The paper describes a relative entropy procedure for imposing moment restrictions on simulated forecast distributions from a variety of models. Starting from an empirical forecast distribution for some variables of interest, the technique generates a new empirical distribution that satisfies a set of moment restrictions. The new distribution is chosen to be as close as possible to the original in the sense of minimizing the associated Kullback-Leibler Information Criterion, or relative entropy. The authors illustrate the technique by using several examples that show how restrictions from other forecasts and from economic theory may be introduced into a model’s forecasts.
JEL classification: E44, C53
Keywords: approximate prior information, Kullback-Leibler Information Criterion, relative numerical efficiency
The authors thank David Aadland, William Roberds, Frank Schorfheide, and Tao Zha for helpful discussions. They also received helpful comments from the participants in the Atlanta Fed brown bag lunch series, the Western Economics Association Meetings in Seattle 2002, the NBER Summer Workshop on Forecasting in July 2002, and seminars at the Economics Departments of the University of Georgia, Vanderbilt University, and the University of Virginia. The views expressed here are the authors’ and not necessarily those of the Federal Reserve Bank of Atlanta or the Federal Reserve System. Any remaining errors are the authors’ responsibility.
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