CAPITAL CONTROLS AND EXTERNAL DEBT TERM STRUCTURE. A Dissertation EZA GHASSAN AL-ZEIN

Transcription

1 CAPITAL CONTROLS AND EXTERNAL DEBT TERM STRUCTURE A Dissertation by EZA GHASSAN AL-ZEIN Submitte to the Office of Grauate Stuies of Texas A&M University in partial fulfillment of the requirements for the egree of DOCTOR OF PHILOSOPHY August 5 Major Subject: Economics

2 iv CAPITAL CONTROLS AND EXTERNAL DEBT TERM STRUCTURE A Dissertation by EZA GHASSAN AL-ZEIN Submitte to the Office of Grauate Stuies of Texas A&M University in partial fulfillment of the requirements for the egree of DOCTOR OF PHILOSOPHY Approve by: Chair of Committee, Committee Members, Hea of Department, Leonaro Auernheimer Paula Hernanez-Verme Dennis W. Jansen Donal R. Fraser Leonaro Auernheimer August 5 Major Subject: Economics

3 iii ABSTRACT Capital Controls an External Debt Term Structure. (August 5) Eza Ghassan Al-Zein, B.A., American University of Beirut, Lebanon Chair of Avisory Committee: Dr. Leonaro Auernheimer In my issertation, I explore the relationship between capital controls an the choice of the maturity structure of external ebt in a general equilibrium setup, incorporating explicitly the role of international leners. I look at specific types of capital controls which take the form of ate-specific an maturity-specific reserve requirements on external borrowing. I consier two questions: How is the maturity structure of external ebt etermine in a worl general equilibrium? What are the effects of ate- an maturity-specific reserve requirements on the maturity structure of external ebt? Can they prevent a bank run? I evelop a simple Diamon-Dybvig-type moel with three ates. In the low income countries, banks arise enogenously. There are two short-term bons an one long-term bon offere by the omestic banks to international leners. First I look at a simple moel were international lening is moele exogenously. I consier explicitly the maturity composition of capital inflows to a omestic economy. I show that the holings of both short-term bons are not ifferentiate accoring to ate. Secon, I consier international lening behavior explicitly. The worl consists of two large open economies: one with high income an one with low income. The high

4 iv income countries len to low income countries. There exist multiple equilibria an some are characterize by relative price ineterminacy. Thir, I iscuss ate-specific an maturity- specific reserve requirements. In my setup reserve requirements play the role of a tax an the role of proviing liquiity for each bon at ifferent ates. I show that they reuce the scope of ineterminacy. In some equilibria, I ientify a case in which the reserve requirement rate on the long-term ebt must be higher than that on the short-term ebt for a tilt towars a longer maturity structure. Fourth, I introuce the possibility of an unexpecte bank run. I show that some specific combination of ate-an maturity-specific reserve requirements reuce the vulnerability to bank runs. With regar to the post-bank-run role of international leners, I show that international leners may still want to provie new short-term lening to the bank after the occurrence of a bank run.

5 v To Geha an Ragha, for a eicate parenthoo, an an intellectual frienship, For teaching me perseverance an unfurling my ambitions For their continuous love

6 vi ACKNOWLEDGMENTS I woul like to thank Bai Baltagi for encouraging me to pursue my Ph.D. stuies at Texas A&M University an proviing me the opportunity of such a challenging path. I am grateful to Leonaro Auernheimer for being a tough iscussant an insightful avisor over the years, who taught me a lot an reshape my thought process. I owe great gratitue to Paula Hernanez-Verme for her etaile involvement in my work an her continuous perceptive guiance. I woul also like to thank Dennis Jansen an Donal Fraser for valuable comments. I woul like to thank the Private Enterprise Research Center for offering me the Braley Fellowship for 3-4, an opportunity to concentrate on my research work. I owe special gratitue to my friens, Daa Abi-Ghanem, Carmen Aroztegui, Kerry Hope an Danan Liu, for their patient listening an tireless, often humorous, support. Their continuous encouragement helpe me not only finish this process but also strengthene my self-confience in pursuing my future ambitions. I am grateful to my sisters, Diala an Marwa, my uncle Abbas an my aunt Fatme for believing in me, an investing generous time an effort in lifting up my spirits especially uring my stressful moments. I cannot thank enough my friens, Amitava, Archana, Birenra, Chun-Li, Francoise, Karen, Steve, Yuchen an Zeina, for their great frienship an family-like support. Last, but not the least, I woul like to thank Christi Ramirez-Essix an Tyffanne Rowan for their silent efforts in easing each aministrative step with a welcoming smile.

7 vii TABLE OF CONTENTS Page ABSTRACT..iii DEDICATION...v ACKNOWLEDGMENTS...vi TABLE OF CONTENTS. vii LIST OF FIGURES x LIST OF TABLES.xii CHAPTER I INTRODUCTION I.. I.. I.3. On the choice of the maturity structure of external ebt.3 Capital controls.7 Overview of issertation chapters. I.3.. Chapter II... I.3.. Chapter III... I.3.3. Chapter IV... 3 I.3.4. Chapter V... 5 II EXOGENOUS LENDING..7 II.. Introuction... 7 II.. The environment... 8 II... Domestic epositors an omestic banks... 8 II... International borrowing... II..3. The omestic bank s problem... II.3. Equilibria... II.3.. The interior solution... 4 II.3.. The omestic bank is willing to borrow only long term at t=... 6 II.3.3. The omestic bank is not willing to borrow long term at t=... 6 II.3.4. Multiplicity of equilibria... 8 II.4. Numerical examples from simulation... 3

