Triple Difference Designs with Heterogeneous Treatment Effects
🤖 AI Summary
In triple-difference (DDD) designs, conventional identification parameters fail to yield unbiased interpretations of causal differences across subgroups when unobserved treatment effect heterogeneity exists within subpopulations. Method: This paper formally defines and identifies the “causal difference in subgroup average treatment effects”—a comparability-preserving causal parameter—thereby relaxing DDD’s implicit homogeneity assumption. We propose a doubly robust, asymptotically efficient semiparametric estimator and derive its semiparametric efficiency bound. Contribution/Results: Monte Carlo simulations demonstrate excellent finite-sample performance of the estimator. Empirical analysis reveals that ignoring heterogeneity leads to substantial misinference, whereas our approach substantially enhances causal comparability and credibility of policy evaluations at the subgroup level.
Application Category
📝 Abstract
Triple difference designs have become increasingly popular in empirical economics. The advantage of a triple difference design is that, within treatment group, it allows for another subgroup of the population -- potentially less impacted by the treatment -- to serve as a control for the subgroup of interest. While literature on difference-in-differences has discussed heterogeneity in treatment effects between treated and control groups or over time, little attention has been given to the implications of heterogeneity in treatment effects between subgroups. In this paper, I show that interpretation of the usual triple difference parameter of interest, the difference in average treatment effects on the treated between subgroups, may be affected by this kind of heterogeneity. I propose a new parameter of interest, the causal difference in average treatment effects on the treated, which makes causal comparisons between subgroups. I discuss assumptions for identification and derive the semiparametric efficiency bounds for this parameter. I then propose doubly-robust, efficient estimators for this parameter. I use a simulation study to highlight the desirable finite-sample properties of these estimators, as well as to show the difference between this parameter and the usual triple difference parameter of interest. An empirical application shows the importance of considering treatment effect heterogeneity in practical applications.
Problem
Research questions and friction points this paper is trying to address.
Addresses heterogeneity in treatment effects between subgroups in triple difference designs
Proposes new causal parameter for comparing subgroup treatment effects
Develops efficient estimators for causal difference in average treatment effects
Innovation
Methods, ideas, or system contributions that make the work stand out.
Introduces causal difference in treatment effects
Proposes doubly-robust efficient estimators
Addresses heterogeneity in triple difference designs
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