“Correcting for Endogeneity in Models With Bunching”, 2023-09-05 (; backlinks):
We develop a novel control function approach in models where the treatment variable has bunching at one corner of its support. This situation typically arises when the treatment variable is a constrained choice and some observations choose the corner solution. The method exploits distributional shape restrictions but makes no exclusion restrictions.
We provide estimators and establish their asymptotic behavior, prove the convergence of the bootstrap, and develop tests of the identification assumptions.
An application reveals that watching television has no effect on cognitive skills and a negative effect on noncognitive skills in children.
When the treatment variable is constrained to be above or below a certain threshold, bunching of observations is often seen at the threshold itself. 2015 develops a test of exogeneity in these situations based on the idea that unobservables vary discontinuously at the threshold. In this article, we show that the same idea can be leveraged further to build a correction for endogeneity, provided that further structure is imposed. Specifically, we impose a restriction on the shape of the distribution of the confounders conditional on the controls, but we allow the parameters of that distribution to be nonparametric functions of the controls. In particular, all of the controls may be endogenous. The approach does not require exclusion restrictions or specific data structures (eg. a panel), so it can be useful when none of the well-established selection-on-unobservables identification strategies are applicable, either because they are infeasible or because they do not identify the parameter of interest.