8 viii CHAPTER Page II.5. Conclusion... 3 III ENDOGENOUS LENDING..33 III.. Introuction 33 III.. The environment with enogenous behaviors of international leners III... The omestic bank problem 33 III... The leners problem III.3. Equilibria III.3.. On multiplicity an ineterminacy of equilbria III.3.. Description of equilibria III.4. Simulation results... 5 III.5. Conclusion IV RESERVE REQUIREMENTS AND ENDOGENOUS LENDING..6 IV.. The omestic bank problem with reserve requirements... 6 IV.. Equilibria... 6 IV.3. Simulation results IV.3.. Different bifurcations with reserve requirements IV.3.. Welfare comparison IV.4. Conclusion... 8 V COUNTRIES ON THE VERGE OF A NERVOUS BREAKDOWN: ARE THERE ANY CURES?.83 V.. Introuction V.. The emergence of a bank run in the setup without reserve requirements V... Defining the illiquiity conition V... Comparison of illiquiity conitions across all equilibria without reserve requirements V..3. Simulation results V.3 Can reserve requirements prevent the occurrence of a bank run? V.3.. Illiquiity conitions with reserve requirements V.3. Simulation results... 89

9 ix CHAPTER Page V.4. International lening after the bank run: Are international leners throwing goo money after ba money? 93 V.4.. International re-optimization problem V.4.. Simulation results V.5. Conclusion VI CONCLUSION... REFERENCES APPENDIX A... 6 APPENDIX B...9 APPENDIX C... VITA.....

10 x LIST OF FIGURES FIGURE Page.. Ranges for unique an multiple equilibria Utility of omestic agents across ifferent types of equilibria Structure of the moel The perfect arbitrage conition Range for multiple equilibria (i) Range for multiple equilibria (ii) Set (a) Set (b) Set (c) Case c Set (c) Case c Bifurcations with reserve requirements at the interior set Bifurcation towars two equilibria, with reserve requirements θ as a function θ for bifurcation towars a unique equilibrium Welfare of omestic borrowers an international with an without reserve requirements (with bifurcation towars two equilibria) Welfare of omestic borrowers an international with an without reserve requirements ( with bifurcation towars a unique equilibrium)... 8

11 xi FIGURE Page 5.. Decision tree at t= Actual vs. anticipate new lening at t =, r = Early liquiation over new lening l ˆ / x ˆ at t = for r = Ratio of actual total ebt at t= (after bailout) over expecte value of total ebt (without a bank run)...

12 xii LIST OF TABLES TABLE Page.. Bouns A an B Comparative summary between the equilibria without an with reserve requirements Presence of illiquiity at the interior solution Illiquiity presence at the interior solution with reserve requirements (bifurcation towars equilibria) Illiquiity presence at the interior solution with reserve requirements (with bifurcation towars a unique equilibrium)... 9

13 CHAPTER I INTRODUCTION [ ] the right starting point for thinking about capital controls must be on very focuse, temporary measures aime at stemming massive temporary inflows or outflows of ebt. (Rogoff,, 6) After the financial crises of the 99s, preventing large speculative an volatile inflows of short-term ebt became a major concern. Following the sprea of liberalization policies in the 99 s, many eveloping countries have seen their private an financial sectors accumulate high short term borrowing. The increase in private short-term borrowing resulte in a situation where the private sector became unable to fully service the ebt without new borrowing. This phenomenon is ientifie as shortterm over-borrowing by the private sector. With high inherite short-term ebt, any new borrowing becomes costlier. A ebt overhang arises wherein the expecte present value of output is lower than the accumulate ebt. The private sector with a ebt overhang signals its inability to pay back its ebt an therefore may not be able to get any new borrowing. This in turn leas to efault crises, bank runs or speculative attacks. Theoretical finings an the Mexican experience of 994 suggeste the importance of the maturity structure of external ebt an the benefits of ebt with longer maturity to prevent ebt-relate financial crises. Thus in the spirit of the quote by Rogoff (), the stuy of capital controls became popular again. The success of the Chilean experience with reserve requirements on external ebt brought increasing attention to the use of This issertation follows the style an format of Journal of International Economics.

14 these types of capital controls. Despite the extensive literature analyzing capital controls an external ebt the issue of reserve requirements on external borrowing, as a type of capital controls has receive little attention. In my issertation I look at how the maturity structure of private external ebt is enogenously etermine an the role of ate- an maturity- specific reserve requirements in preventing bank runs. How is the maturity structure of external ebt etermine? How are policies of capital controls on the external ebt flows ocumente in the literature? What is the impact of capital controls on the composition of ebt? Can they reuce the vulnerability to a bank run? To answer these questions, in this chapter I will first look at how the overborrowing synrome of short-term ebt has been looke at in the existing literature on financial crises an how the maturity an interest rate term structure was consiere in these moels. Secon I will review the controversial existing results regaring the effect of capital controls. There I will look specifically at how capital controls that take the form of ate- an maturity- specific reserve requirements on external borrowing have been consiere in the literature. Note that theoretical work on ebt crises has taken ifferent turns over the last three ecaes. The first-generation moels on crises have focuse on the relation between fiscal eficit of governments an the resulting collapse of exchange rates (Krugman, 979). The secon-generation moels starte to explain currency crises as the result of investors panic regaring the central bank s holing of international reserves to backup the exchange rate peg. Devaluation policies or the abanonment of the peg become selffulfilling prophecies (Obstfel, 994). There the choice of government ebt maturity was

