On the Disciplining Effect of Short-Term Debt in a Currency Crisis

Transcription

1 On the Disciplining Effect of Short-Term Debt in a Currency Crisis Takeshi Nakata May 1, 2012 Abstract This paper explores how short-term debt affects bank manager behavior. We employ a framework where simultaneous multiple bank runs arise in an economy where a currency crisis could take place. We find that when there is no currency crisis, an increase in the proportion of short- to long-term debt heightens the effect of disciplining bank manager behavior. That is, they become more creditor friendly, a situation often discussed in the emerging market literature. However, when there is a currency crisis, an alternative effect arises: namely, the profitability of one bank affects the profitability of other banks in the same country through the exchange rate. In this situation, we show that the disciplining effect is weakened: in fact, there is even the case where the increase in short-term debt induces bank managers to act against creditors interests. Keywords: Bank runs; Currency crisis; Global game; Short-term debt JEL classification numbers: F34; G15; G21 This study was financially supported by Nomura Foundation. 1

2 1 Introduction Risky forms of finance are crucial when discussing the emerging market economies experiencing large-scale financial crises at the end of the last century. This is because of the very large share of foreign borrowing deriving from bank-related, foreign-currency denominated, short-term debt in Latin America and East Asia. Vulnerable forms of financing were in evidence from the outset of these crises, as banks in these countries rolled over short-term debt and invested in domestic firms over the long run. However, once the uncoordinated foreign creditors panicked, capital flowed out, massive devaluations arose, and banks failed. Although one preventive measure for these crises would appear to be to merely discourage a dependence on short-term debt and to promote long-term borrowing, actual resolution is not so simple. Put simply, and as often pointed out, shortterm debt has a positive role in disciplining debtors to behave in the interest of creditors. The nature of this disciplining effect has also surfaced and been emphasized in the context of emerging market crises. However, there are few examples to show the positive effect of these debts, despite the fact that the ratio of short- to long-term debt was extremely high in many of these borrowing countries. Though we cannot strictly evaluate this situation using the ratio of short- to long-term debt, at the time, the banking systems in some of these countries were far from sound. For instance, many of the loans made by banks were of a low quality, and used for financing investments of dubious profitability or for the speculative purchase of existing financial assets. In particular, in East Asia, estimates of the precrisis share of nonperforming loans (as a proportion of total lending) are 13 percent for Thailand and Indonesia, 8 percent for Korea, 10 percent for Malaysia, and 14 percent for the Philippines (Corsetti et al. 1999). Importantly, all of these economies have a notable feature in common, that is, widespread bank runs accompanied their currency crises. According to empirical work by Kaminsky and Reinhart (1999), financial crises in several countries since 1980 have often included both banking and currency crises, commonly referred to as twin crises. Furthermore, simultaneous multiple bank runs took place, as in the following report on Indonesia from 1997 through to 1998: Several banks were insolvent, or at least suffered from serious weakness, well before the crises; the banks difficulties were compounded by the losses incurred when the rupiah began to depreciate. The closure of some banks, together with the absence of coherent strategy for dealing with the others (including the scope of guarantees for depositors), was followed by widespread bank runs that led to calls for massive liquidity support from Bank Indonesia (IMF Occasional Paper 178, p. 38). While often regarded as a device to discipline debtors without paying attention to these features, with short-term 2

3 debt there must be some interaction between its effects and the characteristics of twin crises. In this paper, we analyze bank managers behavior in the situation where multiple bank runs may occur. In particular, we explore how the share of short-term debt affects this behavior in two cases, both with and without a currency crisis. We find that when a currency crisis does not arise, there is no relationship between banks. In this case, an increase in the share of short-term debt induces bank managers to behave in the best interests of creditors, and this is consistent with their well-known property. However, if a currency crisis does occur, the account is completely different. Here, under twin crises, bank runs occur interdependently among a number of banks. More specifically, when the domestic currency depreciates, if they delay, banks may not be repaid because of the reduction in the amount possible to be repaid in dollars. Therefore, foreign creditors withdraw their claims before maturity. Banks that cannot prepare dollars to respond to these withdrawals then exchange domestic currency for dollars with the monetary authority. Ultimately, if banks exchange too large an amount, the monetary authority exhausts the dollar reserves it holds, and the authority devalues the currency. Consequently, when creditors in one bank withdraw dollar-denominated claims early, the prospect of a domestic currency depreciation increases, and thus creditors in other banks in the same country may also withdraw their dollar claims while they still can. More formally, strategic complementarities exist between creditors in one bank and those in another bank. If the proportion of short- to long-term debt is large, more early withdrawal occurs, and therefore, the amount that banks exchange in domestic currency for dollars with the monetary authority is large. Suppose that early withdrawal occurs in one poor-performing bank. Then, foreign creditors in better-performing banks expect that the currency will depreciate and that they will not obtain repayment if they wait. As a result, bank runs also occur in better-performing banks: this is consistent with the empirical evidence. 1 Therefore, when the proportion of short-term debt is high, bank runs will take place because the early withdrawal of other banks affects even a well-managed bank through the exchange rate. That is, the low-performance bank stands in the way of the high-performance bank. Accordingly, the high-performance bank lose its incentive to make an effort. Formally, we show that this additional exchange rate effect weakens the disciplining effect of short-term debt. Moreover, when the currency devaluation is sufficiently large, an increase in short-term debt induces bank managers to act more against creditors interests. Much of the literature has showed that investors are disciplined by short-term 1 Arena (2008) showed that in Easr Asia and Latin America, systemic macroeconomic and liquidity shocks that triggered the crises destabilized not only weak banks but also strong banks. 3

