Simulated latent variable estimation of models with ordered categorical data

Abstract

This paper addresses the problem that occurs when estimating a linear regression model in which some of the explanatory variables are represented by categorical indicators. We replace the categorical variable with a simulated latent variable (SLV) drawn from a truncated multivariate normal distribution using the Gibbs sampler. Consistent and efficient parameter estimates are derived using generalized two-stage least squares, where the instrument set contains a second SLV drawn from the same distribution. Consistent estimates of the parameter covariance matrix are derived using a two-stage procedure. We illustrate this methodology using a Monte Carlo simulation, and also investigate the consequences of incorrect distributional assumptions. The simulated latent variable procedure is shown to be superior to conventional methods involving dummy variables or conditional means.