Faced with model uncertainty, model selection methods are commonly employed in applied empirical research. Improved estimation and inference can be obtained by model averaging, replacing the discontinuities implicit in selection by smooth averaging. An econometric methodology for model averaging is undeveloped. Bayesian model averaging methods have been developed, but frequentist methods 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 averaging methods appropriate for the Generalized Method of Moments (GMM), which is arguably the most common 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 which contains a bias-variance trade-off. Using this framework, the PIs can calculate the asymptotic MSE of modelaveraged GMM, and propose bias-corrected estimates of the MSE. Estimates of the model average weights are functions of these MSE estimates, and are computed using quadratic programming. The result is the PIs proposed GMM model average estimates. In simulations, these estimates are found to possess good finite sample MSE properties. The research suggested in this proposal is at a preliminary stage of development. The theory needs to be fully worked out. Broader conditions and assumptions need to be incorporated to make the analysis more broadly applicable. Model averaging can be extended to include average over instrument sets (averaging over moment conditions). The theory should also be extended to incorporate large instrument asymptotics. A particularly thorny issue will be inference. Similar to model selection, model averaging produces estimates whose sampling distributions cannot be consistently estimated. Robust inference methods will need to be developed which are sensitive to this issue. These topics and issues will be explored in the execution of this proposal. Broader Impacts Model averaging methods are growing in popularity in applied econometrics. The proposed methods will have broad potential empirical application. It is expected that the theory and methods uncovered by this research will find productive use by applied economists both in academics and the public sector.

National Science Foundation (NSF)
Division of Social and Economic Sciences (SES)
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Nancy A. Lutz
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University of Wisconsin Madison
United States
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