Exchange Rates and Fundamentals: A Generalization

TLDR: In this article, the authors generalize the Engel and West hypothesis to the larger class of open economy dynamic stochastic general equilibrium (DSGE) models and show that all the predictions of the standard PVM carry over to the DSGE PVM.

Abstract: Working Paper 2008-16 June 2008 Abstract: 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 1. INTRODUCTION The search for satisfactory exchange rate models continues to be elusive. This paper studies a workhorse theory of currency market equilibrium determination, the present-value model (PVM) of exchange rates, in the spirit of Engel and West (2005). Starting with the PVM and using uncontroversial assumptions about fundamentals and the discount factor, Engel and West (EW) hypothesize that the PVM generates an approximate random walk in exchange rates if the PVM discount factor approaches one and fundamentals are I(1). An important implication of the EW hypothesis is that fundamentals have no power to forecast future exchange rates, even with the PVM dictating equilibrium in the currency market. EW support their hypothesis with a key theorem and empirical and simulation evidence. This paper complements Engel and West (2005) by generalizing their main hypothesis in two ways. First, the EW hypothesis is generalized using a canonical two-country monetary dynamic stochastic general equilibrium (DSGE) model. Its linearized uncovered interest parity (UIP) and money demand equations yield the DSGE-PVM that coincides with the standard PVM of the exchange rate. Second, we show the standard- and DSGE-PVMs make equivalent predictions for exchange rates. The predictions are summarized in five propositions: (1) the exchange rate and fundamental cointegrate [Campbell and Shiller (1987)], (2) the PVM yields an error correction model (ECM) for currency returns in which the lagged cointegrating relation is the only regressor, (3) the PVM predicts a limiting economy (Le., the PVM discount factor approaches one from below) in which the exchange rate is a martingale, (4) given fundamental growth depends only on the lagged cointegrating relation, the exchange rate and fundamental have a common trend-common cycle decomposition [Vahid and Engle (1993)], and (5) the EW hypothesis is also satisfied when the exchange rate and fundamental share a common feature and the PVM discount factor approaches one. A corollary to (5) is that the exchange rate is unpredictable when the PVM discount factor goes to one. We report evidence from vector autoregression (VARs) about the propositions using quarterly floating rate Canadian-, Japanese-, and U.K.-U.S. samples. The VAR evidence rejects cointegration and reveals substantial serial correlation for the exchange rate and the fundamental. There is also evidence that a common feature exists between the Canadian dollar-, Yen-, and Pound-U.S. dollar exchange rates and the relevant fundamentals. …