Nonparametric Regression Approach to Bayesian Estimation

Estimation of unknown parameters and functions involved in complex nonlinear econometric models is a very important issue. Existing estimation methods include generalised method of moments (GMM) by Hansen (1982) and others, efficient method of moments (EMM) by Gallant and Tauchen (1997), Markov chain Monte Carlo (MCMC) method by Chernozhukov and Hong (2003), and nonparametric simulated maximum likelihood estimation (NSMLE) method by Creel and Kristensen (2011), and Kristensen and Shin (2012). Except the NSMLE method, other existing methods do not provide closed-form solutions. This paper proposes non- and semi-parametric based closed-form approximations to the estimation and computation of posterior means involved in complex nonlinear econometric models. We first consider the case where the samples can be independently drawn from both the likelihood function and the prior density. The samples and observations are then used to nonparametrically estimate posterior mean functions. The estimation method is also applied to estimate the posterior mean of the parameter-of-interest on a summary statistic. Both the asymptotic theory and the finite sample study show that the nonparametric estimate of this posterior mean is superior to existing estimates, including the conventional sample mean.