Consistent estimation of pseudo panels in the presence of selection bias

In the presence of selection bias, traditional estimators of pseudo panel data are inconsistent. In this paper, the authors derive the conditions under which consistence is achieved in pseudo-panel estimation and propose a simple test of selection bias. Specifically, they propose a Wald test for the null hypothesis that there is no selection bias. Under rejection of the null hypothesis, the authors can consistently estimate pseudo-panel parameters. They use cross sections and pseudo-panel regressions to test for selection bias and estimate the returns to education in Colombia. The authors corroborate the existence of selection bias and find that returns to education are around twenty percent.