Nonparametric Bounds on Treatment Effects with Imperfect Instruments

Abstract

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