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Heterogeneous Treatment Effects in Panel Data

Retsef Levi, Elisabeth Paulson, Georgia Perakis, Emily Zhang

TL;DR

This paper introduces PaCE, a two-stage method for estimating heterogeneous treatment effects in panel data with general treatment patterns. It first partitions observations into homogeneous-effect clusters using a regression-tree framework and then estimates cluster-level average treatment effects by exploiting an assumed low-rank panel structure via a de-biased convex estimator. Theoretical results establish polynomial decay of regression-tree bias and an optimal (up to log factors) convergence rate for cluster-ATE estimation when the number of treatments scales as $k=O( ext{log} n)$, with empirical validation on semi-synthetic data showing PaCE often outperforms conventional baselines while remaining interpretable (tree with $ ext{≤}40$ leaves). The work broadens low-rank panel-methods to multiple treatments and offers a practical, interpretable tool for policy and business decision-making in causal inference tasks. Future work includes deriving confidence intervals and expanding evaluations to more diverse treatment patterns and datasets.

Abstract

We address a core problem in causal inference: estimating heterogeneous treatment effects using panel data with general treatment patterns. Many existing methods either do not utilize the potential underlying structure in panel data or have limitations in the allowable treatment patterns. In this work, we propose and evaluate a new method that first partitions observations into disjoint clusters with similar treatment effects using a regression tree, and then leverages the (assumed) low-rank structure of the panel data to estimate the average treatment effect for each cluster. Our theoretical results establish the convergence of the resulting estimates to the true treatment effects. Computation experiments with semi-synthetic data show that our method achieves superior accuracy compared to alternative approaches, using a regression tree with no more than 40 leaves. Hence, our method provides more accurate and interpretable estimates than alternative methods.

Heterogeneous Treatment Effects in Panel Data

TL;DR

This paper introduces PaCE, a two-stage method for estimating heterogeneous treatment effects in panel data with general treatment patterns. It first partitions observations into homogeneous-effect clusters using a regression-tree framework and then estimates cluster-level average treatment effects by exploiting an assumed low-rank panel structure via a de-biased convex estimator. Theoretical results establish polynomial decay of regression-tree bias and an optimal (up to log factors) convergence rate for cluster-ATE estimation when the number of treatments scales as , with empirical validation on semi-synthetic data showing PaCE often outperforms conventional baselines while remaining interpretable (tree with leaves). The work broadens low-rank panel-methods to multiple treatments and offers a practical, interpretable tool for policy and business decision-making in causal inference tasks. Future work includes deriving confidence intervals and expanding evaluations to more diverse treatment patterns and datasets.

Abstract

We address a core problem in causal inference: estimating heterogeneous treatment effects using panel data with general treatment patterns. Many existing methods either do not utilize the potential underlying structure in panel data or have limitations in the allowable treatment patterns. In this work, we propose and evaluate a new method that first partitions observations into disjoint clusters with similar treatment effects using a regression tree, and then leverages the (assumed) low-rank structure of the panel data to estimate the average treatment effect for each cluster. Our theoretical results establish the convergence of the resulting estimates to the true treatment effects. Computation experiments with semi-synthetic data show that our method achieves superior accuracy compared to alternative approaches, using a regression tree with no more than 40 leaves. Hence, our method provides more accurate and interpretable estimates than alternative methods.
Paper Structure (34 sections, 20 theorems, 162 equations, 1 figure, 4 tables, 1 algorithm)

This paper contains 34 sections, 20 theorems, 162 equations, 1 figure, 4 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Regression tree with bounded bias (\ref{['thm: tree']})
  3. Optimal rate for average treatment effect estimation (\ref{['thm: convergence']})
  4. Enhanced empirical accuracy with simple estimator
  5. Related literature
  6. General notation
  7. Model and algorithm
  8. Clustering the observations
  9. Step 1
  10. Step 2
  11. Estimating the average treatment effect within each cluster
  12. Theoretical guarantees
  13. Approximation error
  14. Estimation error
  15. Empirical evaluation
  16. ...and 19 more sections

Key Result

Lemma 2.1

Suppose $(\hat{M}, \hat{m}, \hat{\tau})$ is a minimizer of eq:convex-program. Let $\hat{M} = \hat{U}\hat{\Sigma} \hat{V}^{\top}$ be the SVD of $\hat{M}$, and let $\hat{\mathbf T}$ denote the span of the tangent space of $\hat{M}$ and $\left\{ \alpha \mathbf 1^\top \mid \alpha \in \mathbb R^n \right where $D \in \mathbb {R}^{k \times k}$ is the matrix with entries $D_{ij} = \langle P_{\hat{\mathbf

Figures (1)

  • Figure 1: nMAE for SNAP experiments as the proportion of treated units increases.

Theorems & Definitions (44)

  • Lemma 2.1: Error decomposition
  • Theorem 3.2
  • Theorem 3.5
  • proof : Proof of \ref{['thm: tree']}
  • Lemma A.1
  • proof
  • Lemma A.2
  • proof
  • Lemma B.1
  • proof
  • ...and 34 more