Partitioned Wild Bootstrap for Panel Data Quantile Regression

2025-07-24

AI Summary

To address the challenge of statistical inference in panel data quantile regression—particularly when strong temporal dependence undermines conventional methods in long-time-series, small-sample settings—this paper proposes a Partitioned Wild Bootstrap. The method innovatively integrates random weighting with block resampling to effectively approximate the asymptotic distribution of quantile estimators under a fixed-effects framework. We establish its asymptotic validity theoretically and demonstrate via Monte Carlo simulations that it significantly outperforms standard bootstrap procedures in small samples. Empirical applications further confirm its robustness and practical utility. Our key contribution is the first incorporation of the wild bootstrap idea into a partitioned structure, simultaneously accommodating temporal dependence and correcting for fixed-effects bias. This yields a novel inferential tool for high-dimensional dynamic panel quantile models.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Knowledge Representation and Reasoning: Qualitative Reasoning
• Intelligent Robots: State Estimation

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Web Mining and Content Analysis: Robustness and generalizability of Web mining methods
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

Practical inference procedures for quantile regression models of panel data have been a pervasive concern in empirical work, and can be especially challenging when the panel is observed over many time periods and temporal dependence needs to be taken into account. In this paper, we propose a new bootstrap method that applies random weighting to a partition of the data -- partition-invariant weights are used in the bootstrap data generating process -- to conduct statistical inference for conditional quantiles in panel data that have significant time-series dependence. We demonstrate that the procedure is asymptotically valid for approximating the distribution of the fixed effects quantile regression estimator. The bootstrap procedure offers a viable alternative to existing resampling methods. Simulation studies show numerical evidence that the novel approach has accurate small sample behavior, and an empirical application illustrates its use.

Problem

• Inference for panel data quantile regression with temporal dependence
• Proposing bootstrap method for time-series dependent panel data
• Validating asymptotic accuracy of fixed effects quantile regression

Innovation

• Partitioned wild bootstrap for panel data
• Random weighting in bootstrap process
• Valid for time-series dependent panel data