Interpreting Unconditional Quantile Regression with Conditional Independence

TL;DR

This paper offers a deeper interpretation of unconditional quantile regression methods, clarifying their applicability and limitations under conditional independence assumptions for policy effect estimation.

Contribution

It provides additional insights into the interpretation of unconditional quantile effects and delineates the types of policy changes these methods can accurately estimate.

Findings

Unconditional quantile effects are interpretable under conditional independence.

Methods estimate effects for policies satisfying conditional independence.

Limitations exist for policies that do not meet the conditional independence assumption.

Abstract

This note provides additional interpretation for the counterfactual outcome distribution and corresponding unconditional quantile "effects" defined and estimated by Firpo, Fortin, and Lemieux (2009) and Chernozhukov, Fern\'andez-Val, and Melly (2013). With conditional independence of the policy variable of interest, these methods estimate the policy effect for certain types of policies, but not others. In particular, they estimate the effect of a policy change that itself satisfies conditional independence.