positive Money Growth Shocks . . . . . . . . . . . . . . . . . . . . . 87
2.4 Impulse Responses Led by a 1-? Adverse TFP Shock . . . . . . . . . 90
2.5 Impulse Responses Led by a 1-? Adverse Money Growth Shock . . . 94
2.6 Impulse Responses Led by a 1-? Adverse Financial Shock . . . . . . . 98
A.1 Time Series of Shocks to Productivity and Credit Conditions . . . . . 125
A.2 Real Fluctuations: Benchmark 2 vs. RBC model . . . . . . . . . . . . 126
A.3 Real Fluctuations: Benchmark 2 vs. Only Productivity . . . . . . . . 127
A.4 Real Fluctuations: RBC vs. Only Productivity with Benchmark 2
calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128
A.5 Financial Fluctuations: Benchmark 2 vs. Only Productivity . . . . . 129
A.6 Real Fluctuations: Benchmark 4 vs. RBC model . . . . . . . . . . . . 130
A.7 Real Fluctuations: Benchmark 4 vs. Only Productivity . . . . . . . . 131
A.8 Real Fluctuations: RBC vs. Only Productivity with Benchmark 4
calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 132
A.9 Financial Fluctuations: Benchmark 4 vs. Only Productivity . . . . . 133
A.10 Real Fluctuations: Benchmark 1 vs. Only Productivity model . . . . 135
A.11 Real Fluctuations: RBC vs. Only Productivity . . . . . . . . . . . . . 136
A.12 Financial Fluctuations: Benchmark 1 vs. Only Productivity . . . . . 137
B.1 The E?ect of Adverse TFP Shocks on Real Variables . . . . . . . . . 144
B.2 The E?ect of Adverse TFP Shocks on Financial Variables . . . . . . . 145
B.3 The E?ect of Adverse TFP Shocks on Monetary Variables . . . . . . 146
B.4 The E?ect of Adverse Money Growth Shocks on Real Variables . . . 147
B.5 The E?ect of Adverse Money Growth Shocks on Financial Variables . 148
B.6 The E?ect of Adverse Money Growth Shocks on Monetary Variables . 149
B.7 The E?ect of Adverse Financial Shocks on Real Variables . . . . . . . 150
B.8 The E?ect of Adverse Financial Shocks on Financial Variables . . . . 151
viii
B.9 The E?ect of Adverse Financial Shocks on Monetary Variables . . . . 152
B.10 Impulse Responses Led by a 1-? Adverse TFP Shock . . . . . . . . . 154
B.11 Impulse Responses Led by a 1-? Adverse Money Growth Shock . . . 155
B.12 Impulse Responses Led by a 1-? Adverse Financial Shock . . . . . . . 156
B.13 Impulse Responses Led by a 1-? Adverse TFP Shock . . . . . . . . . 158
B.14 Impulse Responses Led by a 1-? Adverse Money Growth Shock . . . 159
B.15 Impulse Responses Led by a 1-? Adverse Financial Shock . . . . . . . 160
ix
List of Abbreviations
CBRT Central Bank of the Republic of Turkey
FED Board of Governors of the Federal Reserve System
RRR Required Reserves Ratio
TFP Total Factor Productivity
x
Chapter 1
Financial Intermediaries, Credit Shocks, and Business Cycles
1.1 Introduction
What are the cyclical properties of ?nancial ?ows in the U.S. banking sec-
tor? How important are ?nancial shocks relative to standard productivity shocks in
driving real and ?nancial business cycles in the U.S.? To address these questions,
this study proposes an equilibrium real business cycle model with a ?nancial sector,
that is capable of matching both real and ?nancial ?uctuations observed in the U.S.
data. Although the relevance of ?nancial shocks together with an explicit model-
ing of frictions in ?nancial sector has received attention recently, the behavior of
aggregate ?nancial variables in the U.S. banking sector and how they interact with
real variables over the business cycle have not been fully explored in the literature.
1
Most previous studies have not tried to match ?uctuations in both standard macro
variables and aggregate ?nancial variables simultaneously. In this chapter, I show
that ?nancial shocks to the banking sector contribute signi?cantly to explaining the
observed dynamics of real and ?nancial variables. Financial shocks play a major
role in driving real ?uctuations due to their impact on the tightness of bank capital
constraint and hence credit spread.
1
See Christiano et. al. (2010), Dib (2010), Meh and Moran (2010), Gertler and Kiyotaki
(2010), Gertler and Karadi (2011), Kollman et al. (2011).
1
I ?rst systematically document the business cycle properties of aggregate ?-
nancial variables, using the data on U.S. commercial banks from the Federal Reserve
Board.
2
The following empirical facts emerge from the analysis: (i) Bank credit,
deposits, and loan spread are less volatile than output, while net worth and leverage
ratio are more volatile, (ii) bank assets and net worth are procyclical, while deposits,
leverage ratio, and loan spread are countercyclical, and (iii) ?nancial variables lead
the output ?uctuations by one to three quarters.
I then assess the quantitative performance of a theoretical model by its ability
to match these empirical facts. In particular, there are two main departures from
an otherwise standard real business cycle framework. The ?rst departure is that
I introduce an active banking sector with ?nancial frictions into the model, which
are modeled as in Gertler and Karadi (2011). Financial frictions require that banks
borrow funds from households and their ability to borrow is limited due to a moral
hazard (costly enforcement) problem, leading to an endogenous capital constraint
for banks in obtaining deposits.
3
This departure is needed in order to have balance
sheet ?uctuations of ?nancial sector matter for real ?uctuations. The second depar-
ture is that the model incorporates shocks to bank net worth (i.e.“?nancial shocks”)
that alter the ability of banks to borrow and to extend credit to non-?nancial busi-
nesses.
4
In the context of the theoretical model, this shock can be interpreted as
2
I also document the business cycle properties of aggregate ?nancial variables of the whole U.S.
?nancial sector from 1952 to 2009, using the Flow of Funds data. Interested readers may look at
Appendix A.3.
3
Hellmann, Murdock and Stiglitz (2000) argue that moral hazard in banking sector plays a
crucial role in most of the U.S. economic downturns in the last century. Moreover, the presence
of the agency problem makes the balance sheet structure of ?nancial sector matter for real ?uctu-
ations, invalidating the application of Modigliani-Miller theorem to the model economy presented
below.
4
Hancock, Laing and Wilcox (1995), Peek and Rosengren (1997, 2000) empirically show that
2
a redistribution shock, which transfers some portion of the wealth from ?nancial
intermediaries to households.
5
However, because of the moral hazard problem be-
tween households and bankers, it distorts intermediaries’ role of allocating resources
between households and ?rms, inducing large real e?ects.
I construct the time series of ?nancial shocks as the residuals from the law of
motion for bank net worth, using empirical data for credit spread, leverage ratio,
deposit rate and net worth. This approach is similar to the standard method for
constructing productivity shocks as Solow residuals from the production function
using empirical series for output, capital and labor.
6
The shock series show that U.S.
economy is severely hit by negative ?nancial shocks in the Great Recession. Finally,
in order to elucidate the underlying mechanism as clearly as possible, I abstract
from various real and nominal rigidities that are generally considered in medium
scale DSGE models such as Christiano et. al.(2005) and Smets and Wouters (2007).
adverse shocks to bank capital contributed signi?cantly to the U.S. economic downturns of the
late 1980s and early 1990s. Theoretically, Meh and Moran (2010) consider shocks that originate
within the banking sector and produce sudden shortages in bank capital. They suggest that these
shocks re?ect periods of ?nancial distress and weakness in ?nancial markets. Brunnermeier and
Pedersen (2009) introduce shocks to bank capital and interpret them as independent shocks arising
from other activities like investment banking. Curdia and Woodford (2010) introduce exogenous
increases in the fraction of loans that are not repaid and exogenous increases in real ?nancial inter-
mediation costs, both of which reduce net worth of ?nancial intermediaries exogenously. Mendoza
and Quadrini (2010) study the e?ect of net worth shocks on asset prices and interpret these shocks
as unexpected loan losses due to producers’ default on their debt. A complete model of the deter-
mination of the ?uctuations in net worth of banks is beyond the scope of this study, because my
goal is to analyze the quantitative e?ects of movements in net worth of ?nancial sector on business
cycle ?uctuations of real and ?nancial variables.
5
This interpretation is suggested by Iacoviello (2010). He argues that 1990-91 and 2007-09
recessions can be characterized by situations in which some borrowers pay less than contractually
agreed upon and ?nancial institutions that extend loans to these borrowers su?er from loan losses,
resulting in some sort of a redistribution of wealth between borrowers (households and ?rms) and
lenders (banks).
6
I also consider some alternative measures of ?nancial shocks, including the one constructed
based on loan losses incurred by U.S. commercial banks (using the charge-o? and delinquency rates
data compiled by the Federal Reserve Board). The construction of these alternative measures and
their simulation results can be found in Appendix A.4. The main results of the study do not
change under these alternative measures.
3
The business cycle accounting exercise in this study is important in the sense
that explaining the dynamics of balance sheet ?uctuations in the U.S. banking sec-
tor can help us better understand, capture and predict the dynamics of standard
macroeconomic variables as the ?nancial ?ows in the U.S. banking sector are highly
cyclical and lead the output ?uctuations by one to three quarters. Therefore, the
dynamics of ?nancial variables in the U.S. banking sector may serve as additional
state variables for explaining real ?uctuations. This study is one of the ?rst studies,
which rigorously addressed this issue. It is also the ?rst work that tried to match
?uctuations in both standard macro variables and aggregate ?nancial variables of
U.S. banking sector simultaneously. Finally, in order to start thinking about how
di?erent policy tools can be implemented in an environment in which the ?nancial
sector is crucial for business cycle ?uctuations and what the welfare implications of
these policies are, we need a model capable of matching real and ?nancial ?uctua-
tions simultaneously. It could be asserted that the model proposed in this study is
quite successful in this dimension.
In the theoretical model, there are three main results. First, the benchmark
model driven by both standard productivity and ?nancial shocks is able to deliver
most of the stylized cyclical facts about real and ?nancial variables simultaneously.
Second, ?nancial shocks to banking sector are important not only for explaining the
dynamics of ?nancial variables but also for the dynamics of standard macroeconomic
variables. In particular, the model simulations show that the benchmark model
driven by both shocks has better predictions about investment, hours and output
than the frictionless version of the model (which is standard RBC model with capital
4
adjustment costs) and than the model driven only by productivity shocks. The
benchmark model also performs better than the model with only productivity shocks
in terms of its predictions about aggregate ?nancial variables.
7
Third, the tightness
of bank capital constraint given by the Lagrange multiplier in the theoretical model
(which determines the banks’ ability to extend credit to non-?nancial ?rms) tracks
the index of tightening credit standards (which shows the adverse changes in banks’
lending) constructed by the Federal Reserve Board quite well.
The economic intuition for why ?nancial shocks matter a lot for real ?uctua-
tions in the model lies in the e?ect of these shocks on the tightness of bank capital
constraint and credit spread. When ?nancial shocks move the economy around the
steady state, they lead to large ?uctuations in the tightness of bank capital con-
straint as evidenced by the big swings in the Lagrange multiplier of the constraint.
Since credit spread is a function of this Lagrange multiplier, ?uctuations in the
latter translate into variations in the former. Credit spread appears as a positive
wedge in the intertemporal Euler equation, which determines how households’ de-
posits (savings in the economy) are transformed into bank credit to non-?nancial
?rms. Fluctuations in this wedge move the amount of deposits, therefore the amount
of bank credit that can be extended to ?rms. Since productive ?rms ?nance their
capital expenditures via bank credit, movements in the latter translate into the ?uc-
tuations in capital stock. Because hours worked is complementary to capital stock
in a standard Cobb-Douglas production function, empirically-relevant ?uctuations
7
The RBC model with capital adjustment costs has no predictions about ?nancial variables
since balance sheets of banks in that model are indeterminate.
5
in capital stock lead to empirically-observed ?uctuations in hours, which eventually
generate observed ?uctuations in output.
This study contributes to recently growing empirical and theoretical literature
studying the role of ?nancial sector on business cycle ?uctuations. On the empirical
side, Adrian and Shin (2008, 2009) provide evidence on the time series behavior
of balance sheet items of some ?nancial intermediaries using the Flow of Funds
data.
8
However, they do not present standard business cycle statistics of ?nancial
?ows.
9
On the theoretical side, the current work di?ers from the existing literature
on ?nancial accelerator e?ects on demand for credit, arising from the movements
in the strength of borrowers’ balance sheets.
10
I focus on ?uctuations in supply of
credit driven by movements in the strength of lenders’ balance sheets. Meh and
Moran (2010) investigate the role of bank capital in transmission of technology,
bank capital and monetary policy shocks in a medium-scale New Keynesian, double
moral hazard framework. Jermann and Quadrini (2010) study the importance of
credit shocks in non-?nancial sector in explaining the cyclical properties of equity
and debt payouts of U.S. non-?nancial ?rms in a model without a banking sector.
An independent study that is closely related and complementary to our work is
Iacoviello (2011). In a DSGE framework with households, banks, and entrepreneurs
each facing endogenous borrowing constraints, he studies how repayment shocks
8
They argue that to the extent that balance sheet ?uctuations a?ect the supply of credit, they
have the potential to explain real ?uctuations, and they empirically show that bank equity has a
signi?cant forecasting power for GDP growth.
9
The notion of “procyclical” in their papers is with respect to total assets of ?nancial inter-
mediaries, not with respect to GDP as in the current study. In that sense, this study undertakes
a more standard business cycle accounting exercise.
10
For example, see Kiyotaki and Moore (1997), Carlstrom and Fuerst (1998), Bernanke, Gertler,
and Gilchrist (1999)
6
undermine the ?ow of funds between savers and borrowers in the recent recession.
My work is di?erent from his study in terms of both empirical and theoretical con-
tributions. First, in terms of empirical work, I systemically document the business
cycle properties of aggregate ?nancial variables in the U.S. banking sector from 1987
to 2010, which I then use to judge the quantitative performance of the theoretical
model, while his work particularly focuses on the 2007-09 recession. Second, in the
theoretical model presented below, only the banking sector faces endogenous capital
constraints, which gives me the ability to isolate the role of banks in the transmis-
sion of ?nancial shocks from the role of household and production sectors. Finally,
I employ a di?erent methodology of constructing the series of ?nancial shocks from
the data. In terms of normative policy, Angeloni and Faia (2010) examine the role
of banks in the interaction between monetary policy and macroprudential regula-
tions in a New Keynesian model with bank runs, while Gertler and Kiyotaki (2010),
and Gertler and Karadi (2011) investigate the e?ects of central bank’s credit pol-
icy aimed at troubled banks.
11
Finally, in an open-economy framework, Kollmann
(2011) studies how a bank capital constraint a?ects the international business cycles
driven by productivity and loan default shocks in a two-country RBC model with a
global bank.
The rest of the chapter is structured as follows: In Section 1.2, I document
evidence on the real and ?nancial ?uctuations in U.S. data. Section 1.3 describes the
theoretical model. Section 1.4 presents the model parametrization and calibration
together with the quantitative results of the model. Section 1.5 concludes.
11
The latter also features the interbank market.
7
1.2 Real and Financial Fluctuations in the U.S. economy
This section documents some key empirical features of ?nancial cycles in the
U.S. economy. The upper left panel of Figure 1 displays quarterly time series for
loan losses of U.S. commercial banks from 1987 to 2010. The loan loss rates are
expressed as annualized percentages of GDP. The ?gure shows that loan loss rates
increased in last three recessions of the U.S. economy. The loss rates peaked in both
1990-91 and 2007-09 recessions, reaching its highest level of 5% in the latter. The
upper right panel of Figure 1 plots daily time series for Dow Jones Bank Index from
1992 to 2010. The ?gure suggests that the market value of banks’ shares declined
substantially in the recent recession. Finally, the middle left panel of Figure 1
displays real net worth growth of U.S. commercial banks (year-on-year). The ?gure
suggests that banks’ net worth shrank in last three recessions of the U.S. economy,
with a reduction of 40% in the 2007-09 recession. These three plots convey a common
message: substantial loan losses incurred by banks together with the fall in their
equity prices typically cause large declines in banks’ net worth, which might lead to
persistent and mounting pressures on bank balance sheets, worsening the aggregate
credit conditions, and thus causing the observed decline in real economic activity,
which is much more pronounced in the Great Recession.
The middle left panel of Figure 1 plots commercial and industrial loan spreads
over federal funds rate (annualized). The ?gure shows that bank lending spreads
sky-rocketed in the recent crisis, reaching a 3.2% per annum towards the end of
the recession and they keep rising although the recession was o?cially announced
8
0
1
2
3
4
5
88 90 92 94 96 98 00 02 04 06 08 10
Loan losses to GDP ratio
0
100
200
300
400
500
600
92 94 96 98 00 02 04 06 08 10
Dow Jones bank index
-60
-40
-20
0
20
40
60
88 90 92 94 96 98 00 02 04 06 08 10
Net worth growth
1.5
2.0
2.5
3.0
3.5
88 90 92 94 96 98 00 02 04 06 08 10
Interest rate spreads
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Bank credit
-2
0
2
4
6
8
10
88 90 92 94 96 98 00 02 04 06 08 10
Deposit growth
Figure 1.1: Financial Flows in the U.S. Economy
9
to be over. The bottom left panel displays real bank credit growth rates (year-on-
year). The ?gure indicates that bank credit growth fell signi?cantly in the recent
economic downturn. Taken together, these ?gures suggest that the U.S. economy
has experienced a signi?cant deterioration in aggregate credit conditions as total
bank lending to non-?nancial sector declined sharply and the cost of funds for non-
?nancial ?rms increased substantially. Finally, the bottom right panel of Figure 1
plots real deposit growth rates (year-on-year). The ?gure shows that growth rate of
deposits began to fall substantially right after the recent recession.
Table 1.1: Business Cycle Properties of Real and Financial Variables, Quarterly U.S.
Data, 1987- 2010
Standard
Deviation x
t?4
x
t?3
x
t?2
x
t?1
xt x
t+1
x
t+2
x
t+3
x
t+4
Real Variables
Output 1.80 0.15 0.39 0.66 0.87 1.00 0.87 0.66 0.39 0.15
Consumption 0.45 -0.20 0.06 0.37 0.66 0.82 0.80 0.67 0.46 0.25
Investment 2.73 0.27 0.49 0.71 0.87 0.97 0.82 0.59 0.33 0.09
Hours 0.91 -0.01 0.19 0.43 0.65 0.83 0.89 0.83 0.68 0.44
Financial Variables
Bank credit 0.93 -0.20 -0.11 0.02 0.14 0.30 0.47 0.63 0.68 0.63
Deposits 0.69 -0.02 -0.08 -0.18 -0.30 -0.39 -0.42 -0.34 -0.22 -0.07
Net Worth 5.17 -0.15 -0.03 0.14 0.32 0.52 0.70 0.80 0.76 0.63
Leverage Ratio 5.61 0.16 0.05 -0.12 -0.30 -0.49 -0.66 -0.74 -0.70 -0.55
Loan Spread 0.08 0.05 0.04 -0.08 -0.21 -0.39 -0.42 -0.43 -0.32 -0.18
a
Business cycle statistics in the table are based on HP-?ltered cyclical components of quarterly empirical time
series (smoothing parameter:1600).
b
The standard deviation of output is expressed in percent; standard deviations of the remaining variables are
normalized by the standard deviation of output (std(x)/std(GDP)).
c
The correlation coe?cients in bold font are the maximum ones in their respective rows.
d
Data sources are provided in Appendix A.1.
I will assess the performance of the model below by its ability to match empiri-
cal cyclical properties of real and ?nancial variables in the U.S data. Table 1 presents
10
the business cycle properties of aggregate ?nancial variables in U.S. commercial
banking sector together with standard macro aggregates for the period 1987-2010.
12
The standard deviations of real and ?nancial variables except GDP are relative to
the standard deviation of GDP. The correlation coe?cients in bold font are the
maximum ones in their respective rows, which indicate the lead-lag relationship of
variables with output. The aggregate ?nancial variables I consider are U.S. commer-
cial banks’ assets (bank credit), liabilities (deposits), net worth, leverage ratio and
loan spread.
13
Quarterly seasonally-adjusted ?nancial data are taken from the Fed-
eral Reserve Board. Quarterly real data are taken from Federal Reserve Economic
Data (FRED) of St. Louis FED. Financial data at the FED Board is nominal. GDP
de?ator from NIPA accounts is used to de?ate the ?nancial time series. See the data
appendix for a more detailed description.
Table 1.1 gives us the following empirical facts about real and ?nancial vari-
ables. Consumption and hours are less volatile than output, while investment is
more volatile; and consumption, investment, and hours are all strongly procyclical
with respect to output. These are standard business-cycle facts; for example, see
King and Rebelo (1999). Bank credit, deposits, and loan spread are less volatile than
output, while net worth and leverage ratio are nearly 5 times more volatile. Bank
12
I focus on the period that begins in 1987 for two reasons. First, U.S. banking sector witnessed
a signi?cant transformation starting from 1987 such as deregulation of deposit rates, increases in
?nancial ?exibility. Second, it also corresponds to a structural break in the volatility of many
standard macro variables, which is so-called Great Moderation.
13
I also conducted the same empirical exercise for total assets and total liabilities in addition
to the narrow de?nitions of these items here. The business cycle statistics are qualitatively very
similar although there are some negligible quantitative di?erences. The reason might be the fact
that bank credit constitutes a substantial part of total assets of a typical commercial bank and
deposits constitute a big portion of its total liabilities.
11
assets and net worth are procyclical, while deposits, leverage ratio, and loan spread
are countercyclical. Finally, all ?nancial variables lead the output ?uctuations by
one to three quarters.
14
Table 1.2: The Sequence of Events in a Given Time Period
1. Productivity zt and recovery rate ?t are realized.
2. Firms hire labor Ht and use capital Kt they purchased in period t ? 1, which are used for production, Yt.
3. Firms make their wage payments wtHt and dividend payments to shareholders (banks) from period t-1.
4. Banks make their interest payments on deposits of households from period t-1 and bankers exit with prob. (1-?).
5. Households make their consumption and saving decisions and deposit their resources at banks.
6. Firms sell their depreciated capital to capital producers who make investment and produce new capital K
t+1
.
7. Firms issue shares [st = K
t+1
] and sell these shares to banks to ?nance their capital expenditures.
8. Banks purchase ?rms’ shares and their incentive constraints bind.
9. Firms purchase capital K
t+1
from capital producers at the price of qt with borrowed funds.
1.3 A Business Cycle Model with Financial Sector
The model is an otherwise standard real business cycle model with a ?nancial
sector. Market segmentation ensures that households cannot directly lend to ?nal
good ?rms, which makes the ?nancial sector essential for transferring funds from
households to non-?nancial ?rms. Credit frictions in ?nancial sector are modeled as
in Gertler and Karadi (2011). I introduce shocks to bank net worth on top of the
standard productivity shocks. The model economy consists of four types of agents:
households, ?nancial intermediaries, ?rms, and capital producers. The ability of
?nancial intermediaries to borrow from households is limited due to a moral hazard
(costly enforcement) problem, which will be described below. Firms acquire capital
in each period by selling shares to ?nancial intermediaries. Finally, capital producers
14
I also reproduce Table 1.1 for the period 1987:Q1-2007:Q1 in order to see whether the empirical
results are driven or at least substantially a?ected by the recent economic events starting at 2007:Q3
or not. The results show that the key stylized facts about real and ?nancial variables described
above are robust to the sample period taken. The reproduced table can be found in Appendix A.1.
12
are incorporated into the model in order to introduce capital adjustment costs in a
tractable way. Table 1.2 shows the sequence of events in a given time period in the
theoretical model described below. The section below will clarify this timeline.
1.3.1 Households
There is a continuum of identical households of measure unity. Households are
in?nitely-lived with preferences over consumption (c
t
) and leisure (1 ?L
t
) given by
E
0
?
t=0
?
t
U(c
t
, 1 ? L
t
) (1.1)
Each household consumes and supplies labor to ?rms at the market clearing
real wage w
t
. In addition, they save by holding deposits at a riskless real return r
t
at competitive ?nancial intermediaries.
There are two types of members within each household: workers and bankers.
