Exchange rates have raised the ire of economists for more than twenty years. The problem is that few, if any, exchange rate models are known to systematically beat a naive random walk in out-of-sample forecasts. Engel and West (2005) show that these failures can be explained by the standard present value model (PVM) because it predicts random walk exchange rate dynamics if the discount factor approaches one and fundamentals have a unit root. This paper generalizes the Engel and West hypothesis to the larger class of open economy dynamic stochastic general equilibrium (DSGE) models. The Engel and West hypothesis is shown to hold for a canonical open economy DSGE model. We show that all the predictions of the standard PVM carry over to the DSGE PVM. The DSGE PVM also yields unobserved components (UC) models that we estimate using Bayesian methods and a quarterly Canadian-U.S. sample. Bayesian model evaluation reveals that the data support a UC model that calibrates the discount factor to one, implying the Canadian dollar–U.S. dollar exchange rate is a random walk dominated by permanent cross-country monetary and productivity shocks.
JEL classification: E31, E37, F41
Key words: exchange rates, present value model and fundamentals, random walk, DSGE model, unobserved components model, Bayesian model comparison
The authors thank Toni Braun, Fabio Canova, Menzie Chinn, Frank Diebold, John Geweke, Fumio Hayashi, Sharon Kozicki, Adrian Pagan, Juan F. Rubio-Ramírez, Tom Sargent, Pedro Silos, Ellis Tallman, Noah Williams, Farshid Vahid, Kenji Wada, Ken West, Tao Zha, and the Federal Reserve Bank of Atlanta macro lunch study group for useful comments. They also thank seminar participants at the National Bureau of Economics Research's 2006 Summer Institute Working Group on Forecasting and Empirical Methods in Macroeconomics and Finance, the 2007 Norges Bank Workshop "Prediction and Monetary Policy in the Presence of Model Uncertainty," the 2007 Bank of Canada-European Central Bank Exchange Rate Modeling Workshop, the 2007 Reserve Bank of Australia research workshop "Monetary Policy in Open Economies," and individuals at the universities of Ohio State, Houston, Tokyo, and Washington for useful comments. The views expressed here are the authors' and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors' responsibility.
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