Three essays on Bayesian econometrics
My dissertation consists of three essays which contribute new theoretical results to Bayesian econometrics. Chapter 2 proposes a new Bayesian test statistic to test 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 chisquared distribution when the null hypothesis is correct. The new statistic has several important advantages that make it appealing in practical applications. First, it is welldefined under improper prior distributions. Second, it avoids JeffreyLindley’s paradox. Third, it always takes a nonnegative value and is relatively easy to compute, even for models with latent variables. Fourth, its numerical standard error is relatively easy to obtain. Finally, it is asymptotically pivotal and its threshold values can be obtained from the chisquared distribution. Chapter 3 proposes a new Waldtype statistic for hypothesis testing based on Bayesian posterior distributions. The new statistic can be explained as a posterior version of Wald test and have several nice properties. First, it is welldefined under improper prior distributions. Second, it avoids JeffreysLindley’s paradox. Third, under the null hypothesis and repeated sampling, it follows a c2 distribution asymptotically, offering an asymptotically pivotal test. Fourth, it only requires inverting the posterior covariance for the parameters of interest. Fifth and perhaps most importantly, when a random sample from the posterior distribution (such as an MCMC output) is available, the proposed statistic can be easily obtained as a byproduct of posterior simulation. In addition, the numerical standard error of the estimated proposed statistic can be computed based on the random sample. The finitesample performance of the statistic is examined in Monte Carlo studies. Chapter 4 proposes a quasiBayesian approach for structural parameters in finitehorizon lifecycle 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).

History
Document type
 PhD dissertation
Degree awarded
PhD in EconomicsYear degree awarded
2018Supervisor(s)
YU, JunCommittee members
PHILLIPS, Peter C. B.; TU, Jun; SARGENT, Thomas J.SMU School
 School of Economics