Macroprudential Policies and Financial Frictions

by

Hasan Sadik Arik

Department of EconomicsDuke University

Date:Approved:

A. Craig Burnside, Supervisor

Mariano Massimiliano Croce, Supervisor

Cosmin Ilut

Andrea Lanteri

Dissertation submitted in partial fulfillment of the requirements for the degree ofDoctor of Philosophy in the Department of Economics

in the Graduate School of Duke University2017

Abstract

Macroprudential Policies and Financial Frictions

by

Hasan Sadik Arik

Department of EconomicsDuke University

Date:Approved:

A. Craig Burnside, Supervisor

Mariano Massimiliano Croce, Supervisor

Cosmin Ilut

Andrea Lanteri

An abstract of a dissertation submitted in partial fulfillment of the requirements forthe degree of Doctor of Philosophy in the Department of Economics

in the Graduate School of Duke University2017

Copyright c© 2017 by Hasan Sadik ArikAll rights reserved except the rights granted by the

Creative Commons Attribution-Noncommercial Licence

Abstract

This dissertation consists of two essays on macropudential policies and financial fric-

tions. In the first essay, the Reserve Option Mechanism, an unconventional policy

tool invented and used by the Central Bank of the Republic of Turkey, is modeled

and evaluated. The mechanism is designed to act as an automatic stabilizer of large

fluctuations of exchange rate by letting banks use foreign currency to fulfill a portion

of the domestic-denominated required reserves. Hence, the fluctuations in domestic

business cycles due to volatile short-term capital flows are expected to be mitigated.

The mechanism works through easing the frictions faced in the financial sector by

generating a certain level of “confidence” for the banks in terms of having enough

foreign funding as reserves. Banks utilize the mechanism up to a point where this

benefit is offset by the cost of using the mechanism: the Reserve Option Coeffi-

cient, which is the amount of foreign currency that must be held to meet one-unit

domestic-denominated reserve requirement, i.e., an artificially imposed “exchange

rate”. Two channels through which the mechanism is utilized are identified: a) the

funding spread banks face between the foreign and domestic funding rates, and b)

depreciation channel which involves the valuation of already-held foreign reserves

through the mechanism.

In the second essay, I present a dynamic stochastic general equilibrium model

that can be used to evaluate macroprudential policies. In the model, both the fi-

nancial intermediaries and the non-financial firms face financial frictions and make

iv

separate financial decisions. After showing the model’s relative ability to replicate

events like the Great Recession compared to natural benchmark models, I document

that financial shocks were relatively more important than productivity shocks in the

period of the Great Recession. Then, I evaluate a countercyclical capital policy that

can help mitigate both financial and productivity shocks. The policy involves injec-

tion of additional capital to the banks during bad times, which reduces the frictions

banks face; as a result, it is welfare-improving.

v

To Seda Nur

vi

Contents

Abstract iv

List of Tables ix

List of Figures x

Acknowledgements xi

1 Required Reserves as a Capital Flow Management Tool 1

1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.2 The Practice: Reserve Option Mechanism (ROM) as a StabilizingPolicy Tool . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

1.3 Model Economy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

1.3.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.3.2 Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.3.3 Capital Producers . . . . . . . . . . . . . . . . . . . . . . . . . 28

1.3.4 Production Firms . . . . . . . . . . . . . . . . . . . . . . . . . 29

1.3.5 Monetary Authority . . . . . . . . . . . . . . . . . . . . . . . 30

1.4 Quantitative Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

1.4.1 Model Calibration . . . . . . . . . . . . . . . . . . . . . . . . 34

1.4.2 Model vs. Data . . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.4.3 Model Dynamics . . . . . . . . . . . . . . . . . . . . . . . . . 34

1.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

vii

2 Countercyclical Capital Rule and Financial Frictions 40

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.2 Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.2.1 Banks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

2.2.2 Strengthening the Effect of Macroprudential Policy . . . . . . 45

2.2.3 Non-financial Firms . . . . . . . . . . . . . . . . . . . . . . . . 45

2.2.4 Government . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.2.5 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

2.3 Importance of Financial Shocks . . . . . . . . . . . . . . . . . . . . . 50

2.4 Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

2.5 Policy Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54

2.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59

A Model Derivations, Definition of Competitive Equilibrium, and Ad-ditional IRFs for Chapter 1 60

A.1 Model Derivations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.1.1 Households . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

A.1.2 Banks’ Net Worth Maximization . . . . . . . . . . . . . . . . 60

A.1.3 Optimal Utilization Rate of the ROM . . . . . . . . . . . . . . 62

A.1.4 Resource Constraints . . . . . . . . . . . . . . . . . . . . . . . 63

A.2 Definition of Competitive Equilibrium . . . . . . . . . . . . . . . . . . 64

A.3 IRFs in Response to Productivity and Country Risk Premium Shocks 65

Bibliography 67

Biography 70

viii

List of Tables

1.1 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

1.2 Steady State Effects of the ROM. . . . . . . . . . . . . . . . . . . . . 36

2.1 Model Parameters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55

2.2 Welfare Comparison . . . . . . . . . . . . . . . . . . . . . . . . . . . 56

ix

List of Figures

1.1 ROC Schedule in Practice. . . . . . . . . . . . . . . . . . . . . . . . . 8

1.2 ROM Utilization and its Dispersion in Practice. . . . . . . . . . . . . 9

1.3 Sensitivity of Friction λ to its Arguments . . . . . . . . . . . . . . . . 23

1.4 Funding Spread vs Utilization Rate . . . . . . . . . . . . . . . . . . . 27

1.5 ROC Sechedule in Practice vs the Model . . . . . . . . . . . . . . . . 31

1.6 Sensitivity of ROC Schedule to roc1. . . . . . . . . . . . . . . . . . . 32

1.7 Sensitivity of ROC Schedule to roc2. . . . . . . . . . . . . . . . . . . 32

1.8 Sensitivity of ROC Schedule to roc3. . . . . . . . . . . . . . . . . . . 33

1.9 World Interest Rate Shock IRFs. . . . . . . . . . . . . . . . . . . . . 37

2.1 Comparison of IRFs: JQ vs JQGK . . . . . . . . . . . . . . . . . . . 51

2.2 Counterfactual Series vs. the Data: Financial Shock Only . . . . . . . 52

2.3 Counterfactual Series vs. the Data: Productivity Shock Only . . . . . 53

2.4 Counterfactual Series vs. the Data: Both Shocks . . . . . . . . . . . . 54

2.5 Comparison of IRFs in Response to Productivity Shock . . . . . . . . 57

2.6 Comparison of IRFs in Response to Financial Shocks . . . . . . . . . 58

A.1 Productivity Shock IRFs. . . . . . . . . . . . . . . . . . . . . . . . . 65

A.2 Country Risk Premium Shock IRFs. . . . . . . . . . . . . . . . . . . . 66

x

Acknowledgements

I am extremely grateful to my advisors Professors Craig Burnside and Max Croce

for their advice and encouragement. I thank to my committee members Professors

Cosmin Ilut and Andrea Lanteri, and seminar participants of Duke’s Macroeconomics

Lunch Groups for their helpful comments and suggestions. I am also grateful to the

Muoio Family Fellowship Fund for supporting me during the summer of 2015, and

the Central Bank of Turkey where I visited during the same period. I benefited

from discussions with my colleagues Adam Bergeron, Vasco de Castro Botelho, Olga

Kozlova, and Nicolas-Aldebrando Benelli.

My mom and dad, my sister, and Seda have always been there for me. I am

grateful to them for their moral and emotional support, as well as for their patience

and understanding.

I feel extremely lucky to come across these guys in Durham: Mert Aydin, Ilker

Nadi Bozkurt, Menevis Cilizoglu, Ezgi Gulen Kaya, Deniz Ozturk, Selcan Tuncay,

Serkan Yolacan, and Safak Yucel. Of course, a very special shout-out goes to my

roommates: Oguz Cetin, Huseyin Gurkan, and Osman “Rumi” Kocas. I will miss

the fun times we shared.

I also would like to thank to Ibrahim Adil Gullu, Enes Ozel, and Alper Sahan for

being who they are. Do not change.

And last but not least, Faruk Aktay. When is the next 1000 miles?

xi

1

Required Reserves as a Capital Flow ManagementTool

1.1 Introduction

“...one might compare capital account liberalization to putting a race car engine into

an old car and setting off without checking the tires or training the driver. Perhaps

with appropriate tires and training, the car might perform better; but without such

equipment and training, it is almost inevitable that an accident will occur. One might

actually have done far better with the older, more reliable engine: performance would

have been slower, but there would have been less potential for an accident...” Stiglitz

(2000)1.

1990s and 2000s witnessed a series of economic crises in Asia, Latin America, and

Eastern Europe upon liberalization of emerging markets’ capital accounts.2 Conse-

quently, the policy measures of capital flow management have been an important

debate in both policy and academic circles.

1 This chapter of the dissertation is based on a previous unpublished manuscript co-authored withSalih Fendoglu, Yasin Mimir, and Enes Sunel.

2 For instance: 1994 Mexico, 1997 Eastern Asia, 1998 Russia, 1999-2002 Argentina, 2001 Turkey.

1

In the aftermath of global financial crisis of 2008-2009, large-scale quantitative

easing policies, sluggish recovery and unresolved policy uncertainties in developed

economies have once again created a volatile global financial environment. Private

capital flows to emerging markets have decreased by almost half in 2008, quickly re-

covered and have been very volatile since then. Such volatile flows, if not managed by

emerging economy policy makers properly, may lead to large fluctuations in domes-

tic business cycles.3 Accordingly, many emerging market central banks have started

following a flexible policy framework, using many unconventional policies, e.g. active

use of reserve requirements, implementing direct controls on capital flows, to sup-

port financial stability along with conventional policy tools to anchor medium-term

inflation expectations.4

This paper investigates an unconventional macroprudential policy tool, the Re-

serve Option Mechanism (ROM), that in principle acts as an automatic stabilizer of

large fluctuations in exchange rate, hence smooths fluctuations in domestic business

cycles due to volatile short-term capital flows. Historically, during periods of large

capital inflows, many emerging market economies have experienced amplified cycles

of appreciation in the exchange rate, improvements in balance sheet conditions of

firms (which rely mostly on foreign funds), looser credit conditions, increases in do-

mestic inflation, stronger appreciation in the exchange rate, and further increases

in capital inflows. As the economy builds up external imbalances, these large cap-

ital flow periods often times ended up with a sudden stop of capital flows, leading

to a reversed cycle of sharp depreciation of the exchange rate and a large contrac-

tion in output. Recently, experiencing large capital inflows, many emerging market

economies have followed policies to weaken such an amplified cycle. The ROM, in

3 See Bruno and Shin (2013a, 2013b) for an example of financial amplification cycle for a smallopen economy due to short-term capital flows.

4 See, for instance, Brazil, Chile, Colombia, Korea and Turkey.

2

this very regard, can be thought as a novel and alternative way to mitigate the effect

of such flows on the domestic business cycles.

The ROM is a novel policy tool in that the mechanism is to cushion the economy

from volatile capital flows in a market-friendly manner. It is a facility allowing banks

(that are subject to reserve requirements) to fulfill part of their domestic currency

reserve requirements with foreign currency funds. Each bank optimally chooses by

how much to utilize the mechanism, i.e. each bank decides the fraction of domestic

currency required reserves that are to be fulfilled by foreign currency funds, if not

nil. During a surge in capital flows, banks in general find it easier to borrow in

USD (e.g. due to lower cost of borrowing in USD) compared to domestic currency.

Banks in turn would utilize the mechanism more during such episodes, retaining

some portion of the USD inflow at the central bank as reserves. In parallel, during

capital outflow periods, banks would find it harder to have USD funding, and in turn

would like to utilize the mechanism less. In turn, banks’ reserves at the central bank

would decrease, again easing the pressure on the exchange rate. In this regard, the

mechanism can be thought as a way to make private agents (banks) internalize the

social benefit of accumulating reserves during inflow periods as a buffer for outflow

periods, smoothing the effect volatile capital flows on the business cycles.

