A New Instrumental Method for Dealing with Endogenous Selection

This paper develops a new method for dealing with endogenous selection. When selectionis directly driven by the dependent variable, the usual instrumental strategy based onthe independence between the outcome and the instruments is likely to fail. Instead, thearticle suggests to rely on independence between the instruments and the selection variable,conditional on the outcome. This may be particularly suitable for nonignorable nonresponse,binary models with missing covariates or Roy models with unobserved sector. Nonparametricidentification of the joint distribution of variables is obtained under completeness, arank condition which has been used recently in several nonparametric instrumental problems.Even if the conditional independence between the instrument and the selection fails,the approach provides sharp bounds on parameters of interest under weaker monotonicityconditions. Apart from identification, nonparametric and parametric estimation is also considered.Eventually, the method is applied to estimate the effect of grade retention in Frenchprimary schools.