Workers supply labor and return the wages they earn to the household while each
banker administers a ?nancial intermediary and transfers any earnings back to the
household. Hence, the household owns the ?nancial intermediaries that its bankers
administer. However, the deposits that the household holds are put in ?nancial in-
termediaries that it doesn’t own.
15
Moreover, there is perfect consumption insurance
within each household.
At any point in time the fraction 1 ?? of the household members are workers
15
This assumption ensures independent decision-making. Depositors are not the owners of the
bank, so the bankers don’t maximize the depositors’ utility, but the expected terminal net worth
of the banks that they own.
13
and the remaining fraction ? are bankers. An individual household member can
switch randomly between these two jobs over time. A banker this period remains a
banker next period with probability ?, which is independent of the banker’s history.
Therefore, the average survival time for a banker in any given period is 1/(1 ? ?).
The bankers are not in?nitely-lived in order to make sure that they don’t reach
a point where they can ?nance all equity investment from their own net worth.
16
Hence, every period (1 ??)? bankers exit and become workers while the same mass
of workers randomly become bankers, keeping the relative proportion of workers and
bankers constant. Period t bankers learn about survival and exit at the beginning of
period t + 1. Bankers who exit from the ?nancial sector transfer their accumulated
earnings to their respective household. Furthermore, the household provides its new
bankers with some start-up funds.
17
The household budget constraint is given by
c
t
+ b
t+1
= w
t
L
t
+ (1 + r
t
)b
t
+ ?
t
(1.2)
The household’s subjective discount factor is ? ? (0,1), c
t
denotes the house-
hold’s consumption, b
t+1
is the total amount of deposits that the household holds at
the ?nancial intermediary, r
t
is the non-contingent real return on the deposits from
t?1 to t, w
t
is the real wage rate, and ?
t
is the pro?ts to the household from owning
capital producers and banks net of the transfer that it gives to its new bankers plus
16
This assumption ensures that the bankers have to borrow from households to ?nance their
equity purchases.
17
This assumption ensures that banks don’t have zero net worth in any period and is similar to
the one about the entrepreneurial wage in Carlstrom and Fuerst (1998), and Bernanke, Gertler,
and Gilchrist (1999).
14
(minus) the amount of wealth redistributed from banks (households) to households
(banks) induced by the net worth shock.
The household chooses c
t
, L
t
, and b
t+1
to maximize (1.1) subject to the se-
quence of ?ow budget constraints in (1.2). The resulting ?rst order conditions for
labor supply and deposit holdings are given by
U
l
(t)
U
c
(t)
= w
t
(1.3)
U
c
(t) = ?(1 + r
t+1
)E
t
U
c
(t + 1) (1.4)
The condition (1.3) states that the marginal rate of substitution between con-
sumption and leisure is equal to the wage rate. The condition (1.4) is the standard
consumption-savings Euler equation, which equates the marginal cost of not con-
suming and saving today to the expected discounted marginal bene?t of consuming
tomorrow.
1.3.2 Financial Intermediaries
1.3.2.1 Balance Sheets
Financial intermediaries transfer the funds that they obtain from households
to ?rms. They acquire ?rm shares and ?nance these assets with household deposits
and their own equity. At the beginning of period t, before banks collect deposits,
an aggregate net worth shock hits banks’ balance sheets. Let’s denote ?
t
as the
15
time-varying recovery rate of loans as a percentage of bank net worth. Innovations
to ?
t
are shocks to bank net worth. Therefore, ?
t
¯ n
jt
is the e?ective net worth of the
?nancial intermediary. For notational convenience, I denote ?
t
¯ n
jt
by n
jt
. Hence, n
jt
is the net worth of ?nancial ?rm j at the beginning of period t after the net worth
shock hits. The balance sheet identity of ?nancial intermediary j is then given by
q
t
s
jt
= b
jt+1
+ n
jt
(1.5)
where q
t
is the price of a representative ?rm’s shares and s
jt
is the quantity of these
shares owned by bank j, b
jt+1
is the amount of deposits that intermediary j obtains
from the households, n
jt
is the net worth of ?nancial ?rm j at the beginning of
period t after the net worth shock hits.
18
Banks undertake equity investment and
?rms ?nance their capital expenditures by issuing shares. Therefore, the ?nancial
contract between the intermediary and the ?rm is an equity contract (or equivalently
a state-dependent debt contract).
The households put their deposits into the ?nancial intermediary at time t and
obtain the non-contingent real return r
t+1
at t +1. Therefore, b
jt+1
is the liabilities
of the ?nancial intermediary and n
jt
is its equity or capital. The ?nancial inter-
mediaries receive ex-post state-contingent return, r
kt+1
for their equity investment.
The fact that r
kt+1
is potentially greater than r
t+1
creates an incentive for bankers
to engage in ?nancial intermediation.
The ?nancial intermediary’s net worth at the beginning of period t +1 (before
18
In U.S. ?nancial data, household deposits constitute 70% of total liabilities of banks. Boyd
(2007) also suggests that demand (checking) deposits form a substantial portion of bank liabilities.
16
the time t+1 net worth shock hits) is given by the di?erence between the earnings on
equity investment in ?rms (assets of ?nancial intermediary) and interest payments
on deposits obtained from the households (liabilities of ?nancial intermediary). Thus
the law of motion for bank net worth is given by
¯ n
jt+1
= (1 + r
kt+1
)q
t
s
jt
? (1 + r
t+1
)b
jt+1
(1.6)
Using the balance sheet of the ?nancial ?rm given by (1.5), we can re-write (1.6) as
follows:
¯ n
jt+1
= (r
kt+1
? r
t+1
)q
t
s
jt
+ (1 + r
t+1
)n
jt
(1.7)
The ?nancial intermediary’s net worth at time t+1 depends on the premium (r
kt+1
?
r
t+1
) that it earns on shares purchased as well as the total value of these shares,
q
t
s
jt
.
1.3.2.2 Pro?t Maximization
This section describes banks’ pro?t maximization. The ?nancial intermediary
j maximizes its expected discounted terminal net worth, V
jt
, by choosing the amount
of ?rm shares, s
jt
, it purchases, given by
V
jt
= max
s
jt
E
t
?
i=0
(1??)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
?r
t+1+i
)q
t+i
s
jt+i
]+(1+r
t+1+i
)n
jt+i
] (1.8)
17
Since the expected discounted risk premium is positive in any period, the
?nancial intermediary will always have an incentive to buy ?rms’ shares. Obtaining
additional funds (deposits) from the households is the only way to achieve this.
However, an agency problem described below introduces an endogenous borrowing
constraint for banks, thus a limit on the size of the ?nancial intermediaries: At
the end of the period, the ?nancial intermediary may choose to divert ? fraction
of available funds from its shares of ?rms with no legal rami?cation and give them
to the household of which the banker is a member. If the ?nancial intermediary
diverts the funds, the assumed legal structure ensures that depositors are able to
force the intermediary to go bankrupt and they may recover the remaining fraction
1 ? ? of the assets. They are not able to get the remaining fraction ? of the funds
since, by assumption, the cost of recovering these funds is too high.
19
Therefore,
for the banks not to have an incentive to divert the funds, the following incentive
compatibility constraint must be satis?ed at the end of period t:
V
jt
? ?q
t
s
jt
(1.9)
The left-hand side of (1.9) is the value of operating for the bank (or equiva-
lently cost of diverting funds) while the right-hand side is the gain from diverting ?
19
As Christiano (2010) suggests, diverting funds is meant to say that bankers might not manage
funds in the interest of depositors or they might invest funds into risky projects which do not
earn a high return for depositors but a high excess return for bankers themselves (Bankers might
invest ? fraction of funds into very risky projects, which could potentially go bankrupt and reduce
equilibrium return to depositors). Taking this into consideration, depositors put their money at
banks up to a threshold level beyond which if bankers make risky investments, they do this at their
own risk. This threshold level of deposits can be thought as if deposits expand beyond that level,
banks would have an incentive to default. The market discipline prevents deposits from expanding
beyond the default threshold level and interest rate spreads re?ect this fear of default although
defaults are not observed in equilibrium.
18
fraction of assets. The intuition for this constraint is that in order for the ?nancial
intermediary not to divert the funds and for the households to put their deposits
into the bank, the value of operating in ?nancial sector must be greater than or
equal to the gain from diverting assets and going bankrupt.
20
A ?nancial intermediary’s objective is to maximize the expected return to its
portfolio consisting of ?rms’ shares and its capital subject to the incentive compat-
ibility constraint. Then its demand for shares is fully determined by its net worth
position, since as long as the expected return from the portfolio is strictly positive,
it will expand its lending (its size) until the incentive compatibility constraint binds.
1.3.2.3 Leverage Ratio and Net Worth Evolution
Proposition 1 The expected discounted terminal net worth of a bank can be ex-
pressed as the sum of expected discounted total return to its equity investment into
?rms and expected discounted total return to its existing net worth.
Proof : See Appendix A.2.1.
Proposition 1 states that that V
jt
can be expressed as follows:
V
jt
= ?
t
q
t
s
jt
+ ?
t
n
jt
(1.10)
where
20
In equilibrium, given the incentive compatibility constraint binds, the banker is indi?erent
between diverting funds and not diverting them. Here we focus on the equilibrium where banker
chooses to operate in the ?nancial sector rather than diverting money and going bankrupt. There-
fore, we analyze the equilibrium where there are no defaults of banks and the amount of funds
that the bankers can collect from households endogenously depends on bankers’ own net worth.
19
?
t
= E
t
[(1 ? ?)??
t,t+1
(r
kt+1
?r
t+1
) + ??
t,t+1
?
q
t+1
s
jt+1
q
t
s
jt
?
t+1
] (1.11)
?
t
= E
t
[(1 ? ?)??
t,t+1
(1 + r
t+1
) + ??
t,t+1
?
n
jt+1
n
jt
?
t+1
] (1.12)
?
t
can be interpreted as the expected discounted marginal gain to the bank of
buying one more unit of ?rms’ shares, holding its net worth n
jt
constant. The ?rst
term is the discounted value of the net return on shares to the bank if it exits the
?nancial sector tomorrow. The second term is the continuation value of its increased
assets if it survives. Meanwhile, ?
t
can be interpreted as the expected discounted
marginal bene?t of having one more unit of net worth, holding q
t
s
jt
constant. The
?rst term is the discounted value of the return on net worth to the bank if it exits
the ?nancial sector tomorrow. The second term is the continuation value of its
increased net worth if it survives.
Therefore, we can write the incentive compatibility constraint as follows:
?
t
q
t
s
jt
+ ?
t
n
jt
? ?q
t
s
jt
(1.13)
The incentive compatibility constraint above binds as long as 0 < ?
t
< ?. The
intuition is as follows: Assume that ?
t
? ?. Then the left-hand side of (1.13) is
always greater than the right-hand side of (1.13) since ?
t
n
jt
> 0 as can be seen
from (1.12). The franchise value of the bank is always higher than the gain from
diverting funds. Therefore, the constraint is always slack. Moreover, assume that
20
?
t
? 0. Since ?
t
is the expected discounted marginal gain to the bank of increasing
its assets, the intermediary does not have the incentive to expand its assets when
?
t
? 0. In this case, the constraint does not bind because the intermediary does not
collect any deposits from households.
The pro?ts of the ?nancial intermediary will be a?ected by the premium r
kt+1
?
r
t+1
. That is, the banker will not have any incentive to buy ?rms’ shares if the
discounted return on these shares is less than the discounted cost of deposits. Thus
the ?nancial ?rm will continue to operate in period t + i if the following inequality
is satis?ed:
E
t+i
??
t,t+1+i
(r
kt+1+i
?r
t+1+i
) ? 0 ?i ? 0 (1.14)
where ??
t,t+1+i
is the stochastic discount factor that the ?nancial ?rm applies to
its earnings at t +1 +i. The moral hazard problem between households and banks
described above limits banks’ ability to obtain deposits from the households, leading
to a positive premium. The following proposition establishes this fact.
Proposition 2 Risk premium is positive as long as the incentive compatibility con-
straint binds.
Proof : See Appendix A.2.2.
When this constraint binds, the ?nancial intermediary’s assets are limited by
its net worth. That is, if this constraint binds, the funds that the intermediary can
obtain from households will depend positively on its equity capital:
21
q
t
s
jt
=
?
t
? ??
t
n
jt
(1.15)
The constraint (1.15) limits the leverage of the ?nancial intermediary to the
point where its incentive to divert funds is exactly balanced by its loss from doing so.
Thus, the costly enforcement problem leads to an endogenous borrowing constraint
on the bank’s ability to acquire assets. When bank’s leverage ratio and/or bank
equity is high, it can extend more credit to non-?nancial ?rms. Conversely, de-
leveraging or the deterioration in net worth in bad times will limit the bank’s ability
to extend credit. Note that by manipulating this expression using the balance sheet,
I can obtain the bank’s leverage ratio as follows:
b
jt+1
n
jt
=
?
t
? ? ?
t
? 1 (1.16)
The leverage ratio increases in the expected marginal bene?t of buying one
more unit of ?rm share, and in the expected marginal gain of having one more unit
of net worth. Intuitively, increases in ?
t
or ?
t
mean that ?nancial intermediation is
expected to be more lucrative going forward, which makes it less attractive to divert
funds today and thus increases the amount of funds depositors are willing to entrust
to the ?nancial intermediary.
21
21
The amount of deposits at banks does directly depend on banks’ net worth. In good times
banks’ net worth is relatively high and depositors believe that bankers do not misbehave in terms
of managing their funds properly. In these times, credit spreads can be fully explained by observed
bankruptcies and intermediation costs. However, in bad times, banks experience substantial de-
clines in their net worth and depositors are hesitant about putting their money in banks. In these
times, the ?nancial sector operates at a less e?cient level and a smaller number of investment
projects are funded. Large credit spread observed in these times can be explained by the above
factors plus the ine?ciency in the banking system.
22
Using (1.15), I can re-write the law of motion for the banker’s net worth as
follows:
¯ n
jt+1
= [(r
kt+1
?r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)]n
jt
(1.17)
The sensitivity of net worth of the ?nancial intermediary j at t + 1 to the
ex-post realization of the premium r
kt+1
? r
t+1
increases in the leverage ratio.
Proposition 3 Banks have an identical leverage ratio as none of its components
depends on bank-speci?c factors.
Proof : From (1.17), one can obtain the following:
¯ n
jt+1
n
jt
= [(r
kt+1
?r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)] (1.18)
q
t+1
s
jt+1
q
t
s
jt
=
?
t+1
???
t+1
?t
???t
¯ n
jt+1
n
jt
(1.19)
The expressions above show that banks have identical expected growth rates
of assets and net worth, thus have identical leverage ratios.
22
By using Proposition 4, we can sum demand for assets across j to obtain the
total intermediary demand for assets:
q
t
s
t
=
?
t
? ??
t
n
t
(1.20)
22
This immediately implies that ?
t
and ?
t
are independent of j. In Appendix A.2.1, I use this
result in explicit derivation of ?
t
and ?
t
.
23
where s
t
is the aggregate amount of assets held by ?nancial intermediaries and n
t
is the aggregate intermediary net worth. In the equilibrium of the model, move-
ments in the leverage ratio of ?nancial ?rms and/or in their net worth will generate
?uctuations in total intermediary assets.
The aggregate intermediary net worth at the beginning of period t +1 (before
the net worth shock hits but after exit and entry), ¯ n
t+1
, is the sum of the net worth
of surviving ?nancial intermediaries from the previous period, ¯ n
et+1
, and the net
worth of entering ?nancial intermediaries, ¯ n
nt+1
. Thus, we have
¯ n
t+1
= ¯ n
et+1
+ ¯ n
nt+1
(1.21)
Since the fraction ? of the ?nancial intermediaries at time t will survive until
time t + 1, their net worth, ¯ n
et+1
, is given by
¯ n
et+1
= ?[(r
kt+1
? r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)]n
t
(1.22)
Newly entering ?nancial intermediaries receive start-up funds from their re-
spective households. The start-up funds are assumed to be a transfer equal to a
fraction of the net worth of exiting bankers.
23
The total ?nal period net worth of
exiting bankers at time t is equal to (1??)n
t
. The household is assumed to transfer
the fraction
?
(1??)
of the total ?nal period net worth to its newly entering ?nancial
intermediaries. Therefore, we have
23
This assumption is slightly di?erent from that in Gertler&Karadi (2011). They assume that
the net worth of newly entering bankers is a fraction of banks’ total assets rather than its net
worth. Since the fraction is small, it does not change the main results of the study signi?cantly.
24
¯ n
nt+1
= ?n
t
(1.23)
Using (1.21), (1.22), and (1.23), we obtain the following law of motion for ¯ n
t+1
:
¯ n
t+1
= ?[(r
kt+1
? r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)]n
t
+ ?n
t
(1.24)
1.3.3 Firms
There is a continuum of unit mass of ?rms that produce the ?nal output in the
economy. The production technology at time t is described by a constant returns
to scale Cobb-Douglas production function:
Y
t
= z
t
F(K
t
, H
t
) = z
t
K
?
t
H
1??
t
(1.25)
where K
t
is the ?rm’s capital stock, H
t
is the ?rm’s hiring of labor and z
t
is an
aggregate TFP realization.
Firms acquire capital K
t+1
at the end of period t to produce the ?nal output
in the next period. After producing at time t + 1, the ?rm can sell the capital on
the open market.
Firms ?nance their capital expenditures in each period by issuing equities and
selling them to ?nancial intermediaries. Firms issue s
t
units of state-contingent
claims (equity), which is equal to the number of units of capital acquired K
t+1
. The
?nancial contract between a ?nancial intermediary and a ?rm is an equity contract
(or equivalently, a state contingent debt contract). The ?rm pays a state-contingent
25
interest rate equal to the ex-post return on capital r
kt+1
to the ?nancial intermedi-
ary. The ?rms set their capital demand K
t+1
taking this stochastic repayment into
consideration. At the beginning of period t + 1 (after shocks are realized), when
output becomes available, ?rms obtain resources Y
t+1
and use them to make repay-
ments to shareholders (or ?nancial intermediaries). The ?rm prices each ?nancial
claim at the price of a unit of capital, q
t
. Thus, we have
q
t
s
t
= q
t
K
t+1
(1.26)
There are no frictions for ?rms in obtaining funds from ?nancial intermediaries.
The bank has perfect information about the ?rm and there is perfect enforcement.
Therefore, in the current model, only banks face endogenous borrowing constraints
in obtaining funds. These constraints directly a?ect the supply of funds to the ?rms.
Firms choose the labor demand at time t as follows:
w
t
= z
t
F
H
(K
t
, H
t
) (1.27)
Then ?rms pay out the ex-post return to capital to the banks given that they
earn zero pro?t state by state. Therefore, ex-post return to capital is given by
r
kt+1
=
z
t+1
F
K
(K
t+1
, H
t+1
) + q
t+1
(1 ? ?)
q
t
?1 (1.28)
Labor demand condition (1.27) simply states that the wage rate is equal to
the marginal product of labor. Moreover, condition (1.28) states that the ex-post
26
real rate of return on capital is equal to the marginal product of capital plus the
capital gain from changed asset prices.
1.3.4 Capital Producers
Following the literature on ?nancial accelerator, I incorporate capital produc-
ers into the model in order to introduce capital adjustment costs in a tractable way.
Capital adjustment costs are needed to introduce variation in the price of capital;
otherwise the price of capital will not respond to the changes in capital stock and
will always be equal to 1.
24
I assume that households own capital producers and receive any pro?ts. At
the end of period t, competitive capital producers buy capital from ?rms to repair
the depreciated capital and to build new capital. Then they sell both the new and
repaired capital. The cost of replacing the depreciated capital is unity; thus the
price of a unit of new capital or repaired capital is q
t
. The pro?t maximization
problem of the capital producers is given by:
max
It
q
t
K
t+1
?q
t
(1 ? ?)K
t
? I
t
(1.29)
s.t. K
t+1
= (1 ??)K
t
+ ?
_
I
t
K
t
_
K
t
(1.30)
where I
t
) is the total investment by capital producing ?rms and ?
_
It
Kt
_
is the capital
24
There will be no ?nancial accelerator between households and banks if there is no variation
in the price of capital.
27
adjustment cost function. The resulting optimality condition gives the following “Q”
relation for investment:
q
t
=
_
?
?
_
I
t
K
t
__
?1
(1.31)
where ?
?
_
It
Kt
_
is the partial derivative of the capital adjustment cost function with
respect to investment-capital ratio at time t. The ?uctuations in investment expen-
ditures will create variation in the price of capital. A fall in investment at time t
(ceteris paribus) will reduce the price of capital in the same period.
1.3.5 Competitive Equilibrium
A competitive equilibrium of this model economy consists of sequences of allo-
cations {c
t
, L
t
, K
t+1
, s
t
, n
t
, ¯ n
t
, I
t
, ?
t
, ?
t
, H
t
}
?
t=0
, of prices {w
t
, r
kt+1
, r
t+1
, q
t
}
?
t=0
and of
exogenous processes {z
t
, ?
t
}
?
t=0
such that (i) the allocations solve the household’s,
the ?nancial intermediary’s, the ?rm’s and the capital producer’s problems at the
equilibrium prices and (ii) markets for factor inputs clear. The following equilibrium
conditions must be satis?ed:
U
l
(t)
U
c
(t)
= w
t
(1.32)
U
c
(t) = ?(1 + r
t+1
)E
t
U
c
(t + 1) (1.33)
28
r
kt+1
=
z
t+1
F
K
(K
t+1
, H
t+1
) + q
t+1
(1 ? ?)
q
t
?1 (1.34)
w
t
= z
t
F
H
(K
t
, H
t
) (1.35)
n
t
= ?
t
¯ n
t
(1.36)
q
t
s
t
=
?
t
? ??
t
n
t
(1.37)
?
t
= E
t
[(1 ? ?)??
t,t+1
(r
kt+1
?r
t+1
) + ??
t,t+1
?
q
t+1
s
t+1
q
t
s
t
?
t+1
] (1.38)
?
t
= E
t
[(1 ? ?)??
t,t+1
(1 + r
t+1
) + ??
t,t+1
?
n
t+1
n
t
?
t+1
] (1.39)
¯ n
t+1
= ?[(r
kt+1
? r
t+1
)
?
t
? ? ?
t
+ (1 + r
t+1
)]n
t
+ ?n
t
(1.40)
q
t
s
t
= q
t
K
t+1
(1.41)
K
t+1
= (1 ? ?)K
t
+ ?
_
I
t
K
t
_
K
t
(1.42)
29
q
t
=
_
?
?
_
I
t
K
t
__
?1
(1.43)
L
t
= H
t
(1.44)
C
t
+ I
t
= z
t
F(K
t
, H
t
) (1.45)
log(z
t+1
) = ?
z
log(z
t
) + ?
z
t+1
(1.46)
log(?
t+1
) = ?
?
log(?
t
) + ?
?
t+1
(1.47)
1.4 Quantitative Analysis
This section studies the quantitative predictions of the model by examining
the results of numerical simulations of an economy calibrated to quarterly U.S.
data. In order to investigate the dynamics of the model, I compute a second-order
approximation to the equilibrium conditions using Dynare.
30
1.4.1 Functional Forms, Parametrization and Calibration
The quantitative analysis uses the following functional forms for preferences,
production technology and capital adjustment costs:
25
U(c, 1 ? L) = log(c) + ?log(1 ? L) (1.48)
F(K, H) = K
?
H
1??
(1.49)
?
_
I
K
_
=
I
K
?
?
2
_
I
K
??
_
2
(1.50)
Table 1.3 lists the parameter values for the model economy. The preference
and production parameters are standard in business cycle literature. I take the
quarterly discount factor, ? as 0.9942 to match the 2.37% average annualized real
deposit rate in the U.S. for the period 1987.Q1-2010.Q4. I pick the relative utility
weight of labor ? as 1.72 to ?x hours worked in steady state, L, at one third of
the available time. The share of capital in the production function is set to 0.36
to match the labor share of income in the U.S. data. The capital adjustment cost
parameter is taken so as to match the relative volatility of price of investment goods
with respect to output in the U.S. data.
26
The quarterly depreciation rate of capital
is set to 2.25% to match the average annual investment to capital ratio.
