A Simple Measure of Robustness for External Validity under Covariate Shifts

Abstract

This paper studies the robustness of estimated policy effects to changes in the distribution of covariates, a key determinant of the external validity of (quasi)-experimental results. I propose a novel robustness metric $\delta^*$ which measures the smallest covariate shift needed to invalidate an empirical claim about the policy effect (e.g., $ATE > 0$). I estimate $\delta^*$ via de-biased GMM, achieving a parametric rate of convergence while accommodating machine-learning estimators of treatment-effect heterogeneity (e.g., LASSO, random forests, neural networks). I develop benchmarking and calibration exercises to interpret the magnitude of $\delta^*$. I illustrate these tools in an application to the Oregon Health Insurance Experiment. Researchers can report $\delta^*$ alongside the point estimate and standard error as a third number gauging external validity under covariate shifts.