Nonlinear Spatial Dynamic Panel Data Model With Endogenous Dominant Units

This paper develops a nonlinear spatial dynamic panel data model, with one particularly interesting application to a structural interaction model for share data. To account for effects from popular units, the spatial weights matrices in our model can allow for dominant units, with unbounded column sums. To account for heterogeneity, our model includes individual fixed effects and heteroskedastic errors. We further consider the potential time-varying endogeneity in spatial weights when weights are constructed by socioeconomic distances. For parameter estimation, we propose the quasi-maximum likelihood estimator (QMLE), generalized methods of moments estimator (GMME) and root estimator (RTE), and establish their consistency and asymptotic normality based on the near epoch dependence (NED) framework. We show that the RTE is asymptotically as efficient as the QMLE in the homoskedastic case, and is asymptotically as efficient as the GMME in the heteroskedastic case. For the panel data setting, we cover both $n,T\rightarrow\infty$ and large $n$ with finite $T$, and the strength of the dominant units equals to 1 as long as $T\rightarrow\infty$. In the empirical application, we apply our model to China's prefectural city-level data and find significant spillover effects of the employment share of tertiary industry, indicating that the development of tertiary industry in large cities can promote the tertiary industry in small cities