4 debt (e.g., Berglof et al. 1994; Hart and Moore 1998; Jensen and Meckling 1976). Some recent studies have showed that short-term debt also provides a borrower incentive in emerging markets. For instance, Diamond and Rajan (2001) argue that short-term debt is the dominant form of debt financing in emerging markets because with long-term debt, even if the net profit value of a project is negative, creditors cannot liquidate the project and thus suffer a loss. In contrast, with shortterm debt, creditors can liquidate the project by discontinuing rollover. Therefore, the expected repayment of short-term debt is larger than that of long-term debt. Further, with competitive markets, the amount of the loan equals the expected amount of repayment. This is the reason why in an emerging market where borrowing demand is extremely high, debt is the dominant form of borrowing. In other work, Jeanne (2009) and Tirole (2002, 2003) showed that short-term debt can induce the government in an emerging market economy to implement policy respecting foreign creditors interests, which is difficult to do with contracts. These past contributions, however, do not include currency crises and bank runs. For the most part, our basic model economy is similar to that in Nakata (2010), who analyzes how the fraction of dollar to domestic debt influences multiple bank runs. However, in that model, the disciplining effect of short-term debt is not dealt with. To our knowledge, this paper is the first analysis explicitly dealt with twin crises and the disciplining effect of the short-term debt. In this situation, we showed that the disciplining effect suggested by these literature must be reconsidered. The remainder of the paper is as follows. Section 2 presents our model. Section 3 discusses how short-term debt affects a bank manager s behavior in an economy without a currency crisis. Section 4 explores the same relation when a currency crisis takes place. Section 5 concludes. 2 The model 2.1 The basic framework We consider a small open economy where a monetary authority is committed to pegging the exchange rate to the foreign currency. There are three dates indexed by 0, 1, 2. The economy has a banking sector comprising two large banks: Banks 1 and 2. Further, there are foreign creditors who are risk neutral. The exchange rate of the baht (the domestic currency) against the dollar (the foreign currency) is initially fixed at parity, and the authority uses foreign reserves to respond to demands to exchange baht for dollars at that rate. When this exchange is sufficiently large, the authority may abandon pegging at this rate 4

5 because of the depletion in dollar reserves and so devalues the fixed rate to e, where e < 1. 2 We assume that the authority devalues the exchange rate when it exhausts its foreign reserves to the level denoted by k > 0. Moreover, we denote the amount of reserves that the authority loses as L. Therefore, the authority abandons fixing the exchange rate at parity if and only if L L, where L is given by: k L = 0. (1) Eventually, the level of the exchange rate e is determined by the following function: e(l) = { 1 if L < L e if L L. (2) 2.2 The banks Each creditor holds claims in either Bank 1 or Bank 2 at Date 0, and then has to decide whether to demand his/her claim from the bank at Date 1 or wait until Date 2. Bank managers in each bank choose either to invest this money in productive technology or to use it for their private benefit. The productive technology generates for the creditors only the input level of output denominated in baht in all banks at Date 1, or R i (θ, I i ) baht in Bank i (i = 1, 2) at Date 2. 3 In contrast, the banks private benefit does not generate any return to the creditors at any date and only serves to increase the utility of the bank managers. The long-term output R i (θ, I i ) is increasing in θ; that is, banks obtain a larger output at Date 2 when the economy is good. We assume that the fundamentals are not publicly reported. Instead, each agent j obtains a noisy signal x j, where x j = θ + ϵ j, > 0 is a constant, and ϵ j are disturbance terms that are independently distributed according to smooth symmetric density g( ) with mean zero. We denote as G( ) the cumulative distribution function for g( ). We assume that there are increasing returns-to-scale on aggregate investment (or a liquidity constraint) in each bank. Therefore, R i (θ, I i ) is increasing in I i, where I i is the continued investment. Further, we assume 2 R < 0 and 2 R > 0. The continued I 2 I θ investment is defined as follows: I i η i N i, where N i is the number of creditors who withdraw at Date 1 from Bank i and η i is the amount of investment in the productive technology of Bank i at Date 0 (η i (0, 1)). 1 η i is the amount of use 2 Hellwig et al. (2006) make a similar assumption. 3 Goldstein (2005) made a somewhat more realistic assumption in that the bank can obtain part of its short-term return in dollars. For notational simplicity, however, we assume that banks do not have any dollar assets at Date 1. 5

