Abstract: I consider a simultaneous system of spatial panel data models, jointly modeling three effects: simultaneous effects, spatial effects and common shock effects. The simultaneous effect comes from endogeneity between dependent variables in a simultaneous equations system and is important in structural economic modeling. The spatial effect is present in models where dependent variables are spatially interacted in a geographical space or in more general economic, social or production network spaces. Common shocks stem from a common factor structure in panel data models, where the dependent variables' responses to shocks (i.e., factors) are heterogeneous and captured by the factor loadings. For example, this framework including these three effects can be used to establish the causal relationship between trade and GDP: (1) simultaneous effects: within a country, trade is endogenously correlated with GDP; (2) spatial effects: a country's trade (or GDP) might be affected by other countries' trade (or GDP) through trade and financial linkages across countries; (3) common shock effects: global financial, energy or other types of shocks might affect trade and GDP of all countries.
The joint modeling of these three effects and consideration of cross-sectional heteroscedasticity result in a large number of incidental parameters. I propose two estimation approaches, the quasi maximum likelihood (QML) method and an iterative generalized principal components (IGPC) method. I develop a full inferential theory for the two estimation approaches, and study the trade-off between model specification and their respective asymptotic properties. I further investigate the finite sample performance of both methods using Monte Carlo simulations, and find that both methods perform well and simulation results corroborate the inferential theories. Some extensions of the model are considered. Finally, I apply the model to analyze the causal relationship between trade and GDP.
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