25
I choose the functional form of the capital adjustment cost following Bernanke, Gertler and
Gilchrist (1999), Gertler, Gilchrist, and Natalucci (2007).
26
The volatility of price of investment goods is taken from Gomme et al. (2011).
31
Table 1.3: Model Parameterization and Calibration
Description Parameter Value Target Data
Preferences
Quarterly discount factor ? 0.9942 Annualized real deposit rate 2.37%
Relative utility weight of leisure ? 1.7167 Hours worked 0.3333
Production Technology
Share of capital in output ? 0.36 Labor share of output 0.64
Capital adjustment cost parameter ? 3.6 Relative volatility of price of investment 0.37
Depreciation rate of capital ? 0.025 Average annual ratio of investment to capital 10%
Steady-state total factor productivity z 1 Normalization N/A
Financial Intermediaries
Steady-state fraction of assets that can be diverted ? 0.1548 Commercial and industrial loan spread 0.46%
Proportional transfer to the entering bankers ? 0.001 0.1% of aggregate net worth N/A
Survival probability of the bankers ? 0.9685 Leverage ratio of commercial banks 4.62
Steady-state level of net worth shock ? 1 Normalization N/A
Shock Processes
Persistence of TFP process ?z 0.9315 Quarterly persistence of TFP process 0.9315
Standard deviation of productivity shock ?z 0.006424 Quarterly standard dev. of TFP shock 0.0064
Persistence of ? process ?? 0.3744 Quarterly persistence of ? process 0.3744
Standard deviation of net worth shock ?? 0.0512 Quarterly standard dev. of net worth shock 0.0512
The non-standard parameters in our model are the ?nancial sector parame-
ters: the fraction of the revenues that can be diverted, ?, the proportional transfer
to newly entering bankers, ?, and the survival probability of bankers, ?. I set ? to
0.001 so that the proportional transfer to newly entering bankers is 0.1% of aggre-
gate net worth.
27
I pick other two parameters simultaneously to match the following
two targets: an average interest rate spread of 46 basis points, which is the histor-
ical average of the di?erence between the quarterly commercial and industrial loan
spread and the quarterly deposit rate from 1987.Q1 to 2010.Q4, and an average
leverage ratio of 4.61, which is the historical average of U.S. commercial banks’
leverage ratio for the same period. The resulting values for ? and ? are 0.155 and
0.968, respectively.
Finally, turning to the shock processes, I follow the standard Solow residuals
approach to construct the series for productivity shocks.
28
Using the production
27
I keep the proportional transfer to newly entering bankers small, so that it does not have
signi?cant impact on the results.
28
I also perform model-based simulations of macro-?nancial shocks using utilization-adjusted
TFP series constructed by Fernald (2009). The results can be found in Appendix A.5.
32
function, I obtain
z
t
=
y
t
K
?
t
H
1??
t
(1.51)
Using the empirical series for output, y
t
, capital, K
t
, and labor, H
t
, I use equation
(1.51) to obtain the z
t
series. Then I construct the log-deviation of TFP series by
linearly detrending the log of the z
t
series over the period 1987.Q1-2010.Q4.
Similar to the construction of productivity shocks, ?
t
series are constructed
from the law of motion for bank net worth, which is given by
?
t
=
1
?[(r
kt+1
? r
t+1
)
?t
???t
+ (1 + r
t+1
)] + ?
¯ n
t+1
¯ n
t
(1.52)
Using the empirical series for net worth, n
t
, credit spread, r
kt+1
? r
t+1
, leverage,
?t
???t
, and gross deposit rate 1 + r
t+1
, I use equation (1.52) obtain the ?
t
series.
29
Then I construct the log-deviation of ?
t
series by linearly detrending the log of these
series over the period 1987.Q1-2010.Q4. The innovations to ?
t
are net worth shocks.
After constructing the z
t
and ?
t
series over the period 1987.Q1-2010.Q4, I
estimate two independent AR(1) processes for both series:
30
log(z
t+1
) = ?
z
log(z
t
) + ?
z
t+1
(1.53)
29
I constructed two ?
t
series by using the realized and the expected values of credit spread. I
obtain the expected value of credit spread by regressing actual spread on real and ?nancial variables
(such as GDP, consumption, investment, hours, bank credit, deposits, net worth) and getting the
predicted value of it. Both series of ? are very similar to each other (the correlation between the
two series is 0.9934).
30
For the stochastic processes, I also tried ?tting a VAR(1), however, the cross-terms in VAR(1)
are statistically insigni?cant at 5% signi?cance level. I included the main results of the analysis
under the VAR(1) representation into the Appendix A.4. The results are qualitatively very similar
although there are some negligible quantitative di?erences.
33
-.06
-.04
-.02
.00
.02
.04
88 90 92 94 96 98 00 02 04 06 08 10
Level of productivity
-.2
-.1
.0
.1
.2
.3
88 90 92 94 96 98 00 02 04 06 08 10
Level of omega
-.03
-.02
-.01
.00
.01
.02
88 90 92 94 96 98 00 02 04 06 08 10
Innovations to productivity
-.2
-.1
.0
.1
.2
.3
88 90 92 94 96 98 00 02 04 06 08 10
Innovations to omega
Figure 1.2: Time Series of Shocks to Productivity and Credit Conditions
log(?
t+1
) = ?
?
log(?
t
) + ?
?
t+1
(1.54)
where ?
z,t+1
and ?
?,t+1
are i.i.d. with standard deviations ?
z
and ?
?
, respectively.
The resulting parameters are ?
z
= 0.93, ?
?
= 0.37, ?
z
= 0.0064, and ?
?
= 0.05.
The ?rst two panels of Figure 1.2 plot the variables z
t
and ?
t
constructed using
the procedures described above. The ?gures show that the levels of productivity
and credit conditions fell sharply in the recent recession.
31
The bottom panels
31
The level of ?
t
started to decline before the recession o?cially began. However, we see a
sharp increase in the level of ?
t
in the middle of the recession period due to the fact that there
are huge capital transfers from bank holding companies to their commercial banks and injection
of capital from the FED with the capital purchase program. If we remove this spike due to the
capital transfers, we see a decline in the level of ?
t
before the recession starts.
34
plot the innovations ?
z,t
and ?
?,t
. These innovations are unexpected changes in the
levels of productivity and ?nancial conditions. The plots suggest that the U.S.
economy is severely hit by both negative productivity and ?nancial shocks in the
Great Recession.
1.4.2 Long-Run Equilibrium of the Model
This section presents the deterministic steady-state properties of the model
economy. First, I will formally show how the tightness of bank capital constraint
a?ects output. Imposing the steady-state on the competitive equilibrium conditions
of the model economy yields the following analytical expression for output:
y =
_
_
?
(1???)µ?
(1??)?(1+µ)
+
(1??)
?
+ ?
_
_
1
(1??)
L
2??
(1.55)
where µ is the Lagrange multiplier of bank capital constraint. Taking the partial
derivative of output w.r.t. µ, I obtain
?y
?µ
= ?
?
(1 ? ?)
_
_
?
(1???)µ?
(1??)?(1+µ)
+
(1??)
?
+ ?
_
_
?
(1??)
L
2??
_
(1 ? ?)?(1 ? ??)?
[(1 ??)?(1 + µ)]
2
_
?2
< 0
(1.56)
which unambiguously shows that the output will be lower the larger µ. The reason is
simple. As the bank capital constraint gets tighter, the credit spread will be larger,
35
as can be seen from the following expression.
(r
k
? r) =
(1 ???)µ?
(1 ??)?(1 + µ)
(1.57)
The term at the right-hand side of equation (1.57) appears as a positive wedge
in the intertemporal Euler equation, which determines how deposits (savings) are
transformed into credit to ?rms in the economy. This positive wedge reduces the
amount of savings that can be extended as credit to non-?nancial ?rms, lowering
their physical capital accumulation, and thus leading to a lower steady-state output.
The same mechanism is also at work when shocks move the economy around the
steady-state as they tighten or relax the bank capital constraint.
0 0.1 0.2 0.3 0.4
0.8
1
1.2
1.4
1.6
Output
0 0.1 0.2 0.3 0.4
0.7
0.8
0.9
1
Consumption
0 0.1 0.2 0.3 0.4
0.1
0.2
0.3
0.4
0.5
Investment
0 0.1 0.2 0.3 0.4
0.3
0.32
0.34
0.36
Hours
0 0.1 0.2 0.3 0.4
0
5
10
15
Deposits
0 0.1 0.2 0.3 0.4
0
1
2
3
Net Worth
0 0.1 0.2 0.3 0.4
0
5
10
15
20
Leverage Ratio
0 0.1 0.2 0.3 0.4
0
0.5
1
1.5
Credit Spread (%)
0 0.1 0.2 0.3 0.4
5
10
15
20
Total Credit
Figure 1.3: Long-run equilibrium as a function of fraction of diverted funds by
bankers
36
Second, I analytically show how output is a?ected by the severity of credit
frictions in banking sector, which is governed by the fraction of diverted funds by
bankers, ?. Taking the partial derivative of output w.r.t. ?, I get
?y
??
= ?
?L
2??
(1 ? ?)
_
¸
¸
_
?
_
(1???)[(1??)???]
(1??)?(1??)?
_
(1??)
?
(1???)[(1??)???]?
(1??)?(1??)?
+
(1??)+??
?
_
¸
¸
_
?
(1??)
_
(1 ? ??)[(1 ? ?)? ? ?]?
(1 ??)?(1 ? ?)?
+
(1 ? ?) + ??
?
_
?2
< 0
(1.58)
which implies that the steady-state output will be lower the higher the intensity
of ?nancial frictions in banking sector. In order to get the intuition behind this
result, I display long-run equilibria of real and ?nancial variables as a function of
the intensity of the credit friction in the ?nancial sector given by fraction of diverted
funds by bankers, ?. All other parameter values are set to those shown in Table 1.3.
Figure 1.3 shows that the long-run dynamics of the model economy to changes in ?
is monotonic and non-linear. As ? increases, households’ incentive to make deposits
into banks falls since the bankers’ gain from diverting funds rises. Banks have to
?nance their equity investment by internal ?nancing rather than external ?nancing.
Thus, deposits go down and net worth rises, leading to a fall in banks’ leverage ratio.
The decline in leverage ratio is sharper than the rise in net worth, inducing a drop
in total credit to non-?nancial ?rms. Credit conditions tighten for ?rms and their
cost of funds given by credit spread goes up. This leads to a reduction in investment
and output falls.
37
1.4.3 Intermediary Capital and the Transmission of Shocks
I present the dynamics of the model in response to productivity and net worth
shocks. In the ?gures below, credit spread, return to capital, and deposit rate are
expressed in percentage points per annum. The responses of all other variables are
expressed in percentage deviations from their respective steady state values.
1.4.3.1 Impulse Responses to TFP Shocks
Figure 1.4 presents the impulse responses to a one-time, one-standard devi-
ation negative shock to TFP. The negative technology shock reduces the price of
investment goods produced by capital producers by 0.3% on impact, lowering the
value of ?rms’ shares. This makes purchase of their shares less pro?table for banks,
which can also be observed from the 1.2% fall in the return to capital. Thus, banks
have di?culty in obtaining deposits from households since their equity investment
becomes less attractive. This reduces the return to deposits by 0.2%, inducing a
countercyclical credit spread. The spread rises by 0.3% on impact. In order to
compensate the fall in their external ?nancing, banks need to ?nance a larger share
of their purchases of equities from their net worth. However, bank net worth also
falls by 4% due to lower asset prices. Since the decline in net worth is sharper
than the fall in deposits on impact, banks’ leverage ratio rises. Hence, the model
with productivity shocks generates a countercyclical leverage ratio. Because banks
cannot adjust their net worth immediately and the lower price of capital reduces
the value of their net worth, their ?nancing conditions tighten and bank lending in
38
the form of equity purchases falls dramatically (by about 4.6%), inducing aggregate
investment to shrink by 0.9%. Finally, hours fall by 0.15%, and output declines by
1.2%.
39
0 5 10 15 20
?1.2
?1
?0.8
?0.6
?0.4
?0.2
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Output
0 5 10 15 20
?0.4
?0.35
?0.3
?0.25
?0.2
Consumption
0 5 10 15 20
?1
?0.8
?0.6
?0.4
?0.2
0
Investment
0 5 10 15 20
?0.2
?0.15
?0.1
?0.05
0
Hours Worked
0 5 10 15 20
?5.4
?5.2
?5
?4.8
?4.6
?4.4
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Bank Credit
0 5 10 15 20
?5
?4
?3
?2
?1
0
Deposits
0 5 10 15 20
?4
?3
?2
?1
0
Bank Net Worth
0 5 10 15 20
?0.1
0
0.1
0.2
0.3
0.4
Credit Spread (Rk?R)
0 5 10 15 20
?0.3
?0.2
?0.1
0
0.1
Quarters
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Price of Capital
0 5 10 15 20
?1.5
?1
?0.5
0
0.5
Quarters
Return to Capital
0 5 10 15 20
?0.2
?0.15
?0.1
?0.05
0
0.05
Quarters
Deposit Rate
0 5 10 15 20
?0.3
?0.2
?0.1
0
0.1
Quarters
Bank Capital to Asset Ratio
Figure 1.4: Impulse responses to a negative one-standard-deviation productivity shock
4
0
0 5 10 15 20
?1
?0.8
?0.6
?0.4
?0.2
0
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Output
0 5 10 15 20
?0.5
0
0.5
1
Consumption
0 5 10 15 20
?2
?1.5
?1
?0.5
0
0.5
Investment
0 5 10 15 20
?0.4
?0.3
?0.2
?0.1
0
0.1
Hours Worked
0 5 10 15 20
?9
?8
?7
?6
?5
?4
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Bank Credit
0 5 10 15 20
?5
0
5
10
Household Deposits (Bank Liabilities)
0 5 10 15 20
?20
?15
?10
?5
0
Bank Net Worth
0 5 10 15 20
0
0.5
1
1.5
Credit Spread (Rk?R)
0 5 10 15 20
?0.6
?0.4
?0.2
0
0.2
Quarters
D
e
v
i
a
t
i
o
n
f
r
o
m
s
.
s
.
(
%
)
Price of Capital
0 5 10 15 20
?2
?1.5
?1
?0.5
0
0.5
Quarters
Return to Capital
0 5 10 15 20
?1
?0.5
0
0.5
Quarters
Deposit rate
0 5 10 15 20
?1.5
?1
?0.5
0
Quarters
Bank Capital to Asset Ratio
Figure 1.5: Impulse responses to a negative one-standard-deviation net worth shock
4
1
1.4.3.2 Impulse Responses to Financial Shocks
Figure 1.5 presents the impulse responses to a one-time, one-standard devia-
tion negative shock to net worth. The negative net worth shock immediately reduces
net worth of banks. Bank net worth falls roughly by 15% on impact. In order to
compensate the decline in their internal ?nancing, they need to ?nance a larger share
of their purchases of equities from deposits. This induces a rise in their leverage
ratio. Hence, the model driven by net worth shocks also generates a countercycli-
cal leverage ratio. Although they have to ?nance a greater fraction of their equity
investment from deposits, their ability to do so is impaired by the fall in their net
worth, leading deposits to decline after ?ve quarters. Moreover, the fall in their
net worth translates into a reduction in bank credit to ?rms. Bank credit shrinks
by roughly 8% on impact. Since ?rms ?nance their capital expenditures via bank
credit, they cut back their investment severely (by about 2%). The drop in invest-
ment reduces the price of capital by 0.4%, which lowers banks’ net worth further.
Hours fall by 0.4% and output drops by 0.9% on impact. Finally, consumption rises
on impact after the shock hits, which is what was observed at the beginning of the
recent ?nancial crisis. In the context of the model, this seemingly unappealing re-
sult can be explained as follows: On the intratemporal margin, the fall in aggregate
demand caused by lower investment expenditures translates into a reduction in the
demand for labor, which eventually leads to a drop in hours worked. Since wages
are ?exible, the reduction in labor demand also lowers wages, leading to a fall in
households’ wage bill. However, the rise in credit spread on impact raises banks’
42
pro?ts. Since households own banks, the rise in their pro?ts helps households sus-
tain their consumption after the ?nancial shock hits. On impact, the rise in bank
pro?ts dominates the reduction in wage bill, pushing consumption up.
32
1.4.4 Business Cycle Dynamics
This section presents numerical results from stochastic simulations of the
benchmark economy with productivity and net worth shocks. First, I simulate the
model economy 1000 times for 1096 periods each and discard the ?rst 1000 periods
in each simulation so that each simulation has the same length as the data sample.
I then compute the standard business cycle statistics using the cyclical components
of the HP-?ltered series. I also conduct the same quantitative exercise for the fric-
tionless version of the benchmark economy, which is essentially the standard RBC
model with capital adjustment costs, in order to compare the real ?uctuations in
both models. Finally, I simulate the model economy only driven by productivity
shocks to see the contribution of net worth shocks to the observed dynamics of real
and ?nancial variables.
Table 1.4 presents quarterly real and ?nancial statistics in the data and in
the model economies. In particular, it displays the relative standard deviations
of real and ?nancial variables with respect to output and their cross-correlations
with output. Column 3 of the table shows that the standard RBC model with
capital adjustment costs driven by standard productivity shocks is able produce
32
Barro and King (1984) argue that any shock that reduces the quantity of hours worked on
impact has to lead a fall in consumption due to consumption-leisure optimality condition. Ajello
(2010) shows that sticky wages are the key factor in generating a positive comovement between
consumption and investment after a ?nancial shock.
43
the key business cycle facts in the U.S. data as expected: consumption and hours
less volatile than output, while investment is more volatile, all real variables are
highly procyclical. However, this model can only explain 80% of the ?uctuations in
output and less than half of the relative volatility in hours. It also generates roughly
perfect positive correlation between real variables and output, contrary to the data.
Moreover, this model has no predictions about ?nancial variables.
Column 4 of the table shows the business cycle statistics of our model economy
with only productivity shocks. This model is much closer to the data in terms of
real ?uctuations, compared to the RBC model. It now accounts for 85% of the
?uctuations in output and roughly half of the relative volatility in hours. The
model is also able to replicate most of the stylized facts about ?nancial variables:
bank assets, deposits and loan spread is less volatile than output, while net worth
and leverage ratio are more volatile; bank assets and net worth are procyclical, while
leverage ratio and loan spread are countercyclical. However, it generates procyclical
deposits, contrary to the data. Although the model does a good job in terms of key
facts of ?nancial variables, it predicts lower ?uctuations. For example, it can explain
less than half of the relative volatility in bank assets, roughly half of the relative
volatility in deposits, less than one third of the relative volatility in net worth and
leverage ratio. The model virtually matches the relative volatility of credit spread.
44
Table 1.4: Real and Financial Statistics
Statistic Data RBC Only Productivity Benchmark
?
Y
1.80 1.44 1.53 1.81
?
C
0.45 0.41 0.39 0.75
?
I
2.73 2.45 2.98 4.64
?
L
0.91 0.40 0.46 0.84
?
Y,I
0.97 1.00 0.98 0.87
?
Y,C
0.82 0.97 0.85 -0.03
?
Y,L
0.83 0.99 0.96 0.81
?
Assets
0.93 – 0.40 0.58
?
Deposits
0.69 – 0.39 0.87
?
NetWorth
5.17 – 1.36 5.90
?
LeverageR.
5.61 – 1.40 6.40
?
Spread
0.08 – 0.07 0.23
?
Y,Assets
0.30 – 0.90 0.88
?
Y,Deposits
-0.39 – 0.46 -0.23
?
Y,NetWorth
0.52 – 0.87 0.68
?
Y,LeverageR.
-0.49 – -0.71 -0.59
?
Y,Spread
-0.39 – -0.86 -0.67
a
Business cycle statistics in the table are based on HP-?ltered cyclical components of quarterly simulated time
series (smoothing parameter:1600).
b
The standard deviation of output is expressed in percent; standard deviations of the remaining variables are
normalized by the standard deviation of output (std(x)/std(GDP)).
c
In all model economies, capital adjustment cost parameter is set to 3.3, which is calibrated in benchmark model
to match the relative volatility of price of investment.
Column 5 of the table shows the real and ?nancial statistics in the benchmark
economy driven by both shocks. This model is even closer to the data than the
previous model in terms of business cycle properties of real variables. It predicts all
of the ?uctuations in output, almost all of the relative volatility in hours. The cross
correlations of investment and hours with output are quite inline with the data.
45
However, the model generates acyclical consumption due to the reasons explained
in the previous section. This model has better predictions about ?nancial variables.
It is able to reproduce the key facts about aggregate ?nancial variables. Moreover, it
now explains more than half of the relative volatility in bank assets, and somewhat
overpredicts the relative volatility in other ?nancial variables. The last column of
Table 1 establishes the ?rst main result of the ?rst chapter: the benchmark model
driven by both shocks is able to deliver most of the key stylized facts about real and
?nancial variables simultaneously.
1.5 Model-Based Simulations of Macro-Financial Shocks vs. U.S.
Data
I also study the dynamics of the model in response to the actual sequence
of shocks to see whether the model is able to generate the real and ?nancial cycles
observed in the U.S. data.
33
I feed the actual innovations to z
t
and ?
t
into the model
and compute the responses of real and ?nancial variables over the period 1987 to
2010.
Figure 1.6 displays the quarterly time series of output, investment and hours
in the data, in the standard RBC model with capital adjustment costs, and in the
benchmark economy. The RBC model is driven by standard productivity shocks,
while the benchmark model is driven by both shocks. Both the quarterly times se-
33
Although I feed the actual series of shocks into the model, they are not perfectly anticipated
by the agents in the economy as they predict future values of z
t
and ?
t
using the AR(1) processes
given by (1.53) and (1.54).
46
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 1
GDP
corr(data, rbc) = 0.69
corr(data, benchmark 1) = 0.80
-50
-40
-30
-20
-10
0
10
20
30
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 1
Investment
corr(data, rbc) = 0.72
corr(data, benchmark 1) = 0.79
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 1
Hours
corr(data, rbc) = 0.39
corr(data, benchmark 1) = 0.60
Figure 1.6: Real Fluctuations: Benchmark vs. RBC model
47
ries of the variables and their model counterparts are log-linearly detrended over the
period 1987.Q1 - 2010.Q4, and plotted in percentage deviations from their trends.
The correlations between the actual and the model-simulated series are also reported
in the graphs. The ?gure suggests that both the RBC model and the benchmark
economy generate series of real variables that closely follow their empirical coun-
terparts. However, the RBC model predicts lower ?uctuations in all real variables.
In particular, the RBC model predicts a smaller decline in output in the 1990-91
recession. Moreover, it generates declines in investment and hours that are smaller
than the actual declines in the 1990-91 and 2007-09 recessions. On the other hand,
the benchmark model generates larger ?uctuations in real variables, consistent with
the data. Since this model has one additional shock compared to the RBC model,
higher volatility can be expected. However, the benchmark model also improves
upon the RBC model in the sense that for output, investment and hours, the cross-
correlations between the data and the benchmark model is much higher than those
between the data and the RBC model. Moreover, the model’s success in generating
empirically-relevant ?uctuations in hours hinges on the fact that it is able to produce
quantitatively reasonable ?uctuations in capital. Since labor is complementary to
capital stock in a standard Cobb-Douglas production function, empirically-relevant
changes in capital stock lead to observed ?uctuations in hours. The second dimen-
sion that the benchmark model improves upon the RBC model is that the latter has
no predictions about ?nancial variables by construction while the former generates
movements in ?nancial variables consistent with the U.S. ?nancial data.
Figure 1.7 displays the quarterly time series of output, investment and hours
48
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
GDP
corr(data, only prod.) = 0.68
corr(data, benchmark 1) = 0.80
-50
-40
-30
-20
-10
0
10
20
30
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Investment
corr(data, only prod.) = 0.68
corr(data, benchmark 1) = 0.79
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Hours
corr(data, only prod.) = 0.33
corr(data, benchmark 1) = 0.60
Figure 1.7: Real Fluctuations: Benchmark vs. Only Productivity
49
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
GDP
corr(data, rbc) = 0.69
corr(data, only prod.) = 0.68
-40
-30
-20
-10
0
10
20
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Investment
corr(data, rbc) = 0.72
corr(data, only prod.) = 0.68
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Hours
corr(data, rbc) = 0.39
corr(data, only prod.) = 0.33
Figure 1.8: Real Fluctuations: RBC vs. Only Productivity
in the data, in the model driven only by productivity shocks, and in the benchmark
economy. The ?gure suggests that the benchmark economy performs better than
the model with only productivity shocks in terms of both volatilities of real variables
and cross-correlations of those variables with the data. For all the real variables,
the cross-correlations with the data in the benchmark model is higher than those
with the data in the model with only productivity shocks.