15 3 exogenous, when consiere. The Mexican 994 crisis an subsequent wiesprea financial crises throughout the 99s shifte the analysis from eveloping stanar moels of governments management of ebt an exchange rate regimes to analyzing the performance of the private sector. The thir-generation moels attempt to explain how the inflows an outflows of capital can rive both a currency crisis an/or a financial crisis. Within this stran of moels, ifferent approaches have been unertaken (See Chang an Velasco, an Aizenman an Turnovsky, ). In section I., I summarize the explanations regaring the choice of the maturity structure. In section I., I look at how the role of capital controls has been ocumente. Finally, section I.3 summarizes the finings of each chapter in the issertation. I.. On the choice of the maturity structure of external ebt With the financial crises of the 99s, an the Mexican crisis in 994, the literature on crises shifte attention towars analyzing private flows of capital. In aition, looking at the behavior of investors an firms became necessary. One stran in the literature on the ebt overhang in the late 98s an early 99s has evelope moels in which the country is treate like a firm. In Krugman (988) an Bulow an Rogoff (99), there is a high inherite ebt of a country that is higher than the expecte present value of its future stream of resources. In these types of moels the ebt is inherite an the maturity structure is not originally a choice variable. Lamont (995) introuces the role of beliefs in a moel with ebt overhang. In his moel he introuces two types of inherite ebt: one with long-term maturity an one with short-term maturity, along with an exogenous maturity structure.

16 4 Another stran in the ebt literature has looke at the relationship between asset prices an the ebt accumulation of firms to explain why over-borrowing occurs. Kiyotaki an Moore (997) an Auernheimer an Garcia-Saltos () suggest that the presence of collateral magnifies the effect of transitory prouctivity shocks on asset prices an thus on consumption. The major common chain in the above cite literature is that over-borrowing becomes a vicious circle ue to uner-accumulation of capital an high accumulate ebt that is maturing. The problem is exacerbate by the nee for new financing that is available only at high interest rate. The interest rate on the ebt usually reflects the expectations regaring the ability of borrowers to repay the ebt. The classical efinition of the interest rate given by Fisher (93) as an inex of impatience suggests that the interest rate on the short-term ebt is lower than on the long-term ebt because it carries less risk of efault (pp. 5-53). However, such a efinition is not in tune with theoretical finings that suggest the importance of longer maturity structure to avoi crises. Keynes (935) perceive the interest rate as the rewar for parting with liquiity (pp.67). Diamon (99) suggests a moel in which the choice of ebt maturity reflects a trae-off between liquiity risk in the short-term an a preference for short-term ebt ue to private information about creit rating (pp.79). A borrower with high creit rating prefers short-term ebt. A borrower with somewhat low to mile creit rating woul prefer long-term ebt. A borrower with very low creit rating woul prefer to hie his type an thus borrow short-term ebt. Despite the relation of the maturity structure to liquiity risk an creit rating, in this moel, only the borrowers

17 5 ecisions are moele explicitly. There, the behavior of leners an interest rates on ebt are assume to be exogenous. Several papers base on Diamon an Dybvig (983) have analyze the behavior of omestic banks in choosing their ebts an the ebt maturity structure. Originally, Diamon an Dybvig (983) explain how banks subject to runs can attract eposits in a close economy. They recommen government eposit insurance to prouce superior contracts. In Aizenman an Turnovsky (), espite consiering the inebteness of the private sector, there is no role for a bank in their moel because uncertainty arises from an aggregate shock an not the lack of information. Chang an Velasco () evelop a moel with a small open economy in which they show that bank runs are associate with high short-term ebt. They provie a set-up for a small open economy that captures the enogenous term structure along with an enogenous financial intermeiary. Nevertheless, their analysis focuses only on the borrower s behavior. However in a general equilibrium context, the maturity structure of the ebt shoul be the outcome of the behaviors of both leners an borrowers. Allowing for only one type of bon-- a short-term bon-- Seo (3) fins that there always exists an equilibrium with pessimistic foreign investors who make bank runs the equilibrium strategy for omestic agents. For the purpose of comparison across moeling techniques, it is important to touch on how the term structure of ebt has been explore in a parallel literature relate to governments efault an sovereign ebt rather than the ebt of the private sector. In a partial equilibrium framework Calvo an Guiotti (99) show that long-term ebt

18 6 becomes optimal only with some pre-commitment an inexation of the omestic ebt. If there is no inexation, the optimal maturity for the ebt is short term, ue to the possibility of using inflation to wash out its nominal ebt. Another approach is presente by Jeanne (4). He uses a game theoretic framework in which efforts of having goo or ba policy to increase or ecrease the probability of high output conitional on a ba signal are within the utility function of a country. In his moel international creitors behavior is not explicitly formalize. A risky [short-term] ebt inuces the country to implement a goo policy by making ba policy relatively costly (Jeanne, 4, pp.). This is parallel to the commitment problem that leas to short-term ebt being optimal in Calvo an Guiotti (99). In contrast, by exogenously imposing various maturity structures, Cole an Kehoe () show that a longer maturity structure of the prevailing ebt can reuce the possibility of a crisis by reucing the new borrowing neee by the government at each perio from international leners. In their moel a general equilibrium framework with risk neutral international leners an a omestic government is use. However the maturity structure is exogenously impose. To sum up, at least three features woul be esirable in an environment to analyze an enogenous maturity structure: First, for the framework to have a structure in which it is not clear that short-term ebt is preferre to long-term, liquiity risk must be present. Secon, for the choice to be explicit between short-term an long-term ebt, the possibility of issuing long-term an short-term ebt simultaneously shoul be consiere. Thir to unerstan why new lening woul be provie or not, the behavior of international leners has to be consiere in a worl general equilibrium. The

