Adaptive MCMC for Generalized Method of Moments with Many Moment Conditions
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A generalized method of moments (GMM) estimator is unreliable when the number of moment conditions is large, that is, it is comparable or larger than the sample size. While a number of provisions for this problem is proposed in classical GMM literature, the literature on its Bayesian counterpart (i.e., Bayesian inference using a GMM criterion as a quasi-likelihood) has paid scant attention to this problem. This paper fills this gap by proposing an adaptive Markov Chain Monte Carlo (MCMC) approach to a GMM inference with many moment conditions. Particularly, this paper focuses on the adaptive tuning of a weighting matrix on the fly. Our proposal consists of two elements. The first is the random update of a weighting matrix, which substantially reduces computational cost, while maintaining the accuracy of the estimation. The second is the use of the nonparametric eigenvalue-regularized precision matrix estimator, which contributes to numerical stability. A simulation study and a real data application then are presented to illustrate the performance of the proposed approach in comparison with existing approaches.
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