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Correcting for Endogeneity in Models with Bunching
We show that in models with endogeneity, bunching at the lower or upper boundary of the distribution of the treatment variable may be used to build a correction for endogeneity. We derive the asymptotic distribution of the parameters of the corrected model, provide an estimator of the standard errors, and prove the consistency of the bootstrap. An empirical application reveals that time spent watching television, corrected for endogeneity, has roughly no net effect on cognitive skills and a significant negative net effect on non-cognitive skills in children.