A General Approach to Relaxing Unconfoundedness

TL;DR

This paper introduces a comprehensive framework for relaxing the unconfoundedness assumption, enabling comparison of existing models and deriving new bounds for various treatment effect parameters beyond averages.

Contribution

It presents a unified class of relaxations for unconfoundedness, including prior models, and derives novel sharp bounds for parameters like QTE and DTE.

Findings

Includes several previous relaxations as special cases.

Provides sharp bounds for QTE and DTE.

Enables sensitivity analysis beyond average effects.

Abstract

This paper defines a general class of relaxations of the unconfoundedness assumption. This class includes several previous approaches as special cases, including the marginal sensitivity model of Tan (2006). This class therefore allows us to precisely compare and contrast these previously disparate relaxations. We use this class to derive a variety of new identification results which can be used to assess sensitivity to unconfoundedness. In particular, the prior literature focuses on average parameters, like the average treatment effect (ATE). We move beyond averages by providing sharp bounds for a large class of parameters, including both the quantile treatment effect (QTE) and the distribution of treatment effects (DTE), results which were previously unknown even for the marginal sensitivity model.