Are Forecast Combinations Efficient?

Abstract

In this paper we take an in-depth view of one particular type of inefficiency that may be present in the combination of forecasts: Mincer and Zarnowitz (MZ) inefficiency. Under mild assumptions we show that weighted combinations of forecasts are MZ-inefficient with probability one. We also show that convex linear combinations of forecasts will always display MZ-inefficiency when the individual forecasts are MZ-efficient. No assumptions about the availability of private or public information are required for these results. All this implies that greater reductions in Mean Squared Prediction Error are possible and that the traditional optimal weighted combination may not coincide with the optimal weighted MZ-efficient combination. We illustrate our findings with a couple of empirical applications in the context of the combination of inflation forecasts for Chile and the U.S. A simple adjustment based upon a rolling OLS strategy is shown to remove the MZ-inefficiency of the combinations quite well.