Concentrated MCMC estimation

This paper studies a concentrated Markov Chain Monte Carlo (MCMC) estimation method that offers significant computational advantages while delivering valid inference for parameters of interest. By reducing the dimension of parameters to be sampled, this method substantially decreases computational time and memory usage relative to both traditional and some state-of-the-art Bayesian algorithms. Its applicability extends to correctly specified or misspecified likelihood functions, as well as generalized method of moments objective functions. Monte Carlo studies demonstrate that the biases and root mean squared errors of the concentrated MCMC estimators are typically smaller than or comparable to those of conventional Bayesian estimators. Furthermore, this method exhibits reliable model selection performance. We establish the large sample properties of the concentrated MCMC estimator. An empirical application analyzing the network spillover effect of stock returns in the Chinese A-share market further illustrates the advantages of this method.