Understanding Financial Crises

UNDERSTANDING FINANCIAL CRISES

Section 4: Currency Crises (Part 1)

March 4, 2002

Franklin Allen

NEW YORK UNIVERSITY

Stern School of Business

Course: B40.3328

( Website: http://finance.wharton.upenn.edu/~allenf/ )

Spring Semester 2002

1. Introduction

During the period 1945-1971

·  Banking crises were virtually eliminated.

·  Currency crises did occur when government economic policies were inconsistent with fixed exchange rates.

Both before and after 1945-1971, banking crises have been common. Both types of crisis often occur together.

Kaminsky and Reinhart (1999) have investigated the relationship between currency crises and banking crises, which they term “twin crises”

·  In the 1970’s when financial systems were highly regulated currency crises were not accompanied by banking crises

·  After the financial liberalizations that occurred in the 1980’s currency crises and banking crises have become intertwined

·  The usual sequence is that banking sector problems are followed by a currency crisis and this further exacerbates the banking crisis

Kaminsky and Reinhart find that the twin crises are related to weak economic fundamentals. Crises when fundamentals are sound are rare.

Section 2 considers models of twin crises.

·  Given Kaminsky and Reinhart’s finding that twin crises tend to occur when fundamentals are weak it would seem that the fundamental based or business cycle view has some applicability here.

Section 2 therefore starts with a fundamental based analysis, or in the terminology of the previous section, a business cycle view of banking crises and currency crises that extends the banking crisis model of Allen and Gale (1998).

·  It develops a version of the model from Allen and Gale (2000) with an international bond market and considers the relationship between banking and currency crises

·  Initially a closed economy is considered as a benchmark and international finance is incorporated subsequently

There are also examples of twin crises where it is difficult to identify changes in fundamentals. The model of Chang and Velasco (2000) also develops a model of twin crises but this is based on a multiple equilibrium analysis.

Section 3 develops models that were developed to explain pure currency crises of the type that were observed in the period 1945-1971 and subsequently where government policy is inconsistent with a fixed exchange rate.

There are two generations of currency crisis model:

First generation:

Designed to explain currency crises such as Mexico 1973-82, e.g. Krugman (1979)

Shows how a fixed exchange rate plus expansionary pre-crisis fundamentals leads to a currency crisis

Second generation:

Designed to show how speculative attacks such as those in Europe in the early 1990’s can occur, e.g. Obstfeld (1996)

Shows how a conditional government policy can lead to multiple equilibria – one without a speculative attack and one with a speculative attack

Morris and Shin (1998) show how a lack of common knowledge can lead to uniqueness of equilibrium. As in Section 3, Hellwig (2001)’s analysis suggests that this only works part of the time.
2. Models of Twin Crises

2.1 Optimal Risk Sharing

Three dates t = 0, 1, 2

Single consumption good at each date

t = 0 1 2

| | |

Safe asset: 1 1 1

(storage)

Risky asset: x rh(x)

The random return r has a cumulative density function F(r) and density function f(r) with support [r0, r1] where 0 £ r0 < r1 < ¥.

h(x) is a decreasing returns to scale production function (h’>0; h’’<0)

Leading economic Observed at date 1:

indicator: perfect signal of r

(usually non-contractible)

Consumers:

Ex ante identical Non-contractible

(measure 2) type discovered:

Early Late

(measure 1) (measure 1)

consume c1 consume c2

Type is non-observable to outsiders so late consumers can always mimic early consumers

This implies there is a “missing market” since liquidity shocks cannot be insured

Individuals can invest in the safe asset so that late consumers can withdraw at date 1 and consume at date 2

Utility function:

U(c1,c2) = u(c1) + u(c2) with u’>0; u’’<0

Initial assumption as benchmark: r can be contracted upon

Each consumer’s initial date 0 endowment of consumption goods is 1 so the aggregate endowment is 2

x is holding of risky asset

y “ “ “ safe “

Optimal contract is c1(r), c2(r)

Optimal risk sharing problem:

Result 1: Characterization of optimal contract (assuming interior solution x, y > 0):

The optimal x and y are such that:

Implementing the incentive-efficient allocation:

·  Equity markets cannot implement the first best allocation because of missing market for insurance against liquidity shocks

·  Banks can potentially overcome the problem of the missing market

2.3 Banking

Contracts are in real terms and cannot be contingent on r

In the absence of a run

t = 0 1 2

| | |

Each consumer Early consumers Late consumers

deposits 1 and withdraw d1 withdraw

bank invests in

portfolio (x, y)

The problem comes when r is so low that the bank cannot afford to pay its depositors the promised amount. In particular, if late consumers think they will receive less than early consumers’d1 there will be a run at date 1 and the bank will go bankrupt.

Bankruptcy rules:

·  All assets must be liquidated and the proceeds distributed pro rata to claimants.

Liquidation proceeds:

·  When risky asset is liquidated at date 1 the proceeds are rh(x)

·  There are no liquidation costs for the safe asset or the risky asset at date 2

 is sufficiently small that it is never worthwhile for the planner to liquidate the risky asset at date 1

Free entry into the banking industry and a continuum of banks with measure 1 implies banks offer contracts that maximize depositors’ ex ante expected utility

Since there are no liquidation costs at date 2 the bank will set sufficiently high that the consumers withdrawing then receive everything that is left over

Let r* be the critical value of r such that a run occurs:

or

Representative bank’s optimization

In addition to the direct costs of liquidation there is a distortion since the bank reduces its investment in the risky asset

Result 2: When deposit contracts are specified in real terms, the costly liquidation associated with a banking system leads to an allocation that yields depositors a lower ex ante expected utility than in the first-best allocation.

