The isotonic regression approach for an instrumental variable estimation of the potential outcome distributions for compliers

Abstract

This paper discusses an instrumental variable estimation of the potential outcome distributions for compliers. The existing nonparametric estimators have a limitation in that they give non-proper cumulative distribution functions that violate the non-decreasing property. Using the least squares representation of the standard nonparametric estimators, a simple isotonic regression approach has been developed. A nonparametric bootstrap method is proposed as an appropriate method used to estimate the variances of the isotonic regression estimators. A simulation study demonstrates that the isotonic regression estimators provide more proper and efficient cumulative distribution functions, with much smaller standard errors than those of the standard nonparametric estimators when the proportion of compliers is small. The methods are illustrated with a study to estimate the distributional causal effect of a veteran status on future earnings. (C) 2019 Elsevier B.V. All rights reserved.