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This paper provides a framework for simultaneous multiple bank runs in a country experiencing a currency crisis. The correlation of bank runs increases as the proportion of debts from foreign creditors (indexed to the dollar) to domestic creditors (indexed to the domestic currency) increases. Moreover, when the share of dollar debt is sufficiently high, this interlinkage is perfect; that is, runs occur in all banks or not at all. Consequently, a situation exists where even a solvent bank cannot borrow in the interbank market. These findings imply that as the domestic banking sector becomes increasingly dependent on dollar debt, there is a heightened requirement for dollar reserves and a lender-of-last-resort facility.

At the end of the last century, it was commonly held that widespread bank runs accompanied currency crises. For example, Kaminsky and Reinhart (1999) provide empirical evidence of financial crises in several countries since 1980 including both banking and currency crises, commonly referred to as twin crises. Moreover, bank runs, especially in East Asia and Latin America, took the form of simultaneous runs on many banks at this time. For instance, the International Monetary Fund (IMF) reported on Indonesia from 1997 through 1998 as follows: “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.) Arena (2008) showed that in East Asia and Latin America, systemic macroeconomic and liquidity shocks that triggered the crises destabilized not only weak banks but also strong banks. To prevent widespread bank failure, large amounts of public funds were then injected into the banking sectors in these regions.1 When discussing these crises, a common criticism is that local banks borrowed from foreign creditors not in their domestic currency but in dollars. Moreover, each bank lent this money to domestic firms and repaid in the domestic currency. Therefore, when each country’s currency drastically depreciated against the dollar, many banks went into default because the amount repayable in dollars had significantly decreased (a currency mismatch problem). The purpose of this paper is to construct a model where bank runs occur interdependently among a number of banks under twin crises and to analyze how the share of dollar debt in domestic debt affects this interdependency. More specifically, when the domestic currency depreciates, banks may not be repaid if they delay because of the reduction in the possible amount repayable in dollars. Therefore, foreign creditors withdraw their claims before maturity. Each bank that cannot prepare dollars for responding to these withdrawals then exchanges domestic currency for dollars with the monetary authority. If these banks exchange too large an amount, the dollar reserves that the monetary authority holds are exhausted; the fixed exchange rate system then collapses, and the domestic currency depreciates. Consequently, when creditors in one bank withdraw claims denominated in dollars 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. As shown in Table 1, a distinctive feature of the banking sector in Asian and Latin American countries that experienced currency crises is that the share of large bank deposits is high. In this situation, creditors are more concerned with the actions of creditors in other banks than would be the case if deposits were dispersed across several banks. Namely, they decide strategically whether to withdraw early or to wait in anticipation of the currency depreciation. We describe the actions of depositors here as a noncooperative game. Moreover, we show that strategic complementarities exist between creditors in one bank and those in another bank. That is, if creditors in one bank withdraw early, those with claims on another bank also withdraw early.As this strategic behavior is caused by the depletion of dollar reserves because of the withdrawal of dollar claims, the degree of strategic complementariness becomes stronger as the ratio of foreign creditors (who hold dollar claims) to domestic creditors (who have claims denominated in the domestic currency) increases. Consequently, we derive the following property: a bank run occurs only in the low-performance bank whose long-term return is low if the proportion of foreign creditors is small. Conversely, if the proportion of foreign creditors is large, early withdrawal of dollar claims in poorly performing banks makes the prospect of retaining the currency peg weaken because the amount that banks exchange domestic currency for dollars with the monetary authority is so large. Accordingly, 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. Therefore, when the proportion of foreign creditors is sufficiently large, bank runs occur in all banks or not at all. One common argument is that the government does not need to intervene in a banking sector that can hedge risk through interbank borrowing and lending. For instance, Goodfriend and King (1988) argue that when financial markets are efficient, solvent banks can insure perfectly against the possibility of a bank run via a sophisticated interbank market where banks can finance their assets with interbank funds. According to our analysis, however, the interbank market cannot perform this function well when the proportion of foreign creditors is large. Therefore, the injection of public funds into banks that are technically solvent but that do not hold sufficient funds to respond to withdrawal before maturity becomes essential. Moreover, dollar reserves are called for as the proportion of foreign creditors increases because the domestic currency tends to depreciate and because bank runs occur in all banks without these reserves. The technique described in this paper relies on Carlsson and van Damme, 1993 and Goldstein, 2005. The proof of the unique existence of the equilibrium and the manner of classifying the equilibrium in our analysis depend on these studies, particularly Goldstein (2005). However, the