Essays on Bayesian Econometrics

Essays on Bayesian Econometrics Jaeho Kim Chair of the supervisor committee: Professor Chang-Jin Kim Department of Economics This dissertation explores important macroeconomics issues based on Bayesian Econometrics tools developed. One goal of the first chapter of the dissertation is to develop an efficient Markov-Chain Monte Carlo (MCMC) algorithm for estimating an ARMA model with a regime-switching mean, based on a multi-move sampler. Unlike the existing algorithm of Billio et al. (1999) based on a single-move sampler, our algorithm can achieve reasonably fast convergence to the posterior distribution even when the latent regime indicator variable is highly persistent or when there exist absorbing states. Another goal of the first chapter is to appropriately investigate the dynamics of the latent ex-ante real interest rate (EARR) in the presence of structural breaks, by employing the econometric tool developed. We argue Garcia and Perron’s (1996) conclusion that the EARR rate is a constant subject to occasional jumps may be sample-specific. For an extended sample that includes recent data, Garcia and Perron’s (1996) AR(2) model of EPRR may be misspecified, and we show that excluding the theory-implied moving-average terms may understate the persistence of the observed ex-post real interest rate (EPRR) dynamics. Our empirical results suggest that, even though we rule out the possibility of a unit root in the EARR, it may be more persistent and volatile than has been documented in some of the literature including Garcia and Perron (1996). The second chapter of the dissertation investigates the conventional wisdom that in the case of a flat prior Bayesian inference will not be very different from classical inference, as the likelihood dominates the posterior density. This chapter shows that there are cases in which this conventional wisdom does not apply. An ARMA model of real GDP growth estimated by Perron and Wada (2009) is an example. While their maximum likelihood estimation of the model implies that real GDP may be a trend stationary process, Bayesian estimation of the same model implies that most of the variations in real GDP can be explained by the stochastic trend component, as in Nelson and Plosser (1982) and Morley et al. (2003). We show such dramatically different results stem from the differences in how the nuisance parameters are handled between the two approaches, especially when the parameter estimate of interest is dependent upon the estimates of the nuisance parameters for small samples. For the maximum likelihood approach, as the number of the nuisance parameters increases, we have higher probability that the moving-average root may be estimated to be one even when its true value is less than one, spuriously indicating that the data is ‘over-differenced. ’ However, the Bayesian approach is relatively free from this pile-up problem, as the posterior distribution is not dependent upon the nuisance parameters. The last chapter of the dissertation is about Bayesian model comparison. Bayesian model comparison is often achieved by the Bayes Factor which is sensitive to prior assumptions. Various alternative Bayes Factors such as the Intrinsic and Fractional Bayes Factors have been proposed to overcome this problem. However, practical problems arise since they include many marginal likelihoods which are not analytically tractable in most cases. An encompassing prior approach (EP) is a recently proposed method to approximate the Bayes Factor numerically in comparing nested models. We extend EP approach to the alternative Bayes Factors in this chapter. Our method provides a simple and elegant way to conduct robust model comparisons to the prior sensitivity for nested models.