Indirect estimation of (latent) linear models with ordinal regressors A Monte Carlo study and some empirical illustrations

Abstract

This paper investigates the effects of ordinal regressors in linear regression models and in limited dependent variable models. Each ordered categorical variable is interpreted as a rough measurement of an underlying continuous variable as it is often done in microeconometrics for the dependent variable. It is shown that using ordinal indicators only leads to correct answers in a few special cases. In most situations, the usual estimators are biased. In order to estimate the parameters of the model consistently, the indirect estimation procedure suggested by Gourieroux et al. (1993) is applied. To demonstrate this method, first a simulation study is performed and then in a second step, two real data sets are used. In the latter case, continuous regressors are transformed into categorical variables to study the behavior of the estimation procedure. The method is extended to the case of limited dependent variable models. In general, the indirect estimators lead to adequate results.