[Paper Review] Bootstrap inference for panel data quantile regression

Antonio F. Galvao, Thomas Parker+1 more|arXiv (Cornell University)|Nov 5, 2021

Spatial and Panel Data Analysis64 references4 citations

TL;DR

This paper proposes a random-weighted bootstrap method for valid inference in panel data quantile regression with fixed effects, preserving temporal dependence and enabling accurate standard errors, confidence intervals, and hypothesis tests. The method is formally proven asymptotically valid under weak dependence conditions, offering a robust alternative to asymptotic approximations that often distort finite-sample inference.

ABSTRACT

This paper develops bootstrap methods for practical statistical inference in panel data quantile regression models with fixed effects. We consider random-weighted bootstrap resampling and formally establish its validity for asymptotic inference. The bootstrap algorithm is simple to implement in practice by using a weighted quantile regression estimation for fixed effects panel data. We provide results under conditions that allow for temporal dependence of observations within individuals, thus encompassing a large class of possible empirical applications. Monte Carlo simulations provide numerical evidence the proposed bootstrap methods have correct finite sample properties. Finally, we provide an empirical illustration using the environmental Kuznets curve.

Motivation & Objective

• To develop a practical and theoretically valid bootstrap method for inference in panel data quantile regression with fixed effects.
• To address the limitations of asymptotic approximations, which often yield distorted confidence intervals in finite samples due to difficult density estimation.
• To formalize the theoretical properties of the random-weighted bootstrap in the context of panel data quantile regression with temporal dependence.
• To provide a computationally simple method that preserves serial correlation in the bootstrap resampling process.
• To establish consistency of bootstrap standard errors, confidence intervals, and variance-covariance estimators under weak dependence conditions.

Proposed method

• Uses random-weighted bootstrap resampling, where weights are i.i.d. random variables independent of the data, to generate bootstrap samples.
• Applies weighted quantile regression estimation to compute bootstrap estimates of the fixed effects quantile regression parameters.
• Employs a conditional bootstrap procedure that preserves the temporal dependence structure within each individual's time series.
• Establishes asymptotic validity by proving distributional consistency of the bootstrap distribution for the estimated coefficients.
• Demonstrates consistency of the resampled variance-covariance matrix as an estimator of the asymptotic variance-covariance matrix.
• Relies on β-mixing conditions in the time dimension, extending validity to models with weakly dependent errors.

Experimental results

Research questions

• RQ1 Can the random-weighted bootstrap provide asymptotically valid inference for fixed effects quantile regression in panel data with temporal dependence?
• RQ2 How does the bootstrap perform in finite samples compared to asymptotic normal approximations, especially when density estimation is challenging?
• RQ3 Does the bootstrap preserve the serial correlation structure of the original data, and how does this affect inference accuracy?
• RQ4 Is the resampled variance-covariance matrix consistent for estimating the asymptotic variance of the fixed effects quantile regression estimator?
• RQ5 What are the theoretical conditions under which the bootstrap distribution converges to the true sampling distribution of the estimator?

Key findings

• The random-weighted bootstrap is asymptotically valid for inference in panel data quantile regression with fixed effects, even under temporal dependence.
• Monte Carlo simulations show that bootstrap-based confidence intervals have better finite-sample coverage than asymptotic normal approximations, which are often distorted.
• The bootstrap method does not require bandwidth selection or density estimation, avoiding a major source of finite-sample error in asymptotic inference.
• The resampled variance-covariance matrix is consistent for the asymptotic variance-covariance matrix, ensuring reliable inference.
• The method is robust to weak dependence in the time dimension, as formalized under β-mixing conditions.
• Empirical application to the environmental Kuznets curve demonstrates the method’s practical utility in real-world panel data analysis.