Figure 1.8 displays the quarterly time series of output, investment and hours
in the data, in the RBC model, and in the model driven only by productivity
shocks. This ?gure suggests that the model with only productivity shocks is not
50
very di?erent from the RBC model in terms of its quantitative performance in real
variables. Actually, the series of real variables generated by these two models are
almost the same. Therefore, we can say that credit frictions in banking sector
by themselves are not enough to improve upon the RBC model and to produce
real ?uctuations consistent with the data. Financial shocks are quite important in
explaining the observed dynamics of real variables.
Figure 1.9 shows the quarterly time series of bank credit, deposits, net worth,
leverage ratio, and credit spread both in the data, in the model driven only by
productivity shocks and in the benchmark model. Both the quarterly time series of
?nancial variables and their model counterparts are log-linearly detrended over the
period 1987.Q1 - 2010.Q4, and plotted in percentage deviations from their trends.
Credit spread is plotted in annualized percentages. The correlations between the
actual and the model-simulated series are also reported in the graphs. For all the
?nancial variables, the cross-correlations with the data in the benchmark model is
signi?cantly higher than those with the data in the model with only productivity
shocks. Speci?cally, for net worth, leverage ratio and credit spread, the benchmark
model produces highly positively correlated series with the data, while the model
with only productivity shocks predicts negative correlations. Thus, ?gures 1.7 and
1.9 establish the second main result of the chapter that ?nancial shocks contribute
signi?cantly to explaining the observed dynamics of ?nancial variables.
Figure 1.10 plots the ?uctuations in the Lagrange multiplier of bank capital
constraint in the benchmark model and those in the index of credit tightness con-
structed by Federal Reserve Board using the Senior Loan O?cer Opinion Survey
51
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Bank credit
corr(data, only prod.) = 0.66
corr(data, benchmark 1) = 0.75
-10
-8
-6
-4
-2
0
2
4
6
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Deposits
corr(data, only prod.) = 0.48
corr(data, benchmark 1) = 0.50
-80
-60
-40
-20
0
20
40
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Net worth
corr(data, only prod.) = -0.17
corr(data, benchmark 1) = 0.74
-40
-20
0
20
40
60
80
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Leverage ratio
corr(data, only prod.) = -0.07
corr(data, benchmark 1) = 0.72
-2
0
2
4
6
8
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 1
Credit spread
corr(data, only prod.) = -0.09
corr(data, benchmark 1) = 0.45
Figure 1.9: Financial Fluctuations: Benchmark vs. Only Productivity
52
-60
-40
-20
0
20
40
60
80
100
88 90 92 94 96 98 00 02 04 06 08 10
Survey of senior officers
Lagrange multiplier
Index of tightening credit standards
Figure 1.10: Tightness of Credit Conditions in the Benchmark Model
on Bank Lending Practices. Starting with the second quarter of 1990, this sur-
vey basically asks senior loan o?cers whether they have recently tighten the credit
standards for commercial and industrial loans, and the collected responses are used
to create an index of credit tightness as the percentage of respondents, reporting
tightening standards. Increases in both the multiplier and the index show the ad-
verse changes in bank lending to non-?nancial businesses. The ?gure shows that
the multiplier tracks the index well. The multiplier also explains the severity of
credit conditions experienced by the U.S. economy in the last three recessions by
capturing most of the ?uctuations in the index. However, there seems to be a phase
shift between these two series.
34
There might be two reasons behind this. The ?rst
one is the inability of standard RBC models to match the lead-lag relationships of
macro variables. The second one is using lagging ?nancial variables from H.8 tables
34
If I use loan losses data to construct the ?nancial shock series, there is no phase shift in the
tightness of credit conditions.
53
while constructing ?nancial shocks rather than using leading ?nancial variables from
Consolidated Reports of Condition and Income (Call) Reports. Bearing this caveat
in mind, we can say that ?gure 1.10 establishes the third main result of this chapter:
U.S. banks experienced a signi?cant deterioration in their lending ability in the last
recessions, especially in 1990-91 and 2007-09 recessions.
1.6 Conclusion
This study quantitatively investigates the joint role of ?nancial shocks and
credit frictions a?ecting banking sector in driving the real and ?nancial ?uctuations
in the U.S. data. To this end, I ?rst characterize the empirical cyclical behavior of
aggregate ?nancial variables of U.S. banking sector. I then use an otherwise standard
real business cycle model with a ?nancial sector, which features an agency problem
between banks and their depositors, leading to endogenous borrowing constraints
for banks in obtaining funds from households. I incorporate empirically-disciplined
shocks to bank net worth (i.e. “?nancial shocks”) which a?ect the ability of banks
to obtain funds from households and to extend credit to non-?nancial sector.The
time series of ?nancial shocks are constructed from the data. The resulting shock
series show that credit conditions in the U.S. economy deteriorated signi?cantly in
the recent recession.
Several key ?ndings emerge from the quantitative analysis. First, the bench-
mark model driven by both productivity and ?nancial shocks is able to explain
most of the empirical facts about real and ?nancial variables simultaneously. Sec-
54
ond, ?nancial shocks to banking sector contribute signi?cantly not only to the ob-
served dynamics of aggregate ?nancial variables but also to the observed dynam-
ics of standard macroeconomic variables. In particular, the benchmark model has
better predictions about real and ?nancial variables than the model driven only
by productivity shocks. Third, the simulation of the benchmark model points a
signi?cant worsening in banks’ lending ability in 1990-91 and 2007-09 recessions.
The main transmission mechanism of ?nancial shocks is through bank capital chan-
nel. In particular, ?nancial shocks are transmitted to the real economy through
tightening bank capital constraint, which eventually leads to rising credit spread.
Non-?nancial ?rms perceive this rise in credit spread as an increase in their cost of
borrowing from banks, leading to a decline in their external ?nance for investment
expenditures. Falling aggregate demand caused by lower investment reduces the
demand for labor, which brings a drop in hours worked, and hence output.
For further research, one can investigate the normative implications of the
model in the light of the recent ?nancial crisis, as U.S. government has assisted
many ?nancial ?rms in order to raise their franchise value, and hence to support
real economic activity. In order to start thinking about how di?erent policy tools
can be implemented in an environment in which the ?nancial sector is crucial for
business cycle ?uctuations and what the welfare implications of these policies are,
we need a model capable of matching real and ?nancial ?uctuations simultaneously.
We think that the model proposed in this study is quite successful in this dimension.
55
Chapter 2
Required Reserves as a Credit Policy Tool
(joint with Enes Sunel and Temel Ta¸sk?n)
2.1 Introduction
Policymakers in both advanced and emerging countries have been exercising
a variety of measures to mitigate the transmission of ?nancial disruptions to the
real sector. To that end, frictions in the ?nancial sector and macroprudential policy
instruments have been the focal point of the recent literature on macroeconomic
dynamics and policy. Among many, reserve requirements have been used extensively
as a macroprudential policy tool in several emerging countries, recently. China,
Brazil, Malaysia, Peru, Colombia and Turkey are some of the countries among others
who have used this tool mostly to curb excessive credit growth in upturns along with
other reasons.
1
In terms of their main objectives, they employ reserve requirements
either as a monetary policy tool to achieve price stability or as a macroprudential
policy tool to foster ?nancial stability, or both. For example, the Central Bank
of the Republic of Turkey (CBRT, hereafter) regards the interest rate as the main
policy tool for price stability, with a secondary role for ?nancial stability, and reserve
requirements as the main policy tool for ?nancial stability, with a secondary role
1
See Montoro and Moreno (2011), Montoro (2011), Gray (2011), Glocker and Towbin (2012)
for the discussion of country experiences.
56
for price stability.
2
The main idea behind using reserve requirements as the main
instrument for ?nancial stability and interest rate as the main instrument for price
stability might be to separate tasks, which increases transparency and facilitates
communication of these policies. In this regard, this study explicitly focuses on the
?nancial stability of reserve requirements.
Central banks could use reserve requirements to achieve ?nancial stability in
the following manner as Montoro and Moreno (2011) noted: they can raise reserve
requirements to contain credit growth in the boom part of the business cycle in
order to counteract ?nancial imbalances in the economy or in an economic downturn,
they can lower reserve requirements to utilize reserve bu?ers accumulated during the
boom part, having the banking sector extend more credit to non-?nancial businesses.
Therefore, reserve requirements can be used as a cyclical policy instrument to ease
credit ?uctuations in the ?nancial sector, and hence to stabilize the real economy.
The goal of this study is to investigate the e?ectiveness of reserve requirements
that respond to expected credit growth in moderating the real and ?nancial cycles of
an economy. We do so in a model where real and ?nancial ?uctuations are ampli?ed
by a ?nancial accelerator mechanism. Speci?cally, we explore the stabilizing role
of reserve requirements as a credit policy tool, on the transmission mechanism of
productivity, monetary and ?nancial shocks. The results suggest that a time-varying
reserve requirement policy mitigates the ?uctuations in key macroeconomic variables
and improves welfare vis-a-vis a ?xed reserve requirement policy.
3
2
Basci (2010).
3
At this point, we acknowledge that cancelling reserve requirements altogether might improve
aggregate welfare of the economy. However, mostly due to precautionary reasons, positive reserve
requirements do exist in practice and since it is beyond the scope of this paper, we do not bring
57
Figure 2.1: Evolution of Required Reserve Ratios in Turkey
We extend the basic ?nancial intermediation framework to one in which “money”
is explicitly modelled via a cash-in-advance constraint. Consequently, we introduce
required reserves into the model in a very tractable way, since we have the concept
of a monetary base.
After the mid of 2010, the CBRT has determined two policy targets in order to
mitigate macro-?nancial imbalances in Turkish economy as Basci and Kara (2011)
elaborated. The ?rst one is to reduce short-term capital in?ows to lower current
account de?cit, and the second one is to curb excessive credit growth in banking
any micro-foundation to this institutional framework in what follows.
58
sector. In this regard, it was decided that in addition to short-term interest rate,
reserve requirements and interest rate corridor are used to foster ?nancial stability
without compromising price stability. Moreover, in order to increase the e?ectiveness
of reserve requirements as a policy tool, the CBRT let the interest rate ?uctuate in
a controlled manner at overnight market to use interest rate corridor as an active
policy instrument and terminated paying interest on required reserves by September
2010. It also di?erentiated required reserves at di?erent maturities (having a higher
required reserve ratio for short-term liabilities) and hence extended the maturity of
banking sector’s liabilities in order to strengthen ?nancial stability.
We calibrate the model to the Turkish economy which exempli?es the use of
reserve requirements as a macroprudential tool since the end of 2010 (see ?gure 2.1).
In particular, the CBRT has increased weighted average of required reserves ratio –
henceforth, RRR – from 5% to 13% between the period October 2010 and April 2011,
in a stepwise manner. This period also coincides with the aftermath of the second
phase of quantitative easing implemented by monetary authorities in a number of
advanced economies. Evidently, this period is characterized by an increase in the
risk appetite of global investors and excessive credit growth in emerging economies
such as Turkey. On the other hand, same measure of RRR has been reduced to
about 10% around November 2011 by the CBRT following the debt crisis of the
Euro area.
Our quantitative exercise involves comparing a “?xed RRR economy” in which
the RRR is calibrated to its “long-run” value preceding the interventions of the
CBRT and the “time-varying RRR economy” in which the RRR is countercycli-
59
cal with respect to expected credit growth.
4
We approximate the required reserves
policy implemented by the CBRT with this countercyclical rule since the CBRT of-
?cials and economists stated that it used the reserve requirements to curb excessive
credit growth in the banking sector after the second phase of quantitative easing
conducted by many advanced economies’ central banks and to ease credit condi-
tions in the banking sector after the Eurozone debt crisis.
5
Moreover, we model
the rule as the one which reacts to expected credit growth in order to re?ect the
CBRT’s incentive to use this policy tool proactively and in a macroprudential and
forward-looking manner.
6
We also simulate the model under moderate and aggres-
sive required reserve policies in order to understand the e?ectiveness of the policy
as a macroprudential policy tool.
There are three main results of this study: First, the time-varying required
reserve ratio rule mitigates the negative e?ects of adverse macroeconomic and ?nan-
cial shocks and the ?nancial accelerator mechanism on real and ?nancial variables.
As a result, we conclude that RRRs might be used as a macroprudential policy
tool in an economy that exhibits ?nancial frictions. Second, in response to TFP
and money growth shocks, countercyclical reserves policy reduces the volatilities of
key variables such as output, consumption, investment, bank credit, credit spreads
and asset prices in comparison with ?xed reserves policy. This happens because
the ampli?cation e?ect of the ?nancial sector is mitigated by time-varying reserve
4
We also conduct the analysis of a model economy with zero required reserves policy. The
dynamics of this case strongly resemble those of the ?xed RRR economy.
5
Basci and Kara (2011) and Kara (2012).
6
The results seem quite similar if the rule responds to current credit growth. The main idea
behind this rule is to reduce the procyclicality of the banking sector in the face of adverse macro
shocks and hence to stabilize the real economy.
60
requirements. Third, a time-varying reserve requirement policy is welfare superior
to a ?xed reserve requirement policy.
The workings of the model might be elaborated in greater detail as follows:
An adverse TFP shock reduces the demand of ?nancial intermediaries for equity
and drives down its price. The collapse in asset prices feeds back into the endoge-
nous capital constraints of intermediaries and causes banks’ net worth to decline.
Accordingly, the shortage in loanable funds, which manifests itself as a rise in credit
spreads, combined with the collapse in asset prices causes investment to decline
substantially. When the RRR is ?xed, the dynamics of reserves resembles that of
deposits.
When the countercyclical RRR policy is in place, the fall in bank credit led
by the adverse TFP shock calls for a reduction in the RRR. This induces banks to
substitute loans for reserves on the assets side of the balance sheet, because the cost
of raising external ?nance is lower with a smaller RRR. Accordingly, larger supply
of funds extended by banks mitigates the collapse in investment and asset prices,
countervailing the ?nancial accelerator mechanism. This also limits the rise in credit
spreads, which is an intertemporal distortion created by ?nancial frictions in the
consumption-savings margin of workers. The downward response of RRR reduces
the demand for monetary base and shoots up in?ation on impact. Therefore, the
credit policy mitigates the ?nancial accelerator at the expense of higher in?ation.
However, since this immediate surge is transitory and driven by the reserves policy,
the model implies an undershooting of in?ation in the following periods. This implies
a substitution of consumption for leisure on the part of forward looking households
61
and labor supply increases in contrast with the ?xed RRR economy. Increased
labor supply combined with a stronger trajectory for capital mitigates the collapse
in output signi?cantly.
A positive money growth shock increases in?ation and crowds out deposits
and consumption for leisure in our cash-in-advance speci?cation. Therefore, a posi-
tive money growth produces similar dynamics to that of TFP shocks in the model.
Consequently, the counter-cyclical RRR policy rule stabilizes key ?nancial and real
variables in response to money growth shocks again at the expense of higher in?a-
tion.
Lastly, we run a ?nancial crisis experiment in which we consider an exoge-
nous decline in the net worth of ?nancial intermediaries as in Hancock, Laing and
Wilcox (1995), Meh and Moran (2010), Brunnermeier and Pedersen (2009), Curdia
and Woodford (2010), Mendoza and Quadrini (2010), Iacoviello (2010), and Mimir
(2011). This shock crudely captures loan losses, asset write-downs or asset revalu-
ations that we observe in the recent ?nancial crisis. Most importantly, it might be
interpreted as an exogenous variation in the risk appetite of international investors,
that may have destabilizing e?ects on the ?nancial system of an economy such as
Turkey.
Although the initial decline in banks’ net worth led by the ?nancial shock is
exogenous, there will be second round e?ects that amplify the collapse in internal
?nance of banks. This would create a shortage of bank credit and would drive a
drop in investment, and in the price of capital. Banks then increase their demand
for external ?nancing (i.e. increase their deposit demand) to compensate for the
62
decline in bank net worth. This causes reserves to increase and drives down in?ation,
pointing out a di?erence from the case of TFP and money growth shocks on part
of the nominal dynamics. Yet, since the shock is transitory, in?ation overshoots in
the period that follows the shock and workers’ expectations regarding the hike in
future in?ation causes hours to decline substantially on impact. Therefore, output
collapses together with investment.
Credit policy in response to ?nancial shock calls for a reduction in the RRR
and is again in?ationary in the sense that the reduction in in?ation on impact
becomes substantially lower. Accordingly, overshooting in in?ation becomes less as
well, limiting the collapse in hours. In this manner, the analysis shows that the
counter-cyclical RRR policy has a stabilizing e?ect in response to ?nancial shocks
in addition to TFP and money growth shocks and might be used by the central
bank as a macroprudential policy tool.
Related Literature
Our work is mostly related to the studies by Glocker and Towbin (2012) and Mon-
toro (2011) who analyze the role of reserve requirements as a macroprudential policy
tool. Glocker and Towbin (2012) augment required reserves as an additional policy
instrument and variations in loans as an additional target into an open-economy
model with nominal rigidities and ?nancial frictions. Their results imply that re-
quirements are in favor of price stability objective only if ?nancial frictions are non-
trivial and are more e?ective if there is a ?nancial stability objective and debt is
denominated in foreign currency. In their work, due to the endogeneity of monetary
63
base, an increase in the RRR increases loan-deposit spreads only if the remuneration
of reserves is below the market rate. Since they obtain impact of policy change on
consumption and investment, the overall e?ect on aggregate demand and in?ation
is ambiguous.
Montoro (2011) introduces counter-cyclical RRR policy tools in an otherwise
standard New-Keynesian setting that introduce collateral and liquidity constraints
as in Kiyotaki and Moore (2008) and maturity mismatch frictions as in Benes and
Lees (2010). He ?nds that RRRs contain the procyclicality of the ?nancial system
in response to demand shocks but not under supply shocks. The main di?erences
of our work with these papers is that we model ?nancial frictions a-la’ Gertler and
Karadi (2011) that introduces an agency problem between depositors and bankers
and that involves equity ?nancing of non-?nancial ?rms. An important deviation
from the former study is that we also explore the role of RRRs in response to ?nancial
shocks and from the latter study is that we ?nd that RRRs might be stabilizing even
under supply shocks. From an alternative perspective, our ?nding that credit policy
implemented by RRRs is the most e?ective in response to ?nancial shocks is in line
with the ?nding of Glocker and Towbin (2012) that RRRs are mostly e?ective when
?nancial frictions are relevant.
Another closely related work to the current study is that of Christensen et al.
(2011) which explores the role of countercyclical bank capital regulations as a macro-
prudential policy tool. Similar to our experiment, they compare time-varying and
constant bank capital regulations and ?nd that the former regime reduces volatili-
ties of real variables and bank lending. However, as they state in their paper, the
64
type of ?nancial friction that they introduce di?ers from that of Gertler and Karadi
(2011) in that it is driven by asymmetric information between bankers and their
creditors a la’ Holmstrom and Tirole (1997), instead of limited commitment. While
the macroprudential regulation in their work is focused on the “size” of the balance
sheet, in our work it is focused on the “composition of the assets side” of the balance
sheet.
Our work also has linkages to closed economy frameworks of Kashyap and Stein
(2012) and Curdia and Woodford (2011) in which the remuneration of reserves has
been studied. Yet, it is obvious that reserves policy studied in these papers are more
related to the central bank balance sheet considerations of the Federal Reserve at
the onset of the sub-prime ?nancial crisis and do not have the focus of containing
excessive credit growth in contrast with the focus of our work. From another per-
spective, the descriptive work of Gray (2011) on recent reserve requirement policy
experiences and the work of Reinhart and Reinhart (1999) on the use of required
reserves for stability of international capital ?ows relates to the current study.
The rest of the paper is organized as follows. Section 2.2 describes the model
economy and characterizes equilibrium. Section 2.3 undertakes the quantitative
analysis regarding the dynamics introduced by macroeconomic and ?nancial shocks
and section 2.4 concludes.
65
2.2 The Model
The model economy is inhabited by households, banks, ?nal goods producers,
capital producers, and a government. Time is discrete. Two ?nancial frictions
characterize the economy. First, market segmentation ensures that households who
are the ultimate savers in the economy cannot directly lend to non-?nancial ?rms.
This assumption makes the banking sector essential for transferring funds from
ultimate savers (households) to ultimate borrowers (?nal goods producers). Second,
banking sector is characterized by credit frictions that are modelled a la Gertler
and Karadi (2011). Households face a cash-in-advance constraint, which makes
them hold real balances, leading to the existence of monetary equilibria. Finally,
banks are subject to time-varying reserve requirements imposed by the central bank,
which reacts countercyclically to expected credit expansion in the economy. Below
is a detailed description of economic agents that reside in this model economy.
2.2.1 Households
The population consists of a continuum of in?nitely-lived identical households.
We assume that each household is composed of a worker and a banker who perfectly
insure each other. Workers supply labor to the ?nal goods producers and assumed
to deposit their savings in the banks owned by the banker member of “other” house-
holds.
7
A representative household maximizes the discounted lifetime utility ?ow earned
7
This assumption is useful in making the agency problem that we introduce in section 2.2.2
more realistic.
66
from consumption, c
t
and leisure, l
t
,
E
0
?
t=0
?
t
u
_
c
t
, l
t
_
(2.1)
where 0 < ? < 1 the subjective discount factor and E is the expectation operator.
Households face the following ?ow budget constraint,
c
t
+ b
t+1
+
M
t+1
P
t
= w
t
(1 ? l
t
) + R
t
b
t
+
M
t
P
t
+ ?
t
+
T
t
P
t
(2.2)
where b
t
is the beginning of period t balance of deposits held at commercial banks, P
t
is the general nominal price level, w
t
is the real wage earned per labor hour, R
t
is the
gross risk free deposits rate, ?
t
is the pro?ts remitted from the ownership of banks
and capital producers and T
t
is lump-sum transfers remitted by the government.
Households face a cash-in-advance constraint which re?ects the timing assump-
tion that asset markets open ?rst as in Cooley and Hansen (1989):
c
t
?
M
t
P
t
+
T
t
P
t
+ R
t
b
t
?b
t+1
(2.3)
Solution of the utility maximization problem of households yield the optimality
conditions below,
67
u
c
(t) = ?R
t+1
E
t
u
c
(t + 1) (2.4)
u
l
(t)
P
t
w
t
= ?E
t
_
u
c
(t + 1)
P
t+1
_
(2.5)
Condition (2.4) is a standard consumption-savings optimality condition, which equates
marginal bene?t of current consumption to the expected discounted bene?t of sav-
ing in deposits. Equation (2.5) on the other hand is a non-standard consumption-
leisure optimality condition due to the existence of cash-in-advance friction which
transforms the trade-o? between the two into an inter-temporal one. Speci?cally,
increasing leisure demand by 1 unit today reduces savings in cash by
P
P
?
=
1
1+?
?
future units because the yield of cash balances is de?ated by in?ation. Therefore,
the utility cost of leisure is measured only in terms of future utility foregone by
facing a tighter cash-in-advance constraint in the next period.
2.2.2 Banks
The modelling of ?nancial sector closely follows that in Gertler and Karadi
(2011). To summarize the key ingredients, we denote the period t balance sheet of
a bank j as,
q
t
s
jt
= (1 ?rr
t
)b
jt+1
+ n
jt
(2.6)
68
The right hand side of the balance sheet denotes the resources of bank j,
namely, net worth, n
jt
and deposits, b
t+1
needed to ?nance its credit extension to
non-?nancial ?rms, q
t
s
jt
. The loans to ?rms serve as state-contingent claims s
jt
towards the ownership of ?rms and are traded at the market price q
t
. Note that
the bank can only loan (1 ? rr
t
) fraction of deposits to the ?rms where rr
t
is the
required reserve ratio set by the central bank as we describe below. The balance
sheet of banks described in equation (2.6) imply an evolution equation for net worth
as follows:
n
jt+1
=
_
R
kt+1
?