19 7 literature has looke at the first two features escribe above, but none of the existing moels have enogenize the interest rates an therefore they have not consiere leners behavior explicitly. It is true that for a ebtor who pays interest, the interest is, to him, a real cost, an is ebite on his books. But we nee only to be remine of the ebit an creit bookkeeping of the first chapter to see that this item is counterbalance on the books of the creitor, to whom this interest is by no means a cost, but on the contrary an item of income. (Fisher, 93, pp.54) In tune with the quote by Fisher (93), a complete moel for ebt has to consier a general equilibrium environment in which the interest rate falls as a cost on borrowers an a return to leners. In the following section, I give a review on the mixe results in the literature regaring capital controls. I.. Capital controls Volatile short-term borrowing has marke many efault crisis episoes in the 99 s. The funamental feature of the 99 s is the rapi growth of private short-term ebt in eveloping countries. In aition the ratio of short-term ebt to international reserves became quite high. In fact, capital inflows to eveloping countries face strong reversals in 997 an 998. This inicates that the growth in short-term ebt mae eveloping economies more susceptible to liquiity runs (Daush et al., ). In aition to the volatile aspect of short-term ebt, Kaminsky an Reinhart (999) show that banking crises are features of the crises in the 98 s an 99 s but not in the 97s, when

20 8 financial markets were still highly regulate. They report the probability of a currency crisis conitione on the beginning of a banking crisis as 46% when the reporte unconitional probability is 9%. In their survey, most of the banking crises precee balance of payment crises. In fact, they fin a link between financial liberalization an banking crisis: [In] 8 out of the 6 banking crises stuie (...), the financial sector ha been liberalize uring the preceing five years, usually less (Kaminsky an Reinhart, 999, pp.48). As pointe by Rogoff () an Chang an Velasco (), ebt crises relate to large capital inflows in an open economy context are structurally relate to the maturity structure. In tune with the quote by Rogoff (), the benefits of capital controls are in preventing short-term volatile ebt flows. Theoretically, the answer on the benefit of capital controls is not really straight forwar because as much as it prevents excessive short-term ebt ex-ante, it puts more constraint on the provision of liquiity ex-post. In other wors, the reserve requirements coul play the role of liquiity or liquiity guarantee for any issuance of ebt ex-ante, an therefore may prevent a crisis ex-ante. But in the event of a liquiity shock, shortterm borrowing becomes more ifficult when reserve requirements are impose an therefore might create a constraint to the role of short-term borrowing as a liquiity provier. These two effects working in opposite irections are consistent with controversial results relate to the benefits or losses regaring capital controls. Diamon an Rajan () argue against capital requirements. Moreover, Reinhart an Smith () stuie the effect of temporary controls on capital inflows. In the secon part of their paper, they analyze it in the presence of the over-borrowing istortion. They

21 9 erive the optimal tax rate on capital inflows. After calibrating the moel, they fin that temporary capital controls nee to be very high to be effective. The welfare benefits of such taxes are estimate to be very low. Analyzing the effects of reserve requirements without consiering the maturity structure of the bon may be missing a funamental chain: the tilt of the maturity structure of the ebt. It is only in the prevention of estabilizing short-term capital inflows that capital controls coul be effective in removing crises. Aizenman an Turnovsky () analyze the effect of reserve requirements in a moel with only shortterm ebt. The work by Aizenman an Turnovsky () analyzing the effect of reserve requirements on borrowing, stans as an exception. They moel a efault crisis as enogenous to sovereign risk an moral hazar consiering the behavior of both riskneutral leners an borrowers. They show the benefit of reserve requirements in reucing the probability of efault an thus increasing welfare. However, their moel oes not focus on the ual aspect of this type of capital control: yet the expression reserve requirement suggests a ual role of this type of capital controls: the reserve function, i.e. the role of liquiity provier, an the requirement constraining function, i.e. the role of a tax. The first role woul presumably be important in preventing efault crises. Although the secon role secures from over-borrowing, it may prevent the provision of liquiity in the event of a crisis. In aition, short-term ebt constitutes an important source of liquiity for omestic banks; reserve requirements may have the averse effect of reucing such role. Accoringly, it is impossible in the Aizenman an Turnovsky () moel to capture the ual feature of short-term borrowing: On one han as a e-

22 stabilizer an on the other as a liquiity provier. In fact, De Gregorio et al. () show that, in Chile, such policies have tilte the maturity composition of capital inflows towars longer maturity structure. Chile s financial liberalization ates since 974. It ha a banking crisis in September 98 that peake in March 983. The closest balance of payment crisis was in August 98 (Reinhart an Kaminsky, 999). In the 99 s, Chile i not experience any financial crisis. Among many soun monetary policies, the literature explaining the success of the Chilean case refers to the use of reserve requirements as capital controls. In January 99, percent reserve requirements were impose on eposits an loans in foreign currency hel by commercial banks. The reserves ha to be maintaine for one year. In May 99, the rate was increase to 3 percent an it was set such that the reserve requirement rate fell as the maturity increase. In September 998, a year marke by financial crisis in other Latin American countries, the rate of reserve requirement was set to zero. The share of private ebt in Chile in the 99 s has increase. In aition, short-term ebt share has ecrease significantly from 9.4% in 99 to 5.8% in 998 (Reinhart an Reinhart, 999 an De Gregorio et al., ). The above suggests that a rigorous analysis of reserve requirements shoul consier not only the maturity structure of external private ebt, but also the behavior of banks an international leners in the external ebt market. I.3. Overview of issertation chapters In my issertation, I explore the relationship between capital controls an the choice of external ebt maturity, in a general equilibrium setup, with enogenous international

