[Paper Review] Identifying spatial interdependence in panel data with large N and small T

Deborah Gefang, Stephen Hall+1 more|arXiv (Cornell University)|Sep 7, 2023

Spatial and Panel Data AnalysisEconomics, Econometrics and Finance3 citations

TL;DR

This paper proposes a two-stage variational Bayesian algorithm for estimating panel spatial autoregressive models with large N and small T, using Dirichlet-Laplace priors for variable selection and parameter shrinkage without predefining spatial weights. The method efficiently identifies spatial interdependence from data, outperforming existing approaches in speed and accuracy, with Monte Carlo studies showing strong recovery of true spatial weight matrices and empirical application revealing novel cross-country growth linkages in EU regions.

ABSTRACT

This paper develops a simple two-stage variational Bayesian algorithm to estimate panel spatial autoregressive models, where N, the number of cross-sectional units, is much larger than T, the number of time periods without restricting the spatial effects using a predetermined weighting matrix. We use Dirichlet-Laplace priors for variable selection and parameter shrinkage. Without imposing any a priori structures on the spatial linkages between variables, we let the data speak for themselves. Extensive Monte Carlo studies show that our method is super-fast and our estimated spatial weights matrices strongly resemble the true spatial weights matrices. As an illustration, we investigate the spatial interdependence of European Union regional gross value added growth rates. In addition to a clear pattern of predominant country clusters, we have uncovered a number of important between-country spatial linkages which are yet to be documented in the literature. This new procedure for estimating spatial effects is of particular relevance for researchers and policy makers alike.

Motivation & Objective

• To address the challenge of identifying spatial interdependence in panel data with large cross-sectional units (N) and few time periods (T).
• To develop a computationally efficient estimation method that does not rely on pre-specified spatial weighting matrices.
• To enable data-driven discovery of spatial linkages through flexible prior structures.
• To improve estimation accuracy and speed in high-dimensional spatial panel models.

Proposed method

• A two-stage variational Bayesian algorithm is proposed for estimating panel spatial autoregressive models.
• Dirichlet-Laplace priors are used to enable simultaneous variable selection and parameter shrinkage.
• The method avoids imposing any a priori spatial structure on linkages, allowing data to determine spatial dependencies.
• Spatial weights matrices are estimated directly from the data without assuming a fixed or known connectivity structure.
• The algorithm is designed to be computationally efficient, suitable for large N and small T settings.
• The approach enables robust inference on spatial effects even when the true spatial structure is unknown.

Experimental results

Research questions

• RQ1 How can spatial interdependence be reliably identified in panel data with large N and small T when no prior spatial structure is assumed?
• RQ2 To what extent can a data-driven Bayesian method recover the true spatial weight matrix without pre-specified spatial weights?
• RQ3 What are the key spatial linkages between regional growth rates in the European Union that remain undetected in existing literature?
• RQ4 How does the proposed method compare in speed and accuracy to conventional estimation techniques in high-dimensional spatial panel models?
• RQ5 Can the method uncover meaningful regional clusters and interdependencies in real-world economic data?

Key findings

• The proposed method is significantly faster than conventional approaches, enabling efficient estimation in large-N, small-T settings.
• Monte Carlo studies demonstrate that the estimated spatial weight matrices closely resemble the true underlying matrices.
• The method successfully identifies predominant country clusters in EU regional growth dynamics.
• Novel between-country spatial linkages in EU regional gross value added growth are uncovered, which have not been previously documented.
• The use of Dirichlet-Laplace priors enables effective shrinkage and variable selection, improving model interpretability.
• Empirical results reveal previously undetected spatial interdependence patterns, highlighting the method's potential for policy-relevant insights.