Welfare Analysis via Marginal Treatment Effects

TL;DR

This paper demonstrates that social welfare can be identified using marginal treatment effects in models with endogeneity and unobserved confounders, enabling improved treatment decision rules.

Contribution

It introduces a novel representation of social welfare via MTE as an operator kernel, applicable to various treatment choice rules, including empirical welfare maximization.

Findings

Welfare function can be identified via MTE in endogenous models.

Provides convergence rates for welfare loss in EWM framework.

Applicable to a range of statistical decision rules.

Abstract

Consider a causal structure with endogeneity (i.e., unobserved confoundedness) in empirical data, where an instrumental variable is available. In this setting, we show that the mean social welfare function can be identified and represented via the marginal treatment effect (MTE, Bjorklund and Moffitt, 1987) as the operator kernel. This representation result can be applied to a variety of statistical decision rules for treatment choice, including plug-in rules, Bayes rules, and empirical welfare maximization (EWM) rules as in Hirano and Porter (2020, Section 2.3). Focusing on the application to the EWM framework of Kitagawa and Tetenov (2018), we provide convergence rates of the worst case average welfare loss (regret) in the spirit of Manski (2004).