In order to analyze the ROM, a two-sector small-open-economy dynamic stochas-

tic general equilibrium (DSGE) model of banking is built. The modeling of the finan-

cial sector closely follow the framework by Gertler et al. (2010) (GK henceforth). The

key feature of the model is that banks are subject to endogenous capital constraints

due to agency problems. This constraint in turn feeds into a financial acceleration

in its general sense, amplifying the initial response of economy to macroeconomic

shocks. The model deviates from the general setup in GK in two ways: First, banks

are subject to domestic currency reserve requirements. Second, banks are allowed

to fulfill part of their domestic currency required reserves with foreign currency.

3

Note that the banking sector described in this model can easily be embedded into

a bigger model to analyze the interaction of the ROM with other, conventional or

unconventional, policy tools.

Management of capital flows are implemented through direct capital controls

and/or macroprudential policy measures. There are numerous studies examining

the effectiveness of the capital flow management tools. I now would like to review

the literature, first briefly discussing the papers on macroprudential policies, then

reviewing the studies on direct capital controls.

CBRT took some other macroprudential measures including currency-based and

maturity-based reserve requirements, and time-varying interest rate corridor. At the

same time, Banking Regulation and Supervision Agency (BRSA) complemented the

policies of CBRT with increasing the risk weight of certain type of loans. Moreover,

the loan-loss provisions were increased for banks which give more than a certain level

of high loan-to-value ratio credits.

Turkey has not been the only country implementing macroprudential measures to

curb adverse effects of volatile global financial system. Most of the emerging counties

including Brazil, Korea, China, Colombia, Indonesia, and Poland took macropruden-

tial measures or capital controls aftermath of the crisis.5

Despite the extensive use of the macroprudential tools, the effects of the policies

are not explored in detail neither in empirical nor in model-based dimensions. The

number of studies has been growing since the Great Recession, though. For instance,

Lim et al. (2011) analyze the effects of several macroprudential policies using cross-

country panel data. They find that caps on loan-to-value ratio and debt-to-income

ratio, ceilings on credit, reserve requirements, capital requirements, and dynamic

provisioning are effective on dampening the procyclicality of credit, leverage, and

5 See Lim et al. (2011) for a detailed discussion of the policies taken by each country and theireffectiveness.

4

foreign liabilities.

Angelini et al. (2012) and Unsal (2011) augment a DSGE model with a banking

sector and study the role of macroprudential policies in this environment. They both

find that macroprudential policies complement monetary policy successfully under a

financial shock and bring sizable benefits.

Beau et al. (2012) study the interaction between monetary policy objectives and

macroprudential policies within a DSGE model extended with financial sector fric-

tions. They find that the macroprudential policies are most effective in price sta-

bility when the monetary policy takes the objectives of macroprudential policy into

account.

Kannan et al. (2009) analyze the role of macroprudential policies in a DSGE

model with financial accelerator mechanism and house price booms. They show

that macroprudential measures targeting credit cycles, especially those implemented

time-varying, are useful for macroeconomic stability.

Some countries including many Latin American and Asian countries used in sev-

eral occasions and still have been using direct capital controls over short term inflows

and/or outflows.6 Regarding the effectiveness of direct capital controls, the findings

in the literature are mixed. For instance Nadal-De Simone and Sorsa (1999) find that

Chilean controls over capital inflows had temporary effect on reducing the volume

and composition of inflows. Edwards (1999) provides evidence on the fact that re-

serve requirement policy of Chile protected the economy from external shocks during

1990s.

Findings of Fengjuan and Kimball (2005) suggest that China’s capital control

measures were effective in reducing the flow volatility. Shah and Patnaik (2007)

provides a similar result for India.

Dooley (1996) surveys the empirical literature on the capital controls of a broad

6 For a detailed survey on country experiences, see Ariyoshi et al. (2000).

5

set of countries and concludes that most of the studies are skeptical about effective-

ness of the capital controls on policy objectives of the governments.

Reinhart and Smith (1998)find that capital controls were effective on reducing

the net outflows and alter the composition for Brazil and Chile, whereas it was not

effective for the case of Colombia and was effective only altering the composition for

Czech Republic.

Magud and Reinhart (2006) provides a more recent survey on country experiences.

They find that capital controls change the relative interest rate and composition of

inflows, however their effect on real exchange rates and net flows is ambiguous.

The paper is mostly related to the quantitative DSGE literature. It is different

from the rest of the literature in the sense that it analyzes a novel macroprudential

rule - unique to the CBRT - namely the Reserve Option Mechanism. This study

is the first attempt to a quantitative evaluation of the effects of the aforementioned

policy measure.

The paper proceeds as follows. Section 1.2 presents the details of the mechanism,

and its use by the banks over the course of its implementation. Section 1.3 presents

the model with a banking sector in an environment with the ROM. Section 1.4

provides the calibration and main empirical results. Section 1.5 concludes.

1.2 The Practice: Reserve Option Mechanism (ROM) as a StabilizingPolicy Tool

The mechanism allows domestic banks to hold their domestic-currency required re-

serves in foreign currency (USD or EUR) up to a certain fraction (e.g. 50%). For

instance, if a bank is obliged to hold 10 units of domestic currency as reserves at

the central bank, the bank can voluntarily retain an equivalent amount of USD at

the central bank to meet up to 5 units of domestic-currency required reserves. The

central bank can steer banks’ use of the mechanism by cyclically adjusting the re-

6

serve option coefficient (ROC), though, the amount of USD that should be held to

meet one-unit domestic-currency- reserve requirement. For instance, if the ROC is

2, then the bank should hold 2 units of domestic currency-worth of USD (at the

central bank) to meet one unit of domestic-currency required reserves (provided that

the bank would like to utilize the mechanism).

Central bank can set different ROCs for different domestic required reserve trenches.

For example, banks may be obliged to hold 1 domestic-currency worth of USD to

meet up to 20% of domestic-currency required reserves, and 2 domestic-currency-

worth of USD to meet 20% to 50% of the domestic currency required reserves (hence

the ROC is 1 for up to %20, and 2 for 20%-50% to meet domestic currency required

reserves, see Figure 1.1 below for the actual ROC schedule used by the CBRT).

For practical policy making, setting increasingly higher ROCs for higher trenches

appears to be important for the effective functioning of the ROM. A lower ROC (e.g.

1) for a lower trench (e.g. first %10) welcomes banks who in general find USD funding

harder. Higher ROCs for higher trenches, on the other hand, ensures that some of

the banks (who in general find USD funding relatively easy) does not fully utilize

the mechanism, since they will otherwise be not able to utilize the mechanism more

during capital inflow periods, hitting the upper bound of the utilization threshold (the

50% in the example). Hence, setting increasingly higher ROCs for higher trenches is

important for the stabilizing role of the mechanism.

The CBRT has implemented the ROM gradually starting in late 2011, setting the

maximum fraction at 10% (i.e. banks can hold up to 10% of their required domestic

reserves in USD) with a ROC 1. The central bank then has gradually increased the

maximum fraction to 60% and set different (and increasing) ROCs for the trenches.

The mechanism so far has been heavily used by the banks (in 2014, the utilization

rate of the mechanism has reached to almost 60%) (Figure 1.2 plots the utilization

rate of the mechanism overtime).

7

Figure 1.1: ROC Schedule Used by CBRT in Practice (as of Feb.27.2015)Note: This figure is taken directly from Akturk et al. (2015). Their caption reads: Data has biweekly frequency (perrequired reserves maintenance period) covering the period from 9/30/2011 to 3/27/2015. The figures inside thestacked bar chart show effective foreign exchange (FX) Reserve Option Coefficients (ROCs) and the correspondingtranches as of the given dates (required reserves maintenance periods) on the horizontal axis. For instance, effectiveFX ROCs as of Aug.31.2012 are 1.1, 1.4, 1.7, 1.9, and 2.0 for the corresponding tranches of 0-30, 30-35, 35-40, 40-45, 45-50, 50-55, and 55-60 percent. The ROCs 3.30, 3.50, 3.70, 3.90, and 4.10 located at the top right corner of thediagram correspond the tranches of 55-56, 56-57, 57-58, 58-59, and 59-60 percent, respectively. The solid black lineis obtained by connecting fifteen realized average FX ROC data points for the banking sector for the correspondingfifteen dates (required reserves maintenance periods) on the horizontal axis. Realized average FX ROCs are obtainedby taking the ratio of required reserves kept in FX to total required reserves multiplied by the percentage use of FXROM facility. Source: Electronic Data Delivery System (EDDS) of the Central Bank of Republic of Turkey.

8

Figure 1.2: ROM Utilization Rates Over Time and its Dispersion

note: The red line represents the monthly average usage rate, and the shaded area around is its dispersion

1.3 Model Economy

The analytical framework is a small open economy monetary model inhabited by

households, banks, non-financial firms, capital producers, and a central bank. Fi-

nancial frictions define bankers as a key agent in the economy. The modeling of the

banking sector is similar to Mimir and Sunel (2015) so that bankers make external

financing from both domestic depositors and international lenders bearing currency

risk. The agency problem as in Gertler et al. (2012) is modified so that as banks’

liability structure gets riskier, financial frictions become non-linearly more severe.

In order to limit the focus of the paper to reserve requirements policy, model does

not contain nominal rigidities so that the central bank is assumed to determine the

exogenous money supply as in Cooley and Hansen (1991) under flexible prices. Note

9

however, that the central bank in the model also implements the ROM. Unless oth-

erwise stated, variables denoted by upper (lower) case characters represent nominal

(real) values in domestic currency. Variables that are denominated in foreign cur-

rency or related to the rest of the world are indicated by an asterisk. For brevity,

key model equations are included in the main text. Interested readers might refer

to Appendix A for detailed derivations of the optimization problems of agents and a

definition of the competitive equilibrium.

1.3.1 Households

There is a large number of infinitely-lived identical households, who derive utility

from consumption ct and leisure (1´ht), where ht is the fraction of daytime devoted

to labor activities. The consumption good is a constant-elasticity-of-substitution

(CES) aggregate of domestically tradable and non-tradable goods,

ct “”

ω1τ pcNt q

τ´1τ ` p1´ ωq

1τ pcTt q

τ´1τ

ıττ´1, (1.1)

where τ ą 0 is the elasticity of substitution between traded and non-traded goods

and 0 ă ω ă 1 is the relative weight of non-traded goods in the consumption basket,

capturing the degree of openness. Let PNt and P T

t represent domestic currency de-

nominated prices of non-traded and traded goods. Then, the expenditure minimiza-

tion problem of households subject to the consumption aggregator (1.1) produces

the domestic consumer price index (CPI),

Pt “”

ωpPNt q

1´τ` p1´ ωqpP T

t q1´τ

ı1

1´τ(1.2)

and the condition that determines the optimal demand frontier for non-tradable and

tradable goods,

10

cNtcTt“

ω

1´ ω

ˆ

PNt

P Tt

˙´τ

. (1.3)

It is assumed that workers constitute % fraction of households and pool their re-

sources for consumption with bankers so that the two subgroups perfectly insure each

other. Each period bankers transform into workers with an exogenous probability

1 ´ θ and are replaced by same number of new bankers so that the household com-

position stays intact. Workers consume the consumption bundle and supply labor

ht. They also can save in local currency assets which are deposited within financial

intermediaries owned by the banker members of other households. The balance of

these deposits is denoted by Bt`1, which promises to pay a gross real risk-free rate

Rt in the next period. Similar to Mimir and Sunel (2015), workers are not allowed

to directly save in productive capital, and only banker members of households are

able to borrow in foreign currency.

Preferences of households over consumption and leisure are represented by the

lifetime utility function that is CRRA in consumption,

E0

8ÿ

t“0

βt„

c1´σt

1´ σ´

χ

1` ξh1`ξt

. (1.4)

Et is the mathematical expectation operator conditional on the information set avail-

able at t, β P p0, 1q is the subjective discount factor, σ ą 0 is the inverse of the

intertemporal elasticity of substitution, χ is the utility weight of labor, and ξ ą 0

determines the Frisch elasticity of labor supply.

