Testing Endogeneity of Spatial Weights Matrices in Spatial Dynamic Panel Data Models

TL;DR

This paper introduces a robust score test for detecting endogeneity in spatial weights matrices within spatial dynamic panel data models, addressing bias and misspecification issues, supported by simulations and an empirical application.

Contribution

It develops a bias-corrected Rao's Score test for endogeneity in spatial weights matrices, improving accuracy under misspecification in spatial dynamic panel models.

Findings

The test performs well in finite samples according to simulations.

It effectively detects endogeneity in empirical data.

The method accounts for fixed effects and local misspecification.

Abstract

I propose Robust Rao's Score (RS) test statistic to determine endogeneity of spatial weights matrices in a spatial dynamic panel data (SDPD) model (Qu, Lee, and Yu, 2017). I firstly introduce the bias-corrected score function since the score function is not centered around zero due to the two-way fixed effects. I further adjust score functions to rectify the over-rejection of the null hypothesis under a presence of local misspecification in contemporaneous dependence over space, dependence over time, or spatial time dependence. I then derive the explicit forms of our test statistic. A Monte Carlo simulation supports the analytics and shows nice finite sample properties. Finally, an empirical illustration is provided using data from Penn World Table version 6.1.