Econometric Shrinkage and Model Averaging

University Of Wisconsin-Madison, Madison WI

Investigators

Abstract

In the course of empirical research, economists typically estimate multiple models. This is partially because there is uncertainty about correct model specification, and is partially because of the desire to avoid over-parameterization. One might ask the question: Which of these models should be used? This is the question of model selection, which has been deeply explored in econometrics and statistics. In contemporary work, model selection has evolved into model averaging. Rather than selecting one model among a set of models, the entire ensemble can be averaged. Averaging reduces estimation variance. Averaging is quite popular in forecasting--newspapers and other outlets will commonly report the average forecast across a set of established forecasting models. This is one example of model averaging, but it extends to all areas of statistical and econometric estimation. In the context of model averaging, the critical question is how to select the weights. In the forecasting example listed above, the convention is to use equal weights. But this is a convention without justification. Instead, what is the best method to select model weights? This research is part of the attempt to answer this question. This research expands the application of shrinkage in econometric estimation. When there are two nested models, model averaging is equivalent with shrinkage estimation. The PI will show that we can apply the modern theory of statistical shrinkage to parametric econometric estimators. The result is that we can construct shrinkage estimators which are more efficient than conventional estimators. This research also extends the theory of shrinkage to the general model averaging case where the number of models exceeds two. The Pi will develop non-Bayesian model averaging methods for econometric estimators. Model averaging methods are growing in popularity in applied econometrics. The methods proposed in this research project will have broad empirical application. It can be expected that the theory and methods uncovered by this research will find productive use by applied economists, statisticians, and other social scientists both in academics and the public sector.