Instrumental Variable Quantile Regression with Misclassification

TL;DR

This paper develops identification and inference methods for instrumental variable quantile regression models with binary endogenous treatments when treatment data is misclassified or measured with error, providing bounds and sharp identified sets.

Contribution

It introduces novel identification results and inference procedures for IV quantile regression with misclassified or error-prone treatment variables, extending prior work.

Findings

Reduced-form quantile regression bounds the structural quantile treatment effect.

Sharp identified set derived under measurement error assumptions.

Proposed inference method accommodates additional covariates.

Abstract

This paper considers the instrumental variable quantile regression model (Chernozhukov and Hansen, 2005, 2013) with a binary endogenous treatment. It offers two identification results when the treatment status is not directly observed. The first result is that, remarkably, the reduced-form quantile regression of the outcome variable on the instrumental variable provides a lower bound on the structural quantile treatment effect under the stochastic monotonicity condition (Small and Tan, 2007; DiNardo and Lee, 2011). This result is relevant, not only when the treatment variable is subject to misclassification, but also when any measurement of the treatment variable is not available. The second result is for the structural quantile function when the treatment status is measured with error; I obtain the sharp identified set by deriving moment conditions under widely-used assumptions on the measurement error. Furthermore, I propose an inference method in the presence of other covariates.