Abstract
We consider a simultaneous spatial panel data model, jointly modeling three effects: simultaneous effects, spatial effects and common shock effects. This joint modeling and consideration of cross-sectional heteroscedasticity result in a large number of incidental parameters. We propose two estimation approaches, a quasi-maximum likelihood method and an iterative generalized principal components method. We develop full inferential theories for the estimation approaches and study the tradeoff between the model specifications and their respective asymptotic properties. We further investigate the finite sample performance of both methods using Monte Carlo simulations. We find that both methods perform well and that the simulation results corroborate the inferential theories. Some extensions of the model are considered. Finally, we apply the model to analyze the relationship between trade and gross domestic product using a panel data over time and across countries.
Highlights
In this paper, I consider a simultaneous spatial panel data model, jointly modeling three effects: simultaneous effects, spatial effects and common shock effects.1 First, the simultaneous effect comes from the endogeneity of the dependent variables in a simultaneous equation system, and is important in many structural economic modeling
In the iterative generalized principal components (IGPC) approach, I do not specify the model for the explanatory variables but allow them to be arbitrarily correlated with the common factors and loadings, which is a more general approach than that used in quasi-maximum likelihood (QML)
Based on DGP1 when the model of explanatory variables is correctly specified in the QML approach, I find that the bias of IGPCE is relatively obvious compared to QMLE whose bias is close to zero
Summary
I consider a simultaneous spatial panel data model, jointly modeling three effects: simultaneous effects, spatial effects and common shock effects. First, the simultaneous effect comes from the endogeneity of the dependent variables in a simultaneous equation system, and is important in many structural economic modeling. Neither approach can be directly applied to my model due to the additional common shock effect In all these papers, the errors are assumed to be idiosyncratic (i.e., uncorrelated over time and cross section), which is too strong in applications, and potential correlation of the errors would cause their estimation methods to be inconsistent. Unlike those papers that use a single-equation approach, I study the same type of question by modeling trade and GDP as a system of simultaneous equations and taking into account the endogeneity between them naturally Despite their importance, global common shocks have not been well captured in the existing literature, whereas they can be captured using my model through a factor structure.
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