Accounting for Regressor-Error Dependencies in Educational Data: A Bayesian Mixture Approach

Abstract

Because frequently random assignment is not feasible in educational studies, our understanding of causal effects of student characteristics on academic performance has made little progress over the years. Omitted variables inducing correlations between regressors and error terms in multilevel data are a major hurdle. If the independence assumption of regressors and error components is not met, standard multilevel regression models yield biased and inconsistent results. This paper focusses on within-level regressor-error dependencies, caused by omitted variables, which are difficult to diagnose and remedy when additional data in the form of instrumental variables are not available. Specifically, we develop a multilevel mixture model that can account for correlations between regressor and error terms. The proposed approach allows for different specifications such as choice- or self-selection models. We present a flexible Bayesian estimation method that can be adapted easily to researchers' specific needs. Investigating the relationship between IQ and educational performance, we find empirical support for self-selection effects that distort substantially the observed relation between these measures.

Keywords: endogeneity, mixture model, fixed-effects estimator, random-effects estimator, omitted variables, regressor-error dependencies