Domestic bank runs and speculative attacks on foreign currencies

Journal of International Money and Finance 17 Ž1998. 331]338

Domestic bank runs and speculative attacks on foreign currencies V. Miller U,1 Uni¨ ersite´ du Quebec des sciences ´ economiques, Case postale 8888, ´ a` Montreal, ´ Departement ´ succursale A, Montreal, Canada H3C 3P8 ´ Quebec, ´

Abstract The paper extends the international-transmission-of-financial-crisis literature by illustrating how a domestic bank run can cause a speculative attack on foreign currencies. The idea is that when domestic banks invest abroad, a domestic bank run will give way to a repatriation of foreign capital. If the repatriation causes a depletion of the foreign central bank’s foreign exchange reserves, then the foreign currency will be devalued. As such a devaluation will render domestic banks insolvent, in the rational equilibrium, domestic bank runs will Ž1. cause a speculative attack on the foreign currency and Ž2. be self-justified. Q 1998 Elsevier Science B.V. All rights reserved. JEL classifications: F3, G2 Keywords: Currency crisis; Bank runs

The literature on balance-of-payments crises and banking crises is by now quite extensive.2 To date these two crises have been primarily treated as separate phenomena.3 However, there exist several events, both historical and present day, U

e-mail: [email protected] I thank an anonymous referee for helpful comments. 2 See Agenor ´ et al. Ž1992. and Blackburn and Sola Ž1993. for reviews of the speculative attack literature and Goldberg Ž1994. and Obstfeld Ž1994. for more recent contributions. Diamond and Dybvig Ž1983., Waldo Ž1985., Chari and Jagannatthan Ž1988., Garber and Grilli Ž1989. and Calomiris and Gorton Ž1991. provide theoretical studies and Williamson Ž1989., Hasan and Dwyer Ž1994., and Canova Ž1994. provide empirical investigations of banking crises. 3 Notable exceptions are Kaminsky and Reinhart Ž1995., Miller Ž1996a,b., Rojas-Suarez and Weisbrod Ž1995. and Velasco Ž1987.. 1

0261-5606r98r$19.00 Q 1998 Elsevier Science B.V. All rights reserved. PII: S 0 2 6 1 - 5 6 0 6 Ž 9 8 . 0 0 0 0 6 - 0

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which suggest that a banking crisis may influence the severity andror magnitude of a currency crisis and vice versa. Consider what happened in the United States just before the turn of the century. Contemporary sentiment along with a large drop in Treasury gold reserves indicated that investors were speculating on the US dollar from 1890 to 1896. In 1893, there was an internal drain Ži.e. bank runs. that culminated in a cash payments restriction. As currency and gold sold at a premium to deposits during the restriction, and as it was not expected to last for very long, the restriction encouraged the importation of gold and halted gold exports. The cash payments restriction therefore interrupted the speculative attack on the US dollar.4 The events that transpired in the United States in 1893 indicate that an internal drain may frustrate an external drain Ži.e. speculative selling attack on a currency.. Miller Ž1996a. shows that if deposit money is used to speculate on the currency and banks are loaned up, then a speculative attack on a currency Ži.e. external drain. will actually cause a crisis for the domestic banking sector.5 The 1994]1995 experience of Mexico, on the other hand, suggests that a banking crisis may contribute to a speculative attack on the national currency.6 Here we consider how an internal drain may provoke a speculative selling attack on a foreign currency when the home country is a net investor in the foreign country with banks being the most important investors. The idea here might be well illustrated by reference to past events in the Japanese financial system. In Japan, the biggest capital exporters are banks and institutional investors. When there has been weakness in the Japanese financial system Žas reflected by falling asset values., these two groups of investors have found it optimal to liquidate their foreign holdings in order to shore up domestic balance sheets and meet liquidity needs. Such repatriation of capital puts pressure on the yen to appreciate and foreign currencies to depreciate.7 While the past weakness of the Japanese financial system has stemmed from a strong yen8 and weak real estate market, one can imagine that a generalized run on Japanese banks could necessitate a repatriation of capital so great that the currencies of those countries to which Japan is an important net investor, depreciate.9 If those depreciations are anticipated, then a Japanese banking crisis could provoke selling attacks on foreign currencies. The paper illustrates that a run on the domestic banking system will cause a 4 Miller Ž1996b. illustrates that a speculative attack was unprofitable during the short period that gold flowed into the United States. 5 Noyes Ž1909. argues that the internal drain of 1893 was caused by the external drain at the time. 6 In 1994, Mexican policymakers increased liquidity to circumvent a banking crisis. However, as the increase in liquidity was inconsistent with the fixed parity, it contributed to the speculative attack on the peso at the end of the year. 7 A similar situation occurred in 1890 when Baring Brothers, a British investment bank, suspended payments and caused a repatriation of British capital which put pressure on the US dollar to fall. 8 A strong yen prevents companies from exporting and reduces the value of financial institutions’ overseas portfolios. 9 The bank runs in Japan in the late summer of 1995 were restricted to a small number of banks and were not generalized.

