Inference for Distributional Treatment Effects in Instrumental Variable Models

• Activity Number: 181
• Type: Contributed
• Date/Time: Monday, August 10, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Kwonsang Lee* and Jing Qin and Dylan Small
• Companies: University of Pennsylvania and National Institute of Allergy and Infectious Diseases and University of Pennsylvania
• Keywords: Causal inference ; Instrumental variable ; Simultaneous confidence band estimation ; Binomial likelihood approach ; Pool Adjacent Violator Algorithm

Abstract

In observational studies, the causal effect of a treatment on the distribution of outcomes is of interest but this can be confounded by unmeasured variables. Instrumental variable methods allow for causal inference controlling for unmeasured confounding in observational studies. The existing nonparametric method of using instrumental variables to estimate the effect of treatment on the distribution of outcomes for compliers has several drawbacks such as producing estimates that violate the non-decreasing and non-negative properties of CDFs. We suggest a binomial likelihood approach and a combined method of EM algorithm and Pool Adjacent Violators Algorithm (PAVA) to estimate the cumulative distribution functions (CDF) of outcomes for compliers. We show that our proposed method overcomes the limitation of previous methods and also show via a series of simulations that our method improves estimation accuracy of the CDFs. Furthermore, we construct a 95% simultaneous confidence band of the estimated CDFs by calibration method. Finally, we apply our method to a study of the effects of Vietnam veteran status on the distribution of civilian annual earnings.