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.
We study labor productivity between 1968 and 2016 and compare recent productivity growth to its past behavior. We find that though recent productivity data are unambiguously weak, they are not greatly out of line with the variation of productivity over the historical record. We find that when labor productivity has been weak in the past, it did not persist at those levels. In addition, we find a systematic tendency to understate growth in real time, suggesting that the average rate of the past six years will likely be revised up in future.
