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

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.