Residualised Treatment Intensity and the Estimation of Average Partial Effects

TL;DR

This paper proposes R-OLS, a new estimator for the average partial effect of a continuous treatment, addressing confounding issues with a novel identification approach and demonstrating superior performance through simulations and empirical application.

Contribution

It introduces R-OLS, a novel estimator for the APE of continuous treatments that accounts for complex confounding and extends Stein's Lemma for identification.

Findings

R-OLS outperforms existing methods in simulations

The estimator is robust to moderate assumption violations

Application to Fetzer (2019) illustrates practical utility

Abstract

This paper introduces R-OLS, an estimator for the average partial effect (APE) of a continuous treatment variable on an outcome variable in the presence of non-linear and non-additively separable confounding of unknown form. Identification of the APE is achieved by generalising Stein's Lemma (Stein, 1981), leveraging an exogenous error component in the treatment along with a flexible functional relationship between the treatment and the confounders. The identification results for R-OLS are used to characterize the properties of Double/Debiased Machine Learning (Chernozhukov et al., 2018), specifying the conditions under which the APE is estimated consistently. A novel decomposition of the ordinary least squares estimand provides intuition for these results. Monte Carlo simulations demonstrate that the proposed estimator outperforms existing methods, delivering accurate estimates of the true APE and exhibiting robustness to moderate violations of its underlying assumptions. The methodology is further illustrated through an empirical application to Fetzer (2019).