## 1. INTRODUCTION

Testing the unbiased forward exchange rate (UFER) hypothesis, that is the hypothesis that the forward foreign exchange rate is an unbiased predictor of the corresponding spot exchange rate, has attracted a considerable amount of interest in the literature. The results concerning its empirical validity have however been rather mixed. Engel (1996), for example, surveyed studies which assumed rational expectations and attempted to attribute the forward rate bias to a foreign exchange risk premium. His main conclusion was that standard general equilibrium models are unsuccessful in explaining the magnitude of the risk premium and the empirical failure of the unbiasedness hypothesis.

The aim of the present paper is to offer a possible explanation for the rejection of the UFER hypothesis that is often reported in the literature. In particular, we exploit an implication of the consumption capital asset pricing model (CAPM) under structural changes in consumption to reconcile this empirical evidence with general equilibrium models. The motivation for this approach is the empirical finding that consumption dynamics can be characterized successfully by models that allow for structural changes that are driven by a Markov process (see, e.g., Cecchetti *et al.*, 1990; Hall *et al.*, 1997). When combined with the hypothesis of time-varying risk premium, such dynamic behaviour for consumption implies that the risk premium itself is subject to Markov changes in regime.

Allowing for the presence of a Markov switching risk premium leads to a model for the spot rate and the forward premium whose parameters switch stochastically between regimes. A difficulty with such a model, however, is that the right-hand side variables are correlated with the disturbances within each regime. It is, therefore, a plausible conjecture that the standard pseudo-maximum likelihood (S-PML) estimator for Markov switching models (see, e.g., Hamilton, 1994, chapter 22), which ignores such correlation, is likely be inconsistent. This inconsistency of the S-PML estimator, combined with the often poor quality of conventional asymptotic inference procedures even in situations where the estimator is consistent (cf. Psaradakis and Sola, 1998), increases considerably the probability of misleading inferences being drawn from the fitted model.

As argued in Psaradakis *et al.* (2002), the difficulties associated with within-regime orthogonality failures in Markov switching models can be overcome by using instrumental variables (IV), much in the same way as in single-regime models. Using this approach, we consider the problem of testing the UFER hypothesis using monthly data for the sterling/dollar exchange rate. It is demonstrated that the UFER hypothesis cannot be rejected in the context of a model that allows for a time-varying risk premium with Markov regimes, provided that instrumental variables are used to account for the failure of orthogonality between right-hand side variables and disturbances. Moreover, such a model outperforms the forward rate when it comes to forecasting the spot exchange rate.

To fix ideas and notation, the next section of the paper outlines a simple theoretical model for forward exchange pricing and explains how a Markov switching foreign exchange risk premium can arise. Section 3 discusses the results of standard regression-based tests of the UFER hypothesis and examines the stochastic properties of the risk premium. Section 4 presents our empirical Markov switching model and a small-scale simulation study of the properties of the tests of the UFER hypothesis that are used in our analysis. It also reports and discusses the results from a post-sample analysis that examines whether the model proposed in the paper could be used to improve forecasts of the spot exchange rate. Section 5 summarizes and concludes.