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repatriation of capital from the foreign country when domestic banks are net investors in the foreign country. If the repatriation is expected to cause a devaluation of the foreign currency, then the bank runs will cause a speculative selling attack on the foreign currency. Moreover, if the foreign currency is devalued as a consequence, then the bank runs will be self-justified in the sense that banks will become insolvent in the face of a run. The paper proceeds as follows: in Sec. 1 we illustrate the no-run equilibrium. Then in Sec. 2 we discuss under what conditions a generalized bank run will Ž1. cause a speculative attack on the foreign currency and Ž2. be self-justifying. Sec. 3 sums up.

1. The model and its no run equilibrium The model of bank runs described below is inspired by Garber and Grilli Ž1989.. Like their model, it is a representative agent model with three periods and a competitive banking system. However, unlike their model, currency-risk rather than liquidity-risk is the focus. Thus, while in Garber and Grilli Ž1989. bank solvency problems occur when the forced early liquidation of long-term securities causes a drop in asset values, here solvency problems arise when the forced repatriation of foreign investments causes a devaluation of the foreign currency and thus a drop in the domestic currency value of assets denominated in foreign currencies.10 Here the home country is large while the foreign one is small, the foreign central bank pegs its currency to the domestic one, and expectations are rational. We first solve for the equilibrium assuming no-bank runs and the continuance of the fixed exchange rate regime. In the domestic economy, there are an infinite number of identical individuals that each lives for three periods: period zero denotes the past, period one the present and period two, the future. In period 0, the endowment is given and initial allocations are chosen to maximize utility. The representative agent’s utility function is given by U Ž C1 . q b U Ž C2 . , 0 - b - 1,

Ž1.

where C1 and C2 denote consumption in periods one and two, respectively. From the definition of the utility function, we see that consumption occurs only in periods one and two. There are two ways to transfer wealth from one period to another. They are storage with no depreciation and investment in a project which yields a one-period return of r. Because investments are lumpy, agents must pool their resources to invest in these projects and banks act as the pooling institutions. Individuals can deposit their wealth in domestic or foreign banks. The periodspecific budget constraints of the representative domestic agent are given by: 10

Garber and Grilli Ž1989. studied the case in which there were assets of different maturities. As they implicitly assumed no currency risk, the currency of denomination was unimportant.

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334

A 0 s S0 q D 0 q D 0)

in period 0,

Ž2.

S0 q Ž 1 q i . D 0 q Ž 1 q i 0) q ˙ e1 . D 0) s S1 q D 1 q D 1) q C1 S1 q Ž 1 q i . D 1 q Ž 1 q i1) q ˙ e2 . D 1) s C2

in period 2,

in period 1,

Ž3. Ž4.

where A0 Sj Dj DUj Cj i iUj

˙e j

s s s s s s s

period zero endowment, storage from period j to period j q 1, deposits held in domestic banks from period j to period j q 1, deposits held in foreign banks from period j to period j q 1, consumption in period j, one-period return on deposits held in domestic banks, one-period return on deposits held in foreign banks from period j to j q 1, and s rate of depreciation of domestic currency from period j y 1 to j.