6 for private benefit in Bank i. We describe the bank managers decision problem later. The long-term return is uncertain for all agents at Date 0. At Date 1, certain information about the future returns of Bank i becomes available to all agents. 4 The realized value of long-term returns differs between Bank 1 and Bank 2; that is, whether R 1 (θ, Ī) > R 2(θ, Ī) or R 2(θ, Ī) > R 1(θ, Ī) for all θ and Ī. Moreover, we assume that a continuum [0, 1] of creditors hold claims in Bank 1 and another continuum [0, 1] of creditors hold claims in Bank 2 in the situation where all creditors do not know which bank s long-term return is higher at Date 0. 5 Creditors hold claims in dollars. 6 More specifically, each creditor deposits one dollar in each bank in the form of either short- or long-term claims. Creditors who hold short-term claims (short-term creditors) in Bank i receive one dollar with early withdrawal (when they do not roll over the short-term debt) or er i dollars after maturity (when they roll over the debt). 7 That is, when short-term creditors wish to withdraw their money at Date 1, each bank only has to liquidate a portion of their investments to serve them. In addition, each bank must exchange baht output for dollars with the monetary authority and serve these creditors. If creditors withdraw their claims early, they obtain one dollar. If they wait until Date 2 and the peg is maintained, they receive R i dollars. If the peg is broken, however, they can obtain only er i dollars where e < 1. Therefore, foreign creditors consider the exchange rate as well as the fundamentals along with the proportion of creditors withdrawing early. On the other hand, creditors who hold long-term claims (long-term creditors) are resigned to waiting until Date 2. Therefore, these creditors for Bank i receive either R i dollars or er i dollars after maturity. We do not consider term premia as in Jeanne (2009), and the proportion of short- to long-term debt is exogenously given. The timing of events in the economy is as follows. Date 0 Creditors hold claims in either Bank 1 or 2. The long-term returns in Banks 1 and 2 are observed. Banks invest the money either in the productive technology or assign it to their 4 Allen and Gale (1998) made similar assumptions. 5 If we modify the setting so that one creditor holds claims in both Bank 1 and Bank 2, the main result does not change. What is important is that there are many creditors for both banks, and this invokes the noncooperative strategic actions we observe below. 6 Here, we assume that all creditors are foreign creditors. Nakata (2010) considers both domestic and foreign creditors and analyzes how the proportion of foreign creditors affects the interdependency between banks. 7 Following Goldstein (2005) and Takeda (2003), we assume that the peg is maintained at Date 0 and Date 1, so large early withdrawals by creditors may cause the banks to fail at Date2. 6

7 private benefit. Date 1 Signals of fundamentals are observed. Creditors observe the banks long-term returns. Short-term creditors decide whether they run or wait until maturity. The monetary authority decides whether to abandon the fixed exchange rate. Date 2 Long-term outcomes are realized. Following Goldstein (2005) and Morris and Shin (1998), we assume that uniform dominance regions exist. That is, when the true state of fundamentals lies above θ i, waiting until maturity is the dominant action for a short-term creditor in Bank i, no matter what he/she believes other creditors will do (we show that I i [0, 1] in equilibrium later). Conversely, when the true state of fundamentals lies below θ i, a short-term creditor in Bank i prefers to withdraw early, even if other creditors wait until maturity. More formally, we assume that θ i and θ i for i = 1, 2 exists such that: 1 > = Prob(θ = y x j )R i (y, 1)dy + Prob(θ θ i x j )R i (θ i, 1) θ i ( ) ( ) xj y θi x j g R i (y, 1)dy + G R i (θ i, 1), θ i 1 < Prob(θ θ i x j )R i ( θ i, 0)e + θi ( xj = G θ ) θi i R i ( θ i, 0)e + g Prob(θ = y x j )R i (y, 0)edy ( xj y ) R i (y, 0)edy. Here, Prob(Ω x j ) is the probability that Ω holds under the condition that agent j receives signal x j. 2.3 Short- and long-term debts Let δ denote the proportion of short-term creditors (the fraction of short-term debt) and 1 δ denote the proportion of long-term creditors (the fraction of longterm debt) in each bank. Moreover, we denote n i as the proportion of creditors who withdraw from Bank i at Date 1. Therefore, the total number of creditors who withdraw early from Bank i is N i = δ n i + (1 δ) 0 = δn i. We can also interpret δ as the degree of maturity mismatch. For instance, when δ = 1, all debt is demand deposit as in Diamond and Rajan (2001a) and Goldstein (2005). In this case, banks must liquidate the project before mature when early withdrawal 7