Households face the flow real budget constraint,

ct ` bt`1 `mt`1 “ wtht `Rtbt `mt

1` πt` Πt `

TrtPt

. (1.5)

11

On the right hand side are the real wage income, real balances of the domestic

currency interest bearing assets inclusive of the earned interest at the beginning of

period t, real money balances at the beginning of period t deflated by gross rate of

inflation 1 ` πt “PtPt´1

between periods t ´ 1 and t and real profits remitted from

firms owned by the households (banks, intermediate home goods producers, and

capital goods producers). Trt represents nominal lump-sum transfers provided by

the government as a result of money creation. On the left hand side are the outlays

for consumption expenditures and asset demands.

Households are also subject to a cash-in-advance constraint, which imposes that

consumption shall be less than or equal to total real monetary asset balances. There-

fore consumption has to satisfy,

ct ďmt

1` πt`TrtPt`Rtbt ´ bt`1. (1.6)

Implicit in this condition is the intraperiod timing of the model. Specifically, govern-

ment determines the new level of money supply and bonds market opens before the

goods market. Households then adjust their interest bearing deposits portfolio and

pool their net deposits with beginning of period real money balances and monetary

transfers provided by the government to purchase consumption goods. Finally, they

earn wage income and receive profits from the ownership of firms during the current

period and determine their demand for real balances to support consumption in the

next period.

Households choose ct, ht, bt`1, and mt`1 to maximize preferences in (1.4) subject

to (1.5), (1.6) and standard transversality conditions imposed on asset demands,

bt`1, and mt`1. The first order conditions of the utility maximization problem of the

households are given by

12

c´σt “ βEt“

c´σt`1Rt`1

‰

, (1.7)

χhξtwt

“ βEt

„

c´σt`1

1` πt`1

, (1.8)

and condition (1.6) holding with equality, if the cash-in-advance constraint is binding.

Equation (1.7) represents the Euler equation for deposits and sets the consumption-

savings margin. Equation (1.8) on the other hand, is a non-standard consumption-

leisure optimality condition, due to the existence of the cash-in-advance friction,

which transforms the trade-off between the two into an intertemporal one. Specifi-

cally, increasing leisure demand by one unit reduces wages in cash by 11`πt`1

future

units because the yield of cash balances is deflated by inflation. 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.

The nominal exchange rate of the foreign currency in domestic currency units

is denoted by St. It is assumed that the law of one price holds for the prices of

traded goods, that is, P Tt “ StP

T˚t , where P T˚

t is the foreign currency denominated

international price of traded goods. For simplicity, the small open economy takes

P T˚t as given and all prices in the rest of the world are constant and normalized to

one. Consequently, the real exchange rate of the foreign currency in terms of real

home goods becomes st “StP

˚t

Pt. Using the definition of the real exchange rate and the

law of one price, the definition of the domestic CPI index (1.2) and the consumption

goods demand frontier (1.3) might be simplified to

1 “”

ω´

pNt

¯1´τ

` p1´ ωq´

st

¯1´τı 11´τ

(1.9)

and

13

cNtcTt“

ω

1´ ω

ˆ

pNtst

˙´τ

, (1.10)

with pNt “PNtPt

denoting the relative price of the non-traded good.

1.3.2 Banks

The modeling of banks closely follows Mimir and Sunel (2015) so that banks in the

model borrow in local currency from domestic households and in foreign currency

from international lenders. They combine these funds with their net worth and

finance capital expenditures of non-traded goods producers by purchasing securities

issued by these firms against their capital demand. For tractability, it is assumed

that banks only lend to home based production units.

A moral hazard problem between bankers and their funders leads to an endoge-

nous borrowing constraint on the former. The agency problem suggests that both

domestic and foreign depositors believe that bankers might divert a certain fraction

of their assets. When diversion realizes, it results in a run and bank liquidates.

Therefore, to rule out runs in equilibrium, banks limit their borrowing to satisfy an

incentive compatibility condition, which defines equilibrium leverage. Furthermore, a

variant of the assumption in Gertler et al. (2012) is used and the financial constraint

is formulated so that banks become riskier (that is, they intend to divert more) if

their liability structure features a larger foreign (non-core) debt share. This assump-

tion also resembles the work of Broner et al. (2014) in which domestic borrowers

discriminate against foreign lenders and pledge a smaller return to foreigners than to

domestic lenders. In those lines, the model endogenously generates a positive spread

between the costs domestic and foreign borrowing as a result of increasing risk due

to non-core funding.

Banks are also subject to a reserve requirement on domestic deposits, i.e. they

14

are obliged to maintain a certain fraction of domestic deposits rr, within the central

bank.7 In this setup, the ROM is introduced as it is designed by the CBRT. That is,

banks are allowed to fulfill part of their domestic currency reserve requirements in

foreign currency denominated funds. The central bank does not impose any utiliza-

tion rate but makes two types of announcements: (i) it sets the upper bound for the

fraction of local currency reserves to be fulfilled with foreign currency denominated

funds and (ii) it determines the cost of utilizing the mechanism as it is elaborated in

greater detail below. Once the instrument is introduced, banks optimally decide on

their utilization rate of the mechanism depending on the funding spread between the

sources of external finance and fluctuations in the exchange rate. Below the bankers’

problem and the modeling of the ROM will be presented in detail.

Balance sheet

The period-t balance sheet of a banker j, without the ROM mechanism, denominated

in domestic currency units is,

Qtljt “ Bjt`1p1´ rrqq ` StB˚jt`1 `Njt, (1.11)

The period-t balance sheet of a banker j, with the ROM mechanism, denominated

in domestic currency units is,

Qtljt “ Bjt`1p1´ rr p1´ xjtqlooomooon

Decrease inTL Reserves

q`StB˚jt`1

˜

1´rrxjtROCpxjtqBjt`1

StB˚jt`1looooooooooooooomooooooooooooooon

Increase in$ Reserves

¸

`Njt (1.12)

where Bjt`1 and B˚jt`1 denote domestic deposits and foreign debt (in nominal foreign

currency units), respectively, Njt denotes banker’s net worth, Qjt is the nominal price

7 For simplicity, it is assumed that there are no reserve requirements on foreign deposits and thebase reserve requirement ratio on domestic deposits is set to a fixed level. Note however that as itis demonstrated below, the use of the ROM by banks endogenizes both domestic and (self-imposed)foreign currency denominated reserves.

15

of claims purchased from nonfinancial firms and ljt is the quantity of such claims. rr

is the required reserves ratio on domestic deposits. xjt denotes the utilization rate

of the ROM, satisfying 0 ă xjt ă x, where x is exogenously set and fixed by the

central bank. Equation (1.12) demonstrates that banks can transform their domestic

currency reserve requirements into and endogenous reserves portfolio comprised of

both domestic and foreign funds. Specifically, when the ROM is utilized, domestic

reserves of bankers are reduced by rrxjtBjt`1, whereas voluntary reserves in FX funds

becomerrxjtROCpxjtqBjt`1

St.

Two observations regarding the mechanism stand out. First, it should be noted

that utilizing the mechanism is costly. The reserve option coefficients (ROC)ROCpxjtq

are penalty coefficients set by the central bank, with ROCpxjtq ą 1 and ROC 1pxjtq ą

1 @xjt, which determines the magnitude of funds required to maintain the ROM

reserves.8 Second, it is straight forward to see that the mechanism is subject to

valuation effects driven by fluctuations in the exchange rate. Specifically, when ex-

change rate depreciates, the real amount of funds required to maintain ROM reserves

decline.

It is useful to divide equation (1.12) by the aggregate price index, Pt, and re-

arrange terms to obtain banker j’s balance sheet in real terms. Those manipulations

imply

qtljt “ bjt`1p1´ROMpxjtqq ` b˚jt`1 ` njt, (1.13)

where qt is the relative price of the security claims purchased by bankers and b˚jt`1 “

StB˚jt`1

Ptis the foreign borrowing in real domestic units. Notice that if the exogenous

8 The ROCs are specified as an increasing function of the ROM utilization rate, xjt, to ensurethat the mechanism can serve as an automatic stabilizer during reversals in capital flows. Namely,lower ROCs for lower utilization rates encourage banks to utilize the mechanism more, and higherROCs for higher utilization rates prevents banks to fully utilize the mechanism. Hence, banks areexpected to increase their use of ROM during inflows and vice versa. Please refer to Section 1.3.5for the specification of the functional form for the ROC schedule that is used in the analysis.

16

foreign price index, P ˚t is assumed to be equal to 1 at all times, then b˚jt`1 incorpo-

rates the impact of the real exchange rate, st “StPt

on the balance sheet. The term

ROMpxjtq on the other hand, satisfiesROMpxjtq “ rrp1´xjt`xjtROCpxjtqq. There-

fore, by utilizing the ROM, bankers endogenize the reserves ratio that they face in de-

positing funds within central bank. Moreover, since ROCpxjtq ą 1, ROMpxjtq ą rr

laying out the inherent trade-off introduced by the mechanism. That is, bankers

gain flexibility of swapping their domestic currency reserves with foreign funds in

response fluctuations in the excess cost of domestic funds and in the exchange rate

at the expense of incurring a larger reserve requirement ultimately.9

Next period’s real net worth, njt`1, is determined by the difference between the

return earned on assets (i.e., loans and reserves) and the cost of borrowing. Therefore,

njt`1 “ Rkt`1qtljt `ROMpxjtqbjt`1 ´Rt`1bjt`1 ´R˚t`1b

˚jt`1, (1.14)

where Rkt`1 denotes the state-contingent real return earned on the purchased claims

issued by the production firms. Rt`1 is the real risk-free deposit rate offered to do-

mestic workers, and R˚t`1 is the country borrowing rate of foreign debt, denominated

in real domestic currency units. Rt and R˚t both satisfy Fisher equations,

Rt “ Et

"

p1` rntqPtPt`1

*

(1.15)

R˚t “ Et

"

Ψtp1` r˚ntqSt`1

St

PtPt`1

*

@t, (1.16)

where rn denotes the net nominal deposit rate and r˚n denotes the net nominal inter-

national borrowing rate.10 Bankers face a premium over this rate while borrowing

9 Notice also that ROM 1pxjtq “ rrpROCpxjtq ´ 1 ` xjtROC 1pxjtqq ą 0, since ROCpxjtq ą 1and ROC 1pxjtq ą 0. Therefore, a higher degree of utilization of this facility further increases theeffective required reserves ratio.

10 Recall that in this flexible price environment, there is no targeting rule for nominal interest rates

17

from abroad. Specifically, the premium is an increasing function of foreign debt that

is, Ψt “ exp´

ψ1ˆb˚t`1

¯

ψt, where ˆb˚t`1 represents the log-deviation of the aggregate

foreign debt of bankers from its steady-state level, ψ1 ą 0 is the foreign debt elas-

ticity of country risk premium, and ψt is a random disturbance to this premium.11

Particularly, it is assumed that ψt follows,

logpψt`1q “ ρψ logpψtq ` εψt`1 (1.17)

with zero mean and constant variance innovations εΨt`1. ρr˚n is the autoregressive

coefficient of the process with |ρr˚n | ă 1. Introducing ψt enables us to study the

domestic business cycle responses to exogenous cycles in global capital flows. In order

to capture the impact of world interest rates on emerging economies, it is assumed

that exogenous world interest rates follow an autoregressive process denoted by,

r˚nt`1 “ p1´ ρr˚n qr˚n ` ρ

r˚nr˚nt ` εr˚nt`1. (1.18)

The innovations εr˚nt`1 are normally distributed with zero mean and constant variance

σr˚n . ρr

˚n is the autoregressive coefficient of the process r˚n denotes a long run level

for the net nominal world interest rate.

Solving for bjt`1 in equation (1.13) and substituting it in equation (1.14), and

re-arranging terms imply that bank’s net worth evolves as,

njt`1 “

”

Rkt`1 ´ Rt`1

ı

qtljt `”

Rt`1 ´R˚t`1

ı

b˚jt`1 ` Rt`1njt. (1.19)

with Rt`1 “Rt`1´ROMpxjtq

1´ROMpxjtqrepresenting the reserves adjusted domestic deposit rate.

This equation illustrates that individual bankers’ net worth depends positively on the

so that rn is determined endogenously by the Fisher equation.

11 By assuming that the cost of borrowing from international capital markets increases in the netforeign indebtedness of the aggregate economy, it is ensured that the stationarity of the foreignasset dynamics as in Schmitt-Grohe and Uribe (2003).

