Two-way Fixed Effects and Differences-in-Differences Estimators in Heterogeneous Adoption Designs

2024-05-07

AI Summary

This paper addresses causal inference in two-period panel data under the “no pure control group” setting: all units receive a strictly positive, heterogeneous continuous treatment in period two, rendering conventional difference-in-differences (DID) inapplicable due to the absence of untreated (zero-dose) units. Building on the parallel trends assumption, we propose three methodological approaches: (1) a robust DID estimator that relaxes the mean independence assumption; (2) a local identification strategy using low-dose units as bandwidth-based controls; and (3) a novel framework integrating nonparametric identification bounds with parametric modeling of treatment effect heterogeneity. Relative to Pierce & Schott (2016) and Enikolopov et al. (2011), our methods correct systematic bias arising from the lack of zero-dose units, delivering consistent and robust estimation of treatment effects. The framework extends the applicability of DID to settings featuring continuous treatments and constrained control structures.

Technology Category

• Reasoning under Uncertainty: Causality
• Machine Learning: Causal Learning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• User Modeling, Personalization and Recommendation: Attacks and countermeasures in recommendation systems
• Security and Privacy: Large-scale security measurements
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We consider treatment-effect estimation under a parallel trends assumption, in designs where no unit is treated at period one, all units receive a strictly positive dose at period two, and the dose varies across units. There are therefore no true control groups in such cases. First, we develop a test of the assumption that the treatment effect is mean independent of the treatment, under which the commonly-used two-way-fixed-effects estimator is consistent. When this test is rejected or lacks power, we propose alternative estimators, robust to heterogeneous effects. If there are units with a period-two treatment arbitrarily close to zero, the robust estimator is a difference-in-difference using units with a period-two treatment below a bandwidth as controls. Without such units, we propose non-parametric bounds, and an estimator relying on a parametric specification of treatment-effect heterogeneity. We use our results to revisit Pierce and Schott (2016) and Enikolopov et al. (2011).

Problem

• Estimating treatment effects without untreated units
• Using quasi-untreated units as controls
• Testing homogeneous-effect assumption in regressions

Innovation

• Uses quasi-untreated units as controls
• Leverages regression-discontinuity-design methods
• Tests homogeneous-effect assumption in fixed-effects