SIMULATED LATENT VARIABLE ESTIMATION OF MODELS WITH ORDERED CATEGORICAL-DATA

This paper addresses the problem that occurs when estimating a linear regression model in which some of the explanatory variables are repres ented by categorical indicators. We replace the categorical variable w ith a simulated latent variable (SLV) drawn from a truncated multivari ate normal distribution using the Gibbs sampler. Consistent and effici ent 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 m atrix are derived using a two-stage procedure. We illustrate this meth odology using a Monte Carlo simulation, and also investigate the conse quences of incorrect distributional assumptions. The simulated latent variable procedure is shown to be superior to conventional methods inv olving dummy variables or conditional means. (C) 1998 Elsevier Science S.A. All rights reserved.