8 occurs. This corresponds to the case maturity mismatched. We assume that δ ranges from δ to δ, where δ (0, 1), δ (0, 1), and δ < δ < 2δ. We denote the aggregate proportion of short-term creditors who withdraw early as D (note that D = n 1 + n 2 ). Because the aggregate number of short-term creditors who do not rollover at Date 1 is δd and each bank must exchange baht output for dollars with the monetary authority for that amount, the authority s loss of reserves is L = δd. 8 Substituting L = δd into equations (1) and (2), we obtain the following: k δd = 0, (3) { 1 if D < D e(δd) = (4) e if D D. Put simply, the fixed exchange rate regime is broken if and only if D D. Moreover, the creditors long-term return in each bank can be denoted by e(δd)r i (θ, I i ) (i = 1, 2). If δ increases, D decreases from equation (3), and therefore e decreases from equation (4). In turn, the decrease in e lowers the foreign creditors long-term return. We can rewrite (3) and (4) as follows: k δ[n 1(n 2 ; δ) + n 2 ] = 0, (5) { 1 if n1 < n e(δ(n 1 + n 2 )) = 1(n 2 ; δ) e if n 1 n 1(n 2 ; δ). (6) That is, the currency peg collapses if and only if n 1 n 1(n 2 ; δ). If n 2 increases, n 1(n 2 ; δ) decreases from equation (5), and therefore e tends to decrease from equation (6) and the assumption e < 1. This in turn decreases the long-term return of foreign creditors in Bank 1: er 1. Similarly, an increase in n 1 decreases the long-term return of foreign creditors in Bank 2: er 2. These interactions, however, would only occur in the case where the currency peg at parity is prone to collapse. On the contrary, when the baht is sufficiently stable to maintain the peg, it would appear that the creditors behaviors in Bank 1 and Bank 2 are independent. We show this in the following section. 3 Where a currency crisis does not occur In this section, we assume that k > 2δ. This implies k > 2δ for all δ [δ, δ]. As a result, even if all creditors in both banks withdraw at Date 1, the pegging 8 Recall that banks must return one dollar to each creditor who withdraws early, and the exchange rate is parity fixed at Date 1. Therefore, the aggregate amount that all banks exchange baht output for dollars with the monetary authority is L δd dollars. 8

9 never collapses. This is because there is strategic behavior within each bank: the incentive of each creditor to withdraw his/her money early is higher when more creditors of the same bank withdraw early. This behavior strengthens when the proportion of short-term debt increases. This, in turn, affects the decision problem of banks: how much they invest in the productive technology at the cost of their private benefit. In this section, we explore this relation analytically. Suppose that all creditors in Bank i withdraw early if they observe a signal below x i and wait until Date 2 if they observe a signal above x i. Then, the threshold value x i is decided by the following equation for i = 1, 2: ( xi θ R i (θ, η i δg )) 1 g ( xi θ ) dθ = 1. (7) The left-hand side is the long-term return of the creditors in Bank i denominated in dollars (which is equivalent to baht), and the right-hand side is the payoff (one dollar) to the domestic creditors in Bank i when they withdraw early. Note that the exchange rate of the baht against the dollar is always one in this section 1 as we assume that the peg never collapses. On the left-hand side, g ( x i ) θ is the posterior density over θ under the condition on the signal x i. This is the proportion of creditors in Bank i who withdraw early. 9 Changing the variable of integration from θ to n i, we obtain the following equation for i = 1, 2 (note that G[(x i θ)/] = n i )): 1 0 R i (x i, η i δn i ) dn i = 1. (8) The left-hand side of equation (8) is monotonically increasing in x i for a given η i and δ. Moreover, the left-hand side of (8) is larger than one for a sufficiently large x i, while it is smaller than one for a sufficiently small x i. Therefore, for i = 1, 2, x i is uniquely solved for a given η i and δ. This threshold signal x i depends on η i. When the banks invest more in the productive asset, the long-term return of the creditors increases and, therefore, they are more likely to wait until maturity. Consequently, the threshold level decreases as the value of η i increases. Now, we see the decision problem of bank managers in each bank at Date 0. Bank managers in Bank i maximize their own benefit B i (1 η i ) at Date 2, where B i( ) > 0 and B i ( ) < 0 (1 η i is the amount of investment for private benefit). We also assume that B (1 δ) = 0 and B (0) =. Consequently, the equilibrium value of η i lies between δ and 1 and, therefore, I i [0, 1] holds. Banks cannot liquidate their private investment once they invest. In addition to pursuing the private benefit, bank managers wish to prevent bank runs as much as possible 9 Assuming a productive technology where banks can only invest at Date 0. Consequently, creditors in one bank cannot move their credit to another bank at Date 1, the so-called flight to quality. Nakata (2010) discusses an allowance for the flight to quality. 9

