Unbalanced or Incomplete Spatial Panel Data Models with Fixed Effects

We consider estimation and inferences for fixed effects spatial panel data models based on unbalanced panels that arise from nonparticipation or inaction of some spatial units in certain time periods. The unbalanced nature of the panel data renders the standard transformation method of estimation inapplicable. In this paper, we propose an M-estimation method where the estimating functions are obtained by adjusting the concentrated quasi scores to account for the estimation of fixed effects and/or the presence of unknown spatiotemporal heteroskedasticity. The method allows for general time-varying and non-normalized spatial weight matrices, and is able to give a full control of all individual and time specific fixed effects involved in the model. Consistency and asymptotic normality of the proposed estimators are established. Inference methods are introduced and their consistency is proved. Monte Carlo results show that the proposed methods perform well in finite sample and are fairly robust against mild departures from the postulated unbalancedness mechanism. Various extensions of the methods, including an incomplete spatial panel data model with missing-on-response-only, are critically discussed