Including Prior Information in Probit Model Estimation

The effects of including different kinds of prior information in estimation of the probit model is examined within the framework of Bayesian inference. Of interest is the effect on posterior information for coefficients, probabilities and elasticities. In a model designed to explain choice between fixed and variable interest-rate mortgages, we show that using Bayesian inference to include inequality information on the signs of coefficients yields inferences about probabilities and elasticities that are substantially different from those obtained using maximum likelihood estimation. In a second model, concerned with state voting behavior, we find that putting prior information on probabilities, rather than coefficients, has a dramatic effect on the posterior density functions for the model coefficients, probabilities and elasticities.