Triple Changes Estimator for Targeted Policies
TL;DR.
Triple changes combines the third comparison dimension of triple differences with the distributional identification of changes-in-changes. The result identifies an entire counterfactual outcome distribution rather than only an average effect and remains useful in nonlinear settings where mean-based triple differences can be biased.
Why this matters.
For targeted policies, the scientifically interesting effect may be distributional rather than just an average. Triple changes expands the changes-in-changes paradigm to a richer three-way design while retaining scale invariance.
Abstract
The renowned difference-in-differences (DiD) estimator relies on the assumption of ‘parallel trends,’ which may not hold in many practical applications. To address this issue, economists are increasingly considering the triple difference estimator as a more credible alternative. Both DiD and triple difference are limited to assessing average effects exclusively. An alternative avenue is offered by the changes-in-changes (CiC) estimator, which provides an estimate of the entire counterfactual distribution by relying on assumptions imposed on the distribution of potential outcomes. In this work, we extend the triple difference estimator to accommodate the CiC framework, presenting the ‘triple changes estimator’ and its identification assumptions, thereby expanding the scope of the CiC paradigm. Subsequently, we empirically evaluate the proposed framework and apply it to a study examining the impact of Medicaid expansion on children’s preventive care.
The paper at a glance
An informal guide to the problem, the idea, and the main results.
1. The problem
Average effects can miss the most important consequences of a targeted policy, especially when the policy reshapes the outcome distribution. Standard difference-based methods also impose assumptions that can be too rigid in applications.
2. The key idea
We combine the third comparison dimension of triple differences with the distributional logic of changes-in-changes. That yields a design that can recover counterfactual distributions rather than only a single mean effect.
3. Distributional identification
We introduce the triple changes estimator and derive identification assumptions for the counterfactual outcome distribution of the treated group. The construction combines the extra comparison dimension of triple differences with the monotone-transport logic of changes-in-changes.
4. Beyond average effects
Because the method identifies a counterfactual distribution, it supports distributional treatment-effect questions rather than only a mean ATT. The paper also develops partial-identification results when the point-identification conditions are relaxed.
5. How it works
- Use a third comparison dimension to relax standard trend restrictions.
- Import the distributional logic of changes-in-changes.
- Construct the target counterfactual distribution under the targeted policy.
- Estimate the resulting distributional treatment effects.
What the simulations and application show
Where this helps
Good fit
- You care about distributional policy effects rather than only average effects.
- Your policy is targeted and naturally suggests a third comparison dimension.
- You want a design-based estimator that is richer than ordinary DID or DDD.
Keep in mind
- Triple changes is designed for targeted-policy settings where a third comparison dimension is scientifically meaningful.
- Because the estimand is distributional, the framework can study changes that would be hidden by a purely average-effect analysis.
Cite this paper
@InProceedings{pmlr-v235-akbari24a,
title = {Triple Changes Estimator for Targeted Policies},
author = {Akbari, Sina and Kiyavash, Negar},
booktitle = {Proceedings of the 41st International Conference on Machine Learning},
pages = {666--695},
year = {2024},
volume = {235},
series = {Proceedings of Machine Learning Research},
publisher = {PMLR},
url = {https://proceedings.mlr.press/v235/akbari24a.html}
}