GMM Model Averaging

在应用实证研究中，面对模型不确定性的智能优点，模型选择方法是常用的方法。改进的估计和推断可以通过模型平均，用平滑平均代替选择中隐含的不连续性。模型平均化的计量经济学方法还没有开发出来。贝叶斯模型平均方法已经得到了发展，但频率方法还没有，除了Hjort和Claeskens(2003)最近的贡献之外。后者的贡献与基于似然的模型有关。广义矩方法(GMM)是计量经济学中最常用的估计框架，但目前还没有适用的模型平均方法。PIS的建议是发展广义矩方法的模型平均方法。PI遵循Hjort和Claeskens(2003)的方法，通过使用局部到零的参数化来开发包含偏差-方差权衡的渐近均方误差计算。利用该框架，PI可以计算模型平均GMM的渐近均方误差，并提出修正后的均方误差估计。模型平均权重的估计是这些均方误差估计的函数，并使用二次规划来计算。其结果是PI提出的GMM模型的平均估计。在模拟中，这些估计被发现具有良好的有限样本均方误差性质。这一理论需要得到充分的解决。需要纳入更广泛的条件和假设，以使分析更广泛地适用。模型平均化可以扩展到包括仪器集的平均数(平均矩条件)。该理论还应扩展到包含大型工具渐近性。一个特别棘手的问题将是推论。与模型选择类似，模型平均产生的估计其抽样分布不能被一致地估计。需要开发出对这个问题敏感的可靠的推理方法。这些主题和问题将在本提案的执行过程中进行探讨。广泛影响模型平均方法在应用计量经济学中越来越受欢迎。所提出的方法将具有广泛的经验应用潜力。预计这项研究发现的理论和方法将被应用经济学家在学术界和公共部门找到富有成效的用途。

Intellectual MeritFaced with model uncertainty, model selection methods are commonly employed in applied empiricalresearch. Improved estimation and inference can be obtained by model averaging, replacing thediscontinuities implicit in selection by smooth averaging. An econometric methodology for modelaveraging is undeveloped. Bayesian model averaging methods have been developed, but frequentistmethods are missing, with the notable exception of the recent contribution of Hjort and Claeskens (2003).The latter contribution is concerned with likelihood-based models. There are no model averagingmethods appropriate for the Generalized Method of Moments (GMM), which is arguably the mostcommon estimation framework in econometrics.The PIs proposal is to develop model averaging methods for GMM. The PIs follow Hjort and Claeskens (2003)by using a local-to-zero parameterization to develop an asymptotic mean-square-error calculation whichcontains a bias-variance trade-off. Using this framework, the PIs can calculate the asymptotic MSE of modelaveragedGMM, and propose bias-corrected estimates of the MSE. Estimates of the model averageweights are functions of these MSE estimates, and are computed using quadratic programming. Theresult is the PIs proposed GMM model average estimates. In simulations, these estimates are found to possessgood finite sample MSE properties.The research suggested in this proposal is at a preliminary stage of development. The theory needs to befully worked out. Broader conditions and assumptions need to be incorporated to make the analysis morebroadly applicable. Model averaging can be extended to include average over instrument sets (averagingover moment conditions). The theory should also be extended to incorporate large instrumentasymptotics. A particularly thorny issue will be inference. Similar to model selection, model averagingproduces estimates whose sampling distributions cannot be consistently estimated. Robust inferencemethods will need to be developed which are sensitive to this issue. These topics and issues will beexplored in the execution of this proposal.Broader ImpactsModel averaging methods are growing in popularity in applied econometrics. The proposed methods willhave broad potential empirical application. It is expected that the theory and methods uncovered by thisresearch will find productive use by applied economists both in academics and the public sector.