Nonparametric bounds on treatment effects with imperfect instruments

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.

Identification with Possibly Invalid IVs

“…Wang (2023) point identifies the LATE with an exogenous quasi-IV satisfying the standard monotonicity assumption of Imbens and Angrist (1994) and another exogenous and excluded IV that can violate monotonicity. Some other works bound the treatment effects with an exogenous quasi-IV IV, see Manski and Pepper (2000); Nevo and Rosen (2012); Conley et al (2012); Flores and Flores-Lagunes (2013); Mealli and Pacini (2013); Ban and Kédagni (2022) among others. Bartels (1991) also uses the term "quasi-IV", but referring to variables that can be both included and endogenous, but only slightly deviating from the exclusion/exogeneity requirements.…”