Sequential Monte Carlo Sampling for DSGE Models

Working Paper: NBER ID: w19152

Authors: Edward P. Herbst; Frank Schorfheide

Abstract: We develop a sequential Monte Carlo (SMC) algorithm for estimating Bayesian dynamic stochastic general equilibrium (DSGE) models, wherein a particle approximation to the posterior is built iteratively through tempering the likelihood. Using three examples consisting of an artificial state-space model, the Smets and Wouters (2007) model, and Schmitt-Grohé and Uribe's (2012) news shock model we show that the SMC algorithm is better suited for multimodal and irregular posterior distributions than the widely-used random walk Metropolis- Hastings algorithm. We find that a more diffuse prior for the Smets and Wouters (2007) model improves its marginal data density and that a slight modification of the prior for the news shock model leads to drastic changes in the posterior inference about the importance of news shocks for fluctuations in hours worked. Unlike standard Markov chain Monte Carlo (MCMC) techniques, the SMC algorithm is well suited for parallel computing.

Keywords: Bayesian estimation; Dynamic Stochastic General Equilibrium; Sequential Monte Carlo

JEL Codes: C11; C15; E10

Causal Claims

Cause	Effect
SMC algorithm (C69)	better approximation of multimodal posterior distributions (C11)
more diffuse prior for the Smets and Wouters model (E19)	improves marginal data density (C55)
more diffuse prior for the Smets and Wouters model (E19)	multimodal posterior distribution (C11)
RWMH algorithm struggles to capture (C69)	multimodal posterior distribution (C11)
slight modification of prior for news shock model (E19)	alters posterior inference regarding news shocks (E39)
anticipated shocks (D84)	explain variance of hours worked (J22)
SMC algorithm (C69)	greater stability and reliability in generating draws from posterior distributions (C46)
RWMH algorithm fails to explore (C45)	posterior surface (Y20)