18

premium of the return earned on assets over the reserves adjusted cost of borrowing,

Rkt`1 ´ Rt`1. The second term on the right-hand side shows the benefit of raising

foreign debt as opposed to domestic debt. Finally, the last term highlights the

contribution of internal funds, that are multiplied by Rt`1, the opportunity cost of

raising one unit of external funds via domestic borrowing.

Banks would find it profitable to purchase securities issued by non-financial firms

only if

Et

!

Λt,t`i`1

”

Rkt`i`1 ´ Rt`i`1

ı)

ě 0 @t, (1.20)

where Λt,t`i`1 “ βi`1Et

”

Ucpt`i`1qUcptq

ı

denotes the i ` 1 periods-ahead stochastic dis-

count factor of households, whose banker members operate as financial intermedi-

aries. Notice that in the absence of financial frictions, an abundance in intermediated

funds would cause Rk to decline until this premium is completely eliminated. In the

following, it is also established that

Et

!

Λt,t`i`1

”

Rt`i`1 ´R˚t`i`1

ı)

ą 0 @t, (1.21)

so that the cost of domestic debt entails a positive premium over the cost of foreign

debt at all times.

In order to rule out any possibility of complete self-financing, it is assumed that

bankers have a finite life and survive to the next period only with probability 0 ă

θ ă 1. At the end of each period, 1 ´ θ measure of new bankers are born and are

remitted ε1´θ

fraction of the assets owned by exiting bankers in the form of start-up

funds.

19

Net worth maximization

Bankers maximize expected discounted value of the terminal net worth of their fi-

nancial firm Vjt, by choosing loans measured by the amount of securities purchased

ljt, the amount of foreign debt b˚jt`1 and the ROM utilization rate xjt. For a given

level of net worth, the optimal amount of domestic deposits can be solved for by

using the balance sheet. Specifically, bankers solve the following value maximization

problem,

Vjt “ maxljt`i,b

˚jt`1`i,xjt`i

Et

8ÿ

i“0

p1´ θqθiΛt,t`1`injt`1`i,

In order to make this problem more tractable, it is assumed that ROM utilization

decision is made after bankers decide on their assets and debt portfolio.12 Therefore,

the first focus will be on the assets and borrowing side of the net worth maximization

problem. This assumption modifies the maximization problem in recursive form to

be written as,

Vjt “ maxxjt

"

maxljt,b

˚jt`1

Et

„

Λt,t`1rp1´ θqnjt`1 ` θVjt`1s

*

. (1.22)

For a nonnegative premium on credit, the solution to the value maximization problem

of banks would lead to an unbounded magnitude of assets. In order to rule out

such a scenario, an agency problem between depositors and bankers is introduced

following Gertler and Kiyotaki (2011). Specifically, lenders believe that banks might

divert an endogenous λ fraction of their total assets. When lenders become aware of

the potential confiscation of assets, they would initiate a bank run and lead to the

liquidation of the bank altogether. In order to rule out bank runs in equilibrium,

12 One might think that they are choosing the utilization rate of the ROM facility during the night.This assumption is reasonable in the sense that the reserves maintenance periods do not constantlyoverlap with balance sheet decisions of banks.

20

in any state of nature, bankers’ optimal choices of loans and borrowing should be

incentive compatible. Therefore, the following constraint is imposed on bankers,

Vjt ě λ

ˆ

fjtxjt

˙

qtljt, (1.23)

where fjt “b˚jt`1

qtljtdenotes the foreign debt-to-assets ratio of bank j. This inequality

suggests that the liquidation cost of bankers from diverting funds Vjt, should be

greater than or equal to the diverted portion of assets. When this constraint binds,

bankers would never choose to divert funds and lenders adjust their position and

restrain their lending to bankers accordingly.

It is assumed that the fraction of diverted funds, λ, is actually an endogenous

function of the ratio of foreign debt to total assets and the utilization rate of the

ROM. In particular, λ takes a quadratic form of λ´

fjtxjt

¯

“ λ0` λ1

´

fjtxjt

¯

` λ22

´

fjtxjt

¯2

with λ1p.q “ λ1 ` λ2

´

fjtxjt

¯

ą 0.13 In other words, bankers are able to divert a

larger fraction of their total assets, when the share of foreign debt financing in total

assets, f increases. This feature reflects the idea that domestic depositors would

have comparative advantage over foreign depositors in monitoring domestic bankers

and recovering funds when banks are liquidated. This assumption is instrumental in

creating a trade-off for bankers while deciding their liability structure. Specifically,

bankers face an elastic supply of funds in the international markets at an exogenous

borrowing rate, whereas funds provided by domestic depositors are bounded by the

size of the small open economy. Therefore, the co-existence of both types of external

financing is ensured, by making the moral hazard problem more severe when the

liability structure is biased towards non-core debt. This, in equilibrium would also

13 This feature is a variant of the assumption made by Gertler et al. (2012) who introduce a trade-offbetween debt and equity financing, in which the latter provides better hedging opportunities.

21

create a premium in the cost of domestic debt over the cost of foreign borrowing.14

Lastly, in order to ensure that the ROM is utilized by banks in equilibrium, it

is assumed that the moral hazard friction becomes less severe as banks utilize the

ROM facility more. This assumption captures the idea that foreign funds utilized

in the ROM become safe assets deposited at the central bank and this becomes

common knowledge both for domestic and foreign depositors, rendering it harder for

bankers to divert assets funded by foreign funds. In that sense the ROM works as

a commitment device, which reduces the riskiness of the banking system.15 Figure

1.3 shows how the friction λ changes as the arguments change in their respective

acceptable intervals.

The methodological approach applied here is to linearly approximate the stochas-

tic equilibrium around the deterministic steady state. Therefore, cases in which the

incentive constraint of banks is always binding is of interest, which implies that

(1.23) holds with equality. This is the case in which the loss of bankers in the event

of liquidation is just equal to the amount of loans that they can divert.

It is conjectured that the optimal value of financial intermediaries to be a linear

function of bank loans, foreign debt-to-assets ratio and bank capital, that is,

Vjt “ pνlt ` fjtν

˚t qqtljt ` νtnjt. (1.24)

Among these recursive objects νlt represents the marginal value of assets, ν˚t stands

for the excess value of borrowing from abroad, and νt denotes the marginal value

of bank capital at the end of period t. The solution to the net worth maximization

problem involves two crucial conditions. First, it pins down the optimal foreign

14 Broner et al. (2014) also show that when domestic borrowers discriminate against foreign lenders,an excess premium for domestic debt emerges.

15 Apart from this intuitive reason, one has to assume that the ROM provides some insurancebenefit for banks in order to obtain positive utilization rates in equilibrium. Without such abenefit, the reserve option coefficients would penalize banks only increase the maintained reservesso that banks would never utilize the mechanism.

22

Figure 1.3: Sensitivity of Friction λ to its Arguments

Note: Friction λ is plotted on the vertical axis. Its arguments are on the horizontal axes. Upper and lower boundsof variables are reasonably selected to contain the steady state values. See 1.2 for the steady state values

debt-to-assets ratio,

fjt “ ´νltν˚t`

«

ˆ

νltν˚t

˙2

`2

λ2

ˆ

λ0 ´ λ1νltν˚t

˙

ff12

. (1.25)

Since f 1´

νltνxt

¯

ă 0, the ratio of foreign debt to total assets increases when the relative

value of foreign borrowing with respect to making new loans rises. Second, one solves

the endogenous leverage constraint of banks as

qtljt “νt

λ´

fjtxjt

¯

´ ζtnjt “ κjtnjt, (1.26)

23

where ζt “ νlt ` fjtν˚t . This endogenous constraint, which emerges from the costly

enforcement problem described above, ensures that banks’ leverage of risky assets is

always equal to κjt and is decreasing with the fraction of divertable funds λ´

fjtxjt

¯

.

Replacing the left-hand side of (1.24) to verify the linear conjecture on bankers’

value and using equation (1.19), it is found that νlt, νt, and ν˚t should consecutively

satisfy,

νlt “ Et

!

Ξt,t`1

”

Rkt`1 ´ Rt`1

ı )

, (1.27)

νt “ Et

!

Ξt,t`1Rt`1

)

, (1.28)

and

ν˚t “ Et

!

Ξt,t`1

”

Rt`1 ´R˚t`1

ı )

, (1.29)

with Ξt,t`1 “ Λt,t`1

”

1´θ`θ´

ζt`1κt`1`νt`1

¯ı

representing the augmented stochastic

discount factor of bankers, which is a weighted average defined over the likelihood of

survival.

Equation (1.27) suggests that bankers’ marginal valuation of total assets is the

premium between the expected discounted total return to loans and the benchmark

cost of domestic funds. Equation (1.28) shows that marginal value of net worth

should be equal to the expected discounted opportunity cost of domestic funds, and

lastly, equation (1.29) demonstrates that the excess value of raising foreign debt is

equal to the expected discounted value of the premium in the cost of raising domestic

debt over the cost of raising foreign debt. One can show that this spread is indeed

positive, that is, ν˚t ą 0 by studying first order condition (A.7) and observing that

λ´

fjtxjt

¯

, µ ą 0 and rrt ă 1 with µ denoting the Lagrange multiplier of bankers’

24

problem.

The definition of the augmented pricing kernel of bankers is useful in understand-

ing why banks shall be a veil absent financial frictions. Specifically, the augmented

discount factor of bankers can be re-written as Ξt,t`1 “ Λt,t`1

”

1´ θ` θλ´

fjtxjt

¯

κt`1

ı

by using the leverage constraint. Financial frictions would vanish when none of the

assets are diverted, i.e. λp.q “ 0 and bankers never have to exit, i.e. θ “ 0. Conse-

quently, Ξt,t`1 simply collapses to the pricing kernel of households Λt,t`1. This case

would also imply efficient intermediation of funds driving the arbitrage between the

lending and deposit rates down to zero.

Observe that equation (1.29) equates marginal value of foreign debt to the funding

premium between domestic versus foreign borrowing. This equality suggests that in

equilibrium, domestic depositors have to be compensated more than foreigners since

their supply of core funding reduces the riskiness of banks. In another dimension, the

result that ν˚ ą 0 brings foundation to the violation of the uncovered interest parity

in that even the country risk premium adjusted interest rates differentials deviates

from the expected exchange rate depreciation.

Optimal utilization of the ROM

The next step of the maximization problem covers the choice of the optimal uti-

lization rate of the ROM facility xjt, given ljt and fjt. The detailed derivation of

the optimal utilization condition is provided in Appendix A. Observe that Rt`1 “

Rt`1´ROMpxjtq

1´ROMpxjtq, which is a function of xjt. Therefore, the Lagrangian, (A.5), is now

resolved with respect to xjt incorporating the solutions to the recursive objects νlt, νt

and ν˚t , listed above. Using these conditions and solving for the first order condition

with respect to utilization, one obtains

25

xjt “Et

!

Ξt,t`1

”

Rt`1 ´R˚t`1

ı )

b˚jt`1

Et

!

Ξt,t`1pRt`1 ´ 1qROM 1pxjtq)

bjt`1

. (1.30)

This condition establishes that all else equal, xjt would increase when the debt ser-

vice differential of domestic debt, which depends on the funding premium, R ´ R˚

increases. This builds in the what is called the spread channel through which banks

would adjust their reserve holdings denominated in different currencies accordingly.

In particular, when the funding cost wedge between domestic and foreign deposits

further increases, banks would choose fulfill reserve requirements by relying on the

ROM more, since borrowing in FX in those periods is relatively cheaper. Note also

that the usage of the facility is also affected by a depreciation channel because the

foreign currency denominated counterpart of ROM reserves are subject to a valuation

effect driven by exchange rate fluctuations.

The Figure 1.4 compares Optimal ROM Utilization Rate against the Funding

Spread under high and low ROC environments. The model is simulated 5000 times

to generate each of these environments. Each red and blue dot in the figure represents

an individual simulation. For the Low ROC environment the parameter roc1 is set

to 1 which is the benchmark calibration and for the High ROC environment it is

increased to 1.2. As it can be seen from the Figure 1.4, when the cost of foreign

funding decreases, the utilization rate increases. Also, for a given level of funding

spread, lower ROC requirement leads to higher ROM utilization. See Equation 1.43

where the parameter roc1 is formally introduced.

