Identification and Estimation of Nonseparable Triangular Equations with Mismeasured Instruments

TL;DR

This paper develops a nonparametric method to identify and estimate the effect of an endogenous variable on an outcome using potentially mismeasured instruments, addressing measurement error and nonseparability without linearity assumptions.

Contribution

It introduces a novel nonparametric identification and estimation approach for models with mismeasured instruments and nonseparable functions, extending existing methods.

Findings

Proposes a deconvolution-based identification strategy.

Develops nonparametric estimators with proven convergence rates.

Monte Carlo simulations demonstrate good finite sample performance.

Abstract

In this paper, I study the nonparametric identification and estimation of the marginal effect of an endogenous variable $X$ on the outcome variable $Y$, given a potentially mismeasured instrument variable $W^*$, without assuming linearity or separability of the functions governing the relationship between observables and unobservables. To address the challenges arising from the co-existence of measurement error and nonseparability, I first employ the deconvolution technique from the measurement error literature to identify the joint distribution of $Y, X, W^*$ using two error-laden measurements of $W^*$. I then recover the structural derivative of the function of interest and the "Local Average Response" (LAR) from the joint distribution via the "unobserved instrument" approach in Matzkin (2016). I also propose nonparametric estimators for these parameters and derive their uniform rates of convergence. Monte Carlo exercises show evidence that the estimators I propose have good finite sample performance.