Quasi-Bayesian Alternative to M-Estimation

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This research develops a class of econometric estimation procedures, called quasi-bayesian estimators, which are computationally and practically attractive. The estimator is simply defined as the mean or median (or other quantity alike) of the quasi-posterior distribution of economic parameter interest. Unlike in the conventional bayesian approach, the quasi-posterior distribution is generated by transforming a criterion or objective function (such as that in GMM) which may not have any likelihood interpretation. The approach is useful and new for a class of ``semi-parametric" problems that do not impose rigid parametric structure on the economic model of interest. The main application of this estimation consists of nonlinear generalized method-of-moments and various other structural econometric models, such as instrumental median regression, in which the conventional estimates are very hard or practically infeasible to compute . All of these models allow, in principle, to answer very interesting economic questions in the context of microeconomic models and economic policy evaluation. However, the practical estimation and use of such models faces very severe implementation challenges. Quasi-bayesian estimation overcomes this problem by relying on the markov chain monte carlo methods. This allows us to form a class of estimators that are practical, easy to use, and that have excellent statistical properties. The project develops the formal statistical and computational properties of quasi-bayesian estimators for a class of semi-parametric models that fall outside the conventional bayesian inference. Asymptotic normality and consistency of the estimates are proven, and it is shown that the quasi-posterior quantiles can be used for making inferential statements about parameters of interest. The project also implements computer programs and demonstrates the usefulness of the entire approach through simulations. An empirical application is also presented. It deals with estimation of dynamic market risk forecasts using the recursive nonlinear quantile (value-at-risk) models. This application is of great interest to the financial firms and banks who are required by law to asses value-at-risk on a daily and a weekly basis.