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The Generalized Method of Moments in the Bayesian Framework and a Model of Moment Selection Criterion

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  • Jae-Young Kim

    (SUNY at Albany)

Abstract

While the classical framework has a rich set of limited information procedures such as GMM and other related methods, the situation is not so in the Bayesian framework. We develop a limited information procedure in the Bayesian framework that does not require the knowledge of the likelihood function. The developed procedure is a Bayesian counterpart of the classical GMM but has advantages over the classical GMM in practical applications. The necessary limited information for our approach is a set of moment conditions, instead of the likelihood function, which has a counterpart in the classical GMM. Such moment conditions in the Bayesian framework are obtained from the equivalence condition of the Bayes' estimator and the GMM estimator. From such moment conditions, a posterior probability measure is derived that forms the basis of our limited information Bayesian procedure. This limited information posterior has some desirable properties for small and large sample analyses. An alternative approach is also provided in this paper for deriving a limited information posterior based on a variant of the empirical likelihood method where an empirical likelihood is obtained from the moment conditions of GMM. This alternative approach yields asymptotically the same result as the approach explained above. Based on our limited information method, we develop a procedure for selecting the moment for GMM. This moment selection procedure is an extension of the Bayesian model selection procedure to the Bayesian semi-parametric, limited information framework. It is shown that under some conditions the proposed moment selection procedure is a consistent decision rule.

Suggested Citation

  • Jae-Young Kim, 2000. "The Generalized Method of Moments in the Bayesian Framework and a Model of Moment Selection Criterion," Econometric Society World Congress 2000 Contributed Papers 1779, Econometric Society.
  • Handle: RePEc:ecm:wc2000:1779
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    1. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    2. Kitamura, Yuichi & Phillips, Peter C. B., 1997. "Fully modified IV, GIVE and GMM estimation with possibly non-stationary regressors and instruments," Journal of Econometrics, Elsevier, vol. 80(1), pages 85-123, September.
    3. Song Chen, 1993. "On the accuracy of empirical likelihood confidence regions for linear regression model," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 45(4), pages 621-637, December.
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