Identification and inference of outcome conditioned partial effects of general interventions

TL;DR

This paper introduces outcome conditioned partial policy effects (OCPPEs), a new distributional causal measure that estimates the impact of interventions across outcome quantiles with improved statistical properties.

Contribution

It develops a novel OCPPE framework, deriving its efficiency bounds, proposing an estimator, and enabling uniform inference, with applications to policy impact analysis.

Findings

OCPPE is $\

An efficient debiased estimator for OCPPE is proposed.

Application to anti-smoking policies shows effects on birthweight percentiles.

Abstract

This paper proposes a new class of distributional causal quantities, referred to as the \textit{outcome conditioned partial policy effects} (OCPPEs), to measure the \textit{average} effect of a general counterfactual intervention of a target covariate on the individuals in different quantile ranges of the outcome distribution. The OCPPE approach is valuable in several aspects: (i) Unlike the unconditional quantile partial effect (UQPE) that is not $\sqrt{n}$-estimable, an OCPPE is $\sqrt{n}$-estimable. Analysts can use it to capture heterogeneity across the unconditional distribution of $Y$ as well as obtain accurate estimation of the aggregated effect at the upper and lower tails of $Y$. (ii) The semiparametric efficiency bound for an OCPPE is explicitly derived. (iii) We propose an efficient debiased estimator for OCPPE, and provide feasible uniform inference procedures for the OCPPE process. (iv) The efficient doubly robust score for an OCPPE can be used to optimize infinitesimal nudges to a continuous treatment by maximizing a quantile specific Empirical Welfare function. We illustrate the method by analyzing how anti-smoking policies impact low percentiles of live infants' birthweights.