Consistent estimation in pseudo panels in the presence of selection bias

In the presence of selection bias the traditional estimators for pseudo panel data models are inconsistent. This paper discusses a method to achieve consistency in static linear pseudo panels in the presence of selection bias and a testing procedure for sample selection bias. The authors' approach uses a bias correction term proportional to the inverse Mills ratio with argument equal to the "normit" of a consistent estimation of the conditional probability of being observed given cohort membership. Monte Carlo analysis shows the test does not reject the null for fixed T at a 5% significance level in finite samples. As a "side effect" the authors utilize the enlarged pseudo panel to provide a GMM consistent estimation of the pseudo panel parameters under rejection of the null and apply the procedure to estimate the rate of return to education in Colombia.