GMM Model Averaging

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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.