Chapter 11

Balance of Payments Crises

In chapter 10 we argued that there is a presumption that any Þxed exchange rate regime must eventually collapse–a presumption that the data supports. Britain and the U.S. were forced o of the gold standard during WWI and the Great Depression. More recent collapses occurred in the face of crushing speculative attacks on central bank reserves. Some well-known foreign exchange crises include the breakdown of the 1946—1971 IMF system of Þxed but adjustable exchange rates, Mexico and Argentina during the 1970s and early 1980s, the European Monetary System in 1992, Mexico in 1994, and the Asian Crisis of 1997. Evidently, no Þxed exchange rate regime has ever truly been Þxed.

This chapter covers models of the causes and the timing of currency crises. We begin with what Flood and Marion [57] call Þrst generation models. This class of models, developed to explain balance of payments crises experienced by developing countries during the 1970s and 1980s. These crises were often preceded by unsustainably large government Þscal deÞcits, Þnanced by excessive domestic credit creation that eventually exhausted the central bank’s foreign exchange reserves. Consequently, Þrst-generation models emphasize macroeconomic mismanagement as the primary cause of the crisis. They suggest that the size of a country’s Þnancial liabilities (the government’s Þscal deÞcit, short term debt and the current account deÞcit) relative to its short run ability to pay (foreign exchange reserves) and/or a sustained real appreciation from domestic price level inßation should signal an increasing likelihood of a crisis.

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Clearly this policy is inconsistent with the long-run maintenance of the Þxed exchange rate since the government will eventually run out of foreign exchange reserves.

Non-attack exhaustion of reserves. If reserves are permitted to decline at the rate in (11.6) without interruption, it is straightforward to determine the time tN at which they will be exhausted. Reserves at any time 0 < t < tN are the initial level of reserves minus reserves lost between 0 and t

Since reserves are exhausted at tN , set r(tN ) = 0 = r(0)−γµ/(1−γ)tN . Solving for tN gives

Time of attack. The time-path for reserves described above is not your typical balance of payments crises. Central banks usually do not have the luxury of watching their reserves smoothly decline to zero. Instead, Þxed exchange rates usually end with a balance-of-payments crisis in which speculators mount an attack and instantaneously acquire the remaining reserves of the central bank.

Economic agents know that the exchange rate must ßoat at tN . They anticipate that the exchange rate will make a discrete jump at the time of abandonment. To avoid realizing losses on domestic currency assets, agents attempt to convert the soon-to-be over-valued domestic currency into foreign currency at tA < tN . This sudden rush into long positions in the foreign currency will cause an immediate exhaustion of available reserves. Call tA the time of attack.

To solve for tA, let s˜(t) be the shadow-value of the exchange rate. It is the hypothetical value of the exchange rate given that the central bank has run out of reserves.1 Market participants will attack if s¯ <

1The home currency is ‘overvalued’ if s¯ < s˜(t). A proÞtable speculative strategy

Money

Money

Figure 11.1: Time-path of monetary aggregates under the Þx and its collapse.

s˜(t). They will not attack if s¯ > s˜. But if s¯ < s˜(t), the attack will result in a discrete jump in the exchange rate of s˜(t) − s¯. The jump presents an opportunity to proÞts of unlimited size which is a violation of uncovered interest parity. We rule out such proÞts in equilibrium.

Thus, the time of attack can be determined by Þnding t = tA such that s˜(tA) = s¯. First obtain for s˜(t) by the method of undetermined coe cients. Since the ‘fundamentals’ are comprised only of m(t) conjecture the solution s˜(t) = a0 + a1m(t). Taking time-derivatives of the guess solution yields sú(t) = a1mú (t) = a1γµ, where the second equality follows from mú (t) = γdú(t) = γµ. Substitute the guess solution into the basic di erential equation (11.5), and equate coe cients on the constant and m(t), to get a0 = αγµ and a1 = 1. You now have

would be to borrow the home currency at an interest rate i(t), use the borrowed funds to buy the foreign currency from the central bank at s¯. After the Þx collapses, sell the foreign currency at s˜(t), repay the loans, and pocket a nice proÞt.

When reserves are exhausted, r(t) = 0, and the money supply becomes

Setting s˜(tA) = s¯ = m(0) = γd(0) + (1 − γ)r(0) and solving for the time of attack gives

Figure 11.1 illustrates the time-path of money and its components when there is an attack. One of the key features of the model is that episodes of large asset market volatility, namely the attack, does not coincide with big news or corresponding large events. The attack comes suddenly but is the rational response of speculators to the accumulated e ects of domestic credit creation that is inconsistent with the Þxed exchange rate in the long run.

One dissatisfying feature of the deterministic model is that the attack is perfectly predictable. Another feature is that there is no transfer of wealth. In actual crises, the attacks are largely unpredictable and typically result in sizable transfers of wealth from the central bank (with costs ultimately borne by taxpayers) to speculators.

A stochastic Þrst-generation model.

Let’s now extend the Flood and Garber model to a stochastic environment. We will not be able to solve for the date of attack but we can model the conditional probability of an attack. In discrete time,

where vt is drawn from the exponential distribution.2. Also, assume that the domestic credit process has an upward drift µ > 1/λ. At time t, agents attack the central bank if s˜t ≥ s¯, where s˜ is the shadow exchange rate.

Let the publicly available information set be It and let pt be the probability of an attack at t + 1 conditional on It. Then,

where θt ≡ (1/γ)¯s − (1 − α)µ − dt + (1/λ). The rational exchange rate forecast error is

and is systematic if pt > 0.

2A random variable X has the exponential distribution if for x ≥ 0, f(x) = λe−λx. The mean of the distribution is E(X) = 1/λ.

Thus there will be a peso problem as long as the Þx is in e ect. By (11.17), we know how pt behaves. Now let’s characterize Et(˜st+1) and the forecast errors. First note that

Et(vt+1) is computed conditional on a collapse next period which will occur if vt+1 > θt. To Þnd the probability density function of v conditional on a collapse, normalize the density of v such that the probability that vt+1 > θt is 1 by solving for the normalizing constant φ in

(222) 1 = φ Rθ∞t λe−λudu. This yields φ = eλθt . It follows that the probability density conditional on a collapse next period is

Now substitute (11.20) into (11.19) and simplify to obtain

Substituting (11.21) into (11.18) you get the systematic but rational forecast errors predicted by the model