Estimation and Inference on Average Treatment Effect in Percentage Points under Heterogeneity

Abstract

In semi-logarithmic regressions, treatment coefficients are often interpreted as approximations of an average treatment effect (ATE) in percentage points. This paper highlights the overlooked bias of this approximation under treatment effect heterogeneity, arising from Jensen's inequality. The issue is particularly relevant for difference-in-differences designs with log-transformed outcomes and staggered treatment adoption, where treatment effects may vary across groups and periods. This paper proposes new estimation and inference methods for an estimand that accounts for heterogeneity across observable subgroups and can improve upon conventional measures. The estimand provides a lower bound on the ATE in percentage points for the relevant target (sub)population, and coincides with it in the absence of within-group heterogeneity. I establish the methods' large-sample properties and study their finite-sample performance through Monte Carlo experiments, which reveal substantial discrepancies between conventional and proposed measures when systematic heterogeneity is large. Two empirical applications further underscore the practical importance of these methods.