As the banking system is competitive, i s r. Perfect capital mobility and perfect foresight assure that i s iU0 q ˙ e1 and i s iU1 q˙ e2 . The equality of the expected returns on foreign and domestic deposits implies that there is an indeterminacy of the division of deposits between domestic and foreign banks. This indeterminacy is resolved by assuming that for identical expected returns, individuals choose deposits in their home country.11 As foreign and domestic residents have the same preferences, in equilibrium foreign depositors will not invest in domestic banks. The maximization problem therefore simplifies to max U Ž C1 . q b U Ž C2 . , 0 - b - 1 s.t. A 0 G S0 q D 0 ,

l0

S0 q Ž 1 q r . D 0 G S1 q D 1 q C1 , S1 q Ž 1 q r . D 1 G C2 ,

l2

l1 Ž5.

where l j is the Lagrange multiplier corresponding to the period j budget constraint. Non-negativity constraints are also added for S0 , D 0 , S1 , and D 1 which are assigned multipliers lS 0 , l D 0 , l S1 and l D1 , respectively. The first-order conditions for this problem are thus: C1 : C2 : S0 : D0 : S1: D 1: 11

U9Ž C1 . s l1 , b U9Ž C2 . s l2 , S0 Ž l1 y l0 . s 0, D 0 Ž l1Ž1 q r . y l0 . s 0, S1Ž l2 y l1 . s 0, D 1Ž l2 Ž1 q r . y l1 . s 0,

The perfect capital mobility assumption stems from a large competitive banking sector that is risk neutral.

V. Miller r Journal of International Money and Finance 17 (1998) 331]338

l0 : l1: l2 : lS 0 : lS1: lD 0 : l D1:

335

l0 Ž A 0 y S0 y D 0 . s 0, l1Ž S0 q Ž1 q r . D 0 y S1 y D 1 y C1 . s 0, l2 Ž S1 q Ž1 q r . D 1 y C2 . s 0, lS 0 S0 s 0, lS1 S1 s 0, l D 0 D 0 s 0, l D1 D 1 s 0.

S0 and S1 will both be zero since these investments are dominated by D 0 and D 1 , respectively.12 Therefore, in equilibrium we have D 0 s A 0 , Ž1 q r . D 0 s D 1 q C1 and Ž1 q r . D 1 s C2 . To complete the set-up, banks’ solvency constraints must be specified. As the banking system is competitive, banks take foreign and domestic interest rates as given and plan their investments so that expected inflows and outflows are equal Ži.e. profits are zero.. It is assumed that each period depositors withdraw only that portion of deposits that is needed to finance consumption. Withdrawals in period one are therefore Ž1 q r . D 0 y D 1 and those in period two are Ž1 q r . D 1. Thus, banks choose investments in period zero so that the following constraints are satisfied. Ž 1 q r . I0 q Ž 1 q r 0) q ˙ e1 . I0) s wŽ 1 q r . D 0 y D 1 x q I1 q I1) Ž 1 q r . I1 q Ž 1 q r 1) q ˙ e2 . I1) s Ž 1 q r . D 1

in period 2.

in period 1,

Ž6. Ž7.

I j and I jU are investments from period j to period j q 1 in domestic and foreign projects, respectively, and r Uj is the one-period return on the foreign investment from period j to j q 1. Assuming that in the absence of capital mobility, the rate of return on foreign investments would exceed the domestic return, some positive amount of domestic resources Ži.e. bank assets . must be invested in the foreign country. However, if banks only invested abroad, the foreign expected return would be less than the domestic one. Thus, I jU is that which ensures that the returns on foreign and domestic investment projects are equal for period j Ži.e. r s r Uj q ˙ e jq1 . and I j is positive.13 Finally, as banks will invest I1U in the foreign country from period one to period two, banks will repatriate Ž1 q r 0U q ˙ e1 . I0U y I1U of their capital from abroad in U U period one and Ž1 q r 1 q ˙ e2 . I1 in period two. Assuming that Ž1 q r . I0U y I1U is positive, these two amounts, denoted by R1 and R 2 , respectively, will be positive. An example of the no-run equilibrium with a constant relative risk aversion utility function is provided in the Appendix.

12

As D obviously dominates S, one might be tempted to drop S from the model. However, as depositors will redeem S for D, the existence of S is necessary. 13 For simplicity it is assumed that there is a unique I jU that will make ˙ e jq1 q r U j s r.

