Relaxing monotonicity in endogenous selection models and application to surveys
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This paper considers endogenous selection models, in particular nonparametric ones. Estimating the law of unselected (or censored or unobserved) outcomes or the unconditional one is feasible when one uses instrumental variables. Using a selection equation which is additively separable in a one dimensional unobservable has the sometimes undesirable property of instrument monotonicity. We present models and nonparametric identification results allowing for non instrument monotonicity and which are based on nonparametric random coefficients indices. We apply these results to inference on nonlinear statistics such as the Gini index in surveys when the nonresponse is not missing at random.
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