10 because they obtain higher estimates as the equilibrium threshold level of the creditors becomes lower. From equation (8), this is equivalent to the situation where bank managers obtain higher utility as he/she obtains a higher long-term return at Date 2 for a constant x i and n i : R i ( x, η i δ n). Consequently, the bank managers problem in Bank i (i = 1, 2) becomes the following: max η i B i (1 η i ) + R i ( x, η i δ n). (9) Note that we assume that the discount rate is 0 for simplicity. From the first-order condition, we obtain the following equation: R i ( x, η i δ n) I = B i(1 η i ). (10) Because both functions are strictly concave, the left-hand side is decreasing in η i and the right-hand side is increasing η i. That is, there is a trade-off between preventing bank runs and obtaining a private benefit. Here, suppose that the proportion of short-term debt, namely, the value of δ, increases. Then, the value of the left-hand side increases and therefore the equilibrium value of η i also increases. The increase in the proportion of short-term debt increases the prospect of early withdrawal and this decreases investment in the productive technology. This, in turn, increases the marginal revenue of the technology. Consequently, managers increase investment in the productive technology at a cost of decreasing the private benefit. 10 Proposition 1 Suppose that there is no currency crisis. In both Bank 1 and Bank 2, the increase in the proportion of the short-term debt increases the investment in the productive technology and decreases the investment in the bank manager s private benefit. Although the account is somewhat different, this result is consistent with that in Diamond and Rajan (2001), Jeanne (2009), and Tirole (2002, 2003): put simply, short-term debt provides an incentive for the borrower to implement creditorfriendly investment. 4 Where a currency crisis occurs We assume that k > δ and k < 2δ are satisfied. k > δ implies k > δ for all δ [δ, δ]. Therefore, even if all foreign creditors in either Bank 1 or Bank 2 withdraw at Date 1, pegging never collapses when none of the short-term creditors 10 This proposition holds whether R 1 (θ, Ī) > R 2(θ, Ī) or R 2(θ, Ī) > R 1(θ, Ī) for all θ and Ī. 10

11 in another bank withdraws early. Similarly, k < 2δ implies k < 2δ for all δ [δ, δ]. As a result, if all short-term creditors in both banks withdraw at Date 1, pegging necessarily collapses. Therefore, whether the peg is maintained or not depends on how many creditors withdraw early in both banks, as described in Subsection Strategic complementarities among creditors When creditors in Bank 1 (Bank 2) demand early withdrawal, Bank 1 (Bank 2) must exchange baht for dollars. This reduces the amount of government reserves and therefore increases the possibility that the currency peg fails and the baht depreciates. Because banks have a mismatch between f oreign liabilities and domestic technology, foreign creditors long-term return in Bank 2 (Bank 1) will be lower. As a result, the incentive for foreign creditors in Bank 1 (Bank 2) to withdraw their money at Date 1 is higher when more foreign creditors in Bank 2 (Bank 1) withdraw early. In this section, we explore this behavior analytically. To start with, we show that there are strategic complementarities between the creditors in Bank 1 and the creditors in Bank 2. In this situation, we show that the bank managers behavior differs from that described in the preceding section. We again solve for the threshold levels of the creditors. At this time, we must consider the exchange rate because it is no longer ensured to be parity. Similarly suppose, as in the previous section, that all creditors in Bank 1 withdraw early if they observe a signal below x 1 and wait until Date 2 if they observe a signal above x 1. In addition, suppose that creditors in Bank 1 believe that all creditors in Bank 2 will withdraw early if they observe a signal below x 2 and will wait until Date 2 if they observe a signal above x 2. Given x 2, the threshold value x 1 is then decided by the following equation: [ ( ( ) ( ))] ( ( )) ( ) x1 θ x2 θ x1 θ 1 e δ G + G R 1 θ, η 1 δg g x1 θ dθ = 1. (11) The left-hand side is the long-term return of creditors in Bank 1 denominated in dollars, and the right-hand side is the payoff (one dollar) to creditors in Bank 1 when they withdraw early. Changing the variable of integration from θ to n 1, we 11 In the case of k < δ, pegging at parity breaks when all of the creditors in one bank withdraw early, even if there is no bank run in another bank. Therefore, the interaction between the creditors in Banks 1 and 2, which we describe in this section, does not come about as in the preceding section. 11