_
R
t+1
?rr
t
1 ? rr
t
__
q
t
s
jt
+
_
R
t+1
? rr
t
1 ?rr
t
_
n
jt
(2.7)
It is evident in equation (2.7) that an increase in the required reserve ratio
rr
t
decreases the returns to assets and increases the returns to equity all else equal.
That induces banks to substitute internal ?nancing (n
t
) for external ?nancing (b
t+1
).
Bankers have a ?nite life and survive to the next period with probability ?. At
the end of each period 1 ?? number of new bankers are born and are remitted
?
1??
of the net worth owned by the exiting bankers. Bankers’ objective is to maximize
the present discounted value of the terminal net worth of their ?nancial ?rm, V
jt
,
by choosing the amount of claims against the ?rm ownership, s
jt
. That is,
69
V
jt
= max
s
jt
E
t
?
i=0
(1??)?
i
?
i+1
?
t,t+1+i
__
R
kt+1+i
?
_
R
t+1+i
? rr
t+i
1 ? rr
t+i
__
q
t+i
s
jt+i
+
_
R
t+1+i
? rr
t+i
1 ? rr
t+i
_
n
jt+i
_
(2.8)
The ?nite life of bankers, ? < 1, ensures that bankers never accumulate enough net
worth to ?nance all their equity purchases of non-?nancial ?rms via internal funds
so that they have to borrow from households in the form of deposits.
The key feature of the ?nancial sector unfolds around a moral hazard problem
between banks and households: In this model of banking, households believe that
banks might divert ? fraction of their total assets for their own bene?t. This might
be thought of as investing part of q
t
s
jt
in excessively risky projects that go bankrupt
eventually and not paying back the corresponding liability to the depositor. In this
case, depositors shall cause a bank run and lead to the liquidation of the bank
altogether. Therefore, bankers’ optimal plan regarding the choice of s
jt
at any date
t should satisfy an incentive compatibility constraint,
V
jt
? ?q
t
s
jt
(2.9)
This inequality suggests that the loss of bankers, V
jt
, from diverting the funds
and investing them in risky projects that would likely fail should be greater than or
equal to the diverted portion of the assets, ?q
t
s
jt
.
By using an envelope condition and algebraic manipulation, one can write the
70
optimal value of banks as
V
?
jt
= ?
t
q
t
s
?
jt
+ ?
t
n
?
jt
(2.10)
where the recursive objects,
8
?
t
= E
t
_
(1 ??)??
t,t+1
_
R
kt+1
?
_
R
t+1
? rr
t
1 ?rr
t
__
+ ???
t,t+1
?
t
?
t+1
_
(2.11)
and
?
t
= E
t
_
(1 ??)??
t,t+1
_
R
t+1
? rr
t
1 ?rr
t
_
+ ???
t,t+1
?
t
?
t+1
_
(2.12)
represent the marginal values of relaxing credit and accumulating net worth for the
bank respectively. The growth rates of assets and net worth of banks are denoted
with ?
t
=
q
t+1
s
jt+1
qts
jt
and ?
t
=
n
jt+1
n
jt
.
One can obtain the following by combining equations (2.9) and (2.10):
?
t
q
t
s
jt
+ ?
t
n
jt
? ?q
t
s
jt
(2.13)
The above constraint binds only if 0 < ?
t
< ?. This happens because ?
t
n
jt
is
greater than zero. If ?
t
? ?, then left hand side would be strictly greater than right
8
Proofs of equations (2.10), (2.11), and (2.12) are available in technical appendix upon request.
71
hand side in equation (2.13). Under plausible values of parameters, this constraint
always binds in equilibrium, which in turn produces the endogenous borrowing con-
straint for the bank as follows:
q
t
s
jt
=
?
t
? ??
t
n
jt
= ?
t
n
jt
. (2.14)
This endogenous constraint which emerges from the costly enforcement prob-
lem described above ensures that banks’ leverage might always be equal to
?t
???t
and
is decreasing with the fraction of funds (?) that depositors believe that banks will
divert.
Due to the fact that ?
t
does not depend on j, one can aggregate equation
(2.14) and obtain the following aggregate relationship:
q
t
s
t
= ?
t
n
t
(2.15)
where s
t
and n
t
represent aggregate levels of banks’ assets and net worth, respec-
tively.
The evolution of aggregate net worth depends on that of the surviving bankers
(n
et+1
) and the start-up funds of the new entrants (n
nt+1
):
n
t+1
= n
et+1
+ n
nt+1
. (2.16)
72
The net worth of new entrants is de?ned as an ? fraction of banks’ aggregate
net worth, that is:
9
n
nt+1
= ?n
t
(2.17)
The fact that ? fraction of banks survive over next period equates the net
worth of surviving banks to the following:
n
et+1
= ?
__
R
kt+1
?
_
R
t+1
? rr
t
1 ? rr
t
__
?
t
+
_
R
t+1
?rr
t
1 ? rr
t
__
n
t
(2.18)
One can sum up equations (2.17) and (2.18) to obtain the evolution of net
worth for the entire set of banks:
n
t+1
=
_
?
__
R
kt+1
?
_
R
t+1
? rr
t
1 ?rr
t
__
?
t
+
_
R
t+1
? rr
t
1 ? rr
t
__
+ ?
_
n
t
(2.19)
Equation (2.19) shows that the evolution of net worth depends on e?ective
spread and leverage ratio of banks.
9
This assumption is slightly di?erent from that in Gertler&Karadi (2011). They assume that
the net worth of newly entering bankers is a fraction of banks’ total assets rather than its net
worth. Since the fraction is small, it does not change the main results of the study signi?cantly.
73
2.2.3 Firms
Firms produce the consumption good by using physical capital and labor as
production factors. They operate with a constant returns to scale technology F(., .)
that is subject to total factor productivity shocks, z
t
y
t
= exp(z
t
)F(k
t
, h
t
) (2.20)
where
z
t+1
= ?
z
z
t
+ ?
zt+1
(2.21)
with zero mean and constant variance innovations, ?
zt+1
.
Firms ?nance capital at date t by issuing claims s
t
to ?nancial intermediaries
and acquire capital k
t+1
from capital producers. Therefore,
q
t
s
t
= q
t
k
t+1
(2.22)
with q
t
is the market price of the ?rms’ equity and capital.
Banks’ claim against the ownership of the ?rm pays out its dividend via the
marginal product of capital in the next period. Hence, the cost of credit to the ?rm
is state-contingent. As a result, the cost of credit to the ?rm must satisfy
R
kt
=
z
t
F
k
(k
t
, h
t
) + q
t
(1 ??)
q
t?1
(2.23)
74
Finally, the optimal labor demand of the ?rm must satisfy the usual static
condition,
w
t
= exp(z
t
)F
h
(k
t
, h
t
) (2.24)
which equates marginal product of labor to the marginal cost of it.
2.2.4 Capital Producers
Capital producers are introduced in order to obtain variation in the price
of capital which is necessary for the ?nancial accelerator mechanism to operate.
To that end, capital producers provide physical capital to the ?rms and repair the
depreciated capital and incur the cost of investment. Consequently, the optimization
problem of capital producers reads,
max
it
q
t
k
t+1
? q
t
(1 ??)k
t
?i
t
(2.25)
subject to the capital accumulation technology,
k
t+1
= (1 ??)k
t
+ ?
_
i
t
k
t
_
k
t
(2.26)
where the function ?(·) represents the capital adjustment cost. The optimality
condition that emerges from the solution to this problem is the well-known “q”
relation that pins down the price of capital,
75
q
t
=
_
?
?
_
i
t
k
t
__
?1
(2.27)
2.2.5 Government
The government is essentially responsible for coordinating monetary policy.
To that end, it controls the supply of money M
0t+1
and determines the required
reserve ratio rr
t
. Any growth of the monetary base is remitted to households in the
form of lump-sum transfers, T
t
. The monetary base grows at the rate µ
t
,
M
0t+1
= exp(µ
t
)M
0t
(2.28)
where the growth rate of money supply is subject to zero mean, constant variance
normally distributed innovations so that,
µ
t+1
= (1 ? ?
µ
)¯ µ + ?
µ
µ
t
+ ?
µt+1
(2.29)
In order to contain the ?nancial accelerator mechanism, the government uses
required reserves as a macroprudential rule. Speci?cally, the required reserves ratio
is assumed to follow a rule that reacts to the expected growth rate of bank credit
at date t + 1 compared to its level in the current period.
10
rr
t
= ¯ rr + ?E
t
[log(q
t+1
s
t+1
) ? log(q
t
s
t
)] (2.30)
10
We also consider a rule which reacts to current credit growth rather than expected future
credit growth. The main results of the study remain unchanged as can be seen from Appendix
B.2.
76
where, ¯ rr is the steady-state value of the required reserves ratio and ? > 0. Con-
sequently, the central bank increases the e?ective pro?t to banks of extending new
loans when credit in the aggregate economy is shrinking, and vice versa. The gov-
ernment budget constraint is given by
T
t
= M
t+1
? M
t
+ P
t
rr
t
b
t+1
? P
t
rr
t?1
b
t
(2.31)
The government uses the seignorage revenue plus the increases in its reserves to
?nance the lump-sum transfer payments to households, which include both workers
and bankers.
11
Within this framework, the money market equilibrium turns out as
the following condition:
M
0t+1
= M
t+1
+ P
t
rr
t
b
t+1
(2.32)
where P
t
is the general price level of the consumption good. The money supply
equals to the currency demand by workers plus the reserve demand by bankers. Since
the left hand side is exogenously determined by the central bank, equilibrium in the
money market might call for adjustments in price level in response to ?uctuations
in reserves. That being said, we also want to emphasize the fact that ?exible-price
models are not good models in explaining the dynamics of in?ation. The only reason
to talk about in?ation dynamics here is to show that using reserve requirements leads
to a possibly interesting trade-o? between price stability and ?nancial stability faced
11
The lump-sum transfer payments to the households equals to the change in money demand
by workers plus the change in reserves demand by bankers.
77
by many emerging market central banks recently. To be precise, this trade-o? is to
reduce the intertemporal distortions created by the credit spread at the expense of
generating higher in?ation volatility.
2.2.6 Competitive Equilibrium
Notice that nominal monetary base and prices grow constantly in this model,
which renders the equations listed above non-stationary. Therefore, following Coo-
ley and Hansen (1989), we make the model stationary by applying the following
normalizations:
´
P
t
= P
t
/M
0t+1
and ˆ m
t
= M
t+1
/(
´
P
t
M
0t+1
) and solve the model
locally around a deterministic steady state.
A competitive equilibrium of this model economy is de?ned by sequences of al-
locations {c
t
, k
t+1
, i
t
, l
t
, h
t
, s
t
, n
t
, n
e
t, n
n
t, b
t+1
, ?
t,t+1
, ?
t
, ?
t
, ?
t
, ?
t,t+1
, ?
t,t+1
, ˆ m
t+1
, ?
t
}
?
t=0
,
prices {q
t
, R
kt+1
, R
t+1
, w
t
,
´
P
t
}
?
t=0
, shock processes {z
t
, µ
t
}
?
t=0
and the government pol-
icy {rr
t
}
?
t=0
that satisfy the following optimality and market clearing conditions:
?
t,t+1
=
u
c
(t + 1)
u
c
(t)
(2.33)
1 = ?E
t
R
t+1
?
t,t+1
(2.34)
c
t
=
exp(µ
t
) ? 1 + ˆ m
t
ˆ
P
t
ˆ
P
t
exp(µ
t
)
+ R
t
b
t
?b
t+1
(2.35)
78
u
l
(t)
w
t
ˆ
P
t
= ?E
t
_
u
c
(t + 1)
ˆ
P
t+1
exp(µ
t+1
)
_
(2.36)
?
t
=
?
t
? ? ?
t
(2.37)
q
t
s
t
= ?
t
n
t
(2.38)
q
t
s
t
= (1 ?rr
t
)b
t+1
+ n
t
(2.39)
?
t,t+1
=
_
R
kt+1
?
R
t+1
?rr
t
1 ? rr
t
_
?
t
+
R
t+1
? rr
t
1 ? rr
t
(2.40)
?
t,t+1
= ?
t,t+1
?
t+1
?
t
(2.41)
n
et
= ??
t?1,t
n
t?1
(2.42)
n
nt
= ?n
t?1
(2.43)
n
t
= n
et
+ n
nt
(2.44)
79
?
t
= E
t
_
(1 ??)??
t,t+1
_
R
kt+1
?
R
t+1
?rr
t
1 ? rr
t
_
+ ??
t,t+1
??
t,t+1
?
t+1
_
(2.45)
?
t
= E
t
_
(1 ? ?)??
t,t+1
_
R
t+1
?rr
t
1 ? rr
t
_
+ ??
t,t+1
??
t,t+1
?
t+1
_
(2.46)
w
t
= exp(z
t
)F
h
(k
t
, h
t
) (2.47)
R
kt
=
exp(z
t
)F
k
(k
t
, h
t
) + q
t
(1 ? ?)
q
t?1
(2.48)
k
t+1
= (1 ??)k
t
+ ?
_
i
t
k
t
_
k
t
(2.49)
q
t
=
_
?
?
_
i
t
k
t
__
?1
(2.50)
exp(z
t
)F(k
t
, h
t
) = c
t
+ i
t
(2.51)
s
t
= k
t+1
(2.52)
1 = l
t
+ h
t
(2.53)
80
exp(?
t
) = exp(µ
t
)
´
P
t
¯
P
t?1
(2.54)
z
t+1
= ?
z
z
t
+ ?
zt+1
(2.55)
µ
t+1
= (1 ? ?
µ
)¯ µ + ?
µ
µ
t
+ ?
µt+1
(2.56)
rr
t
= ¯ rr + ?E
t
[log(q
t+1
s
t+1
) ? log(q
t
s
t
)] (2.57)
1
´
P
t
= ˆ m
t+1
+ rr
t
b
t+1
(2.58)
2.3 Quantitative Analysis
2.3.1 Functional Forms
Preferences: We use a standard CRRA utility function and separable utility
for leisure:
u(c
t
, l
t
) =
c
1??
t
1 ? ?
??
h
1+?
t
1 + ?
(2.59)
with ? > 1, ?, ? > 0.
Production: Firms produce according to a constant returns to scale Cobb-Douglas
81
production function:
exp(z
t
)F(k
t
, h
t
) = exp(z
t
)k
?
t
h
1??
t
(2.60)
with 0 < ? < 1.
Capital Producers: Capital producers are subject to a convex adjustment cost
function:
?
_
i
t
k
t
_
=
?
2
_
i
t
k
t
??
_
2
(2.61)
The parameter values used in the quantitative analysis are reported in Table
2.1. The preference and production parameters are standard in business cycle liter-
ature. The share of capital in the production function is set to 0.4, and the capital
adjustment cost parameter is 2.75. We borrow the standard values of ? and v from
literature as 2 and 2, respectively. We take the quarterly discount factor, ? as 0.9885
to match the 2006-2011 average annualized real deposit rate, 4.73%, in Turkey. We
pick the relative utility weight of labor ? to ?x hours worked in steady state, L, at
one third of the available time. The quarterly depreciation rate of capital is set to
3.7% to match the 1987-2011 average annual investment to capital ratio of 14.8% in
Turkey.
Parameters related to the ?nancial sector are calibrated to match ?nancial
statistics of the Turkish economy in the period 2006-2011. We set ? to 0.001 so
that the proportional transfer to newly entering bankers is 5.71% of aggregate net
82
Table 2.1: Paremeter Values in the Benchmark Model
Description Value Target
Preferences
Quarterly discount factor (?) 0.9885 Annualized real deposit rate (4.73%)
Relative utility weight of consumption (?) 2
CRRA parameter in the utility (v) 2 Literature
Relative utility weight of leisure (?) 15.182 Hours worked (0.33)
Production Technology
Share of capital in output (?) 0.4 Labor share of output (0.64)
Capital adjustment cost parameter (?) 2.75 Relative volatility of investment = 2.25
Depreciation rate of capital (?) 0.037 Average annual ratio of investment to capital (14.8%)
Government
Steady-state value of RRR ( ¯ rr) 0.05 Pre macroprudential policy period
Adjustment parameter in the RRR rule (?) 5.15 Standard deviation of di?erences in RRR for 2009:4-
2012:2 (1.73%)
Financial Intermediaries
Fraction of diverted loans (?) 0.5 Annual commercial & industrial loan spread (1.96%)
Prop. transfer to the entering bankers (?) 0.001 5.71% of aggregate net worth
Survival probability of the bankers (?) 0.962 Capital adequacy ratio of 16% for commercial banks
Shock Processes
Persistence of TFP process (?z) 0.9821 Estimated from detrended log TFPt = ?z log TFP
t?1
+ ?zt
Std. deviation of productivity shocks (?z) 0.0183
Persistence of money growth process (?µ) 0.5702 Estimated from log ?M1t = ?µ log ?M1
t?1
+ ?µt
Std. deviation of money growth shocks (?µ)0.0275
worth. We pick the fraction of diverted funds, ?, and the survival probability, ?,
simultaneously to match the following two targets: an average interest rate spread of
48 basis points, which is the historical average of the di?erence between the quarterly
commercial and industrial loan rates and the quarterly deposit rate from 2006:Q1
to 2011:Q4, and an average capital adequacy ratio of 16%, which is the historical
average of Turkish commercial banks’ capital adequacy ratio for the same period.
12
12
The legal target of risk-weighted capital adequacy ratio set by the Banking Regulation and
Supervision Agency in Turkey is 8%, however, commercial banks in Turkey maintain 16% for this
83
The resulting values for ? and ? are 0.5 and 0.962, respectively. The benchmark
model involves the macroprudential policy rule illustrated in equation (2.30) which
does not alter the steady state of the model but a?ects the dynamics around it. We
calibrate the response parameter of the RRR rule ? to 5.15 in order to match the
standard deviation of the di?erences in RRR of 1.73% for the Turkish economy in
the period 2009:4-2012:2.
We estimate an AR(1) process for the log of TFP for the period 1988:Q2-
2011:Q2 and ?nd a persistence of, ?
z
= 0.9821, and a standard deviation of in-
novations to TFP, ?
z
= 0.0183. The money growth process on the other hand is
estimated for the period 2003:Q1-2011:Q4 using M1 series, following Cooley and
Hansen (1989).
13
Estimation results implied a persistence of, ?
z
= 0.5702, and a
standard deviation of innovations to money growth shocks, ?
µ
= 0.0275.
With the parameterized economy, we ?rst illustrate the role of ?nancial accel-
erator driven by credit frictions in the banking sector. We then study the dynamics
of the model by focusing on impulse responses to one standard deviation nega-
tive productivity and positive money growth shocks in environments that involve
alternative required reserves policies. We also document implications of using a
time-varying required reserves ratio in terms of its e?ect on the volatilities of real
and ?nancial variables in order to understand its e?ectiveness as a macroprudential
policy tool. Finally, we analyze the welfare implications of alternative RRR policies.
ratio in practice.
13
The choice of estimation period re?ects the structural disin?ation that the Turkish economy
has experienced, see Sunel (2011). Moreover, we also estimated an AR(1) for the money growth
process using M0 series. The parameters of the process are quite similar.
84
2.3.2 Findings
In the following subsections, we ?rst display the role of ?nancial accelerator by
comparing the usual cash-in-advance model with the model described in section 2.2.
We then compare the dynamics of negative TFP and positive money growth shocks
under two model economies with time-varying and ?xed RRR policies. Lastly, we
run a ?nancial crisis experiment, in which the net worth of banks are hit by a one-
time exogenous shock, and compare the implications of the two reserve requirement
regimes.
14
2.3.2.1 Amplifying E?ect of Financial Frictions
The dashed plots in ?gures 2.2 and 2.3 represent the monetary economy that
exhibits ?nancial accelerator mechanism and the straight plots represent the cash-
in-advance model with no ?nancial frictions. Required reserves ratio in the former
economy is set to zero to isolate the impact of ?nancial frictions.
Figure 2.2 below illustrates that the collapse in output, investment, price of
capital and loan-deposit spreads is ampli?ed when ?nancial frictions are in place.
We especially want to highlight the almost tripling increase in the reduction of
investment and asset prices and 250 basis points of increase in the credit spreads in
annualized terms. The last one is even more striking because in the economy with
no ?nancial frictions, there is no-arbitrage between return to capital and return
to deposits. The evident ampli?cation owes to the reduced demand of banks for
14
We also analyzed the case with zero reserve requirements policy. Since the dynamics are quite
similar to a ?xed RRR regime, we do not report those results, which are available upon request.
85
0 10 20 30 40
?1.8
?1.6
?1.4
?1.2
?1
Output
%
?
f
r
o
m
S
.
S
.
FA
DSGE
0 10 20 30 40
?4
?3.5
?3
?2.5
?2
?1.5
Investment
0 10 20 30 40
?0.4
?0.3
?0.2
?0.1
0
0.1
Price of Equity
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?50
0
50
100
150
200
250
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
Figure 2.2: Negative Productivity Shocks
86
0 10 20 30 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
FA
DSGE
0 10 20 30 40
?0.8
?0.6
?0.4
?0.2
0
Investment
0 10 20 30 40
?0.06
?0.04
?0.02
0
0.02
Price of Equity
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
0
5
10
15
20
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
Figure 2.3: Positive Money Growth Shocks
87
deposits in case of lower productivity. This stems from the decline in the return to
state-contingent equity issued by ?rms when productivity is lower. This depresses
the price of equity issued by ?rms and results in a collapse in the value of funds
provided to them. As a result, ?rms acquire less capital and investment declines
more.
Figure 2.3 illustrates the dynamics in response to a positive money growth
shock. An important feature of this cash-in-advance economy is that as equa-
tions (2.3) (with equality) and (2.5) illustrate, investment and leisure are cash and
credit goods, respectively. Therefore, when in?ation rises following a positive money
growth shock, labor supply and investment decreases causing a decline in output.
We again obtain ampli?ed responses of investment, asset prices, output and credit
spreads on impact following the shock. Yet, the trajectory of all variables except the
last appears to be similar to the economy with no ?nancial frictions. The ampli?ed
response of investment is coupled with larger degree of declines in asset prices and
credit spreads as in the case of TFP shocks. We also note that the quantitative
impact of monetary shocks are much smaller compared to TFP shocks.
We now analyze the implications of the RRR policy on the dynamics of real,
?nancial, and monetary variables. In ?gures 2.4 and 2.5, we compare the dynamics
of these variables in response to one standard deviation negative TFP and positive
money growth shocks. In ?gure 2.6 we explore the implications of RRR policy
on the dynamics model variables in a ?nancial crisis scenario. The speci?c ?nancial
disruption is a balance sheet shock that bankers face as in mostly recent literature.
15
15
Hancock, Laing and Wilcox (1995), Meh and Moran (2010), Brunnermeier and Pedersen
88
In ?gures 2.4 to 2.6, the dashed plots correspond to the benchmark econ-
omy with the countercyclical RRR rule and the straight plots correspond to an
economy with ?xed RRR. The dynamics of the economy with no reserves closely
resemble those with a ?xed RRR. Therefore for space considerations, we do not
discuss them here and only present the comparison of ?xed RRR economy with
the benchmark economy that displays a countercyclical RRR.
16
Unless otherwise is
stated, the numbers in the y-axes correspond to percentage deviations of variables
from their long-run values. For the case of in?ation and RRR, we plot percentage
“point changes” and for the case of credit spreads we plot “basis point changes” in
annualized terms. In addition, we explore the impact of implementing aggressive
credit policy rules by increasing the response parameter ?. In these experiments, as
anticipated, the impact of the time-varying RRR rule is enhanced when ? is larger.
17
(2009), Curdia and Woodford (2010), Mendoza and Quadrini (2010), Iacoviello (2010), and Mimir
(2011).
16
The dynamics of the economy with no reserves can be found in Appendix B.3.
17
Charts regarding policy intensity experiments can be found in Appendix B.4.
