Bayesian Inference in Regime-Switching ARMA Models with Absorbing States: The Dynamics of the Ex-Ante Real Interest Rate Under Structural Breaks

One goal of this paper 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 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).