Testing for sample selection bias in pseudo panels: Theory and Monte Carlo

Sample selection bias is commonly used in economic models based on micro data. Despite the continuous generalization of panel data surveys, most countries still collect microeconomic information on the behavior of economic agents by means of repeated independent and representative cross-sections. This paper discusses a simple testing procedure for sample selection bias in pseudo panels. In the context of conditional mean independence panel data models we describe a pseudo panel model in which under convenient expansion of the original specification with a selectivity bias correction term the method allows us to use a Wald test of H0: ρ=0 as a test of the null hypothesis of absence of sample selection bias. We show that the proposed selection bias correction term is proportional to Inverse Mills ratio with an argument equal to the normit" of a consistent estimation of the observed proportion of individuals in each cohort. This finding can be considered a cohort counterpart of Heckman´s selectivity bias correction for the individual case and generalizes to some extent previous existing results in the empirical labour literature. Monte Carlo analysis shows the test does not reject the null for fixed T at a 5% significance level in finite samples and increases its power when utilizing cohort size corrections as suggested by Deaton (1985). As a "side effect" our method enables us to make a consistent estimation of the pseudo panel parameters under rejection of the null."