Three Chapters in Bayesian Econometrics

We make three contributions to Bayesian Econometrics. The first is a new Bayesian test statistic for testing a point null hypothesis based on a quadratic loss. The proposed test statistic may be regarded as the Bayesian version of the Lagrange multiplier test. Its asymptotic distribution is obtained based on a set of regular conditions and follows a chi-squared distribution when the null hypothesis is correct. The second contribution is a new Wald-type statistic for hypothesis testing based on Bayesian posterior distributions. The new statistic can be explained as a posterior version of the Wald test. Both tests have several nice properties, including being well-defined under improper prior distributions, and avoiding the Jeffreys-Lindley paradox. They are both asymptotically pivotal, relatively easy to compute, and applicable to latent variable models. Finally, we propose a quasi-Bayesian approach for structural parameters in finite-horizon life-cycle models. This approach circumvents the numerical evaluation of the gradient of the objective function and alleviates the local optimum problem. The asymptotic normality of the estimators with and without approximation errors is derived. The proposed estimators reach the efficiency bound in the general methods of moment (GMM) framework. Both the estimators and the corresponding asymptotic covariance are readily computable. The estimation procedure is easy to parallel so that the graphic processing unit (GPU) can be used to enhance the computational speed. The estimation procedure is illustrated using a variant of the model in Gourinchas and Parker (2002)