Fixed-$T$ Dynamic Spatial Panel Model with Common Shocks

We study a dynamic spatial panel model with observed regressors, interactive effects, and contemporaneous and lagged dependence in a large-$N$, fixed-$T$ framework. The spatial model constitutes an $N$-dimensional simultaneous-equations system. In this $N$-equation view, the interactive effects introduce $N$ unit-specific loading vectors. Estimating them individually when $T$ is fixed creates the type of incidental-parameters problem underlying Nickell bias. We use the $N$-equation view to account for spatial simultaneity through the spatial Jacobian. Crucially, however, we view the same model as a $T$-equation system with $N$ observations. Together with a spatially enriched random-loadings (SERL) specification, this $T$-equation view yields a quasi-likelihood without unit-specific incidental parameters. We propose a computationally tractable block-coordinate algorithm. Simulations show small estimation errors and generally near-nominal coverage probabilities. Applying the method to U.S. county female labor-force participation, we find substantial dynamic and spatial dependence and an important role for education in explaining the rise in female labor-force participation.