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

TL;DR

This paper addresses bias in estimating average treatment effects in percentage points within semi-log regressions, proposing new methods that account for heterogeneity and improve inference accuracy, especially in difference-in-differences designs.

Contribution

It introduces a new estimand that bounds the ATE in percentage points, accounting for heterogeneity, and develops estimation and inference methods with proven large-sample properties.

Findings

Monte Carlo simulations show significant differences between conventional and proposed measures under heterogeneity.

The new estimand provides a lower bound on the true ATE in percentage points.

Empirical applications demonstrate the practical relevance of the proposed methods.

Abstract

In semi-logarithmic regressions, treatment coefficients are often interpreted as approximations of the 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 often vary across groups and periods. This paper proposes new estimation and inference methods for an estimand that accounts for heterogeneity across observable subgroups and improves upon conventional measures. The estimand provides a lower bound on the ATE in percentage points, 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.