12 obtain the following equation (note that G[(x 1 θ)/] = n 1 )) 12 : 1 [ ( ( e δ n 1 + G G 1 (n 1 ) + x ))] 2 x 1 R 1 (x 1, η 1 δn 1 ) dn 1 = 1. (12) 0 We obtain the threshold values for creditors in Bank 2 in a similar manner. The threshold value x 2 is decided by the following equation given x 13 1 : 1 [ ( ( e δ n 2 + G G 1 (n 2 ) + x ))] 1 x 2 R 2 (x 2, η 2 δn 2 ) dn 2 = 1. (13) 0 As shown in the Appendix, only a single pair of threshold equilibriums (ˆx 1, ˆx 2 ) exist that solve equations (12) and (13) given η 1, η 2, and δ. We next explore the strategic interaction between two groups of creditors. By analyzing equations (12) and (13), we can see that creditors have the following features: Lemma 1 ˆx 1 (ˆx 2 ) is increasing in ˆx 2 and ˆx 2 (ˆx 1 ) is increasing in ˆx 1. Namely, there are strategic complementarities between the creditors in Banks 1 and 2. That is, when creditors in Bank 1 believe that creditors in Bank 2 may withdraw early at a higher (lower) level of fundamentals, they run on Bank 1 at a higher (lower) level of fundamentals. Conversely, when creditors in Bank 2 believe that creditors in Bank 1 may withdraw early at a higher (lower) level of fundamentals, they run on Bank 2 at a higher (lower) level of fundamentals. When creditors in Bank 1 withdraw their money before maturity, the dollar reserve that the monetary authority holds falls because Bank 1 must exchange the proportion δ of baht output for dollars with the monetary authority. Therefore, the prospect of collapsing the fixed exchange rate and depreciating the baht becomes likelier. The payoff to creditors in Bank 2 (recall the promise that they would receive their payoff in dollars) when they wait until maturity may then become lower than the payoff when they withdraw early (one dollar). As a result, when creditors in Bank 2 believe that more creditors in Bank 1 will withdraw early, they withdraw early in more cases. We intuitively saw this in Subsection Bank managers behavior under a currency crisis In this section, we analyze the bank managers problem under a currency crisis. 12 The left-hand side of equation (12) is increasing in x 1. Moreover, the left-hand side of (12) is larger than one for a sufficiently large x 1 and smaller than one for a sufficiently small x 1. Therefore, x 1 is uniquely solved given x We can show that x 2 is uniquely solved given x 1 from (13) in a similar manner to Footnote 9. 12

13 From here on, we focus on the case where approaches zero. 14 We firstly focus on equations (12) and (13), and define the threshold values (x 1, x 2) that satisfy the following equations: e(δn 1 )R 1 (x 1, η 1 δn 1 ) dn 1 = 1, (14) e(δn 2 )R 2 (x 2, η 2 δn 2 ) dn 2 = 1. (15) That is, threshold x i characterizes the behavior of creditors in Bank i when they believe that none of the creditors in the other bank will withdraw early. From assumption k > δ, e(δn) = 1 holds for all δ [δ, δ], and N [0, 1]. Therefore, equations (14) and (15) turn out to be the following: R 1 (x 1, η 1 δn 1 ) dn 1 = 1, (16) R 2 (x 2, η 2 δn 2 ) dn 2 = 1. (17) Put simply, if the depositors in one bank believe that none of the creditors in the other bank will withdraw early, they also believe that the pegged exchange rate at parity will never collapse, and therefore there is no difference in the long-term return for foreign and domestic creditors. Consequently, x 1 and x 2 are unaffected by the exchange rate, as in the previous section. In contrast, we define the threshold values (x 1, x 2 ), where x i denotes the threshold level where creditors in Bank i believe that all creditors in the other bank withdraw early. More specifically, these threshold values satisfy the following equations: e [δ (n 1 + 1)] R 1 (x 1, η 1 δn 1 ) dn 1 = 1, (18) e [δ (1 + n 2 )] R 2 (x 2, η 2 δn 2 ) dn 2 = 1. (19) In Section 2, we assumed that the realized value of long-term returns differs between Bank 1 and Bank 2 and that this value is uncertain for all agents at Date 0. Here we assume that the ex post value of long-term returns in Bank 1 is higher than in Bank 2 such that er 1 (θ, δ N) > R 2 (θ, 1 N) for all θ [θ 1, θ 2 ] and N; that is, even if the managers in Bank 1 invest the minimum amount and those in 14 As in Corsetti et al. (2004) and Goldstein (2005), comparative statics of the (improper) prior probability of a bank run, which is difficult without approaching zero, can be reduced to the behavior of x 1, x 1, x 2, and x 2 in the later analysis making approach zero. See Section 4 in Corsetti et al. (2004) for details. 13