Aggregation

The equilibrium in which all households behave symmetrically is of interest, so the

equation (1.26) can be aggregated over j to obtain the following relationship:

26

Figure 1.4: Funding Spread vs Utilization Rate

Note: Comparison Optimal ROM Utilization Rate against the Funding Spread under high and low ROC environ-ments. Each dot represents an individual simulation. For the low ROC environment the parameter roc1 is set to 1which is the benchmark calibration and for the high ROC environment it is increased to 1.2

qtlt “ κtnt, (1.31)

where qtlt and nt represent aggregate levels of banks’ assets and net worth, respec-

tively. Equation (1.31) shows that aggregate credit financed by domestic banks can

only be up to an endogenous multiple of aggregate bank capital. Furthermore, fluc-

tuations in asset prices qt, would feed back into fluctuations in bank capital via this

leverage constraint. This would be the source of the financial accelerator mechanism

in the model.

The evolution of the aggregate net worth depends on that of the surviving bankers

net`1 and the start-up funds of the new entrants nnt`1. Surviving bankers’ net worth

might be obtained by substituting the aggregate bank capital constraint (1.31) into

27

the net worth evolution equation (1.19),

net`1 “ θ!”

Rkt`1 ´ Rt`1 ` ft

´

Rt`1 ´R˚t`1

¯ı

κt ` Rt`1

)

nt. (1.32)

The start-up funds for new entrants, on the other hand, are equal to ε1´θ

fraction of

exiting bankers assets p1´ θqqtlt. Therefore,

nnt`1 “ εqtlt. (1.33)

As a result, the transition for the aggregate bank capital becomes,

nt`1 “ net`1 ` nnt`1. (1.34)

1.3.3 Capital Producers

Capital producers play a pivotal role in the model since variations in the price of

capital drives the financial accelerator. It is assumed that capital producers operate

in a perfectly competitive market, purchase investment goods and transform them

into new capital. They also repair the depreciated capital that they buy from the

final good producing firms. At the end of period t, they sell both newly produced and

repaired capital to the final good production firms at the unit price of qt. Production

firms then use this new capital for production at time t ` 1. Capital producers are

owned by households and return any earned profits to their owners. It is also assumed

that they incur capital adjustment costs while producing new capital, given by the

following quadratic function of the investment rate Φp ikq “

φ2p ik´ δq2. Specifically,

capital producers maximize

maxit

qtkt`1 ´ qtp1´ δqkt ´ it (1.35)

subject to the capital accumulation technology,

28

kt`1 “ p1´ δqkt ` Φ´ itkt

¯

kt, (1.36)

The optimality condition that emerges from the solution to this problem is the well-

known Tobin’s q relation that pins down the price of capital,

qt “”

Φ1´ itkt

¯ı´1

. (1.37)

1.3.4 Production Firms

Firms produce the consumption good by using physical capital and labor as produc-

tion factors. They operate with a constant returns to scale technology F pk, hq that

is subject to total factor productivity shocks, zt,

yt “ exppztqF pkt, htq, (1.38)

where

zt`1 “ ρzzt ` εzt`1 (1.39)

with zero mean and constant variance innovations, εzt`1.

Firms finance next period’s capital at date t by issuing claims kt`1 to financial

intermediaries at the price of capital. The banks’ claim against the ownership of the

firm pays out its dividend via the marginal product of capital in the next period.

Hence, the cost of credit to the firm is state contingent. Indeed, the cost of credit to

the firm must satisfy

Rkt “ztFkpkt, htq ` qtp1´ δq

qt´1

. (1.40)

Finally, the optimal labor demand of the firm must satisfy the usual static con-

dition,

29

wt “ exppztqFhpkt, htq, (1.41)

which equates the marginal product of labor to its marginal cost.

1.3.5 Monetary Authority

The government is responsible for (i) meeting workers’ and bankers’ cash-in-advance

and local currency required reserves demands and (ii) setting the ROM. For the

former, it controls the supply of monetary baseM0t`1, and for the latter, it determines

the ROC schedule and the maximum utilization rate of the mechanism for a given

required reserves ratio rr on local currency deposits.

The monetary base grows at the constant rate g, that is,

M0t`1 “ exppgqM0t. (1.42)

The growth of the monetary base is remitted to households in the form of lump-sum

transfers, Trt.16 Therefore, Trt “

´

exppgq ´ 1¯

M0t.17

In order to contain the financial accelerator mechanism driven by fluctuations in

capital flows, central bank uses the ROM in order to operationalize local currency

reserves maintained within the central bank. Specifically, the ROC schedule that

corresponds to the rate of utilization xt is defined as

ROCpxtq “ roc1 `roc2

πarcsin

ˆ

c

xtproc3 ´ 0q

˙roc4

(1.43)

where roc1, roc2, roc3 and roc4 are calibrated to match the level and the curvature of

16 The monetary policy is modeled in a simplistic manner in order to isolate the impact of theROM described below.

17 Perfect insurance within family members of households ensures that the increase in real balancesand reserves demand is lumped into Trt, which does not alter the optimality conditions of theutility maximization problem.

30

the ROC schedule implemented by the CBRT. In particular, roc1 targets the aver-

age ROC that the banking system faces, roc2 and roc4 helps capture the curvature

features of the schedule and roc3 exactly mimics the maximum ROM utilization rate

imposed by the CBRT.

The arcsin function is successful in producing the features of the ROC schedule

that it is relatively flat for small rates of utilization and increases convexly as uti-

lization rates converge to the upper bound announced by the authorities. This is

illustrated by comparing empirical and model generated ROC schedules in Figure

1.5. It is precisely this eventually convex schedule that prohibits banks from utiliz-

ing the mechanism at its maximum and change it freely in between in response to

fluctuations in the funding premium and the exchange rate. Figures 1.6, 1.7, and

1.8 shows the changes in the ROC schedule used in the model when the respective

parameters change one by one.

Figure 1.5: ROC Sechedule in Practice vs the ModelNote: Comparison of the actual ROC Schedule used by the CBRT against the ROC Schedule used in the model.Blue solid line plots Equation 1.43 which is the ROC Schedule used in the model as a function of the utilization rate.The red solid line plots the actual ROC Schedule used by the CBRT

31

Figure 1.6: Changes in ROC Schedule in the Model for Different Values of theParameter roc1

Figure 1.7: Changes in ROC Schedule in the Model for Different Values of theParameter roc2

Finally, money market clearing necessitates that

M0t`1 “Mt`1 ` Ptrrtp1´ xtqbt`1, (1.44)

where Pt is the general price level of the consumption good. Since the left-hand side

32

Figure 1.8: Changes in ROC Schedule in the Model for Different Values of theParameter roc3

of equation (1.44) is exogenously determined by the central bank, equilibrium in the

money market might call for adjustments in the price level in response to fluctuations

in reserves. Note also that when commercial banks utilize the ROM, they reduce

their local currency denominated reserves demand. The dynamics of inflation driven

by these two sources of fluctuations shall then feed back into the intertemporal

consumption leisure margin and have real effects via the cash-in-advance constraint

shown by equation (1.6).

The resource constraints and the definition of competitive equilibrium are in-

cluded in Appendix A.

1.4 Quantitative Analysis

This section analyzes the quantitative predictions of the model. First the calibration

and the steady state targets are discussed, then the IRFs of selected variables in

response to different shocks are presented.

33

1.4.1 Model Calibration

Table 1.1 provides the list of parameters calibrated in the model with their respective

targets. Note that there is still room for trying to match targets by jointly calibrating

several parameters, especially parameters related to financial intermediaries. Future

studies using of the framework in bigger models can take advantage of the parameter-

target relations presented below. Shock processes estimated for the Turkish economy

for 2003-2011. The ROC-related parameters are used to replicate the actual ROC

schedule used in practice by the CBRT. The relationship between these parameters

and the ROC schedule is further explored in Section 1.3.5.

1.4.2 Model vs. Data

Table 1.2 represents the steady states of several variables of interest. As it is stated

in the previous section though, it is possible to further get close to the data using

a better calibration. One caveat at this point is that, adding the ROM mechanism

to an otherwise exactly the same model changes the steady state levels slightly. It

is still possible to achieve the same steady state targets by changing the calibration.

Values in Table 1.2, however, are a result of the exact same calibration of parameters

for both models.

1.4.3 Model Dynamics

In this section, 3 different models are compared in response to shocks. These models

are 1) Flexible ROM model which is what is presented in this chapter, 2) Fixed ROM

model where the utilization rate xt is fixed at its steady state level, and 3) No-ROM

model which is the model without the ROM mechanism.

The comparison of the Flexible ROM and the No-ROM models sheds light on

the way ROM mechanism works. Note that in Section 1.3.2, two channels through

which the ROM mechanism works are mentioned: a) the spread channel and b) the

34

Table 1.1: Model Parameters

Description Parameter Value Target

Households

Quarterly discount factor β 0.9821 Annualized real deposit rate (7.48%)Relative risk aversion γ 2 LiteratureRelative weight of non-tradables in the consumption basket ω 0.54 Average Consumption to GDP ratioelasticity of substitution for consumption basket τ 0.99 Gertler et al. (2007)Relative utility weight of labor ψ 324.5 1/3 working timeLabor supply elasticity ν 3 Literature

Financial Intermediaries

Survival probability of the bankers θ 0.9346 Leverage ratioProp. transfer to the entering bankers ε 0.0035 1.33% of aggregate net worthDiversion function level parameter λ0 0.55 Core to non-core ratioDiversion function slope parameter λ1 -0.4 Spread between R˚ and RkDiversion function curvature parameter λ2 1.56 Variable f in the model

Firms

Capital adjustment cost parameter ψq 35 Elasticity of price of kt wrt it{kt ratioShare of capital in output α 0.4 Labor share of output (0.60)Depreciation rate δ 0.033 Investment to capital ratio

Shock Processes

Persistence of TFP process ρa 0.962 EstimatedStd. deviation of productivity shocks σa 0.0283 EstimatedPersistence of money growth ρµ 0.5702 EstimatedStd. deviation of money growth shocks σµ 0.0275 EstimatedPersistence of risk premium process ρψ 0.963 EstimatedStd. deviation of risk premium shocks σψ 0.0032 EstimatedPersistence of world interest rate ρa 0.977 EstimatedStd. deviation of world interest rate σa 0.00097 Estimated

Govt and Rest of the parameters

Domestic currency required reserve ratio rr 0.09 required reserve ratio for 2003-2011roc1 roc1 1 ROC Schedule used by the CBRTroc2 roc2 1.3 ROC Schedule used by the CBRTroc3 roc3 0.6 ROC Schedule used by the CBRTroc4 roc4 6 ROC Schedule used by the CBRTEndowment of Tradable good Y T 1.5 Tradable/Non-Tradable RatioCountry risk premium parameter ψr˚ 0.0001 -

depreciation channel. Fixed ROM model is added to the analysis to isolate the effects

of these two channels. Albeit imperfectly, the Fixed ROM model only involves the

depreciation channel, since the banks are unable to change the utilization rate xt

optimally, in response to changes in the funding spread.

35

Table 1.2: Steady State Effects of the ROM and Comparison with the Data for theVariables of Interest.

Variable No-ROM ROM Data

b˚{pb˚ ` bq 0.33 0.3638 0.39

b˚{pqlq 0.27 0.2953 0.26

λ 0.70 0.63 N{A

κ 4.22 4.55 4.05

x N{A 0.52 0.52

ROCpxq N{A 1.15 1.66

Rk ´ R 112bp 126bp 75bp

Effprrq 0.09 0.10 0.09

World Interest Rate shock

Figure 1.9 plots the impulse response functions of several variables of interest to a

one-standard-deviation world interest rate shock. The IRFs in response to produc-

tivity shock and country risk premium shock can be found in the appendix. Despite

an increase in the world interest rate, an increase in domestic funding premium is ob-

served, which is commonly observed in small open economies. Note that the increase

is smaller in the models with ROM, which shows the stabilizing effect of ROM. The

ROM utilization rate jumps up, mainly as a result of the increase in the domestic

funding premium. The third subplot in the first row plots the amount of foreign

currency used to fulfill the required reserves through the ROM mechanism. More

precisely, this variable is equal to: rr ˚ xt ˚ ROCt ˚ bt`1{et. It can be seen that this

amount is decreasing over time in the Flexible ROM model. This decrease is mainly

because of a decrease in the utilization rate over time, since the foreign funding is

not more expensive compared to before. In the Fixed ROM model though, the drop

in this variable is immediate, since the ROM utilization rate is fixed, and therefore

does not jump up on impact.

