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This paper presents conditions for the identification of the AVERAGE effect of training CONSTRAINED to the population of trainees. All of the identification conditions we consider are based on a variety of conditional independence assumptions. More specifically, they assume the participation status and post-training latent earnings are conditionally (mean) independent. The identification conditions differ according to the conditioning set they use. Nowhere are any functional-form imposed. In either words, a nonparametric approach has been taken. Moreover, the conditions are robust to choice-based sampling.

The Impact of Social Interventions: Nonparametric Identification from Choice-Based Samples