"Comparing Information in Forecasts from Econometric Models," (with R. J. Shiller), The American Economic Review, 1990.Paper: pdf file
The information contained in one model's forecast compared to that in another can be assessed from a regression of actual values on predicted values from the two models. We do this for forecasts of real GNP growth rates for different pairs of models. The models include a structural model (the Fair (1976) model), various versions of the vector autoregressive (VAR) model, and various versions of a model we call the "autoregressive components" (AC) model. Our procedure requires that forecasts make no use of future information, and we have been careful to try to insure this, including using the version of the Fair model that existed in 1976, the beginning of our test period.
The method proposed in this paper is useful for comparing forecasts from alternative models, and I have used it in a number of applications aside from those in this paper. One other application is evaluating ex ante forecasts in 1989#1, and another is evaluating forecasts from exchange rate equations in 1997#5. The material in Chapter 7, Section 7.8, and Chapter 8, Section 8.7, in 1994#2 is based on this paper.
A second contribution of this paper is to introduce the AC model, which seems better than the VAR model in some cases.