89
0 20 40
?2
?1.5
?1
?0.5
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy Fixed RR Ratio
0 20 40
?4
?3
?2
?1
0
1
Investment
0 20 40
0
0.5
1
1.5
2
2.5
Hours
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?6
?4
?2
0
2
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?2
0
2
4
Leverage
0 20 40
?2
?1.5
?1
?0.5
0
Bank Credit
0 20 40
?100
0
100
200
300
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?1.5
?1
?0.5
0
0.5
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
0
5
10
15
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
1.5
Inflation
Quarters
0 20 40
?25
?20
?15
?10
?5
0
Reserves
Quarters
Figure 2.4: Impulse Responses Led by a 1-? Adverse TFP Shock
9
0
2.3.2.2 Impulse Responses to TFP Shocks
The general observation that emerges from ?gure 2.4 is that the time-varying
RRR policy dampens the impact of the ?nancial accelerator on key macroeconomic
real and ?nancial variables at the expense of higher in?ation in response to TFP
shocks.
In the economy with ?xed RRR, as expected, households reduce their demand
for consumption and supply of deposits in response to the adverse TFP shock since
output and the pro?ts that accrue from the ownership of banks and capital producers
are lower. On the banks’ side, the reduced TFP highlights the reduction in the
pro?tability of equity loans to ?rms, inducing them to reduce their demand for
deposits.
Under ?xed RRR economy, as ?gure 2.4 shows, the net worth of banks collapse
by 4% re?ecting the feedback e?ect of a 0.6% decline in asset prices through the
endogenous capital constraint of banks, represented by equation (2.15). The decline
in net worth in accordance with the decline in deposits downsizes the total ?nancing
for non-?nancial ?rms (see ?gure 2.4). However, since the decline in bank capital
is larger than that of the value of bank assets, the model implies a countercyclical
bank leverage, which increases by 3.5%. On the other hand, the scarcity of funds
for ?rms shoots up loan-deposits spreads by about 250 basis points in annualized
terms (see the middle panel of ?gure 2.4). The reduction in the quantity of equities
traded and the collapse in asset prices trigger a downsizing in bank credit of about
0.75%. As a combined outcome of these dynamics, investment falls by 3.75% and
91
output declines by about 1.75%.
The nominal price level increases (the bottom panel of ?gure 2.4) because the
economy is now less productive in generating output. Hence, in?ation increases by
0.2 percentage points causing the real balances demand to decline and consumption
velocity of monetary base to increase by about 1%.
Now, we explain how the credit policy de?ned by a countercyclical RRR rule
mitigates the impact of the ?nancial accelerator on key macroeconomic real and
?nancial variables (see the dashed plots in ?gure 2.4). Since bank credit declines in
response to the adverse TFP shock, the policy rule implies a reduction in the RRR
by about 1 percentage point, which can be seen in the bottom panel of the ?gure.
This reduces the cost of extending credit for banks and induces a substitution from
reserves balances to loans in the asset side of their balance sheet. Consequently,
the stronger demand for ?rm equity stabilizes the price of it on impact, and the
peak of decline in equity price is about 0.2% less than how much it is in the ?xed
RRR economy. The substitution in the balance sheet of banks combined with the
better outlook of asset prices reduce the collapse in bank credit from 0.8% to 0.2%.
Accordingly, output and investment decline by 1.3% and 3.5% less than how much
they decline in the ?xed RRR economy.
The support of the central bank via lower reserve requirements cause credit
spreads to rise by about 150 basis points less compared to the ?xed RRR econ-
omy over 5 quarters. We emphasize this ?nding because credit spreads introduce
an intertemporal wedge to the savings decision of the aggregate economy and are
created by ?nancial frictions. The relatively muted response of spreads stems from
92
the reduced decline in return to ?rm equity. The stronger outlook of the economy
re?ects into the balance sheet of banks and bank capital declines by 4% less com-
pared to the ?xed RRR economy and even increases above its long-run level for 20
quarters, since RRR is lower than its long-run value for about 30 quarters. The
immediate implication of stronger trajectory of net worth is a rise of virtually zero
in bank leverage on impact (against a 3.25% hike with ?xed RRR) and even implies
a decline of it up to 2% caused by the increase in bank capital.
The substantial collapse in reserves demand (about 20%) drives down the price
of money and ampli?es the upwards response of in?ation obtained in the ?xed RRR
economy (see bottom panel of ?gure 2.4). However, since this immediate surge is
transitory and driven by the reserves policy, the model implies an undershooting of
in?ation in the coming 7 quarters. This implies a substitution of consumption for
leisure on the part of forward looking households and labor supply increases by 2%
more compared to the ?xed RRR economy. Hence, we obtain the stabilizing impact
of the countercyclical RRR rule on the dynamics of output displayed in the top
panel of ?gure 2.4. Consistent with these ?ndings, real balances demand collapses
on impact but outweighs its steady state level along the transition and consumption
velocity increases by 11% more than the ?xed RRR economy.
To sum up, we obtain the interesting result that the countercyclical RRR
policy mitigates the impact of ?nancial accelerator triggered by TFP shocks on
real and ?nancial variables at the expense of higher in?ation. Now, we explore the
dynamics driven by money growth shocks.
93
0 20 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy Fixed RR Ratio
0 20 40
?0.6
?0.4
?0.2
0
0.2
Investment
0 20 40
?0.3
?0.2
?0.1
0
0.1
Hours
0 20 40
?0.08
?0.06
?0.04
?0.02
0
0.02
Price of Equity
0 20 40
?0.6
?0.4
?0.2
0
0.2
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?0.1
0
0.1
0.2
0.3
0.4
Leverage
0 20 40
?0.1
?0.08
?0.06
?0.04
?0.02
0
Bank Credit
0 20 40
?5
0
5
10
15
20
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.06
?0.04
?0.02
0
0.02
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.5
0
0.5
1
1.5
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.1
0
0.1
0.2
0.3
Inflation
Quarters
0 20 40
?1.5
?1
?0.5
0
0.5
Reserves
Quarters
Figure 2.5: Impulse Responses Led by a 1-? Adverse Money Growth Shock
9
4
2.3.2.3 Impulse Responses to Money Growth Shocks
In this section, we analyze the dynamics of model economies in response to
a one-standard deviation positive money growth shock. Figure 2.5 displays the
impulse responses of key real, ?nancial and monetary variables. Although the impact
of a money growth shock on those variables is an order of magnitude smaller than
that of a productivity shock, these ?gures deliver the same message as in the previous
section that the time-varying RRR policy mitigates the adverse e?ects of money
growth shocks on real and ?nancial variables driven by the ?nancial accelerator
mechanism while creating higher in?ation rates compared to ?xed RRR policy.
We should ?rstly note that the dynamics of the model with ?xed required
reserves ratio policy strongly resemble the properties of a standard stochastic cash-
in-advance economy by Stockman (1981) and Cooley and Hansen (1989), which is
modi?ed to cover bank deposits in the cash-in-advance constraint. In this sense, we
follow the timing assumption of Cooley and Hansen (1989) that asset markets open
?rst for workers, but with the di?erence that b
t+1
is not necessarily (and actually
never) equal to zero, and higher rates of in?ation discourage household savings in
the form of deposits. In the end, the general mechanism in this basic model is
broadly summarized by the idea that an expansionary shock to the growth rate
of money supply raises in?ation rate and induces households to substitute credit
goods for cash goods. The re?ection of that mechanism to the current model is that
consumption and deposit savings decline and leisure demand increases as implied by
equations (2.3) and (2.5). Since deposit savings are intermediated to non-?nancial
95
?rms’ equity ?nancing, investment declines in response to a positive money growth
shock. Lower investment and the decline in labor supply then reduce output and
consumption.
In the ?xed RRR economy, in?ation rate increases by about 0.2% percentage
points on impact. This reduces hours worked by 0.25% since consumption and
deposits are the cash goods and leisure is the credit good. The fall in household
deposits leads to a reduction in bank credit in the form of equity purchases. As the
demand for non-?nancial ?rms’ shares decline, the price of equity falls by 0.07%.
The decline in equity prices causes bank net worth to shrink by 0.4% on impact,
leading to a rise in credit spreads by about 20 annualized basis points. Since the cost
of ?nancing capital expenditures is now higher for non-?nancial ?rms, investment
and output drop by 0.4% and 0.15%, respectively. In terms of monetary variables,
as in?ation rate rises, real money balances decrease and consumption velocity surges
by 0.4%.
When the central bank puts the credit policy to work, RRR declines about
0.06 percentage points as bank credit falls in response to a positive money growth
shock. There is an immediate decline of 1.25% in the reserves, and deposit demand
by banks. The reduced cost of extending credit induces banks to substitute away
their assets from reserves to ?rm equity, and accordingly the initial decline in bank
credit is 0.07% smaller. As equity purchases by banks are larger, the decline in
the price of equity on impact is totally eliminated in comparison to the ?xed RRR
policy. This is re?ected into the balance sheet of banks and intermediary capital
does not decline at all compared to a reduction of 0.45% in the ?xed RRR economy.
96
Furthermore, the rise in credit spreads are about 15 annualized basis points lower
and the stronger trajectory of bank net worth causes leverage to decline by 0.05%
over 5 quarters instead of an increase of about 0.4%. Since credit spreads are the
main source of intertemporal distortion caused by the credit frictions in ?nancial
sector, the central bank e?ectively mitigates the adverse impact of this distortion
on the economy via implementing a lower reserve requirement policy. As another
favorable result of these dynamics, investment falls by 0.3% less in the case of time-
varying reserve requirements.
The initial fall in reserves by 1.2% creates an excess supply of monetary base
in the economy and raises the in?ation rate by 0.25% percentage points to restore
equilibrium in the money market (see ?gure 2.5). Therefore the trade-o? between
price and ?nancial stability is still evident under money growth shocks. This causes
the real money demand to decline and consumption velocity of monetary base to
rise by 0.6% more. Lastly, we again obtain the undershooting of in?ation following
the ?rst period as opposed to the case with ?xed RRR. This feeds back into the
consumption-leisure margin of workers and hours decline by about 0.2% less com-
pared to the ?xed RRR economy. This results in stabilizing output on impact and
obtaining 0.1% less decline in it over 5 quarters when the rule is in place.
97
0 20 40
?2
?1.5
?1
?0.5
0
0.5
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy Fixed RR Ratio
0 20 40
?6
?4
?2
0
Investment
0 20 40
?3
?2
?1
0
1
Hours
0 20 40
?1
?0.5
0
0.5
Price of Equity
0 20 40
?15
?10
?5
0
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
0
2
4
6
8
10
Leverage
0 20 40
?1.5
?1
?0.5
0
Bank Credit
0 20 40
0
100
200
300
400
500
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?8
?6
?4
?2
0
2
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
Inflation
Quarters
0 20 40
?15
?10
?5
0
5
Reserves
Quarters
Figure 2.6: Impulse Responses Led by a 1-? Adverse Financial Shock
9
8
2.3.2.4 Financial Crisis Experiment and Credit Policy
The previous two sections illustrated that the macroprudential reserves policy
stabilizes key macroeconomic and ?nancial variables in response to conventional
shocks along the business cycle. In this section, we explore how countercyclical
reserve requirements perform during a ?nancial crisis. The speci?c experiment is
to consider an exogenous decline in the net worth of ?nancial intermediaries. This
shock crudely captures loan losses, asset write-downs or asset revaluations that we
observe in the recent ?nancial crisis. As stated in the Introduction, it might be
though of as a sharp reversal in the risk appetite of international investors, which
is an exogenous factor that threatens the ?nancial stability of a country such as
Turkey.
Although the initial decline in banks’ net worth that we introduce is exogenous,
there will be second round e?ects that endogenously trigger an adverse ?nancial
accelerator mechanism. The initial fall in the net worth reduces the amount of
bank credit that can be extended to non-?nancial ?rms as banks are not able to
compensate the decline in their internal ?nancing with households’ deposits. Since
non-?nancial ?rms ?nance their capital expenditures via bank credit, there will be
a drop in investment, and hence in the price of capital. The value of intermediary
capital depends on asset prices. The endogenous decline in asset prices leads to a
further deterioration in banks’ net worth, creating an adverse feedback loop of falling
aggregate demand, declining asset prices, and deteriorating intermediary balance
sheets.
99
Speci?cally, we consider an initiating disturbance of a 5% decline in the net
worth of ?nancial intermediaries. This disturbance will be a one-time shock and we
want to think of it as a rare event. We analyze the e?ects of this shock in the model
economy with ?xed RRR policy and then illustrate the mitigating e?ects of time-
varying RRR policy on real, ?nancial and monetary variables. Figure 2.6 shows the
impulse responses of real, ?nancial and monetary variables under di?erent policy
regimes.
In the economy with ?xed RRR, the negative net worth shock immediately
reduces bank capital by 11% on impact (see the middle panel of ?gure 2.6). Although
deposits rise due to banks’ increased demand for deposits to compensate the decline
in their internal ?nancing, the deterioration of bank capital causes total ?nancing by
?nancial intermediaries to shrink. This translates into a reduction in bank credit in
the form of equity purchases to ?rms by 1.2% on impact. As the demand for ?rms’
shares is lower, the price of equity falls by 1%. This ampli?es the exogenous impact
of the ?nancial shock via endogenous capital constraint of banks and explains the
substantial decline of 11% in the net worth. The decline in bank capital rises their
leverage by 10% on impact. Induced by the shortage in credit and collapse in asset
prices, credit spreads rise by 450 basis points in annualized terms. This in turn
causes ?rms to cut back their investment severely (by about 6%) due to lower bank
credit and higher cost of ?nancing.
The increase in bank deposits driven by banks’ e?ort to compensate for the
net worth loss increases reserves balances by 1% in the ?xed RRR economy. This
creates an excess demand for monetary base and in?ation declines on impact by 0.6
100
percentage points (see the bottom panel of ?gure 2.6). However, since the shock is
transitory, in?ation overshoots by 0.7 percentage points in the period that follows the
shock and workers’ expectations regarding the hike in future in?ation causes hours
to decline by 2.75% on impact. Therefore, output shrinks by 1.6% as shown in the
top panel of the ?gure. The dynamics of real balances demand and consumption
velocity of monetary base resemble the expected implication of the dynamics of
in?ation.
In the model economy with credit policy, the time-varying rule induces a fall
in the RRR of about 0.6 percentage points since bank credit declines in response to
the negative ?nancial shock. Reserves immediately drop by 11% and eliminate the
collapse in in?ation almost completely. Most importantly, the dynamics of reserves
moves in?ation in such a way to induce hours and accordingly output to increase
on impact (see the bottom and top panels of ?gure 2.6).
Following the reduced cost of making equity loans to ?rms, banks substitute
away their assets from reserves to ?rm equity, therefore the initial decline in bank
credit is 1% smaller. As the demand for ?rm equity is higher in the model with credit
policy, the 1% reduction in the price of equity is in the model economy with ?xed
RRR policy is almost totally eliminated. This reinforces the intermediary capital
via the leverage constraint and reduces the collapse in bank net worth by 5%. We
emphasize this ?nding that the macroprudential policy reduces the ampli?ed impact
of the ?nancial shock on bank capital by 50%. Accordingly, the rise in credit spreads
are 200 basis points lower in annualized terms and bank leverage increases by 5%
instead of 10%. As another favorable outcome, investment falls by 5% less than how
101
much it declines in the ?xed RRR economy over 5 quarters. To sum up, we obtain
the result that a macroprudential reserve requirements policy that has a ?rst order
impact on the balance sheet of ?nancial intermediaries is the most e?ective in the
event of a ?nancial turmoil.
For all shocks, the higher the intensity of required reserves policy, which is
measured by a larger ? parameter, the lower is the contraction in real macroeco-
nomic and ?nancial variables. Most importantly, the adverse hike in credit spreads,
which is the indicator of ?nancial frictions in this model economy are eliminated
to substantial degrees as the credit policy is implemented more aggressively. Ad-
ditionally, as expected, the in?ationary cost of macroprudential intervention is also
magni?ed as the policy becomes more intense.
Now we proceed to the next section in which we report the impact of coun-
tercyclical reserve requirement policy on the volatilities of key macroeconomic real
and ?nancial variables.
2.3.2.5 E?ects of Time-Varying RRR Policy on Volatilities
Table 2.2 below displays the volatilities of real and ?nancial variables when
TFP and money growth shocks are realized over su?ciently long simulations of
the model economy with three di?erent regimes: (i) ?xed RRR, (ii) a moderate
required reserve policy (? = 5.15), and (iii) an aggressive required reserve policy
(? = 10). As indicated in the table, the economy with a moderate credit policy
features lower volatilities in real variables such as output, consumption, investment
102
as well as in ?nancial variables such as bank credit, loan-deposit spread, and asset
prices, compared to the economy with a ?xed RRR policy. Column 4 of the table
shows that as the required reserve policy gets more aggressive, the volatilities of
output, consumption, investment, bank credit, loan-deposit spread, and asset prices
are even lower. We especially want to highlight the 50% decline in the volatilities of
credit spreads and leverage ratio, the 22% decline in the volatilities of investment
and asset prices, and 77% decline in the volatility of bank net worth when the
moderate credit policy is in place. Since volatilities over the business cycle are lower
under credit policy, we consider exploring welfare implications of it worthwhile.
Accordingly, in the following section, we carry out welfare comparisons of di?erent
reserve requirement policies. Finally, we emphasize that as the time-varying RRR
policy gets aggressive, in?ation volatility gets higher.
Table 2.2: Volatilities of Real and Financial Variables
Variable Fixed Reserves Credit Policy (? = 5.15) Credit Policy (? = 10)
Real Variables
Output 2.77 2.26 2.07
Consumption 1.59 1.47 1.41
Investment 6.01 4.70 4.22
Hours 0.35 2.44 2.62
Financial Variables
Credit 1.08 0.89 0.82
Deposits 1.22 1.76 2.57
Net Worth 4.35 1.24 1.31
Leverage Ratio 4.04 2.01 2.04
Credit Spread 0.28 0.14 0.12
Asset Prices 0.62 0.48 0.43
Monetary Variables
In?ation 0.18 0.27 0.37
103
2.3.2.6 Credit Policy and Welfare
Consider the time-varying reserve requirement policy, denoted by trp, and the
?xed reserve requirement policy, denoted by frp. We de?ne the welfare associated
with the time-invariant equilibrium given by the countercyclical reserve requirement
policy conditional on a particular state of the economy in period 0 as
V
trp
0
= E
0
?
t=0
?
t
U(c
trp
t
, l
trp
t
) (2.62)
where E
0
denotes conditional expectation over the initial state, and c
trp
t
and l
trp
t
stand for the contingent plans for consumption and leisure under the time-varying
reserve requirement policy. Similarly, the welfare associated with the time-invariant
equilibrium given by the ?xed reserve requirement policy conditional on a particular
state of the economy in period 0 as
V
frp
0
= E
0
?
t=0
?
t
U(c
frp
t
, l
frp
t
), (2.63)
where c
frp
t
and l
frp
t
stand for the contingent plans for consumption and leisure under
the ?xed reserve requirement policy.
We then compute consumption-based welfare gains for each alternative time-
varying reserve requirement policy (moderate or aggressive). Let ?
c
stand for the
welfare gain of adopting time-varying reserve requirement policy instead of the ?xed
one conditional on a particular state in period 0. We de?ne ?
c
as the proportional
increase of regime frp’s consumption plan that a household must demand to be as
104
well o? under policy regime trp. Therefore, ?
c
is implicitly de?ned by
V
trp
0
= E
0
?
t=0
?
t
U
_
(1 + ?
c
)c
frp
t
, l
frp
t
_
(2.64)
Hence, a positive value for ?
c
implies that the time-varying reserve requirement
policy is welfare superior to the ?xed reserve requirement policy.
In order to obtain accurate welfare rankings, we perform a second-order ap-
proximation to the policy functions and the welfare given by V
0
. It is very well-known
that welfare levels would be equal to each other under alternative policy regimes if
we conduct a ?rst-order approximation to the policy functions since the expected
value of endogenous variables would be equal to their non-stochastic steady state
levels across all alternative reserve policies. We then de?ne welfare in the following
recursive form to conduct a second-order approximation to V
0
:
V
0,t
= U(c
t
, l
t
) + ?E
t
V
0,t+1
. (2.65)
Schmitt-Grohe and Uribe (2006) show that V
0
can also be represented as
V
0,t
= V
0
+
1
2
?(V
0
) (2.66)
where V
0
is the level of welfare evaluated at the non-stochastic steady-state, and
?(V
0
) is the constant correction term, denoting the second-order derivative of the
policy function for V
0,t
with respect to the variance of shock processes. Therefore,
equation (2.66) is an approximation to the welfare V
0,t
, capturing the ?uctuations
105
of endogenous variables at the stochastic steady state.
We compare three di?erent policy regimes in terms of their welfare gains:
(i) a ?xed reserve requirement policy, frp, (ii) a moderate time-varying reserve
requirement policy (? = 5.15), mtrp and (iii) an aggressive time-varying reserve
requirement policy (? = 10), atrp. We ?nd that the welfare gain of the central
bank following mtrp rather than frp is 0.05% in consumption-equivalent welfare
terms. Moreover, the welfare gain of the central bank following atrp rather than
frp is 0.13% in consumption-equivalent welfare terms. These results indicate that
following an operational time-varying reserve requirement policy is always welfare
improving compared to an inactive reserve policy. Additionally, on quantitative
grounds, these welfare gains are non-trivial as far as closed economy models are
concerned.
2.4 Conclusion
There are certain advantages and drawbacks of using reserve requirements to
achieve ?nancial stability. The main advantages are (i) it is one of the two main
policy tools that most central banks can use, (ii) the central bank does not directly
face any costs since reserve requirements e?ectively alter the ?nancial sector’s own
balance sheet in order to provide liquidity to the system, and (iii) the central bank
can employ reserve requirements without requiring banks to have low-risk assets as
collateral, which is unlike the re-discount window. On the other hand, there are
some drawbacks of using reserve requirements, including (i) their role as a tax on
106
the banking sector, putting depository institutions at a competitive disadvantage
compared to unregulated ?nancial institutions, and (ii) they may lead to rise in the
credit spreads as they put additional costs on ?nancial intermediation. One can
assess the e?ectiveness of reserve requirements as a ?nancial stability tool through
their e?ects on credit spreads and bank credit to non-?nancial sector. Other things
being equal, we expect countercyclical implementation of reserve requirement ratios
to mitigate the decline in credit growth and accordingly moderate the rise in credit
spreads in economic downturns, and curb excessive credit growth in boom periods.
To that purpose, we build a quantitative monetary DSGE model with a bank-
ing sector that is subject to time-varying reserve requirements imposed by the central
bank and endogenous capital constraints due to an agency problem. We model re-
serve requirements as an exogenous policy rule that countercyclically responds to
credit growth in the ?nancial sector in a forward looking sense. We consider the
e?ects of three di?erent types of shocks: productivity, money growth and ?nancial
shocks. For each type of shock, we ?nd that the time-varying required reserve ra-
tio rule mitigates the negative e?ects of adverse shocks ampli?ed by the ?nancial
accelerator mechanism on real and ?nancial variables. In each case, it reduces the
intertemporal distortions created by the credit spread at the expense of generating
higher in?ation, pointing out the clear trade-o? between price stability and ?nancial
stability faced by many central banks nowadays. It also reduces the volatilities of
key variables such as output, consumption, investment, bank credit, loan spread
and asset prices, indicating the role of reserve requirements as a macroprudential
policy instrument. Finally, we ?nd that a time-varying reserve requirement policy
107
achieves a higher welfare than a ?xed reserve requirement policy.
This study illustrates that when ?nancial frictions are important, monetary
policy that adopts macroprudential reserve requirement ratios as an instrument
might have real e?ects even if there are no nominal or real rigidities. Our work is
also timely in the sense that academicians and policy makers are expressing their
doubts about in?ation targeting contemporaneously, and accordingly, quantity of
money has emerged as an explicit policy instrument.
There are several further research avenues: one can introduce liquidity shocks
in order to bring a microfoundation to holding reserves in order to rationalize the
optimality of positive reserve requirements. It might also be interesting to focus on
the tradeo? between price stability and ?nancial stability in a framework in which an
interest rate feedback rule is introduced under nominal rigidities such as Christiano
et al. (2005) and Smets and Wouters (2007). Lastly, it might also be worthwhile
to study an open economy model to explicitly consider the e?ects of international
capital ?ows in the design of required reserves policies.
