Spatial Panel Data Models with Temporal Heterogeneity

This dissertation studies the fixed effects (FE) spatial panel data (SPD) models with temporal heterogeneity (TH), where the regression coefficients and spatial coefficients are allowed to change with time. The FE-SPD model with time-varying coefficients renders the usual transformation method in dealing with the fixed effects inapplicable, and an adjusted quasi score (AQS) method is proposed, which adjusts the concentrated quasi score function with the fixed effects being concentrated out. AQS tests for the lack of temporal heterogeneity (TH) in slope and spatial parameters are first proposed. Then, a set of AQS estimation and inference methods for the FE-SPD model with temporal heterogeneity is developed, when the AQS tests reject the hypothesis of temporal homogeneity. Finally, an attempt is made to extend these methodologies to allow the idiosyncratic errors of the model to be heteroskedastic along the cross-section dimension, where a method called outer-product-of-martingale-differences is proposed to estimate the variance of the AQS functions which in turn gives a robust estimator of the variance-covariance matrix of the AQS estimators. Asymptotic properties of the AQS tests are examined. Consistency and asymptotic normality of the AQS estimators are examined under both homoscedastic and heteroskedastic errors. Extensive Monte Carlo experiments are conducted and the results show excellent finite sample performance of the proposed AQS tests, the proposed AQS estimators of the full model, and the corresponding estimates of the standard errors. Empirical illustrations are provided.