Vector autoregressions with Markov-switching parameters (MS-VARs) offer substantial gains in data fit over VARs with constant parameters. However, Bayesian inference for MS-VARs has remained challenging, impeding their uptake for empirical applications. We show that Sequential Monte Carlo (SMC) estimators can accurately estimate MS-VAR posteriors. Relative to multi-step, model-specific MCMC routines, SMC has the advantages of generality, parallelizability, and freedom from reliance on particular analytical relationships between prior and likelihood. We use SMC’s flexibility to demonstrate that model selection among MS-VARs can be highly sensitive to the choice of prior.
This paper develops a new class of structural vector autoregressions (SVARs) with time-varying parameters, which I call a drifting SVAR (DSVAR). The DSVAR is the first structural time-varying parameter model to allow for internally consistent Bayesian inference under exact--or set--identification, nesting the widely used SVAR framework as a special case. I prove that the DSVAR implies a reduced-form representation, from which structural inference can proceed similarly to the widely used two-step approach for SVARs: first estimating reduced-form parameters and then imposing identifying restrictions to choose among the set of observationally equivalent structural parameters consistent with the reduced-form estimates. In a special case, the reduced form implied by the DSVAR is a tractable known model for which I provide the first algorithm for Bayesian estimation of all free parameters. I demonstrate the framework in the context of Baumeister and Peersman's (2013) work on time variation in the elasticity of oil demand.
We develop a sequential Monte Carlo (SMC) algorithm for Bayesian inference in vector autoregressions with stochastic volatility (VAR-SV). The algorithm builds particle approximations to the sequence of the model's posteriors, adapting the particles from one approximation to the next as the window of available data expands. The parallelizability of the algorithm's computations allows the adaptations to occur rapidly. Our particular algorithm exploits the ability to marginalize many parameters from the posterior analytically and embeds a known Markov chain Monte Carlo (MCMC) algorithm for the model as an effective mutation kernel for fighting particle degeneracy. We show that, relative to using MCMC alone, our algorithm increases the precision of inference while reducing computing time by an order of magnitude when estimating a medium-scale VAR-SV model.
Debates among policy makers about the appropriate response of fiscal policy to the Great Recession centered on the size of the fiscal multiplier, defined as the number of dollars that output increases in response to a dollar of fiscal stimulus.Mostly using the structure of micro-founded Dynamic Stochastic General Equilibrium models, macroeconomists have argued that fiscal multipliers may vary over time and be particularly large in liquidity traps or during recessions. I extend existing techniques for the Bayesian estimation of vector autoregressions with Markov-switching in selected coefficients to empirically investigate both the extent of time-variation in fiscal multipliers and what factors cause the variation. In contradiction to recent results in the literature, my estimates suggest that the value of the government spending multiplier is likely smaller in recessions than in expansions, while tax cuts have a greater effect in recessions than in expansions. I find little evidence that regime change in monetary policy rules and fiscal policy rules have caused time variation in the value of the fiscal multiplier.