Essays on Bayesian econometrics

In this thesis we consider several topics in Bayesian econometrics. The first chapter addresses the issues of estimation and tests of exogeneity and overidentifying restrictions in the simultaneous equation model with white noise and an autocorrelated error term. Using Markov Chain Monte Carlo algorithms within the limited information Bayesian framework, we estimate the parameters of the structural equation of interest and test exogeneity and overidentifying restrictions, first with white noise and then with autocorrelated error terms. This type of analysis has not been considered in the Bayesian literature. We develop a test of exogeneity on a single parameter and a test of overidentifying restrictions that can be used to test just-identifying restrictions. We apply the proposed procedures to estimate supply and demand equations of the U.S. gasoline market.; In the second chapter we test Friedman's Money Supply Volatility Hypothesis to explain the decrease in velocity of money that happened in 1982--83, 1985--87 and in 1992--94. We test for Granger causality between the velocity of money and volatility of money growth. The test of Granger causality in the Bayesian framework is robust to the presence of possibly integrated or cointegrated variables; it does not require preliminary tests of unit roots and cointegration. We use a new proxie for the volatility of money growth, the estimated volatility of money growth from an ARMA-GARCH regression model. We conclude that Friedman's Money Supply Volatility Hypothesis is supported by the empirical evidence. The conclusion is opposite to the conclusion of previous researchers.; In the third chapter we discuss issues of cointegration testing. After surveying Bayesian tests of cointegration in the error-correction mechanism models, we propose a new Bayesian test of cointegration rank. The test that we propose can be conducted by either computation of the posterior odds or by deriving the posterior densities of singular values of the reduced rank matrix. We develop the Metropolis-Hasting algorithm to sample the parameters from the posterior distribution and derive the posterior densities of the singular values. We provide simulated examples to give some insights about the performance of the cointegrating test based on the computed highest posterior density interval and the test based on computation of the posterior odds.