2.3.1 Optimal Monetary Policy

Suppose deposit contracts promise a fixed nominal return and there is a central bank

·  The central bank can ensure banks can meet their commitments when the leading economic indicator shows that r will be low by setting the price level high and making the output from the storage technology valuable in nominal terms

·  This ensures the deposits of the early consumers can be paid and the bank will have enough assets to make it worthwhile for late consumers not to withdraw

Result 3: If the central bank chooses the appropriate price level and banks use nominal contracts, there are no banking crises and the first-best allocation can be implemented as an equilibrium.

2.4 International Finance

Initially suppose there is a short-term international bond market – a long-term market is considered later

t = 0 1 2

| | |

International 1 r r2

bond market

To ensure an interior solution: E[r]h’(0) > r2

Country is small so bond market is risk neutral

Now y represents investment in the international bond market, i.e., it is a foreign currency investment

Individuals have access to the international bond market just as they had access to the storage technology previously

2.4.1 Optimal Risk Sharing

Suppose r can be contracted on and let I(r) be the transfer from the international market. The planner’s problem is:

Solution is such that

·  Full insurance is provided so early and late consumers bear no risk and receive the expected returns from the bank’s portfolio

·  The allocation between early and late consumers depends on the form of the utility function and involves if the incentive constraint binds and otherwise

·  Production efficiency: E[r]h’(x) = r2

In practice such fully state contingent contracts are not possible. We consider what happens when there is an international debt market. Two cases are considered

·  Debt is denominated in domestic currency

·  Debt is denominated in foreign currency

For ease of exposition we focus below on the case where the incentive constraint binds.
2.4.2 Domestic Currency Debt

Suppose that a short-term international bond market denominated in domestic currency exists at dates 0 and 1.

·  In the date 0 market uncertainty has not been resolved and the bond issue price reflects this.

·  At date 1 uncertainty has been resolved so we can simply write everything in present value terms using r as the discount rate.

0 1 2

| | |

Borrow qB Repay B

Borrow L/r Repay L

Date 0 budget constraint: x + y £ 2 + qB

No arbitrage condition: p1(r) = rp2(r) º p(r)

Date 1 budget constraint:

Depositors have access to the international bond market so instead of the incentive constraint becomes

Substituting the budget constraints and the incentive constraint becomes

If r is large enough that this constraint is satisfied the bank is solvent and there is no need to liquidate the assets at date 1 but if it is not then the bank must liquidate and

In the closed economy the central bank sets the price level so that crises and the associated costly liquidation were avoided. In the open economy the counterpart is that the central bank sets the exchange rate 1/p(r) so that there is no banking crisis.

To see how equilibrium is analyzed consider the following situation and remember that we are focussing on the case where the incentive constraint binds.

·  All banks choose D, , x and y.

·  The central bank sets the exchange rate

and there are no banking crises.

Can a bank improve its depositors’ welfare by changing its choice from D, , x and y? Suppose that in addition to and y it adopts the following strategy (work in foreign currency):

0  1

Issue domestic currency bond: +q -1/p(r)

Invest in foreign currency assets: -q rq

Net payoff in foreign currency: rq – 1/p(r)

Since the bond is fairly priced to reflect exchange rate risk the expected payoff to this strategy is zero.

·  The strategy effectively transfers resources from high return states to low return states for late consumers which allows depositors’ welfare to be improved

The fact that each bank would like to borrow more than other banks indicates existence of equilibrium may be problematical. We therefore analyze a “pseudo-equilibrium” with a constraint on borrowing. As

·  As each bank borrows more and invests it in safe international bonds its portfolio becomes dominated by these assets. Domestic investors “own” a smaller proportion of the portfolio and bear less risk and foreign lenders “own” a larger proportion of the portfolio and bear more. Because the portfolio is becoming larger the risk of the domestic assets becomes relatively small and the exchange rate can fluctuate less.

Result 4: In the limit as all risk is eliminated for depositors and the allocation is optimal.

Comment: The form of the equilibrium is consistent with the observation that foreign exchange transactions and international financial flows are so large.

So far we have focussed on short-term debt but it turns out introducing long-term debt makes little difference.

Result 5: Because uncertainty is resolved at date 1 and short-term debt can be rolled over there is no difference between short and long-term debt except the cost. When the yield curve is flat or upward sloping, short-term debt is strictly preferred to long-term debt.

2.5 Foreign Currency Debt

·  When foreign debt is denominated in terms of domestic currency there is a temptation for governments to inflate and expropriate the foreign lenders.

·  For developed countries with sophisticated political institutions this will not be an issue.

·  For emerging economies this possibility may be quite likely in which case an “inflation premium” will be charged. This may make borrowing in domestic currency expensive.

·  The inflation premium can be avoided by denominating the international debt in foreign currency rather than domestic currency.

·  However, if the foreign debt is denominated in foreign currency the benefits that a central bank and international bond market can bring are reduced.

·  The central bank may no longer be able to prevent financial crises and inefficient liquidation of assets

·  It may not be possible to share risk with the international bond market

2.5.1 The Dollarized Economy

·  Deposit contracts and foreign debt in foreign currency (i.e. real) terms.

·  In the event that r is low and commitments to depositors and foreign lenders cannot be met, there is bankruptcy and costly liquidation. As in Section 3 there is equal priority for all claimants.

Result 6: The optimal policy for the representative bank is to borrow an infinite amount in the international bond market and invest the proceeds in the international bond market. This eliminates risk for depositors when there is bankruptcy so that early consumers always obtain the same consumption level.