Long-Horizon Forecasts of Asset Prices when the Discount Factor is close to Unity- Institute Working Paper no. 36 - FRB Dallas

Abstract Engel and West (EW, 2005) argue that as the discount factor gets closer to one, presentvalue asset pricing models place greater weight on future fundamentals. Consequently, current fundamentals have very weak forecasting power and asset prices in these models appear to follow approximately a random walk. We connect the Engel-West explanation to the studies of long-horizon regressions. As expected, we find that under EW’s assumption that fundamentals are I(1) and observable to the econometrician, long-horizon regressions generally do not have significant forecasting power when the discount factor is large. However, when EW’s assumptions are violated in a particular way, our analytical and simulation results show that long-horizon regressions can have substantial power, even when the discount factor is close to one and the power of short-horizon regressions is low. One example for the substantial power improvement at long horizons is the existence of unobservable stationary fundamentals, such as the risk premium, in present-value asset pricing models. Consistent with our model’s prediction, we find that the risk premium calculated from survey data can forecast exchange rates at long horizons. These results suggest that the presence of stationary unobservable fundamentals may have played a large role in the power improvement of long-horizon regressions found in empirical studies.