14 Bank 2 invest the maximum amount in the productive sector, the long-term return of Bank 1 is higher than that of Bank 2. Therefore, x 1 < x 2 and x 1 < x 2 hold for all η i [ δ, 1]. Moreover, because e(2δ) < 1 is satisfied from the assumption, and because of Lemma 1, x 1 < x 1 and x 2 < x 2 also hold for all δ [δ, δ] and η i [ δ, 1]. Moreover, x 1 < x 2 holds. To sum up, x 1 < x 1 < x 2 < x 2 is satisfied. Under this relation, the equilibrium becomes the following. Lemma 2 For a given δ [δ, δ] and η i [ δ, 1] (i = 1, 2), as approaches 0, the equilibrium ˆx 1 converges to x 1 and the equilibrium ˆx 2 converges to x 2. Bank runs occur only in Bank 2 but not in Bank 1 in the range of fundamental values from x 1 to x 2. We can compare threshold levels between no currency crisis and a currency crisis from equations (8), (14), and (15). Lemma 3 Compared with the case of no currency crisis, the threshold level of Bank 2 does not change but the threshold level of Bank 1 increases from x 1 to x 1. In currency crises, even a strong bank become vulnerable because of a weak bank through the exchange rate, which we can see in Subsection 2.3. This is a key feature of this section, which considerably affects the decision problem of the bank managers in Bank 1. Here, let us consider the decision problem of bank managers in each bank at Date 0 under a currency crisis. The bank managers problem in Bank 2 is the same in the no currency crisis case because equation (17) determines the equilibrium threshold level, which is similar to that in the previous section. However, the objective function of the bank managers in Bank 1 is different: the equilibrium threshold level is now solved using equation (18). Consequently, the bank managers problem in Bank 1 becomes the following: max η 1 B 1 (1 η 1 ) + e [δ (n 1 + 1)] R 1 ( x, η 1 δ n). (20) From the first-order condition, we obtain the following equation: e [δ (n 1 + 1)] R i( x, η i δ n) I = B i(1 η i ). (21) Similar to the previous section, an increase in the proportion of short-term debt raises the value of the left-hand side and, therefore, the equilibrium value of η 1 increases. However, there is another effect in this problem. The left-hand side depends on the exchange rate, which is no longer ensured to retain parity. If the proportion of short-term debt increases, more early withdrawal occurs. This 14

15 reduces the government s foreign reserves more. It results that the peg is more likely to be broken; that is, it becomes more possible for e to become lower than one. Therefore, in contrast to the first effect, this effect reduces the left-hand side and lowers the equilibrium value of η 1. Proposition 2 Suppose that a currency crisis occurs and that er 1 (θ, δ N) > R 2 (θ, 1 N) for all θ [θ 1, θ 2 ] and N [0, 1] is satisfied. We can see that in Bank 2 (a low profit bank), the increase in the proportion of short-term debt increases investment in the productive technology and decreases investment in the bank manager s private benefit. In contrast, in Bank 1 (a high profit bank), an increase in the proportion of short-term debt does not necessarily increase investment in the productive technology and decrease investment in the bank manager s private benefit. Bank 2 affects the profitability of Bank 1 through the exchange rate. Even if managers attempt to increase the long-term return as much as possible, they cannot prevent the baht devaluation because of the low return of Bank 2. Therefore, the long-term return in Bank 1 becomes lower in dollar terms compared with the case without a currency crisis. Corollary 1 Suppose that a massive devaluation occurs when the foreign reserve is considerably reduced. In this case, an increase in the proportion of short-term debt decreases investment in the productive technology and increases investment in the bank manager s private benefit in Bank 1. If the value of e is sufficiently low, the negative externality through the exchange rate becomes dominant and, therefore, an increase in the value of δ lowers the equilibrium value of η 1. Put differently, short-term debt does not discipline bank managers in Bank 1; on the contrary, it induces them to act against their creditors interests. 5 Conclusion This paper explores how short-term debt affects bank manager behavior in a framework where simultaneous multiple bank runs arise in two situations; that is, where a currency crisis does and does not take place. In the case of no currency crisis, an increase in the proportion of short- to long-term debt induces the bank manager to increase the return of creditors in all banks. In the case of a currency crisis, however, this effect is ambiguous because the profitability in a low-profit bank affects that of a high-profit bank in the same country through the 15

16 exchange rate. When a massive devaluation occurs, short-term debt then assists bank managers to decrease the return of creditors. Therefore, we must reconsider the positive effect of short-term debt as often discussed in the context of emerging market economies. 16

17 References [1] Arena, M., Bank failures and bank fundamentals: a comparative analysis of Latin America and East Asia during the nineties using bank-level data. Journal of Banking and Finance 32, [2] Berglof, E., von Thadden, E., Short-term versus long-term interests: capital structure with multiple investors. Quarterly Journal of Economics 109 (4), [3] Corsetti, G., Pesenti, P., Roubini, N., What caused the Asian currency and financial crisis? Japan and World Economies 11, [4] Corsetti, G., Dasgupta, A., Morris, S., Shin, H.S., Does one Soros make a difference? A theory of currency crises with large and small traders. Review of Economic Studies 71 (1), [5] Diamond, D., Rajan, R.G., Banks, short-term debt and financial crises: theory, policy implications and applications. Carnegie Rochester Conference Series on Public Policy 54, [6] Goldstein, I., Strategic complementarities and the twin crises. Economic Journal 115 (503), [7] Hart, O., Moore, J., Default and renegotiation: a dynamic model of debt. Quarterly Journal of Economics 113 (1), [8] Hellwig, C., Mukherji, A., Tsyvinski, A., Self-fulfilling currency crises: the role of interest rates. American Economic Review 96 (5), [9] Jeanne, O., Debt maturity and the international financial architecture. American Economic Review 99 (5), [10] Jensen, M., Meckling, W., Theory of the firm: managerial behavior, agency costs and ownership structure. Journal of Financial Economics 3 (4), [11] Kaminsky, G.L., Reinhart, C.M., The twin crises: the causes of banking and balance-of-payments problems. American Economic Review 89 (3), [12] Morris, S., Shin, H.S., Unique equilibrium in a model of self-fulfilling currency attacks. American Economic Review 88 (3),