36

Figure 1.9: Impulse Response Functions of Selected Variables to a Negative OneStandard Deviation World Interest Rate Shock

Note: The dashed red lines are for the model where the utilization rate is fixed at its steady state value, the solidblue lines are for the model where the utilization rate is a choice variable of the banks, and black dotted lines are forthe model where there is no ROM policy

AS for the credit given the non-financial firms, the drop in the Flexible ROM

model is much smaller than the drop in the No-ROM model, which is another ev-

idence to the stabilizing effect of ROM mechanism. The drop in the Fixed ROM

model though is much smaller. This is because now the banks have. all of a sudden,

some foreign reserves in the form of required reserves that are valued a lot more due

to the increase in the exchange rate. This means banks can release some of the funds

in the form of credit to the non-financial sector. This leads to smaller decrease in

37

credit relative to the case where utilization rate is a decision variable.

The third subplot in the second row plots the λt variable, namely fraction of

divertable loans. This is also the measure of the financial frictions faced by the

banks in this setup. The benefit of the ROM mechanism comes from the fact that it

lowers the friction faced by the banks, which is apparent in the subplot as well.

In addition, note the smaller drops in loan-foreign debt spread, asset price, in-

vestment and the real exchange rate as an evidence of the stabilizing effect of the

ROM mechanism. The drops are all smaller in the case of fixed ROM model. This

is because the banks find themselves “overfunded” through the increase in the value

of foreign currency used to fulfill the reserves. This leads to releasing some of this

funding to the non-financial sector in the form of additional credit, which mitigates

the shock even more compared to the Fixed ROM model.

IRFs in response to productivity shock and country risk premium shock can be

found in Appendix A.3. The responses of variables of these shocks follow a narrative

similar to what is presented above.

1.5 Conclusion

This paper is the first attempt to quantitatively model and evaluate the Reserve

Option Mechanism, a novel policy tool invented and used by the CBRT. Using a

version of Gertler et al. (2012), the mechanism is modeled in the DSGE realm. In

order for the mechanism to work, it needs to generate certain level “confidence” for

the banks in terms of having enough foreign resources to fund themselves during

bad times. This benefit is incorporated into the model by making the financial

frictions faced by the banks negatively depend on the utilization rate. Banks use

the mechanism up to a point where this benefit is offset by the cost of using the

mechanism: facing the reserve option coefficient. Two channels through which the

mechanism work are identified: a) banks keep an eye on the spread when using the

38

mechanism, and b) valuation of already-held foreign reserves as a result of changes

in the exchange rate is an important determinant of the utilization rate.

39

2

Countercyclical Capital Rule and FinancialFrictions

2.1 Introduction

This chapter introduces an environment useful for evaluating the macroprudential

policies. It includes financial intermediaries and non-financial firms that are both

subject to financial frictions and separately make financial decisions. The model,

in essence, borrows the non-financial firms from Jermann and Quadrini (2012) and

financial intermediaries from Gertler and Karadi (2011). The problem of financial

intermediaries are also augmented following Gertler et al. (2012).

To my knowledge, this model is the first of its kind in the sense that negative

effects of financial shocks, or ability of policies to mitigate such shocks can be parti-

tioned into the two aforementioned sectors. This is important because the literature

so far lacks the ability to compare/contrast the financial intermediaries against the

rest of the economy1. Most models involve only a financial intermediary through

which the shocks and the policies affect the rest of the economy. Such approaches

1 see for instance, the two relatively comprehensive review of the literature: Galati and Moessner(2013) and Lim et al. (2011)

40

might seem acceptable since the Great Recession worked exactly the same way, how-

ever this leads to overweighting of the financial sector in designing the macropruden-

tial policies, possibly, at the cost of the non-financial sector. The benefit of jointly

modeling the financial frictions faced by, and the financial decisions made by both

sectors is apparent in Section 2.3 in terms of the model’s ability to replicate data.

The chapter is organized as follows: Section 2.2 introduces the model used in

this chapter, Section 2.3 compares the importance of financial shocks against the

productivity shocks, documents the model’s ability to generate events like the Great

Recession and also compares the model against the relevant benchmarks, Section 2.4

reports the way model is calibrated, 2.5 evaluates a countercyclical capital rule as

an example, and Section 2.6 concludes.

2.2 Model

2.2.1 Banks

Banks in the model is similar to Gertler and Karadi (2011). They lend to firms in

the form of debt, and use their own net worth and household’s deposits to finance

this lending. Hence period t balance sheet of a bank is:

bt`1{p1` rtq “ bdt`1p1´ rrq ` nt (2.1)

where bt`1 is the lending, which is an asset for the bank, bdt`1 is the household’s

deposit, rr is the required reserve ratio, and nt is the net worth of the bank.

In the next period, the bank gets back bt`1 from the firms, the amount held as

required reserves rrbdt`1, and has to pay household a risk-free rate of Rdt . Hence net

worth next period can be written as:

41

nt`1 “ bt`1 ` rrbdt`1 ´R

dt bdt`1 (2.2)

Combine the two equations to get:

nt`1 “ bt`1

„

1´pRd

t ´ rrq

p1` rtqp1´ rrq

` nt

„

pRdt ´ rrq

1´ rr

(2.3)

“ bt`1AAt ` ntBBt (2.4)

where AAt and BBt are defined accordingly, to ease notation.

Banks has a θ probability of survival. At the end of their lifetime, their net

worth is given to the households. In the same period new bankers are born to hold

the number of banks constant, and households give a small start-up funds to these

banks. As a result, a living bank maximizes:

Vt “ maxbt`1

Et

8ÿ

i“0

p1´ θqθimt`1`int`1`i (2.5)

Recursively, this is equivalent to:

Vt “ maxbt`1

Etmt`1rp1´ θqnt`1 ` θVt`1s (2.6)

However, there are agency issues between the household and the bank. In partic-

ular, households take into account the ability of banks to divert some of their assets

for their own good. Hence banks are subject to an incentive compatibility constraint:

Vt ě λbt`1 (2.7)

where λ is the fraction of assets that banks can divert. To solve the banks’

problem, it is conjectured that the solution is linear in bt`1 and nt:

Vt “ νbt bt`1 ` νnt nt (2.8)

42

All that is left now, is to find the marginal benefits νbt and νnt . After using this

conjecture and equation 2.4, the solution to equation 2.5 can be separated into two

parts:

νbt bt`1 “ Et

8ÿ

i“0

p1´ θqθimt`1`iAAt`ibt`1`i (2.9)

νnt nt “ Et

8ÿ

i“0

p1´ θqθimt`1`iBBt`int`i (2.10)

Start with the first one:

νbt “ Et

8ÿ

i“0

p1´ θqθimt`1`iAAt`ibt`1`i

bt`1

(2.11)

“ p1´ θqmt`1AAt `8ÿ

i“1

p1´ θqθimt`1`iAAt`ibt`1`i

bt`1

(2.12)

“ p1´ θqmt`1AAt ` θmt`1bt`2

bt`1

8ÿ

i“0

p1´ θqθi`1mt`2`iAAt`i`1bt`2`i

bt`2

(2.13)

νbt “ Et

„

p1´ θqmt`1AAt ` θmt`1bt`2

bt`1

νbt`1

(2.14)

Similarly,

νnt “ Et

„

p1´ θqmt`1BBt ` θmt`1nt`1

ntνnt`1

(2.15)

At this point, why the incentive compatibility constraint holds with equality all

the time needs to be clarified. To do that, let us start with banks’ profit maximization

problem:

Vt “ maxbt`1

Et

8ÿ

i“0

p1´ θqθimt`1`irbt`1`iAAt`i ` nt`iBBt`is (2.16)

subject to:

43

Vt ě λbt`1 (2.17)

using conjectured solution, Lagrangian is:

L “ νbt bt`1 ` νnt nt ` µtrν

bt bt`1 ` ν

nt nt ´ λbt`1s (2.18)

FOC:

νbt ` µtνbt ´ µtλ “ 0 (2.19)

Equivalently νbt “µtλp1`µtq

. So IC binds pµt ą 0q, if expected discounted marginal

gain of increasing bank assets is positive. So:

Vt “ νbt bt`1 ` νnt nt “ λbt`1 (2.20)

which is equivalent to what is called endogenous borrowing constraint:

bt`1 “νnt

λ´ νbtnt “ κ

loomoon

Leverage

nt (2.21)

Note that it needs to be the case that 0 ă νbt ă λ for meaningful results. This is

true for acceptable calibration done in the literature.

As it was mentioned earlier, there are new entrants to the banking sector each

period. As a start-up fund from the households, these new entrants get εp1´θq

fraction

of exiting bankers’ net worth , which is p1 ´ θqnt, so nnt`1 “ εnt where nnt`1 is the

net worth of new entrants. For the surviving bankers, the net worth is equal to:

nst`1 “ θnt`1 “ θrbt`1AAt ` ntBBts (2.22)

“ θrκntAAt ` ntBBts “ θrκAAt `BBtsnt (2.23)

44

and finally the aggregate net worth is equal to:

nt`1 “ nnt`1 ` nst`1 (2.24)

2.2.2 Strengthening the Effect of Macroprudential Policy

The policy experiment that will be conducted in Section 2.5 will be about providing

additional capital to banks when they are stressed. To make the banks in the model

are responsive enough to such a policy, it could be assumed that any additional

net worth nt that banks have will reduce the financial friction banks are facing. In

particular, following Gertler et al. (2012), the financial friction λ is assumed to be a

quadratic function of nt:

λpntq “ λ0 ` λ1 ˚ p1{ntq ` λ2 ˚ p1{ntq2 (2.25)

The model is calibrated so that BλBnt

ă 0 so that any increase in the net worth

eases the constraint banks are facing. 2. This assumption is reasonable in the sense

that more net worth banks own, less incentive they will have to divert some of the

assets for their own use. The optimality conditions found previously will not change

as a result of this new assumption since nt is a state variable at period t.

The models with and without this additional property discussed above will be

compared against each other and against a benchmark in Section 2.5.

2.2.3 Non-financial Firms

Non-financial firms in the model follow Jermann and Quadrini (2012). Debt is always

preferred to equity (pecking order assumption), but firms’ ability to use debt is

constrained. To motivate pecking order, literature introduces a tax advantage. Gross

2 Also, with the addition of 3 new parameters, now there is relatively more room to match thedata. Section 2.4 shows the targets of the calibration of these 3 new parameters

45

return on debt is Rt “ 1`rtp1´τq as in Hennessy and Whited (2005) or Jermann and

Quadrini (2012). There are also adjustment costs to change equity: cost “ φpdt´ dq2

where d is equity payout. This adjustment cost helps the model match the moments

of equity and non-financial leverage in the data. Budget constraint of the non-

financial firm is:

bt ` wtht ` kt`1 ` dt “ p1´ δqkt ` F p.q ` bt`1{Rt (2.26)

Suppose that the firm also need an intraday loan lt to finance some of its activities.

It will be assumed that this intraday loan is interest-free, or that the interest is

negligibly small. In the model, lt is needed to finance:

lt “ wtht ` it ` dt ` bt ´ bt`1{Rt (2.27)

which gives lt “ F p.q when combined with the budget constraint.

Similar to the banks’ problem, there are agency issues between the firms and the

lender of this intraday loan. Firms decides to default after revenue realization but

before paying intraday loan. Total liabilities at this point sum up to lt`bt`1{p1`rtq.

After the default decision, the lender decides to liquidate the firm or let it operate.

In case of no default, firm value is Emt`1Vt`1.