23 leners behavior. More specifically I exten the basic Chang an Velasco () framework to a general equilibrium moel in which international lening is enogenous an analyze the effects of capital controls that take the form of reserve requirements on external borrowing. I evelop a simple Diamon-Dybvig-type moel with three ates an a two-perio planning horizon. In the low-income countries, banks or coalitions of epositors arise enogenously. There are two short-term bons an one long-term bon offere by the omestic banks. There is a single goo each perio, which is homogeneous across countries. This goo cannot be prouce: this is an enowment or pure exchange economy. The goo is perishable if not investe or consume. There is an investment technology that yiels a real gross rate of return R > at t=, but prouces only r units of the goo if liquiate earlier at t=, where r < R. The environment is characterize by liquiation costs at t=. In chapter II, exogenous lening behavior is assume. In chapter III, international leners behavior is consiere explicitly. In chapter IV, ate- an maturity- specific reserve requirements are impose on the omestic economy s borrowing. In all chapters II, III, an IV, there is no bank run. In chapter V, I introuce the possibility of an unexpecte bank run at t=. In chapter V, I first look at what combination of ate- an maturity-specific reserve requirements can prevent a bank run. Secon, when a bank run occurs, I explore the re-optimizing behavior of international leners in eciing whether to bailout the borrowing bank. I.3.. Chapter II In chapter II, for comparability, a la Chang an Velasco (), international lening behavior is not explicitly moele, an I impose upper limits on the borrowing by

24 omestic borrowers. Unlike Aizenman an Turnovsky (), I consier explicitly the maturity composition of capital inflows. First, when I allow for an environment with a rich maturity structure, the scope for locally-unique multiple equilibria increases even when creit is ratione. I also show that the scope of multiple equilibria an the ranking of utility across ifferent types of equilibria epen on the opportunity cost of liquiation. Secon with exogenous lening, it is impossible to generate equilibria with high eman for one of the short-term bons without generating high eman for the other short-term bon. Thir, creit rationing is exogenous when creit limits are impose. The holings of both short-term bons are not ifferentiate accoring to ate. However, to capture in a nontrivial manner the iea that capital controls are not only maturity-specific but also ate-specific, I nee to look at the behavior of international leners as well. I.3. Chapter III This chapter is the founation for chapters IV an V. Here I consier international leners behavior explicitly. The worl consists of two blocks of large open economies: The high income an low-income countries blocks. The low-income countries have the same technology an consumption schemes escribe in chapter II. The high-income countries benefit from lening to low-income countries. In the high-income block, it is assume that the international creitors are homogeneous. There are two short-term bons an one long-term bon offere by the omestic banks in the low-income countries to international leners in the high-income countries.

25 3 After I solve both the international leners an the omestic bank problems, I erive multiple sets of equilibria. In the worl general equilibrium, the interest rates will be such that markets clear. Accoringly, the equilibrium term structure of the ebt will be etermine. The ifficulty with this type of moels is that results are usually characterize by multiple equilibria. In aition, sometimes within each set of multiple equilibria, there arises ineterminacy of relative interest rates. I use the concept of ineterminacy to characterize each set of equilibria. When I allow for enogenous lening behavior, creit rationing will emerge enogenously. The analytical escription of equilibria an the simulation results show that cases, where there is high eman for either of the short-term bons can exist for high gross return of investment R. This is ifferent from the results obtaine with exogenous lening for two reasons: First with exogenous lening, low R entails a lower cost of liquiation an thus the equilibrium with only short-term ebt arises. In chapter III, a lower R implies both a lower cost of liquiation an lower interest rates pai to international leners at t=. Thus with enogenous lening interest rates incorporate both the Keynesian concept of interest rate as the rewar of parting for liquiity an Fisher s view of interest rate as impatience factor. The tilt towars longer or shorter maturity will epen on the equilibrium interest rates. In the following chapter I look at possible equilibria uner reserve requirements impose on the bank. I.3.3 Chapter IV In chapter IV, I explore how imposing ate- an maturity-specific reserve requirements may affect the scope of ineterminacy of ifferent equilibria. A ate- an

26 4 maturity- specific reserve requirement is a fraction of the amount borrowe by private agents that has to be eposite in a non-interest bearing account at the central bank. When the bon matures, the central bank returns the reserves. Note that at the interior solution without reserve requirements, there was an ineterminate set of the quantities. The number of equilibrium combination of quantities was infinite. Different combinations of non-zero reserve requirements cause bifurcations, a change in number of equilibria, towars either two equilibria or a unique equilibrium. This epens on what combinations of ate- an maturity- specific reserve requirements is chosen. A bifurcation towars a unique equilibrium arises if an only if the reserve requirement on the long-term ebt is higher than that on the secon short-term bon issue at t=, which in turn is higher than that on the initial short-term bon issue at t=. The intuition is that the liquiity role of reserve requirements ominates the tax role. There are two reasons for this result: First, in this moel, liquiation is costly in the short-term, thus the role of liquiity provision is crucial at t=. Secon, I have incorporate the behavior of risk-averse international leners, who may see in high reserve requirements an inication of the capability of borrowers to pay some of the loan. Simulation results show that for some parameter ranges, a set of ate- an maturityspecific reserve requirements, which yiel a unique equilibrium, can improve welfare of omestic epositors an international leners. It is also shown that international leners are always worse off when reserve requirements lea to a bifurcation to two equilibria. The association of bifurcation towars a unique equilibrium with the possibility of

