Time-Variation and Structural Change in the Forward Discount: Implications for the Forward Rate Unbiasedness Hypothesis

Abstract

It is a well accepted empirical result that forward exchange rate unbiasedness is rejected in tests using the “differences regression ” of the change in the logarithm of the spot exchange rate on the forward discount. The result is referred to in the International Finance literature as the forward discount puzzle. Competing explanations of the negative bias of the forward discount coefficient include the possibilities of a time-varying risk premium or the existence of “peso problems. ” We offer an alternative explanation for this anomaly. One of the stylized facts about the forward discount is that it is highly persistent. We model the forward discount as an AR(1) process and argue that its persistence is exaggerated due to the presence of structural breaks. We document the temporal variation in persistence, using a time-varying parameter specification for the AR(1) model, with Markov-switching disturbances. We also show, using a stochastic multiple break model, suggested recently by Bai and Perron (1998), that for the G-7 countries, with the exception of Japan, the forward discount persistence is substantially less, if one allows for multiple structural breaks in the mean of the process. These breaks could be identified as monetary shocks to the central bank’s reaction function, as discussed in Eichenbaum and Evans (1995). Using Monte Carlo simulations we show that if we do not account for structural breaks which are present in the forward discount process, the forward discount coefficient in the “differences regression ” is severely biased downward, away from its true value of 1. The authors would like to thank Charles Engel and the participants of the macroeconomics seminar at the New York Federal Reserve Bank for helpful comments and suggestions and Jushan Bai for generously providing the GAUSS code to estimate the multiple break models. The usual disclaimer applies