Abstract
Abstract 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.
Highlights
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 (RCS)
We describe a pseudo panel model in which under convenient expansion of the original specification with a selection bias correction term the method allows us to use a Wald test of H0: ρ=0 as a test of the null hypothesis of the absence of sample selection bias
We show that the proposed selection bias correction term is proportional to the inverse Mills ratio of the normit of a consistent estimation of the observed proportion of individuals in each cohort
Summary
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 (RCS). Empirical labour literature utilizes influential articles by Gronau (1974) and Lewis (1974), hereafter G-L, and eliminates selectivity bias by means of a correction term proportional to the inverse Mills ratio with an argument equal to the inverse normal cumulative distribution function (normit) of the proportion of individuals observed in each cohort. We show that the proposed selection bias correction term is proportional to the inverse Mills ratio of the normit of a consistent estimation of the observed proportion of individuals in each cohort. Taking expectations in (11) for fixed t gives: This expression, as we will see, forms the basis to use the selection equation as a relevant element to estimate a bias correction term for the main equation
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