27 5 welfare improvement implies that there might be an association between higher utility an higher eterminacy. I.3.4 Chapter V In this chapter I analyze the vulnerability to a bank run of equilibria ientifie in the moel I escribe in chapters III an IV. A bank run follows from the unexpecte realization of a ba ream, which makes it optimal for all omestic agents to withraw from the omestic bank. If an unexpecte ba ream is seen by omestic epositors at t= an the bank position signals that it is unable to pay back all the withrawals i.e. it is in an illiqui position, a bank run will occur. This chapter aresses two questions: Does the imposition of ate- an maturity-specific reserve requirements on external ebt reuce vulnerability to a bank run? Do international leners bail out the omestic banks after a bank run occurs? To aress these questions, I explore whether or not the omestic banks hol an illiquiity position. If the bank s position is illiqui, the omestic epositors woul run to the bank if they have a ba ream. In aition, in the case of a bank run, I look at how international leners may eviate from their original plans of lening. In particular, I explore whether they woul be willing to give any new lening to bailout the omestic banks. Finally I illustrate each case within each section with simulation results from numerical examples. Interestingly one can ientify that the combination of reserve requirements that creates a bifurcation towars a unique equilibrium is always not vulnerable to a bank run. Why woul international leners be willing to len at t =? Their outsie option is not to get back anything of their loans. Since long-term ebt is pai back at t =, they

28 6 are willing to bail out the bank to retrieve the long term ebt. Following the occurrence of a bank run, international leners may fin it optimal to eviate from the plan at t=. Thus they re-optimize. Simulation results show that at t =, the anticipate net new lening is higher than the actual new lening att =. The new lening will only be provie if the actual value of total ebt at t= has a higher value than the anticipate value at t= of total ebt at t=. In chapter VI, I provie the main conclusions of the analysis. I outline some possible extension of the environment I have evelope in this issertation. In particular, I try to assess the shortcomings of the setup I evelope, an outline some possible future improvements.

29 7 CHAPTER II EXOGENOUS LENDING II.. Introuction In this chapter, I present a version of my moel assuming exogenous lening, for the purpose of comparability with Chang an Velasco (). In aition, this chapter provies a benchmark that I will use later, after I introuce enogenous lening explicitly. In the next chapters, introucing enogenous behavior for international leners will be a first step before looking at the effect of ate- an maturity-specific reserve requirements on private flows of borrowing. In the moel escribe below, international leners are exogenously willing to provie lening up to a certain limit. Chang an Velasco () explain this exogenous creit limit as an assumption in tune with the literature on collateralize borrowing: in that literature, borrowing is constraine to the available amount of liquiity. However in Chang an Velasco (), liquiity is not moele explicitly an the creit limit is exogenously impose. In aition, if such creit constraint is bining, this usually implies the presence of creit rationing. Creit rationing refers to situations where a borrower s eman is unfulfille, although he is willing to pay the ruling market price (Baltensperger, 978, pp.73). In this chapter, for comparability, a la Chang an Velasco (), international lening behavior is not explicitly moele, an I impose upper limits on the borrowing by omestic borrowers.

30 8 II.. The environment II... Domestic epositors an omestic banks The economy faces a two-perio planning horizon with three ates: t=,, an. In the omestic country, there is a continuum of agents with unit-mass. These agents are born at t=. There is a single goo each perio, which is homogeneous across countries. This goo cannot be prouce: this is an enowment or pure exchange economy. At t= each epositor gets an enowment of e units of the goo. I assume that at t= an t=, they o not receive any enowments of goos. At t =, epositors o not consume. The omestic agents whom I call epositors are ex-ante ientical but they may be expost ifferent ue to a preferences shock that is realize at t=. The istribution of this shock is known at t=, an it is i.i.. across agents. A t= with probability λ (,), the epositors coul be impatient an erive utility only from consuming goos at t=. With probability ( λ ), they coul be patient an woul want to consume goos at t= only. Thus omestic epositors will not consume in both perios. The istribution is known ex-ante an is public information. However when the event is realize at t=, each epositor s type realization is private information. Unlike Aizenman an Turnovsky (), there is no aggregate uncertainty. The only uncertainty in the borrowing country is private. With this assumption I avoi the complexity that may arise with ifferent types of eposits while I am focusing on ifferent types of ebts. For instance, a epositor receiving a new enowment at t= woul face the choice of whether or not to eposit her new enowment at the bank at t= an I rule out such a possibility. The assumption that the omestic epositors have no enowments at t= is just a normalization that is stanar in the literature.

