A Dynamic Binary Probit Model with Time-Varying Parameters and Shrinkage Prior*

Abstract

This article studies a time series binary probit model in which the underlying latent variable depends on its lag and exogenous regressors. The regression coefficients for the latent variable are allowed to vary over time to capture possible model instability. Bayesian shrinkage priors are applied to automatically differentiate fixed and truly time-varying coefficients and thus avoid unnecessary model complexity. I develop an MCMC algorithm for model estimation that exploits parameter blocking to boost sampling efficiency. An efficient Monte Carlo approximation based on the Kalman filter is developed to improve the numerical stability for computing the predictive likelihood of the binary outcome. Benefits of the proposed model are illustrated in a simulation study and an application to forecast economic recessions.