Nonparametric Bounds on Treatment Effects with Imperfect Instruments

TL;DR

This paper develops nonparametric bounds for treatment effects using imperfect instruments, leveraging monotonicity assumptions to improve identification and applying the method to estimate returns to schooling.

Contribution

It extends existing identification results to nonparametric models with imperfect instruments, incorporating monotonicity assumptions to tighten bounds.

Findings

Derived nonparametric bounds on treatment effects with imperfect instruments.

Showed how monotone treatment response assumption tightens bounds.

Applied methodology to estimate returns to schooling using survey data.

Abstract

This paper extends the identification results in Nevo and Rosen (2012) to nonparametric models. We derive nonparametric bounds on the average treatment effect when an imperfect instrument is available. As in Nevo and Rosen (2012), we assume that the correlation between the imperfect instrument and the unobserved latent variables has the same sign as the correlation between the endogenous variable and the latent variables. We show that the monotone treatment selection and monotone instrumental variable restrictions, introduced by Manski and Pepper (2000, 2009), jointly imply this assumption. Moreover, we show how the monotone treatment response assumption can help tighten the bounds. The identified set can be written in the form of intersection bounds, which is more conducive to inference. We illustrate our methodology using the National Longitudinal Survey of Young Men data to estimate returns to schooling.