Quantile Treatment Effects in High Dimensional Panel Data

2025-04-01

AI Summary

This paper addresses the estimation of quantile causal effects under sparse interventions (affecting only a few units) in high-dimensional panel data (large N and large T), moving beyond the limitations of conventional average treatment effect (ATE) frameworks. We propose the Quantile Generalized Synthetic Control (QGSC) method—the first extension of synthetic control to quantile regression—accommodating quantile-varying latent factor structures. We establish consistency and asymptotic normality of the estimator and develop a quantile-adaptive bootstrap procedure for valid inference. Monte Carlo simulations demonstrate robust finite-sample performance. An empirical application to China’s 2008 RMB 4-trillion stimulus reveals substantial heterogeneity across the GDP growth distribution: lower-income regions experience significantly larger gains at middle-to-lower quantiles, underscoring the importance of distributional policy evaluation.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Causality
• Game Theory and Economic Paradigms: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Economic ramifications for generative AI infrastructure and applications
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Practical large-scale studies of user experience

Abstract

We introduce a novel estimator for quantile causal effects with high-dimensional panel data (large $N$ and $T$), where only one or a few units are affected by the intervention or policy. Our method extends the generalized synthetic control method (Xu 2017) from average treatment effect on the treated to quantile treatment effect on the treated, allowing the underlying factor structure to change across the quantile of the interested outcome distribution. Our method involves estimating the quantile-dependent factors using the control group, followed by a quantile regression to estimate the quantile treatment effect using the treated units. We establish the asymptotic properties of our estimator and propose a bootstrap procedure for statistical inference, supported by simulation studies. An empirical application of the 2008 China Stimulus Program is provided.

Problem

• Estimating quantile causal effects in high-dimensional panel data
• Extending synthetic control to quantile treatment effects
• Handling factor structure changes across outcome quantiles

Innovation

• Extends synthetic control to quantile treatment effects
• Estimates quantile-dependent factors from controls
• Uses quantile regression for treated units