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V. Miller r Journal of International Money and Finance 17 (1998) 331]338

2. Bank runs and speculative attacks Let Fj denote reserves of domestic currency in the foreign central bank in period j net of net capital inflows for the period.14 The foreign central bank will continue pegging its currency to the domestic one as long as its reserves exceed Fm . If reserves fall below Fm , then the foreign central bank will abandon the currency peg and allow its exchange rate to float. It is assumed that F1 y R1 G Fm and F2 y R 2 G Fm . Thus, in the no-run equilibrium, ˙ e1 s ˙ e2 s 0. Given the initial allocations chosen in period zero based on the no-run scenario, if F1 y Ž1 q r . I0U - Fm , then a generalized bank run which results from a sudden belief that all other depositors will withdraw the entire amount in their accounts will Ž1. cause a speculative attack on the foreign central bank; and Ž2. be self-justified. Proposition 1. If F1 y (1 q r0U )I0U - Fm , then a bank run will generate a speculati¨ e attack on the foreign currency. If a bank run occurs in period 1, then depositors will try to withdraw all of their deposits during that period. To pay-off depositors, banks will have to repatriate all of their foreign investments which is Ž1 q r 0U . I0U if currency values remain unchanged. However, if F1 y Ž1 q r 0U . I0U - Fm , then the foreign currency will be devalued before banks are able to repatriate all of their investments. As a foreign currency devaluation will reduce the domestic currency value of banks’ foreign investments Ži.e. ˙ e 1 - 0., banks will liquidate all of their foreign investments and convert them into domestic currency at the foreign central bank as quickly as possible. In other words, there will be an attack on the foreign central bank’s foreign exchange reserves which is staged by domestic banks. Proposition 2. If F1 y (1 q r0U )I0U - Fm , then a bank run will be self-justifying in the sense that it will make banks insol¨ ent. Suppose that after initial allocations are chosen, depositors stage a bank run during period 1 and so banks are forced to repatriate all of their foreign investments. To finance the external drain without a devaluation, reserves at the foreign central bank must fall by Ž1 q r 0U . I0U . Thus, if the foreign central bank’s reserves are sufficient Ži.e. F1 y Ž1 q r 0U . I0U ) Fm ., then the fixed exchange rate regime will continue uninterrupted. However, if F1 y Ž1 q r 0U . I0U - Fm , then the foreign currency will be devalued when reserves fall to Fm . As the period 1 bank solvency constraint is Ž 1 q r . I0 q Ž 1 q r 0) q ˙ e1 . I0) s Ž 1 q r . D 0

Ž8.

and as I0U and r 0U are set under the assumption that ˙ e1 is zero, if ˙ e1 is negative, as 14

Fj equals Fjy1 plus the current account balance for period j and the capital account balance for period j y 1.

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it will be when the foreign currency is devalued, then banks will be insolvent. Thus, if F1 y Ž1 q r 0U . I0U - Fm , then a bank run will be self-justifying. 3. Conclusion In spite of an extensive literature on internal- Ži.e. banking crises. and externaldrains Ži.e. currency crises., little has been said about how one type of drain may influence the other. Yet there are several episodes, both in history and present day, that suggest that these two types of crises may be related. The present paper investigated one such potential link. It was shown that if domestic banks are important exporters of capital, then a domestic internal drain can give rise to an external drain abroad. In addition to deepening our understanding of how crises may be transmitted across financial sectors Ži.e. the banking sector to the foreign exchange market., the paper illustrated how crises may be transmitted internationally. The paper has thus joined together elements of the literatures on bank runs, speculative currency attacks and the international-transmission-of-financial-crises. An important point to be taken from the study is that creditors Ždebtors. should consider the size and stability of potential borrowers Žlenders. when deciding whether or not to lend Žborrow.. It may be risky for banks in large countries to invest in small ones when the small countries’ foreign exchange reserves are thin. Alternatively, it may be dangerous for small countries to accept the investments of banks in larger ones when those banking systems are vulnerable to attack. Appendix 1: Example of no-run equilibrium with ˙ e1 s ˙ e 2 s 0: constant relative risk aversion utility function. Suppose that UŽ C j . s C j1y arŽ1 y a .. The first order conditions can then be summarized as15 C1 : C2 : D0 : D 1: l0 : l1: l2 :

a Cy s l1 , 1 a b Cy s l2 , 2 Ž1 q r . s l 0rl1 , Ž1 q r . s l1rl2 , A0 s D0 , Ž1 q r . D 0 s D 1 q C1 , Ž1 q r . D 1 s C2 .