108
Appendix A
A.1 Data Appendix
Quarterly seasonally-adjusted data on standard macroeconomic variables ex-
cept Hours are taken from the Federal Reserve Economic Data (FRED) of St. Louis
FED. Hours data are taken from Current Employment Statistics survey published
by the Bureau of Labor Statistics. GDP de?ator from NIPA accounts is used to
de?ate the time series of the nominal macro aggregates. Consumption is the sum of
“Personal consumption expenditures on nondurables” (PCND) and “Personal con-
sumption expenditures on services”. Investment is the sum of “Personal consump-
tion expenditures on durables” (PCDG) and “Gross private domestic investment”
(GPDI). GDP is the sum of Consumption and Investment. Hours is computed as
the multiplication of “average weekly hours in private sector” with “average number
of workers in private sector”. Quarterly time series of capital stock to obtain z
t
se-
ries are constructed using the approach described in the online appendix of Jermann
and Quadrini (2010).
Quarterly ?nancial time series of Bank assets and Bank liabilities are con-
structed using the monthly data on Assets and Liabilities of Commercial Banks in
the U.S. from Data Download Program of Statistical & Historical Database of the
Federal Reserve Board. Financial data at the FED board are seasonally-adjusted
but nominal. GDP de?ator from NIPA accounts is used to de?ate the ?nancial time
109
series. Bank assets are bank credit at the asset side of the balance sheet of the U.S.
commercial banks. Bank liabilities are deposits held at the U.S. commercial banks.
Quarterly time series of Loan spread are taken from Survey of Terms of Business
Lending from Statistical & Historical Database of the FED Board. Loan spread is
commercial and industrial loan spread over intended federal funds rate. Quarterly
deposit rates are constructed using monthly data on 3-month certi?cate of deposit
secondary market rate from FRED. The in?ation rate computed from GDP de?ator
is used to make nominal deposit rate data real.
Table A.1: Business Cycle Properties of Real and Financial Variables, Quarterly U.S.
Data, 1987.Q1-2007.Q1
Standard
Deviation x
t?4
x
t?3
x
t?2
x
t?1
xt x
t+1
x
t+2
x
t+3
x
t+4
Real Variables
Output 1.48 0.15 0.39 0.66 0.88 1.00 0.87 0.66 0.39 0.15
Consumption 0.44 -0.20 0.07 0.37 0.66 0.82 0.80 0.67 0.46 0.25
Investment 2.68 0.27 0.49 0.71 0.87 0.97 0.82 0.59 0.33 0.09
Hours 0.96 -0.01 0.19 0.43 0.65 0.83 0.89 0.83 0.68 0.44
Financial Variables
Bank credit 0.82 0.07 0.21 0.34 0.45 0.54 0.56 0.57 0.50 0.39
Deposits 0.83 0.09 0.00 -0.09 -0.19 -0.29 -0.37 -0.36 -0.31 -0.24
Net Worth 5.29 0.03 0.20 0.38 0.55 0.70 0.76 0.74 0.63 0.47
Leverage Ratio 5.99 0.00 -0.16 -0.34 -0.51 -0.65 -0.70 -0.68 -0.56 -0.39
Loan Spread 0.09 -0.18 -0.23 -0.32 -0.34 -0.35 -0.22 -0.17 -0.09 -0.03
a
Business cycle statistics in the table are based on HP-?ltered cyclical components of quarterly empirical time
series (smoothing parameter:1600).
b
The standard deviation of output is expressed in percent; standard deviations of the remaining variables are
normalized by the standard deviation of output (std(x)/std(GDP)).
c
The correlation coe?cients in bold font are the maximum ones in their respective rows.
110
A.2 Proofs
A.2.1 Proof of Proposition 1
Let’s conjecture that the bank’s franchise value is given by
V
jt
= ?
t
q
t
s
jt
+ ?
t
n
t
(A.1)
Comparing the conjectured solution for V
jt
to the expected discounted terminal net
worth yields the following expressions,
?
t
q
t
s
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
? r
t+1+i
)q
t+i
s
jt+i
] (A.2)
?
t
n
jt
= E
t
?
i=0
(1 ??)?
i
?
i+1
?
t,t+1+i
(1 + r
t+1+i
)n
jt+i
(A.3)
I write ?
t
and ?
t
recursively using the expression above. Let’s begin with ?
t
. To
ease the notation, let’s drop expectations for now.
?
t
=
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
? r
t+1+i
)x
t,t+i
] (A.4)
where x
t,t+i
=
q
t+i
s
jt+i
qts
jt
.
?
t
= (1 ? ?)??
t,t+1
(r
kt+1
?r
t+1
) +
?
i=1
(1 ??)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
? r
t+1+i
)x
t,t+i
]
(A.5)
111
?
t
= (1??)??
t,t+1
(r
kt+1
?r
t+1
)+??
t,t+1
?x
t,t+1
?
i=0
(1??)?
i+1
?
i+1
?
t+1,t+2+i
[(r
kt+2+i
? r
t+2+i
)x
t+1,t+1+i
]
(A.6)
The in?nite sum at the right-hand side of equation (A.6) is one period updated
version of equation (A.4), given by
?
t+1
=
?
i=0
(1 ? ?)?
i+1
?
i+1
?
t+1,t+2+i
[(r
kt+2+i
? r
t+2+i
)x
t+1,t+1+i
] (A.7)
where x
t+1,t+1+i
=
q
t+1+i
s
jt+1+i
q
t+1
s
jt+1
.
Hence, we can re-write (A.6) with the expectations as follows:
?
t
= E
t
[(1 ??)??
t,t+1
(r
kt+1
? r
t+1
) + ??
t,t+1
?x
t,t+1
?
t+1
] (A.8)
Let’s continue with ?
t
. To ease the notation, let’s drop expectations for now.
?
t
=
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
(1 + r
t+1+i
)z
t,t+i
(A.9)
where z
t,t+i
=
n
jt+i
n
jt
?
t
= (1 ? ?)??
t,t+1
(1 + r
t+1
) +
?
i=1
(1 ??)?
i
?
i+1
?
t,t+1+i
(1 + r
t+1+i
)z
t,t+i
(A.10)
112
?
t
= (1??)??
t,t+1
(1+r
t+1
)+??
t,t+1
?z
t,t+1
?
i=0
(1??)?
i+1
?
i+1
?
t+1,t+2+i
(1+r
t+2+i
)z
t+1,t+1+i
(A.11)
The in?nite sum at the right-hand size of equation (A.11) is one period updated
version of equation (A.9), given by
?
t+1
=
?
i=1
(1 ? ?)?
i+1
?
i+1
?
t+1,t+2+i
(1 + r
t+2+i
)z
t+1,t+1+i
(A.12)
where z
t+1,t+1+i
=
n
jt+1+i
n
jt+1
Hence, we can re-write equation (A.11) with the expectations as follows:
?
t
= E
t
[(1 ? ?)??
t,t+1
(1 + r
t+1
) + ??
t,t+1
?z
t,t+1
?
t+1
] (A.13)
A.2.2 Proof of Proposition 2
The pro?t maximization problem by a representative bank is given by
V
jt
= max
s
jt
E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
[(r
kt+1+i
?r
t+1+i
)q
t+i
s
jt+i
+ (1 + r
t+1+i
)n
jt+i
]
(A.14)
s.t. V
jt
? ?q
t
s
jt
(µ
t
) (A.15)
where µ
t
is the Lagrange multiplier associated with the incentive compatibility con-
113
straint. Using the solution for V
jt
in Proposition 2, I can re-write the intermediary’s
maximization problem using the Lagrangian,
L = ?
t
q
t
s
jt
+ ?
t
n
jt
+ µ
t
[?
t
q
t
s
jt
+ ?
t
n
jt
??q
t
s
jt
] (A.16)
The ?rst order conditions w.r.t. s
jt
and µ
t
are given respectively by
(1 + µ
t
)?
t
q
t
= µ
t
?q
t
(A.17)
V
jt
??q
t
s
jt
= 0 (A.18)
Rearranging (A.17) gives us the following expression,
?
t
=
µ
t
?
(1 + µ
t
)
(A.19)
Therefore, we establish that the incentive compatibility constraint binds (µ
t
> 0)
as long as expected discounted marginal gain of increasing bank assets is positive.
Replacing the de?nition of ?
t
, we obtain
E
t
[(1 ??)??
t,t+1
(r
kt+1
? r
t+1
) + ??
t,t+1
?
q
t+1
s
jt+1
q
t
s
jt
?
t+1
] =
µ
t
?
(1 + µ
t
)
(A.20)
Imposing the steady-state, we get the following expression,
114
(1 ? ?)?(r
k
?r)
(1 ? ??)
=
µ?
(1 + µ)
(A.21)
Rearranging gives us
(r
k
? r) =
(1 ???)µ?
(1 ??)?(1 + µ)
(A.22)
As long as µ is positive, i.e. the incentive compatibility constraint binds, risk pre-
mium is positive. Since I solve the model using linear approximation around the
steady-state and the shocks are su?ciently small, the premium is always positive in
numerical simulations.
115
A.3 Business Cycle Statistics of Aggregate Financial Variables of the
whole U.S. Financial Sector
For interested readers, this section documents empirical cyclical properties of
aggregate measures of the leverage ratio, debt and equity of U.S. ?nancial ?rms and
of the credit spread using quarterly data for the period 1952-2009. In particular, I
compute standard business cycle statistics of the aggregate ?nancial variables, such
as their standard deviations, cross-correlations with output.
I use quarterly balance sheet data from the Flow of Funds Accounts of the
Federal Reserve Board.
1
The theoretical model described below treats the entire
?nancial intermediary sector as a group of identical institutions although there is
a considerable amount of heterogeneity among ?nancial institutions in terms of
both their functions and balance sheet structures. For example, some ?nancial
intermediaries such as private pension funds, mutual funds, retirement funds, are
?nanced only by equity while some others such as banks, security-brokers and dealers
use leverage extensively. In order to be consistent with the model, I only select
?nancial institutions that always carry some leverage.
I focus on both depository and non-depository ?nancial institutions. The de-
pository institutions are U.S. chartered commercial banks, savings institutions, and
credit unions. The non-depository institutions are issuers of asset-backed securities,
bank holding companies, security brokers and dealers, ?nance companies, insurance
1
Total ?nancial assets and total liabilities in the Flow of Funds Accounts are partly measured
at book values and may be di?erent from market values. The di?erences between book values
and market values are more likely to disappear when the balance sheet of a particular ?nancial
institution is marked to market and/or when total ?nancial assets or liabilities are short-term.
116
companies, funding corporations, and real estate investment trusts. These institu-
tions perform the majority of activity in the U.S. ?nancial sector as measured by
their total assets.
2
Liabilities are de?ned as the sum of “Total liabilities” of each
of the aforementioned depository and non-depository ?nancial institutions in the
U.S. ?nancial system, while Net Worth is de?ned as the sum of “Total ?nancial
assets” minus the sum of “Total liabilities” of the same institutions. Leverage ratio
is the ratio of Liabilities to Net Worth. Credit spread measure I use is the di?erence
between quarterly real return to capital and quarterly real deposit rate. Quarterly
real return to capital data are taken from Gomme et.al. (2011). Quarterly deposit
rate data is taken from Federal Reserve Economic Data (FRED) of St. Louis FED.
I use quarterly in?ation rate computed using GDP de?ator to make nominal deposit
rates real.
Quarterly ?nancial data are taken from the Flow of Funds Accounts (FFA)
of the Federal Reserve Board. Quarterly real data except Hours and deposit rate
data are taken from Federal Reserve Economic Data (FRED) of St. Louis FED.
Hours data are taken from Current Employment Statistics survey published by the
Bureau of Labor Statistics. The return to capital data are taken from Gomme et
al. (2011). This paper constructs an empirical measure of the return to capital
for the U.S., which directly corresponds to the de?nition of the return to capital
in this paper. The balance sheet data in the level tables of FFA are nominal and
2
The total assets of these institutions is 90% of the total assets of the U.S. ?nancial sector.
Moreover, our de?nition of U.S. ?nancial sector includes important marked based ?nancial insti-
tutions such as security broker&dealers, ?nance companies, asset backed security (ABS) issuers,
and commercial banks as Adrian and Shin (2009) suggest. They argue that the balance sheet
?uctuations of these institutions are important determinants of real ?uctuations.
117
are not seasonally adjusted. All ?nancial data are seasonally adjusted using Census
X12 and are de?ated using GDP de?ator. I use FFA coded level tables released on
March 10, 2011 when I refer to the balance sheet items of ?nancial sector. Financial
and real data sources for ?gures 1 and 2, and tables 1 and 2 are given below.
Liabilities are the sum of “Total liabilities” of each of the following ?nancial
institutions: U.S. chartered commercial banks (Table L.110, Line 23), savings in-
stitutions (Table L.114, Line 23), credit unions (Table L.115, Line 16), issuers of
asset-backed securities (Table L.126, Line 11), bank holding companies (Table L.112,
Line 11), security brokers and dealers (Table L.129, Line 13), ?nance companies (Ta-
ble L.127, Line 10), property-casualty insurance companies (Table L.116, Line 16),
life insurance companies (Table L.117, Line 16), funding corporations (Table L.130,
Line 12), and real estate investment trusts (Table L.128, Line 11).
Net Worth is the sum of “Total ?nancial assets” minus the sum of “Total
liabilities” of each of the following ?nancial institutions: U.S. chartered commercial
banks (Table L.110, Line 1 minus Line 23), savings institutions (Table L.114, Line 1
minus Line 23), credit unions (Table L.115, Line 1 minus Line 16), issuers of asset-
backed securities (Table L.126, Line 1 minus Line 11), bank holding companies
(Table L.112, Line 1 minus Line 11), security brokers and dealers (Table L.129, Line
1 minus Line 13), ?nance companies (Table L.127, Line 1 minus Line 10), property-
casualty insurance companies (Table L.116, Line 1 minus Line 16), life insurance
companies (Table L.117, Line 1 minus Line 16), funding corporations (Table L.130,
Line 1 minus Line 12), and real estate investment trusts (Table L.128, Line 1 minus
Line 11).
118
Leverage Ratio is is the ratio of Liabilities to Net Worth. Finally, Credit
Spread is computed as the di?erence between the quarterly return to capital and
the quarterly deposit rate.
Consumption is the sum of “Personal consumption expenditures on nondurables”
(PCND) and “Personal consumption expenditures on services”. Investment is the
sum of “Personal consumption expenditures on durables” (PCDG) and “Gross pri-
vate domestic investment” (GPDI). GDP is the sum of Consumption and Invest-
ment. Hours is computed as the multiplication of “average weekly hours in private
sector” with “average number of workers in private sector”.
Table A.2: Business Cycle Statistics, Quarterly U.S. Data, 1952-2009
GDP C I Leverage R. Liabilities Net Worth Credit Spread
Standard deviation (%) 1.97 0.89 5.56 5.33 2.16 5.76 0.22
Quarterly autocorrelation 0.83 0.86 0.82 0.74 0.92 0.79 0.75
GDP 1 0.54 0.96 -0.08 0.57 0.28 -0.56
C – 1 0.29 0.10 0.07 -0.08 -0.05
Correlation matrix I – – 1 -0.10 0.63 0.33 -0.62
Leverage R. – – – 1 -0.03 -0.92 0.14
Liabilities – – – – 1 0.40 -0.51
Net Worth – – – – – 1 -0.32
Credit Spread – – – – – 1
a
Business cycle statistics for GDP, consumption and investment are computed using quarterly data from FRED
database. Consumption is the sum of personal consumption expenditures on nondurables and services (PCND +
PCESV). Investment is the sum of personal consumption expenditures on durable goods and gross private domestic
investment (PCDG + GPDI). GDP is the sum of consumption and investment.
b
Business cycle statistics in the table are based on HP-?ltered cyclical components over the period 1952-2009.
c
The correlation coe?cients greater than 0.13 are statistically signi?cant at 5% signi?cance level.
Table A.1 presents business cycle statistics for the aggregate leverage ratio, ag-
gregate liabilities, and aggregate equity of U.S. ?nancial sector together with those
for the credit spread. The volatility of the leverage ratio is nearly 3 times larger
than that of output and is roughly equal to that of investment. Table 1 shows
that the ?nancial leverage ratio is acyclical. The contemporaneous correlation be-
tween the ?nancial leverage ratio and output is -0.08. The volatility of aggregate
119
equity is 3 times larger than that of output, while the volatility of aggregate debt is
roughly equal to that of output.
3
The contemporaneous correlation between aggre-
gate liabilities and output is 0.57 while that between aggregate equity and output
is 0.28, indicating that both series are procyclical.
4
Moreover, the contemporane-
ous correlation with between credit spread and GDP is -0.56, showing that it is
countercyclical.
Table A.3: Cross Correlations of Financial Variables with Lags and Leads of GDP
Variable Y
t?5
Y
t?4
Y
t?3
Y
t?2
Y
t?1
Y
t
Y
t+1
Y
t+2
Y
t+3
Y
t+4
Y
t+5
Liabilities 0.01 0.13 0.27 0.41 0.52 0.57 0.57 0.50 0.39 0.26 0.12
NetWorth 0.00 0.04 0.09 0.14 0.21 0.28 0.34 0.35 0.31 0.20 0.05
LeverageR. 0.00 0.00 0.00 0.00 -0.03 -0.08 -0.14 -0.18 -0.18 -0.10 0.00
Spread 0.28 0.17 0.03 -0.15 -0.34 -0.56 -0.67 -0.60 -0.46 -0.29 -0.11
a
See the footnote (b) in Table 2 for the construction of aggregate ?nancial variables.
b
Business cycle statistics in the table are based on HP-?ltered cyclical components over the period 1952-
2009.
c
The correlation coe?cients greater than 0.13 are statistically signi?cant at 5% signi?cance level.
Table A.2 displays the cross-correlations of ?nancial variables with di?erent
lags and leads of GDP. It shows that aggregate ?nancial variables lead business cy-
cles in the U.S. In particular, the ?nancial leverage ratio, equity and credit spread
lead output by three, two and one quarters, respectively. However, liabilities con-
temporaneously move with output.
The following facts emerge from the empirical analysis above: (1) Financial
3
Using the Flow of Funds database, Jermann and Quadrini (2009) shows that relative volatili-
ties of non-?nancial sector debt and equity to non?nancial business sector GDP are 1.29 and 1.05,
respectively.
4
Jermann and Quadrini (2009) ?nd that debt is countercyclical and equity is procyclical for
non-?nancial ?rms for the same time period. In addition, using Compustat database, Covas and
Den Haan (2006) shows that debt and equity issuance is procyclical for the majority of publicly
listed ?rms.
120
leverage ratio and equity are three times more volatile than output, liabilities are a
little more volatile than output, (2) liabilities and equity are procyclical, ?nancial
leverage ratio is acyclical, and credit spread is countercyclical, and (3) Financial
leverage ratio, equity and credit spread lead output by three, two and one quarters,
respectively, while liabilities contemporaneously move with output.
121
A.4 Alternative Measures of Financial Shocks
This section presents alternative measures of ?nancial shocks and the simula-
tion results of the benchmark models under these alternative measures. I label the
benchmark model presented in the text as Benchmark 1.
The ?rst alternative measure for ?
t
series is constructed using the charge-o?
and delinquency rates of all loans, the level of outstanding loans, and net worth of
U.S. commercial banks from the Federal Reserve Board:
?
t
=
(1 ?Loanlossrates) ? Outstandingloans
Networth
(A.23)
Then I construct the log-deviation of ?
t
series by linearly detrending the log
of these series over the period 1987.Q1-2010.Q4. The ?
t
series can be interpreted
as the level of recovery rates of loans as a percentage of net worth. These recovery
rates determine the level of credit conditions in the economy since banks’ ability to
extend loans to non-?nancial businesses depends on their level of net worth, which
can be seen from equation (1.20). Therefore, the innovations to ?
t
are shocks to
the recovery rates, hence to the level of ?nancial conditions in the economy. First, I
estimate a VAR(1) for both TFP series and this alternative measure of ?. However,
the cross-terms in the VAR coe?cient matrix are not statistically signi?cant at 5%
signi?cance level. Then I estimate two independent AR(1) processes for both series.
The resulting persistence of the ? series is ?
?
= 0.9690 and the standard deviation
of the shock is ?
?
= 0.003111. The levels of z
t
and ?
t
series and the innovations to
those series are plotted in Figure A.1. I label the model driven by both standard
122
productivity shock and this alternative measure of ?nancial shock as Benchmark 2.
The second alternative measure for ?
t
series is constructed by calibrating the
persistence, ?
?
, and the standard deviation of the shock, ?
?
, to match the persistence
and the volatility of net worth in the data. The resulting persistence is ?
?
= 0.55,
and the resulting standard deviation of the shock is ?
?
= 0.04. I label the model
driven by both standard productivity shock and this alternative measure of ?nancial
shock as Benchmark 3.
Finally, the third alternative measure for ?
t
series is constructed as in the main
text. However, this time I estimate a VAR(1) for both TFP and ? series instead of
estimating two independent AR(1) processes as follows:
_
¸
¸
¸
_
´ z
t+1
´ ?
t+1
_
¸
¸
¸
_
=
_
¸
¸
¸
_
?
z
?
z,?
?
?,z
?
?
_
¸
¸
¸
_
_
¸
¸
¸
_
´ z
t
´ ?
t
_
¸
¸
¸
_
+
_
¸
¸
¸
_
?
z,t+1
?
?,t+1
_
¸
¸
¸
_
.
The resulting parameters are ?
z
= 0.9467, ?
z,?
= -0.0142, ?
?,z
= 0.9129, ?
?
=
0.2824, ?
z
= 0.006378, and ?
?
= 0.0489. I assume that the shocks are i.i.d. as the
correlation coe?cient between the innovations is not statistically signi?cant at 5%
signi?cant level. I label the model driven by both standard productivity shock and
this alternative measure of ?nancial shock as Benchmark 4.
Table A.3 presents the business cycle properties of real and ?nancial variables
of four di?erent benchmark models under alternative ?nancial shock measures. The
table suggests that main results of the paper don’t change across under alternative
?nancial shock series: all of the benchmark models are able to reproduce the key
123
business cycle facts about real variables: consumption and hours are less volatile
than output, while investment is more volatile. Investment and hours are highly
procyclical. However, Benchmark 1, 3 and 4 generates a counterfactual negative or
zero correlation between consumption and output. Moreover, Benchmark 4 predicts
higher volatilities in real variables compared to other three models. In terms of
?nancial variables, all of the benchmark models can explain most of the key empirical
regularities about aggregate ?nancial variables: bank assets, deposits, and spread are
less volatile than output, while net worth and leverage ratio are more volatile. Assets
and net worth are procyclical, while leverage ratio and spread are countercyclical.
Benchmark 1 and 3 predict countercyclical deposits, consistent with the data, while
Benchmark 2 and 4 generate procyclical deposits, contrary to the data. Overall,
regardless of which ?nancial shock measure is taken, we can say that ?nancial shocks
help the theoretical model explain ?nancial ?uctuations better, while preserving
most of its predictions about real variables.
For interested readers, I also include the ?gures A.2 to A.9 that display the
quarterly time series of real variables in the data, in the standard RBC model with
capital adjustment costs, and in the benchmark model economies (2 and 4) and
that display the quarterly time series of ?nancial variables in the data, in the model
driven only by productivity shocks, and in the benchmark model economies (2 and
4).