18 [13] Nakata T., Interdependent bank runs under a collapsing fixed exchange rate regime. Journal of the Japanese and International Economies 24, [14] Takeda F., A twin crisis model with incomplete information. Journal of the Japanese and International Economies 18 (1), [15] Tirole, J., Financial crises, liquidity, and the international monetary system Princeton University Press. [16] Tirole, J., Inefficient foreign borrowing: a dual and common agency perspective. American Economic Review 93 (5),

19 A Appendix A.1 The unique existence of equilibrium (ˆx 1, ˆx 2 ) First, we prove that there exists one pair of equilibrium (ˆx 1, ˆx 2 ) that solves equations (12) and (13) in the text. Let us denote (12) as x 1 = χ 1 (x 2 ): x 1 as a function of x 2. Similarly, we denote (13) as x 2 = χ 2 (x 1 ). As shown in Goldstein (2005), we obtain χ 1(x 2 ) < 1 and χ 2(x 1 ) < 1 from (12) and (13). Therefore, the simultaneous equation x 1 = χ 1 (x 2 ) and x 2 = χ 2 (x 1 ) is uniquely solved as (ˆx 1, ˆx 2 ). Next, we show the broader uniqueness; that is, the above equilibrium is the only possible equilibrium in our model. Suppose by way of negation that an equilibrium exists other than ˆx 1. Furthermore, suppose foreign creditors in Bank 1 run on the bank with signals above ˆx 1, and denote the highest signal in the alternative equilibrium, at which they switch from running to waiting, as x H 1. Similarly, we denote the highest signal in the alternative equilibrium, at which creditors in Bank 2 switch from running to waiting, as x H 2. Because of the existence of upper dominance regions, x H 1 and x H 2 have upper bounds. x H 1 is characterized by the following equation: e ( δ ( n A 1 (θ) + n A 2 (θ) )) R 1 ( θ, η1 δn A 1 (θ) ) 1 g ( x H 1 θ ) dθ = 1, (A.1) where n A 1 (θ) and n A 2 (θ) stand for the proportion of creditors in Bank 1 and Bank 2 who withdraw at date 1. Because creditors do not ( run on) Bank 1 at signals above x H 1 (θ) in the alternative equilibrium, n A x H 1 (θ) G 1 θ must be satisfied. ( ) Similarly, n A x H 2 (θ) G 2 θ also have to be satisfied. Therefore: ( )) ( ) x e(x H 1, x H H 2 )R 1 (θ, η 1 δg 1 θ 1 x H g 1 θ dθ 1, (A.2) [ ( ( ) ( ))] where e(x H 1, x H x H 2 ) = e θ, δ G 1 θ x H + G 2 θ. This equation is equivalent to: 1 ( ) e(x H 1, x H 2 )R 1 x H 1 G 1 (n 1 ), η 1 δn 1 dn1 1, (A.3) 0 [ ( ( ))] where e(x H 1, x H 2 ) = e x H 1 G 1 (n 1 ), δ n 1 + G G 1 (n 1 ) + xh 2 xh 1. Let us compare this inequality with (12) in the text. Because x H 1 is larger than ˆx 1, x H 2 x H 1 > ˆx 2 ˆx 1 must hold for (A.3) to be consistent with (12). In a similar way, we can see that x H 1 x H 2 > ˆx 1 ˆx 2 must hold from (13). These conditions do not hold at the same time and are therefore a contradiction. Consequently, creditors in Bank 1 would not run at signals above ˆx 1. We can also show in a similar way that they would not run at signals below ˆx 1. Furthermore, we can also prove that creditors in Bank 2 would behave in a similar way based on ˆx 2. 19

20 A.2 Proof of Lemma 1 The function x 1 = χ 1 (x 2 ) defined Subsection A.1 is increasing in x 2 for all x 2 from (12) and, similarly, x 2 = χ 2 (x 1 ) is increasing in x 1 for all x 1 from (13). Therefore, the lemma is true. A.3 Proof of Lemma 2 We show that when x 1 < x 1 (δ) < x 2 < x 2 (δ) holds and approaches 0, ˆx 1 converge to x 1 (δ), and ˆx 2 converge to x 2 (δ) for a given δ [δ, δ] (following Goldstein (2005), the superscript stands for the change in the equilibrium threshold by the change of the scale of noise). When approaches 0, ˆx 1 could not be larger than x 1 (δ), and ˆx 2 could not be smaller than x 2 because of the continuity of ˆx 1 and ˆx 2 in. Thus, G ( ) G 1 (n 1 ) + x 2 x 1 converges to 1 as approaches 0. Similarly, G ( G 1 (n 2 ) + x 1 x 2 ) converges to 0 as approaches 0. Consequently, as approaches 0, x 2 converges to x 2 from Lemma 1. 20