This paper presents methods for estimating the impact of training on earnings when non-random selection characterizes the enrollment of persons into training. We explore the benefits of cross-section, repeated cross-section and longitudinal data for addressing this problem by considering the assumptions required to use a variety of new and conventional estimators given access to various commonly encountered types of data. We investigate the plausibility of assumptions needed to justify econometric procedures when viewed in the light of prototypical decision rules determining enrollment into training. We examine the robustness of the estimators to choice-based sampling and contamination bias.
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