124
-.06
-.04
-.02
.00
.02
.04
88 90 92 94 96 98 00 02 04 06 08 10
Level of productivity
-.03
-.02
-.01
.00
.01
.02
88 90 92 94 96 98 00 02 04 06 08 10
Level of omega
-.03
-.02
-.01
.00
.01
.02
88 90 92 94 96 98 00 02 04 06 08 10
Innovations to productivity
-.020
-.015
-.010
-.005
.000
.005
.010
88 90 92 94 96 98 00 02 04 06 08 10
Innovations to recovery rates
Figure A.1: Time Series of Shocks to Productivity and Credit Conditions
125
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 2
GDP
corr(data, rbc) = 0.65
corr (data, benchmark 2) = 0.86
-50
-40
-30
-20
-10
0
10
20
30
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 2
corr(data, rbc) = 0.72
corr(data, benchmark 2) = 0.83
Investment
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 2
corr(data, rbc) = 0.39
corr(data, benchmark 2) = 0.64
Hours
Figure A.2: Real Fluctuations: Benchmark 2 vs. RBC model
126
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
corr(data, only prod.) = 0.68
corr(data, benchmark 2) = 0.86
GDP
-50
-40
-30
-20
-10
0
10
20
30
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Investment
corr(data, only prod.) = 0.68
corr(data, benchmark 2) = 0.83
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Hours
corr(data, only prod.) = 0.33
corr(data, benchmark 2) = 0.64
Figure A.3: Real Fluctuations: Benchmark 2 vs. Only Productivity
127
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
GDP
corr(data, rbc) = 0.69
corr(data, only prod.) = 0.68
-40
-30
-20
-10
0
10
20
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Investment
corr(data, rbc) = 0.72
corr(data, only prod.) = 0.68
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
corr(data, rbc) = 0.39
corr(data, only prod.) = 0.33
Hours
Figure A.4: Real Fluctuations: RBC vs. Only Productivity with Benchmark 2
calibration
128
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Bank credit
corr(data, only prod.) = 0.60
corr(data, benchmark 2) = 0.31
-10
-8
-6
-4
-2
0
2
4
6
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Deposits
corr(data, only prod.) = 0.46
corr(data, benchmark 2) = 0.46
-80
-60
-40
-20
0
20
40
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
corr(data, only prod.) = 0.12
corr(data, benchmark 2) = 0.51
Net Worth
-60
-40
-20
0
20
40
60
80
100
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Leverage Ratio
corr(data, only prod.) = 0.03
corr(data, benchmark 2) = 0.44
-1
0
1
2
3
4
5
6
7
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 2
Credit spread
corr(data, only prod.) = -0.10
corr(data, benchmark 2) = 0.32
-60
-40
-20
0
20
40
60
80
100
88 90 92 94 96 98 00 02 04 06 08 10
Survey of senior officers
Productivity shocks
Benchmark
Index of tightening credit conditions
corr(survey, prod) = 0.46
corr(survey, benchmark) = 0.53
Figure A.5: Financial Fluctuations: Benchmark 2 vs. Only Productivity
129
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 4
GDP
corr(data, rbc) = 0.69
corr(data, benchmark 4) = 0.77
-100
-80
-60
-40
-20
0
20
40
60
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 4
Investment
corr(data, rbc) = 0.72
corr(data, benchmark 4) = 0.81
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data RBC Benchmark 4
Hours
corr(data, rbc) = 0.40
corr(data, benchmark 4) = 0.53
Figure A.6: Real Fluctuations: Benchmark 4 vs. RBC model
130
-15
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
GDP
corr(data, only prod.) = 0.73
corr(data, benchmark 4) = 0.77
-100
-80
-60
-40
-20
0
20
40
60
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Investment
corr(data, only prod.) = 0.79
corr(data, benchmark 4) = 0.81
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Hours
corr(data, only prod.) = 0.47
corr(data, benchmark 4) = 0.53
Figure A.7: Real Fluctuations: Benchmark 4 vs. Only Productivity
131
-15
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
GDP
corr(data, rbc) = 0.69
corr(data, only prod.) = 0.73
-100
-80
-60
-40
-20
0
20
40
60
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Investment
corr(data, rbc) = 0.72
corr(data, only prod.) = 0.80
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
RBC
Only Productivity
Hours
corr(data, rbc) = 0.40
corr(data, only prod.) = 0.47
Figure A.8: Real Fluctuations: RBC vs. Only Productivity with Benchmark 4
calibration
132
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Bank credit
corr(data, only prod.) = 0.81
corr(data, benchmark 4) = 0.80
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Deposits
corr(data, only prod.) = 0.48
corr(data, benchmark 4) = 0.62
-80
-60
-40
-20
0
20
40
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Net worth
corr(data, only prod.) = -0.01
corr(data, benchmark 4) = 0.69
-40
-20
0
20
40
60
80
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Leverage ratio
corr(data, only prod.) = 0.01
corr(data, benchmark 4) = 0.73
-4
-2
0
2
4
6
8
10
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
Benchmark 4
Credit spread
corr(data, only prod.) = 0.07
corr(data, benchmark 4) = 0.36
Figure A.9: Financial Fluctuations: Benchmark 4 vs. Only Productivity
133
A.5 Model-Based Simulations of Macro-Financial Shocks using Utilization-
Adjusted TFP series
134
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
GDP
corr(data, only prod) = 0.52
corr(data, benchmark) = 0.77
-40
-30
-20
-10
0
10
20
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Investment
corr(data, only prod) = 0.31
corr(data, benchmark) = 0.70
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Hours
corr(data, only prod) = 0.21
corr(data, benchmark) = 0.63
Figure A.10: Real Fluctuations: Benchmark 1 vs. Only Productivity model
135
-16
-12
-8
-4
0
4
8
12
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
RBC
GDP
corr(data, rbc) = 0.54
corr(data, only prod) = 0.52
-40
-30
-20
-10
0
10
20
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
RBC
Investment
corr(data, rbc) = 0.39
corr(data, only prod) = 0.31
-12
-8
-4
0
4
8
88 90 92 94 96 98 00 02 04 06 08 10
Data
Only Productivity
RBC
Hours
corr(data, rbc) = 0.29
corr(data, only prod) = 0.21
Figure A.11: Real Fluctuations: RBC vs. Only Productivity
136
-10
-5
0
5
10
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Bank credit
corr(data, only prod) = 0.12
corr(data, benchmark) = 0.49
-10
-8
-6
-4
-2
0
2
4
6
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Deposits
corr(data, only prod) = 0.57
corr(data, benchmark) = 0.57
-80
-60
-40
-20
0
20
40
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Net worth
corr(data, only prod) = 0.09
corr(data, benchmark) = 0.77
-40
-20
0
20
40
60
80
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Leverage Ratio
corr(data, only prod) = -0.07
corr(data, benchmark) = 0.73
-60
-40
-20
0
20
40
60
80
100
88 90 92 94 96 98 00 02 04 06 08 10
Data
Benchmark
Only Productivity
Index of tightening credit standards
corr(data, only prod) = -0.38
corr(data, benchmark) = 0.16
Figure A.12: Financial Fluctuations: Benchmark 1 vs. Only Productivity
137
Table A.4: Real and Financial Statistics
Statistic Data Benchmark 1 Benchmark 2 Benchmark 3 Benchmark 4
?
Y
1.80 1.81 1.65 1.83 2.75
?
C
0.45 0.75 0.52 0.77 0.57
?
I
2.73 4.64 3.77 4.68 5.13
?
L
0.91 0.84 0.64 0.88 0.94
?
Y,I
0.97 0.87 0.92 0.88 0.97
?
Y,C
0.82 -0.03 0.34 -0.09 -0.70
?
Y,L
0.83 0.81 0.86 0.81 0.96
?
Assets
0.93 0.58 0.53 0.57 0.69
?
Deposits
0.69 0.87 0.44 0.74 0.74
?
NetWorth
5.17 5.90 2.10 5.17
?
4.21
?
LeverageR.
5.61 6.40 2.18 5.92 3.68
?
Spread
0.08 0.23 0.11 0.22 0.17
?
Y,Assets
0.30 0.88 0.91 0.87 0.86
?
Y,Deposits
-0.39 -0.23 0.48 -0.21 0.19
?
Y,NetWorth
0.52 0.68 0.82 0.67 0.70
?
Y,LeverageR.
-0.49 -0.71 -0.57 -0.66 -0.60
?
Y,Spread
-0.39 -0.67 -0.78 -0.70 -0.83
a
Business cycle statistics in the table are based on HP-?ltered cyclical components of quarterly simulated time series
(smoothing parameter:1600).
b
The standard deviation of output is expressed in percent; standard deviations of the remaining variables are normalized
by the standard deviation of output (std(x)/std(GDP)).
c ?
denotes calibration target.
138
Appendix B
B.1 Banks’ Pro?t Maximization Problem
Let’s conjecture that the bank’s franchise value is given by
V
jt
= ?
t
q
t
s
jt
+ ?
t
n
t
(B.1)
Comparing the conjectured solution for V
jt
to the expected discounted terminal net
worth yields the following expressions,
?
t
q
t
s
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
_
R
kt+1+i
?
_
R
t+1+i
?rr
t+i
1 ?rr
t+i
__
q
t+i
s
jt+i
(B.2)
?
t
n
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
_
R
t+1+i
? rr
t+i
1 ? rr
t+i
_
n
jt+i
(B.3)
Let’s ESP
t+i
stand for
_
R
kt+1+i
?
_
R
t+1+i
?rr
t+i
1?rr
t+i
__
and let’s RR
t+i
stand for
_
R
t+1+i
?rr
t+i
1?rr
t+i
_
.
Therefore,
?
t
q
t
s
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
ESP
t+i
q
t+i
s
jt+i
(B.4)
?
t
n
jt
= E
t
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
RR
t+i
n
jt+i
(B.5)
139
We write ?
t
and ?
t
recursively using the expressions above. Let’s begin with ?
t
. To
ease the notation, let’s drop expectations for now.
?
t
=
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
ESP
t+i
x
t,t+i
(B.6)
where x
t,t+i
=
q
t+i
s
jt+i
qts
jt
. Let’s separate (B.6) into two parts.
?
t
= (1 ? ?)??
t,t+1
ESP
t
+
?
i=1
(1 ? ?)?
i
?
i+1
?
t,t+1+i
ESP
t+i
x
t,t+i
(B.7)
Rearrange the second term at the right-hand size of the expression (B.7),
?
t
= (1??)??
t,t+1
ESP
t
+??
t,t+1
?x
t,t+1
?
i=0
(1??)?
i+1
?
i+1
?
t+1,t+2+i
ESP
t+1+i
x
t+1,t+1+i
(B.8)
The in?nite sum at the right-hand side of equation (B.8) is one period updated
version of equation (B.6), given by
?
t+1
=
?
i=0
(1 ? ?)?
i+1
?
i+1
?
t+1,t+2+i
ESP
t+1+i
x
t+1,t+1+i
(B.9)
where x
t+1,t+1+i
=
q
t+1+i
s
jt+1+i
q
t+1
s
jt+1
.
Hence, we can re-write (B.8) with the expectations as follows:
?
t
= E
t
[(1 ? ?)??
t,t+1
ESP
t
+ ??
t,t+1
?x
t,t+1
?
t+1
] (B.10)
140
Let’s continue with ?
t
. To ease the notation, let’s drop expectations for now.
?
t
=
?
i=0
(1 ? ?)?
i
?
i+1
?
t,t+1+i
RR
t+i
z
t,t+i
(B.11)
where z
t,t+i
=
n
jt+i
n
jt
. Let’s separate (B.11) into two parts.
?
t
= (1 ? ?)??
t,t+1
RR
t
+
?
i=1
(1 ??)?
i
?
i+1
?
t,t+1+i
RR
t+i
z
t,t+i
(B.12)
Rearrange the second term at the right-hand size of the expression (B.12),
?
t
= (1 ??)??
t,t+1
RR
t
+??
t,t+1
?z
t,t+1
?
i=0
(1 ??)?
i+1
?
i+1
?
t+1,t+2+i
RR
t+1+i
z
t+1,t+1+i
(B.13)
The in?nite sum at the right-hand size of equation (B.12) is one period updated
version of equation (B.10), given by
?
t+1
=
?
i=1
(1 ??)?
i+1
?
i+1
?
t+1,t+2+i
RR
t+1+i
z
t+1,t+1+i
(B.14)
where z
t+1,t+1+i
=
n
jt+1+i
n
jt+1
.
Hence, we can re-write equation (B.12) with the expectations as follows:
?
t
= E
t
[(1 ? ?)??
t,t+1
RR
t
+ ??
t,t+1
?z
t,t+1
?
t+1
] (B.15)
The pro?t maximization problem by a representative bank is given by
141
V
jt
= max
s
jt
E
t
?
i=0
(1 ??)?
i
?
i+1
?
t,t+1+i
ESP
t+i
q
t+i
s
jt+i
+ RR
t+i
n
jt+i
] (B.16)
s.t. V
jt
? ?q
t
s
jt
(µ
t
) (B.17)
where µ
t
is the Lagrange multiplier associated with the incentive compatibility con-
straint. Using the conjectured solution for V
jt
above, we can re-write the interme-
diary’s maximization problem using the Lagrangian,
L = ?
t
q
t
s
jt
+ ?
t
n
jt
+ µ
t
[?
t
q
t
s
jt
+ ?
t
n
jt
??q
t
s
jt
] (B.18)
The ?rst order conditions w.r.t. s
jt
and µ
t
are given respectively by
(1 + µ
t
)?
t
q
t
= µ
t
?q
t
(B.19)
V
jt
??q
t
s
jt
= 0 (B.20)
Rearranging (B.19) gives us the following expression,
?
t
=
µ
t
?
(1 + µ
t
)
(B.21)
Therefore, we establish that the incentive compatibility constraint binds (µ
t
> 0)
as long as expected discounted marginal gain of increasing bank assets is positive.
142
B.2 Impulse Responses under an Alternative RRR Policy Rule reacting to Current Credit Growth
1
4
3
0 10 20 30 40
?1.8
?1.6
?1.4
?1.2
?1
?0.8
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?1.4
?1.2
?1
?0.8
?0.6
Consumption
0 10 20 30 40
?4
?3
?2
?1
0
Investment
0 10 20 30 40
0
0.5
1
1.5
2
Hours
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?2
?1.5
?1
?0.5
0
Equity
0 10 20 30 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 10 20 30 40
?2.6
?2.4
?2.2
?2
?1.8
?1.6
Wage
Quarters
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?3
?2
?1
0
1
Ex?post Return to Capital
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?1
?0.5
0
0.5
Deposit Rate
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.1: The E?ect of Adverse TFP Shocks on Real Variables
1
4
4
0 10 20 30 40
?5
?4
?3
?2
?1
0
1
Net Worth
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?2.5
?2
?1.5
?1
?0.5
0
Deposits
0 10 20 30 40
?2
?1
0
1
2
3
4
Leverage
0 10 20 30 40
?1.8
?1.6
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
Bank Credit
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?50
0
50
100
150
200
250
300
Loan?Deposit Spread
Quarters
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
Figure B.2: The E?ect of Adverse TFP Shocks on Financial Variables
1
4
5
0 10 20 30 40
?8
?6
?4
?2
0
2
4
6
Real Balances
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
0
2
4
6
8
10
12
Velocity
0 10 20 30 40
?0.5
0
0.5
1
1.5
Inflation
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?25
?20
?15
?10
?5
0
Reserves
Quarters
Figure B.3: The E?ect of Adverse TFP Shocks on Monetary Variables
1
4
6
0 10 20 30 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.04
?0.03
?0.02
?0.01
0
Consumption
0 10 20 30 40
?0.5
?0.4
?0.3
?0.2
?0.1
0
Investment
0 10 20 30 40
?0.3
?0.2
?0.1
0
0.1
Hours
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.04
?0.03
?0.02
?0.01
0
Equity
0 10 20 30 40
?0.1
?0.05
0
0.05
0.1
Price of Equity
0 10 20 30 40
?0.05
0
0.05
0.1
0.15
Wage
Quarters
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.4
?0.2
0
0.2
0.4
Ex?post Return to Capital
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.05
0
0.05
0.1
0.15
Deposit Rate
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.4: The E?ect of Adverse Money Growth Shocks on Real Variables
1
4
7
0 10 20 30 40
?0.6
?0.5
?0.4
?0.3
?0.2
?0.1
0
0.1
Net Worth
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.07
?0.06
?0.05
?0.04
?0.03
?0.02
?0.01
0
Deposits
0 10 20 30 40
?0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Leverage
0 10 20 30 40
?0.1
?0.08
?0.06
?0.04
?0.02
0
Bank Credit
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?5
0
5
10
15
20
25
Loan?Deposit Spread
Quarters
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.06
?0.05
?0.04
?0.03
?0.02
?0.01
0
0.01
0.02
Required Reserves Ratio
Quarters
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.5: The E?ect of Adverse Money Growth Shocks on Financial Variables
1
4
8
0 10 20 30 40
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
Real Balances
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.2
0
0.2
0.4
0.6
0.8
1
1.2
Velocity
0 10 20 30 40
?0.05
0
0.05
0.1
0.15
0.2
0.25
0.3
Inflation
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
Reserves
Quarters
Figure B.6: The E?ect of Adverse Money Growth Shocks on Monetary Variables
1
4
9
0 10 20 30 40
?2
?1.5
?1
?0.5
0
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.2
?0.1
0
0.1
0.2
0.3
Consumption
0 10 20 30 40
?8
?6
?4
?2
0
Investment
0 10 20 30 40
?4
?3
?2
?1
0
1
Hours
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.5
?0.4
?0.3
?0.2
?0.1
0
Equity
0 10 20 30 40
?1.5
?1
?0.5
0
0.5
Price of Equity
0 10 20 30 40
?0.5
0
0.5
1
1.5
Wage
Quarters
%
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?6
?4
?2
0
2
4
Ex?post Return to Capital
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?1
0
1
2
3
4
Deposit Rate
Quarters
A
n
n
.
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.7: The E?ect of Adverse Financial Shocks on Real Variables
1
5
0
0 10 20 30 40
?14
?12
?10
?8
?6
?4
?2
0
Net Worth
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?0.4
?0.2
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Deposits
0 10 20 30 40
0
2
4
6
8
10
12
Leverage
0 10 20 30 40
?1.4
?1.2
?1
?0.8
?0.6
?0.4
?0.2
0
Bank Credit
%
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
0
100
200
300
400
500
600
Loan?Deposit Spread
Quarters
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 10 20 30 40
?0.6
?0.5
?0.4
?0.3
?0.2
?0.1
0
0.1
Required Reserves Ratio
Quarters
%
P
t
.
?
f
r
o
m
S
.
S
.
Figure B.8: The E?ect of Adverse Financial Shocks on Financial Variables
1
5
1
0 10 20 30 40
?2
0
2
4
6
8
10
Real Balances
%
?
f
r
o
m
S
.
S
.
Credit Policy
Fixed RR Ratio
No Reserves
0 10 20 30 40
?8
?6
?4
?2
0
2
Velocity
0 10 20 30 40
?0.8
?0.6
?0.4
?0.2
0
0.2
0.4
0.6
0.8
Inflation
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 10 20 30 40
?12
?10
?8
?6
?4
?2
0
2
Reserves
Quarters
Figure B.9: The E?ect of Adverse Financial Shocks on Monetary Variables
1
5
2
B.3 Impulse Responses under Zero RRR Policy
1
5
3
0 20 40
?2
?1.5
?1
?0.5
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy (phi = 5.15) Fixed RR Ratio No Reserves
0 20 40
?4
?3
?2
?1
0
Investment
0 20 40
0
0.5
1
1.5
2
2.5
Hours
0 20 40
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?3
?2
?1
0
1
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?4
?2
0
2
4
Leverage
0 20 40
?2
?1.5
?1
?0.5
0
Bank Credit
0 20 40
?100
0
100
200
300
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?1.5
?1
?0.5
0
0.5
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
0
5
10
15
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
1.5
Inflation
Quarters
0 20 40
?25
?20
?15
?10
?5
0
Reserves
Quarters
Figure B.10: Impulse Responses Led by a 1-? Adverse TFP Shock
1
5
4
0 20 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy (phi = 5.15) Fixed RR Ratio No Reserves
0 20 40
?0.6
?0.4
?0.2
0
0.2
Investment
0 20 40
?0.3
?0.2
?0.1
0
0.1
Hours
0 20 40
?0.06
?0.04
?0.02
0
0.02
Price of Equity
0 20 40
?0.4
?0.3
?0.2
?0.1
0
0.1
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?0.1
0
0.1
0.2
0.3
Leverage
0 20 40
?0.08
?0.06
?0.04
?0.02
0
Bank Credit
0 20 40
?5
0
5
10
15
20
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.06
?0.04
?0.02
0
0.02
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.5
0
0.5
1
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.1
0
0.1
0.2
0.3
Inflation
Quarters
0 20 40
?1.5
?1
?0.5
0
0.5
Reserves
Quarters
Figure B.11: Impulse Responses Led by a 1-? Adverse Money Growth Shock
1
5
5
0 20 40
?3
?2
?1
0
1
Output
%
?
f
r
o
m
S
.
S
.
Credit Policy (phi = 5.15) Fixed RR Ratio No Reserves
0 20 40
?8
?6
?4
?2
0
2
Investment
0 20 40
?4
?3
?2
?1
0
1
Hours
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?10
?8
?6
?4
?2
0
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
0
2
4
6
8
10
Leverage
0 20 40
?1
?0.8
?0.6
?0.4
?0.2
0
Bank Credit
0 20 40
0
100
200
300
400
500
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.6
?0.4
?0.2
0
0.2
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?8
?6
?4
?2
0
2
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
Inflation
Quarters
0 20 40
?15
?10
?5
0
5
Reserves
Quarters
Figure B.12: Impulse Responses Led by a 1-? Adverse Financial Shock
1
5
6
B.4 Policy Intensity Experiments
1
5
7
0 20 40
?2
?1.5
?1
?0.5
Output
%
?
f
r
o
m
S
.
S
.
Moderate Credit Policy (phi = 5.15) Fixed RR Ratio Aggressive Credit Policy (phi=10)
0 20 40
?4
?3
?2
?1
0
Investment
0 20 40
0
0.5
1
1.5
2
2.5
Hours
0 20 40
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?3
?2
?1
0
1
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?3
?2
?1
0
1
2
3
Leverage
0 20 40
?2
?1.5
?1
?0.5
0
Bank Credit
0 20 40
?50
0
50
100
150
200
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?2
?1.5
?1
?0.5
0
0.5
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
0
5
10
15
20
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
1.5
2
Inflation
Quarters
0 20 40
?40
?30
?20
?10
0
Reserves
Quarters
Figure B.13: Impulse Responses Led by a 1-? Adverse TFP Shock
1
5
8
0 20 40
?0.2
?0.15
?0.1
?0.05
0
Output
%
?
f
r
o
m
S
.
S
.
Moderate Credit Policy (phi = 5.15) Fixed RR Ratio Aggressive Credit Policy (phi=10)
0 20 40
?0.6
?0.4
?0.2
0
0.2
Investment
0 20 40
?0.3
?0.2
?0.1
0
0.1
Hours
0 20 40
?0.05
?0.04
?0.03
?0.02
?0.01
0
0.01
Price of Equity
0 20 40
?0.4
?0.3
?0.2
?0.1
0
0.1
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
?0.1
0
0.1
0.2
0.3
Leverage
0 20 40
?0.08
?0.06
?0.04
?0.02
0
Bank Credit
0 20 40
?5
0
5
10
15
20
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.08
?0.06
?0.04
?0.02
0
0.02
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.5
0
0.5
1
1.5
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?0.1
0
0.1
0.2
0.3
Inflation
Quarters
0 20 40
?1.5
?1
?0.5
0
0.5
Reserves
Quarters
Figure B.14: Impulse Responses Led by a 1-? Adverse Money Growth Shock
1
5
9
0 20 40
?2
?1.5
?1
?0.5
0
0.5
Output
%
?
f
r
o
m
S
.
S
.
Moderate Credit Policy (phi = 5.15) Fixed RR Ratio Aggressive Credit Policy (phi=10)
0 20 40
?8
?6
?4
?2
0
2
Investment
0 20 40
?3
?2
?1
0
1
Hours
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Price of Equity
0 20 40
?10
?8
?6
?4
?2
0
Net Worth
%
?
f
r
o
m
S
.
S
.
0 20 40
0
2
4
6
8
10
Leverage
0 20 40
?1
?0.8
?0.6
?0.4
?0.2
0
Bank Credit
0 20 40
0
100
200
300
400
Loan?Deposit Spread
A
n
n
u
a
l
i
z
e
d
B
s
.
P
t
.
?
f
r
o
m
S
.
S
.
0 20 40
?0.8
?0.6
?0.4
?0.2
0
0.2
Required Reserves Ratio
%
P
t
.
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?8
?6
?4
?2
0
2
Velocity
%
?
f
r
o
m
S
.
S
.
Quarters
0 20 40
?1
?0.5
0
0.5
1
Inflation
Quarters
0 20 40
?15
?10
?5
0
5
Reserves
Quarters
Figure B.15: Impulse Responses Led by a 1-? Adverse Financial Shock
1
6
0
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