Kalman filtering with truncated normal state variables for Bayesian estimation of macroeconomic models

A pair of simple modifications–in the forecast error and forecast error variance–to the Kalman filter recursions makes possible the filtering of models in which one or more state variables is truncated normal and latent. Such recursions are broadly applicable to macroeconometric models, such as vector autoregressions and estimated dynamic stochastic general equilibrium models, that have one or more probit-type equation.