A Computational Implementation of GMM

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The PI requests funds for research in econometrics that will develop new methods for data analysis. Many theories developed in economics (and other social and behavioral sciences) predict complicated relationships between variables of interest, relationships that do not fit simple linear regression models. Testing these models requires statistical estimation of non-linear models. In general, estimating economic models of this kind involves a complicated numerical optimization problem. This optimization problem is often combined with the use of numerical simulations (for example, as in maximum simulated likelihood estimation). The result is an extremely complicated computational problem. Computational constraints limit the size of datasets and also limit the kinds of models that can be estimated. The PI seeks to develop methods that are not limited in these ways. This project promotes the progress of science because we must use statistical methods to test hypotheses in many circumstances.The PI and others have proposed ideas that combine simulation with nonparametric regression as a way to reduce the computational problem. Here he proposes to use those ideas to study a statistical method of implementing quasi-Bayes estimators for nonlinear and nonseparable GMM (generalized method of moments) models. He will study both kernel and local polynomial methods and allow for both exact and over identification. The project will also demonstrate the asymptotic validity of inference based on simulated posterior quantile regression. The PI will study the combination with sieve and bootstrap methods.