In case of default, with prob ξt lender recovers whole kt`1. To make the lender

indifferent (between liquidation and letting work continue to operate), firm pays

qtkt`1´ bt`1{p1` rtq, and promises to pay bt`1 next period. As a result, expost value

of default (for the firm) is:

lt ` Emt`1Vt`1 ´

„

kt`1 ´bt`1

1` rt

(2.28)

In case of default, with prob p1´ ξtq lender recovers 0. Then it is not optimal to

46

liquidate and so lender waits. Lender gets no payments and the firm keeps lt. Hence

expost value of default (for the firm) is now:

lt ` Emt`1Vt`1 (2.29)

As a result expected liquidation value (for the firm) is:

lt ` Emt`1Vt`1 ´ ξt

ˆ

kt`1 ´bt`1

1` rt

˙

(2.30)

Hence the incentive compatibility constraint that will prevent firm from defaulting

is:

Emt`1Vt`1 ě lt ` Emt`1Vt`1 ´ ξ

ˆ

kt`1 ´bt`1

1` rt

˙

(2.31)

Equivalently:

ξ

ˆ

kt`1 ´bt`1

1` rt

˙

ě lt (2.32)

It will be assumed that this constraint is always binding to solve analytically, this

in fact the case around the deterministic steady state because the Lagrange multi-

plier of this constraint is always positive in the solution of the firm’s problem.

Firm’s problem then:

V pk, b; sq “ maxd,h,k1,b1

d` Em1V pk1, b1; s1q (2.33)

subject to:

47

p1´ δqk ` F p.q ´ wh` b1{R “ b` dt ` φpdt ´ dq2

loooooooomoooooooon

ϕpdq

`k1 (2.34)

ξt

ˆ

kt`1 ´bt`1

1` rt

˙

ě F p.q (2.35)

λ and µ being the Lagrange multipliers of BC and IC, FOCs with respect to

d, h, k1, b1 are:

1` λp´ϕdpdqq “ 0 (2.36)

λpFh ´ wq ` µp´Fhq “ 0 (2.37)

Em1Vkp1q ´ λ` µξ “ 0 (2.38)

Em1Vbp1q `

λ

R` µξp

´1

p1` rqq “ 0 (2.39)

where ϕdpdtq “ 1` 2φpdt ´ dq.

Envelopes:

Vkp.q “ λrp1´ δq ` Fks ` µr´Fks (2.40)

Vbp.q “ ´λ (2.41)

This implies that:

λ “1

ϕdpdq(2.42)

Vb “´1

ϕdpdq(2.43)

µ “λpFh ´ wq

pFh{Xtq“pFh ´ wq

pFhqϕdpdq(2.44)

Vk “1

ϕdpdqrp1´ δq ` pFkqs ´

ppFhq ´ wqpFkq

pFhqϕdpdq(2.45)

As a result the 3rd and the 4th FOCs are equivalent to:

48

Em1

„

1

ϕdpd1qrp1´ δq ` Fkp

1qs ´

pFkp1qqpFhp

1q ´ w1q

pFhp1qqϕdpd1q

(2.46)

´1

ϕdpdq`pFh ´ wqξ

pFhqϕdpdq“ 0 (2.47)

Em1

ˆ

´1

ϕdpd1q

˙

`1

ϕdpdqR`pFh ´ wq

pFhqϕdpdqξ

ˆ

´1

p1` rq

˙

“ 0 (2.48)

Hence equations 2.46,2.48,together with BC and IC solves for k1, b1, h, d.

2.2.4 Government

To keep the model as simple as possible, the government is doing only two things

in the model. First, the tax benefits to firms are financed by taxes levied on the

household. Second, the capital tax/subsidy introduced in Section 2.5 are netted out

in the same manner. Note that there is no government expenditure in the model,

which could easily be added to the the model.

2.2.5 Households

Households in the model have recursive preferences in order to make the welfare

analysis in Section 2.5 meaningful, aside from other obvious benefits of using such

preferences. Following Epstein and Zin (1989), Epstein and Zin (1991), and Weil

(1990), they maximize:

Vt “ maxct,ht

„

p1´ βqUpct, htq1´ 1

ϕ ` β`

Et“

V 1´γt`1

‰˘

1´1{ϕ1´γ

1

1´1{ϕ

(2.49)

where Upct, htq “ cot p1´ htq1´o subject to

wtht ` bdtR

dt´1 ` stpdt ` ptq “ bdt`1 ` st`1pt ` ct ` Tt (2.50)

where Tt “bt`1

1`rtp1´τq´

bt`1

1`rt. FOCs wrt ht, b

dt`1, st`1 are:

49

p1´ oq

o

ctp1´ htq

“ wt (2.51)

Etrmt`1Rdt s “ 1 (2.52)

Et

„

mt`1

ˆ

dt`1 ` pt`1

pt

˙

“ 1 (2.53)

where the stochastic discount factor mt`1 is:

mt`1 “ β

ˆ

ct`1

ct

˙´1 ˆUt`1

Ut

˙1´ 1ϕ

»

–

Vt`1

Et“

V 1´γt`1

‰

11´γ

fi

fl

1ϕ´γ

(2.54)

Together with a second-order Taylor approximation used when solving the model,

these preferences make the models compared in Section 2.5 distinguishable from each

other in terms of welfare.

2.3 Importance of Financial Shocks

Importance of financial shocks and their ability in models to replicate events like the

Great Recession depends on the way the financial frictions are modeled. Jermann

and Quadrini (2012) claims that the financial shocks are more important relative

to productivity shocks. According to Pfeifer (2016) however, this finding heavily

depends on the way data is treated to create shock series. This chapter uses the

“corrected” version of shock series that are borrowed from Pfeifer (2016).

Figure 2.1 compares the impulse response functions of several variables. The

model “JQ” is the corrected version of Jermann and Quadrini (2012), i.e., it is bor-

rowed from Pfeifer (2016). The model “JQGK” is the model presented in Section

2.2 except the modification in Subsection 2.2.2. Addition of that part only strength-

ens the model. As it can be seen from the figure, corrected shock series lead to a

50

relatively bigger role for the TFP shock, relative to the financial shock, especially

in case of output. To understand the ability of the JQGK model in replicating the

Figure 2.1: Comparison of IRFs: JQ vs JQGK

Note: IRFs of selected variables in response to negative one standard deviation TFP (blue lines) and financial (redlines) shocks. Solid lines are the “corrected” version of Jermann and Quadrini (2012) from Pfeifer (2016), anddashed lines are Jermann and Quadrini (2012) augmented by Gertler and Karadi (2011) in Section 2.2 except themodification in Subsection 2.2.2. Off-diagonal elements in auto-correlation matrix of shocks are set to zero as inJermann and Quadrini (2012) and Pfeifer (2016)

data, counterfactual series of selected variables in response to a) financial shocks

only, b) productivity shocks only, c) both shocks together (uncorrelated) are plotted

in Figures 2.2, 2.3, and 2.4, respectively. These figures compare 3 different models

against the data. Data series, JQ Model (which is the replication of Jermann and

Quadrini (2012)), and JQnew Model (which is the “corrected” version of Jermann

and Quadrini (2012)) are all taken from Pfeifer (2016). The JQGK Model uses the

same shock series generated by Pfeifer (2016). Augmenting Jermann and Quadrini

(2012) with Gertler and Karadi (2011) makes the financial shocks far more important

51

than noted by Pfeifer (2016). Financial shock now are able to replicate the Great

Recession single handedly, while the effect of productivity shocks on the output seem

to lie between the effects in JQ and JQnew models. As a result, macroprudential

policies that aim to prevent recessions or financial instabilities are going to be more

effective in JQGK model, which is in line with the real world experience since most

of the macroprudential policies are implemented through the financial system.

Figure 2.2: Counterfactual Series vs. the Data: Financial Shock Only

Note: Counterfactual series are compared against data in response to financial shocks only. Data in green solid line,original model of Jermann and Quadrini (2012) in red dashed line, and the “corrected” version in blue dashed lineare all taken from Pfeifer (2016). Jermann and Quadrini (2012) augmented with Gertler and Karadi (2011) in blacksolid line uses the shock series generated in Pfeifer (2016). Recessions defined by NBER are denoted by shadedvertical areas.

52

Figure 2.3: Counterfactual Series vs. the Data: Productivity Shock Only

Note: Counterfactual series are compared against data in response to productivity shocks only. Data in green solidline, original model of Jermann and Quadrini (2012) in red dashed line, and the “corrected” version in blue dashedline are all taken from Pfeifer (2016). Jermann and Quadrini (2012) augmented with Gertler and Karadi (2011) inblack solid line uses the shock series generated in Pfeifer (2016). Recessions defined by NBER are denoted by shadedvertical areas.

2.4 Calibration

The calibration closely follows that of the literature. In particular, parameters are

mostly borrowed from Bernanke et al. (1999), Gertler and Karadi (2011), Jermann

and Quadrini (2012), and Pfeifer (2016). The list of parameters can be found in table

2.1. The 3 parameters which are introduced in Subsection 2.2.2 plus proportional

transfer to new bankers ε are jointly used to hit 4 targets: a) one hundred basis

point annual credit spread, b) leverage ratio of 4, c) Steady-State net worth, d)

53

Figure 2.4: Counterfactual Series vs. the Data: Both ShocksNote: Counterfactual series are compared against data in response to both productivity and financial shocks. Datain green solid line, original model of Jermann and Quadrini (2012) in red dashed line, and the “corrected” version inblue dashed line are all taken from Pfeifer (2016). Jermann and Quadrini (2012) augmented with Gertler and Karadi(2011) in black solid line uses the shock series generated in Pfeifer (2016). Recessions defined by NBER are denotedby shaded vertical areas.

second moment of net worth. Also note that parameters related to shock processes

exactly follow Pfeifer (2016), so they are not reported in table 2.1.

2.5 Policy Experiment

In the aftermath of Great Recession policies involving capital injections to financial

intermediaries became popular3. This section involves the examination of such poli-

cies. In particular, subsidy to/taxation of bank capital (i.e., net worth as it is called

3 see for instance Bernanke (2009)

54

Table 2.1: Model Parameters

Description Parameter Value Target

Households

Quarterly discount factor β 0.9825 Annualized risk-free rateLabor/consumption weight in Cobb-Douglass utility kernel o 0.3704 1/3 working timeElasticity of Intertemporal Substitution ϕ 2 LiteratureCoefficient of Relative Risk Aversion γ 10 Literature

Financial Intermediaries

Survival probability of the bankers θ 0.972 Gertler and Karadi (2011)Prop. transfer to the entering bankers ε 0.002 See Section 2.4Bank’s asset diversion rate / level λ0 0.1 See Section 2.4Bank’s asset diversion rate / slope λ1 0.31 See Section 2.4Bank’s asset diversion rate / curvature λ2 -0.001 See Section 2.4

Non-Financial Firms

Share of capital in output α 0.33 Labor share of outputDepreciation rate δ 0.025 Investment to capital ratioEquity Adjustment cost parameter φ 0.08 Pfeifer (2016)

Govt and Rest of the parameters

required reserve ratio rr 0.11 Datacorporate debt deduction τ 0.35 Jermann and Quadrini (2012)Output Weight in Capital Subsidy Rule βY -2.20 See section 2.5Credit Weight in Capital Subsidy Rule βb -1.35 See section 2.5

in this chapter) using a simple rule will be analyzed. It is assumed that the regulator

cares about the credit and output only, following the vast literature4.

Suppose that the regulator has the following loss function:

Tnt “ βY pYt ´ Y q ` βbpbt ´ bq (2.55)

where Tnt is the proportional net worth tax, betas are the weights of deviations

of output and credit from their steady state values, and variables with bars are the

steady state values of the respective variables. βY and βb are calibrated to maximize

welfare of the households using a reasonable grid search over these two parameters.

In order to understand the benefit of the introduction of such a policy, three

4 two relatively comprehensive reviews of literature are Galati and Moessner (2013) and Lim et al.(2011)

55

Table 2.2: Welfare Effects of Capital Subsidy/Tax as a Macroprudential Policy

Model Welfare pVtq % Welfare Gain Cons. Equiv.

