Are Forecast Combinations Efficient?

It is well known that weighted averages of two competing forecasts may reduce Mean Squared Prediction Errors (MSPE) and may also introduce certain inefficiencies. In this paper we take an in-depth view of one particular type of inefficiency stemming from simple combination schemes. We identify testable conditions under which every linear convex combination of two forecasts displays this type of inefficiency. In particular, we show that the process of taking averages of forecasts may induce inefficiencies in the combination, even when the individual forecasts are efficient. Furthermore, we show that the so-called "optimal weighted average" traditionally presented in the literature may indeed be suboptimal. We propose a simple testable condition to detect if this traditional weighted factor is optimal in a broader sense. An optimal "recombination weight" is introduced. Finally, we illustrate our findings with simulations and an empirical application in the context of the combination of inflation forecasts.