ESSAYS ON BAYESIAN INFERENCE IN REGRESSION MODELS WITH NON-NORMAL ERROR TERMS

Abstract

OF THE DISSERTATION ESSAYS ON BAYESIAN INFERENCE IN REGRESSION MODELS WITH NON-NORMAL ERROR TERMS by HARUHIKO SHIMIZU Dissertation Director: Professor Hiroki Tsurumi The dissertation consists of three essays on regression models with non-normal error terms. In the first essay, I consider the Bayesian analysis of regression model with the error term following the exponential power distribution (EPD) that includes normal and Laplace distributions as special cases. Many empirical data are known to follow non-normal distributions. If we use a distribution that is flexible enough to include the normal distribution as a special case, we may be able to explain the data better. In estimating the regression model I use a modified efficient jump algorithm for Markov Chain Monte Carlo (MCMC) draws of the parameters of the epd distribution. I also discuss the unbiasedness of the least absolute deviation (LAD) estimator. The LAD estimator of the regression coefficients turns out to be unbiased except for the constant term even if the error term has a skewed distribution. Second essay is about the censored model known as the Tobit. Yu and Stander (2007) proposed a Bayesian quantile regression model using the asymmetric Laplace distribution (ALD). Yu and Staner (2007) formulated the likelihood function based on the quantiles. I construct the likelihood function based on the usual way the Tobit regression model is defined in econometrics. I show by using Monte Carlo simulation experiments that the way I constructed the likelihood function works better than Yu and Stander’s likelihood function judged by the mean squared errors. I present an application using the data on hours worked by women.