نوسانات نرخ ارز واقعی درون زا در بهینه سازی یک مدل اقتصاد باز

This paper constructs a simple intertemporal model of a small open economy inhabited by forward looking agents, in which endogenous fluctuations in the real exchange rate can arise in equilibrium, i.e. fluctuations that are not linked to movements in economic fundamentals. The key condition for the main results is the assumption that the Marshall–Lerner condition does not hold (i.e. that the country's exports and imports are inelastic to its real exchange rate). It is shown that, given that the Marshall–Lerner condition fails, there exist periodic equilibria and/or stationary sunspot equilibria in the neighborhood of the stationary state.

In international macroeconomics, perhaps the most striking features of the data are the large, persistent fluctuations in nominal and real exchange rates. The large volatility of these rates has stimulated the development of various versions of the so-called exchange rate overshooting theory pioneered by Dornbusch (1976), who developed a model in which a monetary expansion induces an immediate depreciation of domestic money in excess of its long-run equilibrium value, i.e. an overshooting of the exchange rate due to an exogenous shock. Subsequent studies (e.g. Calvo and Rodriguez, 1977, Liviatan, 1981, Frenkel and Rodriquez, 1982 and Chen et al., 1989), almost without exception, also attributed large fluctuations in the real exchange rate to exogenous shocks and regarded the wide variability of the real exchange rate as purely a transitory process by which asset holders restore portfolio balance in the new steady state. In this class of models in which a unique equilibrium path tending toward the steady state is ensured, no persistent fluctuations in the real exchange rate could occur in a stationary economy which does not experience any exogenous shock to its economic fundamentals. Fluctuations in real exchange rates are therefore ascribed to fluctuations in underlying fundamental economic variables. Meese and Rogoff (1983) first challenged the explanatory power of existing ‘exogenous’ models of exchange rate determination by showing their inferior out-of-sample forecasting performance relative to a simple random walk model. Many empirical studies since then have seemed to end with the conclusion that the real exchange rate also follows a random walk. However, a failure of structural models to outperform a random walk model does not necessarily mean that the exchange rate follows a random walk. In fact, recently a BDS test for exchange rate changes has actually rejected the random walk hypothesis and indicates that exchange rates contain substantial nonlinearity (Hsieh, 1989 and Brock et al., 1991). One plausible explanation of the nonlinear dependence is that exchange rate fluctuations are endogenous to an important degree. Over the past decade there has been a revival of interest in endogenous models of economic fluctuations, in which fluctuations could persist even in the absence of exogenous shocks to the economy.1 Following this line of research, the present paper investigates the stability of real exchange rate dynamics in the context of an endogenous cycle model. The Brock (1975) model is modified and extended to a fully-employed small, open economy under flexible exchange rates, in which residents who optimize with perfect foresight consume both domestic goods and imported goods. Currency substitution does not exist in the economy and national money is used solely for purchases of goods and assets. The non-monetary assets in the economy are the fixed stock of domestic equities and international bonds denominated in foreign currency. These two different types of assets are assumed to be imperfect substitutes. In the analysis which follows, it is assumed that the utility function of the agent is separable in bond balances and consumption goods. It is shown that even such a simple model can produce cyclical dynamic paths for the real exchange rate. The condition for such cyclical equilibria to occur is that the Marshall–Lerner condition is not satisfied in the short run. When the Marshall–Lerner condition does not hold, a real exchange rate depreciation worsens the balance of trade, which has to be accompanied, in equilibrium, by an increase in capital inflow or a reduction in capital outflow, which, in turn, requires a fall in the expected rate of real depreciation of the domestic currency. Thus, the possibility of monotonic movements and dynamic saddle paths is excluded and cyclical fluctuations in the real exchange rate can arise. As the condition that the import and export demands are inelastic in the short run is well established empirically,2 the result we obtain in this paper may explain the short-run fluctuations in real exchange rates.

Frankel and Meese (1987) and several other econometric studies suggest that actual exchange rate movements are largely not attributable to variations in macroeconomic variables (fundamentals). An endogenous, deterministic model of exchange rate dynamics such as the present one could, in principle, give a plausible explanation to this empirical finding. This paper has shown that even a simple, perfect-foresight model of a small open economy with a finite degree of asset substitutability may generate cyclical dynamic paths for the real exchange rate, when the Marshall–Lerner condition is not satisfied. The crucial point here is that, with a negative trade-balance elasticity, a higher-than equilibrium real exchange rate induces a negative trade balance, which calls for a smaller real exchange rate change in the next period. The possibility of monotonic movements of the real exchange rate is therefore excluded and cyclical fluctuations emerge. The story of real-exchange-rate endogenous fluctuations presented in this paper distinguishes itself from existing models of exchange rate dynamics, which have assumed the fulfillment of the Marshall–Lerner condition and have a unique rational expectations equilibrium. Since the fact that the sum of short-run demand elasticities for imports and exports is less than unity is empirically well-established, our model may be interpreted as explaining short-run fluctuations in the real exchange rate as an endogenous process. The assumption that the Marshall–Lerner condition does not hold is crucial for generating the complex dynamics of the real exchange rate in our model. Assuming that this condition does not hold is only justified if our model is viewed as a model of high frequency exchange rate movements, as empirically net exports do not respond much to exchange rate movements in the very short run. However, for most industrialized countries, the Marshall–Lerner condition does hold for adjustment periods beyond the very short run (six months). See, for example, Krugman and Obstfeld (1997, p. 485). To go beyond this short-term time frame, we will probably have to construct an open-economy endogenous growth model by incorporating physical capital accumulation, which produces differences between long-run and short-run responses of net exports to real exchange rate changes. Endogenous fluctuations in real exchange rates might occur due to specific properties of production functions rather than to the failure of the Marshall–Lerner condition.