Semi-nonparametric estimation of spatial dynamic panel data models with nonparametric spatial weights

2026-06-23

AI Summary

This study addresses the challenge of an unknown spatial weight matrix in spatial dynamic panel models when only economic distance measures are available and no prior structural information exists. The authors develop a semi-nonparametric framework that treats the spatial weights—entering the outcome variable, its lags, and the disturbance term—as unknown functions of economic distance. A unified operator-based approach accommodates both spatial autoregressive and matrix exponential specifications while incorporating two-way fixed effects. Innovatively fully nonparametrizing the spatial weights, the paper proposes a sieve GMM estimator that stacks linear and quadratic moment conditions and employs heteroskedasticity-robust inference. Theoretical results establish √{n(T−1)} convergence and asymptotic normality for the parameter estimates, and Monte Carlo simulations confirm strong finite-sample performance. Empirically, the analysis reveals that economic-geographic proximity significantly intensifies the spatial dependence of witchcraft-related murders.

Abstract

We develop a semi-nonparametric framework for spatial dynamic panel data (SDPD) models with two-way fixed effects when the spatial interaction structure is unknown beyond a distance measure. This is accomplished by modelling spatial weights in the outcome, lagged-outcome, and disturbance channels as unknown functions of underlying economic distances. These enter the SDPD system through matrix-function operators, providing a unified approach that accommodates both spatial autoregressive and matrix exponential spatial specifications. Allowing for unknown heteroskedasticity, we propose sieve GMM estimators based on a stacked set of linear and quadratic moment conditions, and derive a feasible optimal GMM estimator and a more efficient feasible best GMM estimator. As $(n, T) \rightarrow \infty$, the parametric component is $\sqrt{n(T - 1)}$-consistent and asymptotically normal, echoing classical semi-nonparametric results. Monte Carlo experiments indicate excellent finite-sample performance. We apply the method to 'witch' killings as studied by Miguel (2005), and find that economic-geography proximity rather than cultural-geography proximity between communities significantly amplifies spatial dependence in these economic murders.

Problem

• spatial dynamic panel data
• nonparametric spatial weights
• two-way fixed effects
• spatial interaction structure
• economic distance

Innovation

• semi-nonparametric estimation
• spatial dynamic panel data
• matrix-function operators
• sieve GMM
• unknown spatial weights