Efficient Estimation of Ordered Probit Models

Abstract

Abstract This article discusses a model in which both the dependent variable and the explanatory variables are ordinal and have an arbitrary number of categories. Assuming joint normality of the underlying continuous latent variables, we compare estimation based on the joint distribution to estimation based on the conditional distribution. Because the explanatory variables are not weakly exogenous in this model, the latter approach implies a loss in efficiency that can be substantial in many cases, as shown in detail for the special case of trichotomous data with symmetric thresholds. Therefore, latent variables underlying the observed ordinal variables should always be considered to be jointly endogenous; that is, the joint distribution should be considered.