Endogeneity and Heterogeneity in LDV Panel Data Models

Abstract

We extend three existing cross-sectional limited dependent variable (LDV) estimators, that allow for endogenous regressors, to a panel data model. We focus on estimation of effects of timeinvariant endogenous regressors, since to our knowledge, besides joint maximum likelihood, no other alternative consistent parametric estimators than the ones suggested here exist. We compare their small sample performance of estimates of marginal effects to i.i.d. LDV estimators as well as to linear estimators by means of Monte Carlo Studies. Some notable differences in the performance of the LDV estimators appear. One estimator, the 2SIV, performs reasonably well in terms of bias, even with weak instruments. Another type, the AGLS estimators, have a large small sample bias when no endogeneity is present. The 2SCML estimators seem to perform reasonable in most scenarios even under some types of misspecification. In addition, 2SLS performed relatively well, but had a substantial MSE with weak instruments and substantial bias in misspecified scenarios. Although potentially important because of heterogeneity bias, our extension of LDV models to the panel case did not give improvements in small sample performance over the cross-sectional estimators.Two-Step Estimation; Panel Data; Endogenous Regressor; Time-Invariant Regressor; Linear Approximation