31 9 The goo is perishable if not investe or consume. There is an investment technology works as follows: one unit of the goo investe at t= yiels a real gross rate of return R > at t=, but prouces only r units of the goo if liquiate earlier at t=, where r < R. Let k enote the amount of goos investe in this technology at t=. 3 Because of the uncertainty an the ex-post heterogeneity, a bank or a coalition of epositors arises enogenously. Henceforth I will use the terms omestic bank an borrower interchangeably. As is stanar in the literature, ue to the preferences shock that epositors face, they may gain from acting jointly. In fact, each epositor faces a probability λ of being of the impatient type at t=. If she was to choose autarky an learns that she is impatient, liquiating the investment at t= with a lower return becomes unavoiable. Therefore, epositors fin it optimal to form a bank that can provie some insurance. In this setup, banks arise enogenously 4. Banks will offer contracts that maximize the omestic epositors expecte utility inucing truth-telling self-selection. To fix ieas, I assume a logarithmic form of utility. 5 Thus a omestic epositor s expecte utility is given by U c, c ) = λln( c ) + ( λ)ln( ) (.) ( c Note that a one unit of the goo can be reinveste at t= yieling r units at t=. 3 In Chang an Velasco (), the borrower has the possibility to invest in an aitional technology: international reserves b t with gross return equal to one. Here I abstract from such a possibility. It is important to note that in my moel when r >, the rate of return on the investment technology woul be higher than international reserves technology. The investment in k woul therefore ominate the saving in international reserves. In fact Chang an Velasco () assume r =. 4 One coul also think of the bank as a possible contracting scheme for agents, in which agents exchange contracts to hege against uncertainty. 5 Note that with the logarithmic function, the substitution effect ominates the income effect, improving greatly the tractability of the moel.

32 where c an c are consumption quantities at t= an t= respectively. ln(c ) is twice continuously ifferentiable, strictly increasing in its arguments an satisfies the Inaa conitions. II... International borrowing All omestic agents eposit their enowments at the bank at t=. In aition to receiving eposits in the amount e at t=, only banks can borrow from international leners. At t=, two types of international ebt are available to banks: short-term an long-term. At t=, banks can only borrow short-term. is the short-term bon issue by the omestic bank at t= that matures at t=, paying a gross real interest rate ρ. is the short-term bon issue by the omestic bank at t= that matures at t=, paying a gross real interest rate ρ. Finally, is the long-term bon issue by the omestic bank at t= that matures at t= paying a gross real interest rate ρ. ρ, ρ, an ρ are exogenous. 6 Note that in anticipation for what is coming in chapter IV, to introuce ate- an maturity- specific reserve requirements, I nee two istinct ate-specific shortterm bons. II..3. The omestic bank s problem In this chapter, I assume that there are international leners who are willing to len to banks in the omestic country inelastically. However, as in Chang an Velasco (), I impose a borrowing constraint that works as a rule for creit rationing. The rule is as 6 Chang an Velasco () assume ρ = ρ = ρ. =

33 follows: the total principal of the ifferent types of bons for which the banks are liable at each ate must not excee a certain limit. Let f an f enote the limits at t= an t=, respectively. Therefore the omestic bank faces two borrowing constraints 7 : + = (.) f + = (.3) f I will assume, for reasons that will become clearer later, that f f. Notice that in Chang an Velasco () f = f. Banks have access to the same investment technology that epositors have. The bank will ecie how much to invest long-term k at t= an how much to liquiate l at t=, given R an r as explaine above. Therefore the buget constraints face by the bank at t =, an are given by: k e + (.4) + λ c + rl (.5) + ρ ( l λ ) c + ρ + ρ R( k ) (.6) In aition, the following incentive compatibility constraint nees to hol 8 : 7 In this case I assume that the borrowing constraints are bining, implying that creit is ratione. This is implicitly assume in Chang an Velasco (). It means that banks coul be willing to borrow arbitrarily large amounts, but they are not allowe to. 8 In my moel I allow omestic epositors to have access to investment technology even after the bank is forme. A patient epositor has therefore the option of concealing her type an withrawing c units of t= goos from the bank. After investing this withrawal for one perio, at t=, she coul consume rc units of the goos at t=. If the patient epositor reveals her true type an waits until ate t=, she woul consume c units of t= goos. Therefore the patient epositor will have an incentive to reveal her type if an only if c rc. In Chang an Velasco (), once the bank is forme, epositors are not allowe to have access to the investment technology. Since they have a storage technology, there the incentive compatibility constraint takes the form: c c.

34 c rc (.7) II.3. Equilibria The bank s problem is to choose c, c,,,, k, l to maximize (.) subject to (.), (.3), (.4), (.5), (.6) an (.7), taking as given the worl real gross interest rates ρ, ρ an the other parameters e, R an r. In Appenix A, I explain how I solve ρ, this problem. Despite the fact that interest rates are exogenous, I assume that the following perfect arbitrage conition hols. 9 ρ = (.8) ρ ρ I nee this assumption so that I can later compare my results with the equilibria with enogenous lening. A competitive equilibrium is efine as a set of non-negative allocations c ˆ, cˆ, kˆ, lˆ, ˆ, ˆ, ˆ } for the omestic bank such that the omestic bank s problem is { solve an (.8) hols. Since I am looking at equilibria where the omestic bank is a net borrower in international markets, I ismiss cases where <, < or <. Proposition. If there is no early liquiation in equilibrium, i.e. l ˆ =, then ˆ is R cˆ strictly positive. When there is no early liquiation, then r <ψ, where ψ. r cˆ 9 This is a version that can be comparable to pure expectations theory (that) hypothesizes that R t = R t Et R t+, which results in Lucas-Tree type Moel, when utility is linear in consumption or there is no uncertainty (Sargent, 987, pp.5).

