[Paper Review] Inference without smoothing for large panels with cross-sectional and temporal dependence

Javier Hidalgo, Marcia M. A. Schafgans|arXiv (Cornell University)|Jun 25, 2020

Spatial and Panel Data Analysis3 citations

TL;DR

This paper proposes a cluster-based inference method and nonparametric bootstrap schemes for large panel data models with general cross-sectional and temporal dependence, avoiding the need for bandwidth or smoothing parameters. It establishes asymptotic normality via frequency-domain wild bootstraps and spectral decomposition, enabling valid inference without parametric assumptions on dependence structures.

ABSTRACT

This paper addresses inference in large panel data models in the presence of both cross-sectional and temporal dependence of unknown form. We are interested in making inferences that do not rely on the choice of any smoothing parameter as is the case with the often employed "HAC" estimator for the covariance matrix. To that end, we propose a cluster estimator for the asymptotic covariance of the estimators and valid bootstrap schemes that do not require the selection of a bandwidth or smoothing parameter and accommodate the nonparametric nature of both temporal and cross-sectional dependence. Our approach is based on the observation that the spectral representation of the fixed effect panel data model is such that the errors become approximately temporally uncorrelated. Our proposed bootstrap schemes can be viewed as wild bootstraps in the frequency domain. We present some Monte-Carlo simulations to shed some light on the small sample performance of our inferential procedure.

Motivation & Objective

• To develop valid inference procedures for large panel data models when both cross-sectional and temporal dependence are present and unknown.
• To eliminate reliance on bandwidth or smoothing parameters typically required in HAC estimators for covariance matrix estimation.
• To address the limitations of parametric models in capturing complex, heterogeneous dependence across individuals and time.
• To propose bootstrap methods that are nonparametric and robust to unknown dependence forms in both dimensions.
• To establish asymptotic normality and validity of inference under weak dependence and nonparametric error structures.

Proposed method

• Uses spectral decomposition of the fixed-effect panel model to render errors approximately temporally uncorrelated.
• Applies a cluster estimator for the asymptotic covariance matrix that accounts for both cross-sectional and temporal dependence without smoothing.
• Develops frequency-domain wild bootstrap schemes that avoid bandwidth selection by leveraging discrete Fourier transforms.
• Employs Bartlett-type kernel approximations and Parseval’s identity to analyze spectral moments and asymptotic distributions.
• Implements bootstrap procedures based on Fourier coefficients of error processes, ensuring consistency under general dependence.
• Uses Bernstein’s lemma and moment conditions to prove convergence to normal limits under weak dependence and summability of spectral weights.

Experimental results

Research questions

• RQ1 Can valid inference be performed in large panels with unknown cross-sectional and temporal dependence without relying on bandwidth selection or smoothing?
• RQ2 How can bootstrap procedures be designed to be nonparametric and robust to general forms of dependence in both time and cross-section?
• RQ3 What is the asymptotic distribution of estimators under general dependence structures when both n and T grow?
• RQ4 Can spectral methods and frequency-domain bootstraps replace traditional HAC estimators in large panels?
• RQ5 What are the conditions under which cluster-based inference and wild bootstraps yield valid asymptotic approximations?

Key findings

• The proposed cluster estimator consistently estimates the asymptotic covariance matrix without requiring bandwidth or smoothing parameters.
• The frequency-domain wild bootstrap schemes are asymptotically valid and do not require parametric assumptions on the dependence structure.
• Asymptotic normality of the estimator is established under weak dependence and summability of spectral weights.
• The bootstrap procedure achieves convergence in distribution to a normal limit via Bernstein’s lemma and moment bounds.
• The method remains valid even when temporal dependence varies across individuals, avoiding the need for individual-specific bandwidth selection.
• Monte Carlo simulations confirm good small-sample performance, supporting the robustness of the proposed inference framework.