Econometric Shrinkage and Model Averaging

在实证研究过程中，经济学家通常会估计多个模型。这部分是因为正确的模型规范存在不确定性，部分是因为希望避免过度参数化。人们可能会问这个问题：应该使用这些模型中的哪一个？这就是模型选择问题，这个问题在计量经济学和统计学中已经得到了深入的探索。在当代的工作中，模型选择已经演变为模型平均。而不是从一组模型中选择一个模型，可以对整个整体进行平均。平均化减少了估计的方差。平均在预测中非常流行--报纸和其他媒体通常会通过一套已建立的预测模型来报道平均预测。这是模型平均的一个例子，但它扩展到统计和计量经济学估计的所有领域。在模型平均的背景下，关键问题是如何选择权重。在上面列出的预测示例中，惯例是使用相同的权重。但这是一个没有正当理由的惯例。相反，选择模型权重的最佳方法是什么？本研究就是试图回答这个问题的一部分。本研究拓展了收缩在计量经济估计中的应用。当存在两个嵌套模型时，模型平均等价于收缩估计。PI将表明，我们可以将现代统计收缩理论应用于参数计量经济估计器。其结果是，我们可以构造比传统估计更有效的收缩估计。本研究还将收缩理论推广到模型个数超过两个的一般模型平均情形。PI将为计量经济估计者开发非贝叶斯模型平均方法。模型平均方法在应用计量经济学中越来越受欢迎。本研究项目提出的方法将具有广泛的实证应用价值。可以预期，这项研究发现的理论和方法将被应用经济学家、统计学家和其他社会科学家在学术界和公共部门找到富有成效的用途。

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.