Bayesian Inference of State Space Models with Flexible Covariance Matrix Rank: Applications for Inflation Modeling

Abstract

After the introductory chapter, this thesis comprises two further chapters. The main chapters in this dissertation, i.e., chapters 2 and 3 are presented in essay format, each with an independent introduction and conclusion. The contents of these individual chapters are outlined below. Chapter 2 studies the forecasting implications of specifying unobserved components (UC) models with different state correlation structures. While implications for signal extraction from specifying UC models with correlated or orthogonal innovations have been well-investigated, out-ofsample implications are less well understood. This paper attempts to address this gap in light of the recent resurgence of studies adopting UC models for forecasting purposes. Four correlation structures for errors are entertained: orthogonal, correlated, perfectly correlated innovations as well as a novel approach which combines features from two contrasting cases, namely, orthogonal and perfectly correlated innovations. Parameter space restrictions associated with different correlation structures and their connection with forecasting are discussed within a Bayesian framework. As perfectly correlated innovations reduce the covariance matrix rank, a Markov Chain Monte Carlo sampler which builds upon properties of Toeplitz matrices and recent advances in precision-based algorithms is developed. Our results for several measures of U.S. inflation indicate that the correlation structure between state variables has important implications for forecasting performance as well as estimates of trend inflation. Chapter 3 develops an econometric framework to investigate the contribution of monetary policy to the evolution of U.S. trend inflation. We combine two modeling approaches - measuring trend inflation using an unobserved components model and estimation of monetary policy rules with drifting coefficients - to investigate interdependence between policy rule parameters and trend inflation. We employ identification strategies of the policy shock to trend inflation which highlight particular changes in the conduct of systematic monetary policy and overidentify a state space model for inflation and the policy rate. An effcient Markov Chain Monte Carlo algorithm using precision-based methods is proposed for static and dynamic selection of policy drivers behind trend inflation. Our empirical analysis indicates three main results: (1) the influence of monetary policy on trend inflation increased during the Great Moderation relative to the Great Inflation period; (2) non-policy shocks, however, accounted for between 50 and 70 per cent of the variation in trend inflation during each of these episodes; (3) monetary policy's contribution to stabilize trend inflation around the early 1980s reflects a weaker reaction to output gap changes accompanied by a stronger emphasis on inflation gap dynamics and inflation target adjustments.