Bayesian State Space Models in Macroeconometrics

Abstract

State space models play an important role in macroeconometric analysis and the Bayesian approach has been shown to have many advantages. This paper outlines recent developments in state space modelling applied to macroeconomics using Bayesian methods. We outline the directions of recent research, specifically the problems being addressed and the solutions proposed. After presenting a general form for the linear Gaussian model, we discuss the interpretations and virtues of alternative estimation routines and their outputs. This discussion includes the Kalman filter and smoother, and precision based algorithms. As the advantages of using large models have become better understood, a focus has developed on dimension reduction and computational advances to cope with high-dimensional parameter spaces. We give an overview of a number of recent advances in these directions. Many models suggested by economic theory are either non-linear or non-Gaussian, or both. We discuss work on the particle filtering approach to such models as well as other techniques that use various approximations -to either the time t state and measurement equations or to the full posterior for the states -to obtain draws.

Hybrid SV‐GARCH, t‐GARCH and Markov‐switching covariance structures in VEC models—Which is better from a predictive perspective?

“…Finally, it remains an open issue whether the models and methods developed here are actually scalable to large Bayesian VAR/VEC systems, which are presently a popular and promising research area in empirical macroeconomics (see, e.g. Bańbura et al, 2010; Koop, 2013; and more recent works by Chan, 2020; Cross et al, 2020; Chan & Strachan, 2023; and Gefang et al, 2023). Whether the volatility structure in high‐dimensional systems is computationally tractable depends on the specific choice.…”

Flexible Mixture Priors for Large Time-varying Parameter Models

“…implying that α ∼ N (a 0 , Ω 0 ) with prior mean a 0 = Φ −1 γ and prior variance-covariance matrix Chan and Jeliazkov, 2009;Chan and Strachan, 2020). In the special case of φ t = 0 K×K , for all t, Φ (and thus Ω 0 ) reduces to an identity matrix, while φ t = 0 K×K , for any t, induces a (specific) banded lower-triangular (block diagonal) structure of Φ (Ω 0 ).…”

A sparse matrix formulation of model-based ensemble Kalman filter

“…State-space models are frequently used in many applications. Examples of application areas are economics (Creal 2011;Chan and Strachan 2020), weather forecasting (Houtekamer and Zhang 2016;Hotta and Ota 2021), signal processing (Loeliger et al 2007) and neuroscience (Smith and Emery 2003). A state-space model consists of an unobserved latent {x t } discrete time Markov process and a related observed {y t } process, where y t gives information about x t , and the y t 's are assumed to be conditionally independent given the {x t } process.…”