Using these conditions, we have D 1 s Ž1 q r . A 0rw1rŽŽ1 q r .1y ab .x1r a q 14 , 15

The conditions for the multipliers are not explicitly provided but incorporated into the other expressions.

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338

C1 C2 I0 I1

s s s s

Ž1 q r . A 0rwŽ1 q r .1y ab .x1r a q 14 , Ž1 q r . 2A 0rw1rŽŽ1 q r .1y ab .x1r a q 14 , A 0 y I0U , Ž1 q r . A 0rw1rŽŽ1 q r .1y ab .x1r a q 14 y I1U ,

where I0U and I1U ensure that r s r 0U s r 1U . As expected, I0 and I1 are inversely related to I0U and I1U , respectively. In addition D 1 , C2 and I1 are all positively related to r while the effect of an increase in r on C1 is ambiguous and depends on the magnitudes of other parameters Ži.e. the income and substitution effects of a change in r .. If for example, b s 1, a s 0.5 and r s 0.05, equilibrium allocations are D 1 s 0.538 A 0 , C1 s 0.512 A 0 , and C2 s 0.565 A 0 . References Agenor, P., Jagdeep, S.B., Flood, R.P., 1992. Speculative attacks and models of balance-of-payments ´ crises. Staff Pap. 39, 357]394. Blackburn, K., Sola, M., 1993. Speculative currency attacks and balance of payments crises. J. Econ. Surveys 7, 119]144. Calomiris, C., Gorton, G., 1991. The origin of banking panics: models, facts and bank regulation. In: Hubbard, G. ŽEd.., Financial Markets and Financial Crises. Chicago University Press for NBER, Chicago, pp. 110]157. Canova, F., 1994. Were financial crises predictable? J. Money, Credit, Banking 26, 102]124. Chari, V.V., Jagannatthan, R., 1988. Banking panics, information, and rational expectations equilibrium. J. Finance 43, 749]760. Diamond, D.W., Dybvig, P.H., 1983. Bank runs, deposit insurance, and liquidity. J. Political Econ. 91, 401]419. Garber, P.M., Grilli, V.U., 1989. Bank runs in open economies and the international transmission of panics. J. Int. Econ. 27, 165]175. Goldberg, L., 1994. Predicting exchange rate crises: Mexico revisited. J. Int. Econ. 36, 413]430. Hasan, I., Dwyer, G.P., 1994. Bank runs in the free banking period. J. Money, Credit, Banking 26, 271]288. Kaminsky, G.L., Reinhart, C.M., 1995. The twin crises: the causes of banking and balance-of-payments problems. IMF mimeo. Miller, V., 1996a. Speculative currency attacks with endogenously induced commercial bank crises. J. Int. Money Finance 15, 383]403. Miller, V., 1996b. Exchange rate crises with domestic bank runs: evidence from the 1890s. J. Int. Money Finance 15, 637]656. Noyes, A.D., 1909. Forty Years of American Finance. Putnam’s Sons, New York. Obstfeld, M., 1994. The logic of currency crises. NBER working paper no. 4640. Rojas-Suarez, L., Weisbrod, S., 1995. Financial market fragilities in Latin America: the 1980s and 1990s. IMF Occasional Paper, no. 132. Velasco, A., 1987. Financial and balance of payments crises. J. Develop. Econ. 27, 263]283. Waldo, D.G., 1985. Bank runs, the deposit-currency ratio and the interest rate. J. Monet. Econ. 15, 269]278. Williamson, S., 1989. Bank failures, financial restrictions, and aggregate fluctuations: Canada and United States. Federal Reserve Bank of Minneapolis Quarterly Review, 20]40.