Bayesian Inference in Regression Models with Ordinal Explanatory Variables

This paper considers Bayesian inference procedures for regression models with ordinally observed explanatory variables. Taking advantage of a latent variable interpretation of the ordinally observed variable we develop an efficient Bayesian inference procedure that estimates the regression model of interest jointly with an auxiliary ordered probit model for the unobserved latent variable. The properties of the inference procedure and associated MCMC algorithm are assessed using simulated data. We illustrate our approach in an investigation of gender based wage discrimination in the Swedish labor market and find evidence of wage discrimination.