Testing long-horizon predictive ability with high persistence, and the Meese-Rogoff puzzle

A well-known puzzle in the international finance literature is that a random walk predicts exchange rates better than economic models (Meese and Rogoff, 1983a,b and 1988). This paper offers a potential explanation for this finding. When exchange rates and fundamentals are highly persistent, long-horizon forecasts of economic models are asymptotically biased by the estimation error in the parameter that measures the persistence. When this bias outweighs the benefits from exploiting economic information, the random walk model will forecast better. This happens even if the economic model is the true data generating process. The reason is that a random walk model imposes a unit root, rather than estimates it. The paper thus proposes a test for equal predictive ability in the presence of highly persistent variables. When applied to the Meese-Rogoff exercise, this test shows that the poor forecasting ability of economic models does not imply that the models are not a good description of the data.