Separating Variances and Correlation; A New Prior for TVP-VARs

Abstract

Time-Varying parameter models have become more popular in recent years, especially as they are adapted to accommodate larger datasets. However, all recent developments use standard priors, specifically the Inverse-Wishart class of priors over the parameter error covariance matrix. In this paper, I show that Inverse-Wishart priors have a number of negative properties, and that those properties are likely salient in a TVP context since there is little information from the likelihood. Fully aware of these deficiencies, the Bayesian Random Effects literature has developed a series of uninformative priors to correct these weaknesses. In this paper, I adapt one of those priors into an informative and easily understandable prior for covariances. I show that the choice of prior does have an impact on posterior inference and that the new priors have improved frequentist properties. I apply my prior to the canonical Primiceri (2005) dataset and find that their results were sensitive to the choice of prior. Moreover, in a forecasting exercise, the new prior improves forecasts for that same dataset.

Keywords: Time-Varying Parameters, Half-t, Inverse-Wishart