Uniform Inference on High-dimensional Spatial Panel Networks

TL;DR

This paper develops a uniform inference framework for high-dimensional spatial panel networks using a debiased regularized GMM estimator, enabling hypothesis testing on network parameters with proven consistency and asymptotic normality.

Contribution

It introduces a novel debiased-regularized GMM estimator for large-scale spatial networks, with a uniform inference theory applicable to both linear and nonlinear moments.

Findings

Estimator shows superior performance in simulations

Enables hypothesis testing on network structure parameters

Applicable to both linear and nonlinear moment conditions

Abstract

We propose employing a high-dimensional generalized method of moments (GMM) estimator, regularized for dimension reduction and subsequently debiased to correct for shrinkage bias (referred to as a debiased-regularized estimator), for inference on large-scale spatial panel networks. In particular, the network structure, which incorporates a flexible sparse deviation that can be regarded either as a latent component or as a misspecification of a predetermined adjacency matrix, is estimated using a debiased machine learning approach. The theoretical analysis establishes the consistency and asymptotic normality of our proposed estimator, taking into account general temporal and spatial dependencies inherent in the data-generating processes. A primary contribution of our study is the development of a uniform inference theory, which enables hypothesis testing on the parameters of interest, including zero or non-zero elements in the network structure. Additionally, the asymptotic properties of the estimator are derived for both linear and nonlinear moments. Simulations demonstrate the superior performance of our proposed approach. Finally, we apply our methodology to investigate the spatial network effects of stock returns.