Filtering and Smoothing in State-Space Models with Multiple Regimes

Abstract

This paper improves Bayesian filtering techniques in regime-switching state-space models and develops a novel recursion-based smoother for latent variables. The smoother is computationally stable, adaptable to different filters, and easy to implement. We assess its performance in a New Keynesian DSGE model pairing it with three practical filters: the Generalized Pseudo-Bayesian filters of order one (GPB1) and two (GPB2, often referred to as the Kim or Kim–Nelson filter in applied economics), and the Interacting Multiple Model filter (IMM), common in engineering literature but rarely used in economics. The simulation results show that the IMM filter is about three times faster and at least as accurate as the GPB2 filter, while our smoother further reduces errors by approximately 25%. Applied to U.S. data from 1947 to 2023, the IMM filter–smoother pair uncovers important monetary policy regime shifts, including those after COVID-19. This demonstrates the practical relevance of the proposed routines for macroeconomic analysis.