GMM Model Averaging

智力优势面对模型的不确定性，模型选择方法在应用经验研究中被广泛采用。改进的估计和推断可以通过模型平均来获得，用平滑平均代替选择中隐含的不连续性。模型平均的计量经济学方法尚未发展。贝叶斯模型的平均方法已经被开发出来，但缺少频率论方法，Hjort和Claeskens（2003）最近的贡献是一个显著的例外。广义矩法（GMM）可以说是计量经济学中最常用的估计框架，但目前还没有适合GMM的模型平均方法。PI遵循Hjort和Claeskens（2003），使用局部到零参数化来开发包含偏差-方差权衡的渐近均方误差计算。使用这个框架，PI可以计算modelaveragedGMM的渐近MSE，并提出MSE的偏差校正估计。模型平均权重的估计值是这些MSE估计值的函数，并使用二次规划进行计算。其结果是PIs提出的GMM模型的平均估计值.在模拟中，我们发现这些估计具有良好的有限样本均方误差性质。这个理论需要充分研究。更广泛的条件和假设需要纳入，使分析更广泛地适用。模型平均值可以扩展到包括仪器组的平均值（平均力矩条件）。该理论还应扩展到包括大型仪器的渐近性。一个特别棘手的问题将是推理。与模型选择类似，模型平均产生的估计值的抽样分布不能一致估计。需要开发对这一问题敏感的强有力的推理方法。这些主题和问题将在本提案的执行中进行探讨。更广泛的影响模型平均方法在应用计量经济学中越来越受欢迎。所提出的方法将有广泛的潜在的经验应用。预计本研究所揭示的理论和方法将在学术界和公共部门的应用经济学家中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.