JQ+EZ (Benchmark) 0.68621685 - -

JQ+EZ+GK+λp1{ntq 0.64204410 -0.0644 -0.00059784

+Policy 0.66270370 -0.0343 -0.00041140

different models are compared: a) model with capital tax, b) model without capital

tax, c) a benchmark model that will act as a “first best”. Note that this policy is

about subsidizing financial intermediaries so that they can overcome their financial

constraints during bad times. As a result, the model without the financial interme-

diation, which is the RBC model presented in Jermann and Quadrini (2012), is a

natural candidate to be a benchmark. This benchmark model contains other financial

frictions (on non-financial firms) which are explained in this chapter in Section 2.2.3

or in Jermann and Quadrini (2012). Therefore this model is not the universal/fully-

frictionless benchmark. However, it is a good benchmark since the debt flow from

households to firms does not contain financial intermediaries or frictions faced by the

financial intermediaries.

In this section, welfare under these three models are computed and compared. Vt

in household maximization problem in equation 2.49 is used as a welfare measure.

The welfare loss as a result of the introduction of the financial intermediaries, and

financial frictions faced by the intermediaries can be seen in Table 2.2. The table

also presents the consumption equivalent of the welfare loss, which is around 0.05

percent. The consumption equivalent is the amount of consumption households

would require in the benchmark model, so that they are indifferent between staying

in the benchmark model and moving to the respective model. The introduction of

the capital subsidy drops that welfare loss to 0.04 percent in consumption terms. The

56

Figure 2.5: Comparison of IRFs in Response to Productivity Shock

Note: IRFs of selected variables in response to positive one standard deviation TFP shock. Blue lines are for thebenchmark model where the original Jermann and Quadrini (2012) is augmented by Eipstein-Zin preferences, theblack lines are for the model where the financial intermediaries are added to the the blue model, and red lines arefor the mdeol where the capital subsidy/tax policy is added to the black model

welfare changes are relatively small. This is because a) households have another way

to fund firms in the model (through a decrease in equity payout), and b) households

partially get back some of the net worth subsidy they are funding through the policy,

since when banks probabilistically die and give their net worth to the household every

period.

Figure 2.5 and 2.6 plot the IRFs of several variables of interest with respect to on-

standard-deviation productivity and financial shocks in the three models, namely the

benchmark model, the full model presented in Section 2.2, and finally the model with

57

Figure 2.6: Comparison of IRFs in Response to Financial Shocks

Note: IRFs of selected variables in response to positive one standard deviation TFP shock. Blue lines are for thebenchmark model where the original Jermann and Quadrini (2012) is augmented by Eipstein-Zin preferences, theblack lines are for the model where the financial intermediaries are added to the the blue model, and red lines arefor the mdeol where the capital subsidy/tax policy is added to the black model

the policy introduced in this section. The smoothing and welfare increasing effects of

the policy is apparent The response of the output is closer to that of the benchmark

model. The responses of financial variables, namely credit, debt repurchase and

equity payout, are much smoother. And the initial change in net worth is showing

how much, in percentage deviation, net worth changes as a result of the introduction

of the policy.

58

2.6 Conclusion

This chapter introduces a parsimonious model that can be used as an environment

to evaluate macroprudential policies. Both the financial intermediaries (modeled

following Gertler and Karadi (2011) and Gertler et al. (2012)) and non-financial firms

(modeled following Jermann and Quadrini (2012)) are subject to financial frictions

and make financial decisions. The model’s relative ability to replicate events like

the Great Recession is discussed in Section 2.3 which involves the comparison of the

importance of financial shocks against the productivity shocks in generating enough

movement in the output and in some financial variables of interest. The policy

discussed in Section 2.5 belongs to a class of macroprudential policies that operate

through the balance sheet of financial intermediaries. The policy is, in essence,

a countercyclical capital rule that eases the financial frictions faced by the banks

during bad times. Welfare gains of using such policy is relatively small, mainly due

to a)households have also equity payout channel to fund the firms the model, and

b)households are able take back some of the net worth subsidy given to the banks

since banks probabilistically die and give their net worth to households each period.

59

Appendix A

Model Derivations, Definition of CompetitiveEquilibrium, and Additional IRFs for Chapter 1

A.1 Model Derivations

A.1.1 Households

The expenditure minimization problem of households

mincNt ,c

Tt

Ptct ´ PNt c

Nt ´ P

Tt c

Tt (A.1)

subject to (1.1) yields the demand curves cNt “ ω´

PNtPt

¯´τ

ct and cTt “ p1´ωq´

PTtPt

¯´τ

ct,

for non-traded and traded goods, respectively.

A.1.2 Banks’ Net Worth Maximization

Bankers solve the following value maximization problem,

Vjt “ maxljt`i,fjt`i,xjt`i

Et

8ÿ

i“0

p1´ θqθiΛt,t`1`i njt`1`i

60

“ maxljt`i,fjt`i,xjt`i

Et

8ÿ

i“0

p1´ θqθiΛt,t`1`i

! ”

Rkt`1`i ´ Rt`1`i

ı

qt`iljt`i

`

”´

Rt`1`i ´R˚t`1`i

¯ı

fjt`iqt`iljt`i ` Rt`1`injt`i

)

. (A.2)

subject to the constraint (1.23). Since,

Vjt “ maxljt`i,fjt`i,xjt`i

Et

8ÿ

i“0

p1´ θqθiΛt,t`1`i njt`1`i

“ maxljt`i,fjt`i,xjt`i

Et

«

p1´ θqΛt,t`1njt`1 `

8ÿ

i“1

p1´ θqθiΛt,t`1`i njt`1`i

ff

, (A.3)

it can be written that:

Vjt “ maxxjt

"

maxljt,fjt

Et

!

Λt,t`1rp1´ θqnjt`1 ` θVjt`1s

)

*

, (A.4)

reflecting the intraperiod timing assumption for the choice of the ROM utilization.

The Lagrangian which solves the bankers’ profit maximization problem reads,

maxljt,fjt

L “ pνlt ` fjtν˚t qqtljt ` νtnjt ` µt

„

pνlt ` fjtν˚t qqtljt ` νtnjt ´ λ

ˆ

fjtxjt

˙

qtljt

.

(A.5)

where the term in square brackets is due to equations (1.23) and (1.24). The first-

order conditions for ljt, fjt, and µt are:

pνlt ` fjtν˚t qp1` µtq “ λ

ˆ

fjtxjt

˙

µt (A.6)

ν˚t p1` µtq “ λ1ˆ

fjtxjt

˙

1

xjtµt (A.7)

61

ˆ

νlt ` fjtν˚t ´ λ

ˆ

fjtxjt

˙˙

qtljt ` νtnjt ě 0. (A.8)

respectively. Cases in which the incentive constraint of banks is always binding are

of interest, which implies that µt ą 0 and (A.8) holds with equality. Rearranging

(A.8) yields the endogenous leverage condition (1.26). Note also that by (A.6), µ ą 0

implies ν˚ ą 0 so that the funding premium is positive in equilibrium.

Combining equations (A.6) and (A.7) and using the functional form for λp.q, the

following is obtained:

fjt “ ´νltν˚t`

«

ˆ

νltν˚t

˙2

`2

λ2

ˆ

λ0 ´ λ1νltν˚t

˙

ff12

. (A.9)

Finally, Vjt`1 in equation (A.4) is replaced by imposing the linear conjecture in

equation (1.24) and the borrowing constraint (1.26) to obtain,

Vjt “ Et

!

Ξt,t`1njt`1

)

, (A.10)

where Vjt stands for the optimized value. Replacing the left-hand side to verify the

linear conjecture on bankers’ value (1.24) and using equation (1.19), the definition

of the augmented stochastic discount factor Ξt,t`1 “ Λt,t`1r1´ θ` θpζt`1κt`1`νt`1qs

is obtained, and νlt, νt, and ν˚t should consecutively satisfy equations (1.27), (1.28)

and (1.29) in the main text.

A.1.3 Optimal Utilization Rate of the ROM

The first order condition with respect to xjt would read,

„ˆ

BνltBxjt

` fjtBν˚tBxjt

˙

qtljt `BνtBxjt

njt

p1` µtq “ ´fjtx2jt

qtljtλ1

ˆ

fjtxjt

˙

µt. (A.11)

62

this equation can be rewritten by using equations (1.27) and (1.29) to obtain,

BνtBxjt

”

p1´ fjtqqtljt ´ njt

ı

p1` µtq “fjtx2jt

qtljtλ1

ˆ

fjtxjt

˙

µt. (A.12)

This expression might be simplified as follows. First notice that by the first order

condition with respect to fjt (A.7), µt1`µt

“ν˚t xjt

λ1ˆ

fjtxjt

˙ is obtained. By bankers’ bal-

ance sheet (1.13), p1 ´ fjtqljt ´ njt “ bjt`1p1 ´ ROMpxjtqq and lastly, by equation

(1.28) BνtBxjt

“ Et

!

Ξt,t`1pRt`1´1q

1´ROMpxjtqROM 1pxjtq

)

. Using the above conditions and the

definitions, equation (A.12) can be rewritten as,

xjt “Et

!

Ξt,t`1

”

Rt`1 ´R˚t`1

ı )

b˚jt`1

Et

!

Ξt,t`1pRt`1 ´ 1qROM 1pxjtq)

bjt`1

. (A.13)

A.1.4 Resource Constraints

The resource constraint for the final good equates domestic production to the demand

for consumption of the non-traded good and demand for investment. That is,

y “ pNt cNt ` it. (A.14)

For simplicity, it is assumed that the log of traded goods production follows an

exogenous process

logpyTt`1q “ p1´ ρTqyT ` ρT logpyTt q ` ε

Tt`1 (A.15)

with zero mean and constant variance Gaussian innovations εTt`1. Therefore, the

balance of payments vis-a-vis the rest of the world defines the trade balance as a

function of net foreign assets and follows as

63

etrCTt ´ Y

Tt s “ b˚t`1 ´R

˚t b˚t ` rrrxtROCtbt`1 ´ rrxt´1ROCt´1bts (A.16)

Observe that the endogenously determined ROM reserves constitute the international

reserves of the central bank and fluctuate depending on banks’ liability structure and

the utilization rate of the ROM.

A.2 Definition of Competitive Equilibrium

A competitive equilibrium is defined by sequences of prices

!

qt, Rkt, Rt, R˚t , Pt, P

Nt , P

Tt , wt, πt, st

)8

t“0,

government policies

tROCpxtq,M0t, T rtu8

t“0 ,

allocations

!

ct, cNt , c

Tt , ht, bt`1,mt`1, b

˚t`1, lt, xt, ft, nt`1, kt`1, it, yt

)8

t“0,

initial conditions

b0, b˚0 , k0,m0, n0,

and exogenous processes!

εψt`1, εr˚nt`1, ε

zt`1, ε

Tt`1

)8

t“0

such that;

i) Given exogenous processes, initial conditions, government policy, and prices;

the allocations solve the utility maximization problem of households, the net

worth maximization problem of bankers, and the profit maximization problems

of capital producers and consumption goods producers.

64

ii) Home and foreign goods, physical capital, investment, security claims, domes-

tic deposits, money, and labor markets clear. The trade balance and GDP

identities and hold.

A.3 IRFs in Response to Productivity and Country Risk PremiumShocks

Figure A.1: Impulse Response Functions of Selected Variables to a Negative OneStandard Deviation Productivity Shock

Note: The dashed red lines are for the model where the utilization rate is fixed at its steady state value, the solidblue lines are for the model where the utilization rate is a chaoice variable of the banks, and black dotted lines arefor the model where there is no ROM policy

65

Figure A.2: Impulse Response Functions of Selected Variables to a Negative OneStandard Deviation Country Risk Premium Shock

Note: The dashed red lines are for the model where the utilization rate is fixed at its steady state value, the solidblue lines are for the model where the utilization rate is a chaoice variable of the banks, and black dotted lines arefor the model where there is no ROM policy

66

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Biography

My name is Hasan Sadik Arik, and I was born in Denizli/Turkey on February 28th

1987. I earned my B.S. in Mathematics and B.A. in Economics from Koc Univer-

sity/Istanbul in 2010, and my M.S in Economics from the London School of Eco-

nomics and Political Science/London in 2011. I wrote my masters thesis under the

supervision of Professor Nobuhiro Kiyotaki. Since 2012, I have been studying at

Duke University.

70