Relaxing monotonicity in endogenous selection models and application to surveys

TL;DR

This paper introduces nonparametric endogenous selection models that relax the monotonicity assumption, enabling better inference on survey outcomes with nonrandom nonresponse using instrumental variables.

Contribution

It develops models allowing nonmonotonic selection in nonparametric settings and discusses their identification and application to survey statistics.

Findings

Models enable nonmonotonic selection analysis.

Application to Gini index estimation in surveys.

Addresses nonresponse not missing at random.

Abstract

This paper considers endogenous selection models, in particular nonparametric ones. Estimating the unconditional law of the outcomes is possible 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 which allow for nonmonotonicity and are based on nonparametric random coefficients indices. We discuss their nonparametric identification and apply these results to inference on nonlinear statistics such as the Gini index in surveys when the nonresponse is not missing at random.