model presented in this paper differs from Goldstein (2005) in three ways. First, while Goldstein (2005) analyzed how twin crises arise by dealing with the strategic complementarities between creditors who have claims on a bank and speculators who attack the currency, we focus on the strategic complementarities between creditors in one bank and those in another bank. Furthermore, we show how bank runs spread under twin crises. Second, there are four types of players in our model and only two types in Goldstein (2005). Therefore, our analysis is more complex. Finally, unlike Goldstein (2005) we introduce claims denominated in both dollars and the domestic currency. We then examine how the ratio of dollar claims to total claims affects the interlinkages between bank runs. Moreover, we explore several implications that we cannot derive from Goldstein’s (2005) analysis. These include the failure of the interbank market and the necessity of a lender-of-last-resort when opening the domestic banking sector to the international market. Many studies show how banking crises in one region or institution can spread elsewhere. For instance, Chen (1999) showed that the adverse information that precipitates a bank run in one bank implies adverse information in another. Allen and Gale, 2000 and Dasgupta, 2004 provide another instance where banks link to each other through interbank insurance, and they show that bank runs can arise through this channel. To the best of our knowledge, however, none of the literature has analyzed bank runs arising through the channel of a collapsing fixed exchange rate followed by depreciation of the domestic currency. The extant literature has explained various currency crisis phenomena by using currency mismatch models. For example, Burnside et al., 2004 and Schneider and Tornell, 2004 showed that currency mismatch is one of the causes that precipitates the boom–bust cycle often observed in countries experiencing currency crises. Choi and Cook (2004) also analyzed how the currency mismatch affects monetary policy. However, these contributions do not deal with widespread bank runs. As far as the author is aware, this study is also the first to explore how a currency mismatch affects the interlinkages between bank runs. The paper is structured as follows. Section 2 outlines the basic model, and Section 3 presents the strategic complementarities among creditors in different banks. Section 4 examines how the proportion of dollar debt affects the interlinkages between bank runs. Section 5 discusses policies we can derive from the model. Section 6 concludes.

In this paper, we developed a model in which multiple bank runs occur at the same time in a country where the pegged exchange rate breaks down. We showed that a bank run in one bank makes the domestic currency depreciate, and therefore claims denominated by dollars in another bank in the same country are also withdrawn early. This strategic complementarity becomes stronger as the proportion of foreign creditors in the banking system becomes larger. Moreover, when the number of foreign creditors exceeds a certain level, there is a perfect correlation; that is, a bank run occurs in all banks or no bank. Consequently, the interbank market does not function well, and therefore a LLR facility and dollar reserves become more essential as the proportion of foreign creditors increases. Moreover, this serves as an additional reference to recent discussion on how much the government should hold in dollar reserves. Our model implies that if the domestic financial system mainly consists of banks, as the domestic banking sector becomes more dependent on dollar debt, more dollar reserves are required for execution of the LLR. Our model does not include the flight to quality; that is, creditors move from one bank to another at Date 1, perceiving the second as being less likely to fail. In fact, this behavior has been seen in the Asian and Latin American crises (see, for instance, Berg, 1999 and Domac et al., 1999). If foreign creditors simply move their credit to another bank in the same country whose return is higher, the dollar reserves do not fall, and the fixed exchange rate never collapses. Therefore, we must reexamine our results. Nevertheless, actual flight to quality is never sufficiently extensive to stabilize the currency. One possible explanation is that creditors must take the risk of reinvesting the withdrawn credit in the same country because a speculative attack coincides with the bank run, as in Goldstein (2005). We omit this in our model for simplicity. Another explanation is that foreign creditors may not have enough information on other banks in the same developing country and therefore hesitate to reinvest in these banks. However, more elaborate analysis would make these topics of discussion clearer. The technique in our model largely depends on the global game originating in Carlsson and van Damme, 1993 and Morris and Shin, 1998. A key feature is the assumption that an agent does not have common knowledge about the fundamentals, bringing with it the result that the equilibrium is unique. However, recent studies show that the equilibrium is not necessarily unique, even in a situation lacking common knowledge. For instance, Hellwig et al., 2006 and Angeletos and Werning, 2006 have modified the global game framework to allow endogenously determined prices. Likewise, Angeletos (2006) introduced the endogenous information generated by policy interventions into the framework. Moreover, Angeletos et al. (2007) extended the conventional model of a global game, entailing a simultaneous move game, to a sequential move game. In these models, they assure multiplicity under certain conditions. If by introducing these modifications in our analysis these multiple equilibria exist, it would be harder to examine under what conditions widespread bank runs are more likely to occur. However, this extension is worthy of attention and an interesting topic for future research.