Exercise 1 Consider a small, open economy inhabited by a large number of individuals who live for an infinite number of periods and who can perfectly forecast the future. In this economy there is only one good, tradable at no cost, such that its domestic price is determined by the Law of One Price, PðtÞ 5 SðtÞPF, where PðtÞ is the domestic price of the good and PF is the foreign price of the good, which we will assume is equal to 1. Time is continuous and the economy is endowed with a constant and exogenous flow of the consumption good. There is perfect mobility of capital in the sense that agents can lend or borrow at the international interest rate of i . 0, which we assume as constant. The real money supply is defined as mðtÞ 5 MðtÞ

PðtÞ , where MðtÞ is the nominal money supply. This economy finances an exogenous fiscal deficit, BOX 9.7 CONTAGION IN LATIN AMERICA Do Latin America countries suffer from contagion? Forbes and Rigobon (2001) investigate contagion in the region that is not caused by real connections between economies. They compare the propagation of shocks in normal periods with propagation in crisis periods. If there is contagion, the propagation of shocks in crisis periods should be greater. The authors did not find evidence that the transmission diverges over time. They conclude that there are quite strong ties between economies, albeit, they are equal in both normal and crisis periods. Notwithstanding the important role played by trade channels and changes in relative prices, transmission by financial panic, and other factors connected to multiple equilibria, does not appear to be significant.

Latin America presents episodes of lending booms followed by currency crises. Comparing the Latin American experience with the rest of the world, Gourinchas and Landerretche (2001)

observed that, while in the rest of the world lending booms, in general, do not lead to currency crises, in Latin America they do. The authors conjecture that the most probable cause of the crises is the combined financial liberalization effect combined with a deficiency in its regulation and supervision. The results obtained indicate that an economic instrument that limits the taking of loans to avoid lending booms in the region could be beneficial.

Chapter 9 • Currency Crises 257 denoted by d . 0, by issuing money. The rate of growth of the nominal money supply is defined by μðtÞ  M_ ðtÞ

MðtÞ

, and the money supply is given by MðtÞ 5 PðtÞd 1 SðtÞRðtÞ;

where Rt represents the level of international reserves.

The demand for money is given by LðiðtÞÞ 5 λ

1 1 iðtÞ

;

where iðtÞ is the nominal interest rate and λ . 0 is a constant. Inflation is defined as the percentage change of price: πðtÞ  P_ðtÞ

PðtÞ

. The relation between the nominal and real interest rates is given by the Fisher relation, iðtÞ 5 rðtÞ 1 πðtÞ.

a. Show that the rate of growth of the real stock of money is equal to the difference between the rate of growth of money supply and inflation.

b. Assume that the government of this country decides to fix the nominal exchange rate at level S, i.e., SðtÞ 5 S. Show that, if Rð0Þ is sufficiently large, it is possible to temporarily maintain this exchange rate. Also show that, while the nominal exchange rate SðtÞ

remains fixed, the money supply will be constant. Calculate the real money supply.

c. What happens with the international reserves while the nominal exchange rate remains constant? Based on the fiscal policy adopted by the government, explain why the fixed exchange rate regime is not sustainable.

d. Assume that, when the fixed exchange rate regime ends, the international reserves will be null, i.e., RðtÞ 5 0. Show that after the end of the regime there is equilibrium with constant inflation and a constant real money supply. Compute inflation and the real money supply in this equilibrium.

e. Considering that the fixed exchange rate regime is unsustainable, calculate the period T in which the regime is abandoned. Show that in period T the trajectory of price levels remains continuous, however, the real demand for money decreases abruptly. What happens with the level of international reserves in period T? What is the economic intuition for the result?

f. Present illustrative graphs containing the trajectory of the stock of international reserves, the nominal money supply and the nominal exchange rate, both before and after period T. Explain each of these graphs.