Making Exchange Rates Sparkle: Restricting Its Present-Value Model with Common Trends and Common Cycles

Abstract Exchange rates have raised the ire of economists for more than 20 years. A problem is that there appears to be no exchange rate model that systematically beats a naive random walk in out of sample forecasts. Economists also find it irksome that theoretical models are unable to explain short-, medium-, and long-run exchange rate movements. Engel and West (2005) show that these failures can be explained by the present value model (PVM) because it predicts the exchange rate is a random walk if currency traders are highly interest sensitive and fundamentals have a unit root. This paper generalizes Engel and West (2005). We find that the PVM imposes common trend and common cycle restrictions on the exchange rate and its I(1) fundamental. As the interest sensitivity of money demand grows large, the common cycle forces the exchange rate to approximate a martingale. A PVM of the exchange rates is also constructed from a dynamic stochastic general equilibrium (DSGE) open economy model. The DSGE-PVM predicts that the exchange rate is dominated by permanent monetary and productivity shocks, as the world real interest rate becomes small. Thus, our results complement and extend Engel and West (2005) to a larger class of models, while presenting a new challenge to future research.