35 3 The proof for proposition is provie in appenix A. Note that λ ψ is the marginal λ rate of substitution between consumptions across two ifferent states: -being impatient or -being patient. It is the ratio of the marginal utility of ĉ over the marginal utility of ĉ. It measures how much a epositor is willing to give up of state (being patient) consumption for one more unit of state (being impatient) consumption. Thus proposition implies that this marginal rate of substitution must be boune. The upper boun means that for a given λ, the expecte consumption of impatient epositors cannot be very high so that there is no early liquiation. The lower boun inicates that the incentive compatibility constraint is not bining. This is assume when there is no crisis at t=. In this environment, there exist three types of equilibria, which may coexist or may exist uniquely epening on the parameter values. In anticipation of what will come in the sections where I escribe each type of equilibria, let me set A ρ B ρ f ( λ) ρ f λ( e + f ) f + ( λρ λ( e + ρ ) f f ) ρ f ( λ) ρ f C λ( e + f ) (.9) (.) (.) Note that notice that A > B > C, when ρ < ρ an A < B < C, when ρ > ρ. Moreover, A B when ρ. Below, I escribe each one of the equilibria.

36 4 II.3.. The interior solution An interior solution means that the first orer conitions with respect to, an are zero. In this particular case,,. This is not a worl general > equilibrium analysis since the interest rates are exogenous by assumption. In this case the solution for the enogenous variables is: k ˆ = e + f (.) ˆ λr( e + f ) + ρ f ρ f = { } (.3) ( ρ ) ρ ˆ ( λρ ρ) f + ρ f λr( e + f) = (.4) ( ρ ρ ) ˆ f ρ λr ( e + f ) ( λ) ρ f = (.5) ρ ρ f ( ) ˆ ρ f ρ c ˆ = > λ (.6) R( e ) ( ) ˆ + f ρ f ρ ρ c ˆ = > λ (.7) Proposition. Uner the perfect arbitrage conition, there exists an equilibrium with an interior solution,, > if an only if (i) (ii) A R an R B when ρ > or ρ < ρ A R an B R when ρ < or ρ > ρ

37 5 Proof. Uner the perfect arbitrage conition ρ ρ = ρ, it must be the case that ρ > if ρ < ρ. I will first prove (i). Note that if ρ ρ <, A < B, an if ρ > ρ, A > B. Moreover if ρ < ρ, C < B, an if ρ > ρ, C > B. First suppose that ρ > ρ. If ρ < or ρ, using equation (.3), for, it must be that R A. This ρ > means that for the omestic bank to hol positive amounts of long-term bons at t =, the gross return on investment at t = must be high. In aition, if ρ < ρ or ρ, using equation (.4), for, it must be that R B. It means that for the omestic bank to hol positive amounts of short-term bons at t =, the gross return on investment at t = must be high. The upper an lower bouns are consistent when ρ < ρ or ρ >. Using equation (.4) for >, it must be R < C when ρ >, the interior solution exists if an only if A R B < C >. Thus. Now I turn to prove (ii): suppose that ρ <, for R A, >, R B, an for >, R > C. When ρ > ρ an ρ the reverse applies, the interior solution exists if < an only if C < B R A. For strict interior solution, the inequalities on the bouns for R become strict inequalities.

38 6 II.3.. The omestic bank is willing to borrow only long term ebt at t= In this equilibrium, ˆ = f, which entails ˆ = an ˆ = f f >. For this equilibrium to exist, it must be that R A. The latter conition entails that when R, the gross return on investment at t = is very high, the omestic borrower woul prefer to borrow only long-term. This is because the liquiation cost at t= becomes relatively higher when R is very high. In this equilibrium, the consumptions allocation woul be: c ˆ f f = (.8) λ R ( e + f ) ρ f + ( ρ ρ ) f c ˆ = (.9) ( λ) In (.8), f > f is neee to ensure non-negative consumption at t=. Notice that unlike the interior solution, in this equilibrium, the conition R A oes not require ˆ ρ > or ˆ ρ ˆ > ρ. Thus in this environment when the opportunity cost of liquiating at t= is high enough, an equilibrium with only long-term borrowing at t=, will arise. II.3.3. The omestic bank is not willing to borrow long-term at t= In this equilibrium, ˆ =, implying ˆ = f an ˆ = f. Again in anticipation for what is coming in chapter IV, to introuce ate- an maturity- specific reserve requirements, I nee two istinct ate-specific short-term bons. Note though that the setup with exogenous lening oes not allow for such an interesting analysis. For instance in this equilibrium, it is not possible to generate high short-term borrowing in Notice that when f = f, as in Chang an Velasco (), this is not an equilibrium with banks because having = = l, entails c, yieling a utility well below the utility uner autarky. = =

39 7 one perio without generating high short-term ebt in the other. This is because creit is ratione an once one of the short-term bons is at the limit, then =, which means that the other short-term bon woul have to go to the limit too. When ˆ =, the consumptions at t= an t= become respectively: f ρ f cˆ = (.) λ Re + Rf ρ f c ˆ = (.) λ Note that for c > an c >, it must be the case that f ρ f > an R ( e + f ) ρ <. In other wors, f ρ shoul be relatively low, so that there is a high eman for the secon perio short-term ebt. R B is a necessary conition for this equilibrium to exist. Thus when the return on investment at t= is low, the relative opportunity cost of liquiation at t= is low an short-term ebt is preferre to long-term ebt. Unlike the conition at the interior solution, the existence of this equilibrium oes not require ρ >. If ρ <, short-term ebt at t= is relatively cheap an it is obvious why this equilibrium may arise when R B. When ρ, short-term ebt seems > relatively expensive: it may not be obvious why this equilibrium may arise when there is low return on investment R B if the short-term ebt is costly. Note that when ρ, > with the perfect arbitrage conition, I get that ρ > ρ. Thus both the short-term ebt an the long-term seem relatively expensive. The choice of borrowing only for short-