Essays on theories and applications of spatial econometric models

My dissertation is about theories and applications of spatial autoregressive (SAR) models. As an effective method in analyzing interdependence among the observations, the SAR models have witnessed ever-increasing applications in various areas, including Economics, Sociology, Geography and others. This dissertation intends to extend the spatial theoretical literature by studying a more general SAR model and to enrich the social interaction studies by introducing a special SAR model to confront the identifications issues. Chapter 2 studies peer effects in student academic achievement. It is well known that disentangling peer effects from other confounding effects is difficult, and separately identifying endogenous and contextual social effects is impossible for the linear-in-means social interaction model. This study confronts these conceptual problems by using a SAR model with group fixed effects. The nonlinearity introduced by the variations in the peer measurements in the SAR model provides information to identify both endogenous and contextual effects, thus resolving the "reflection problem". The group fixed effects term in the model captures the confounding effects of the common variables faced by the same group members. I use datasets from the National Longitudinal Study of Adolescent Health (Add Health) survey and specify peer groups as friendship networks. I find evidence for both endogenous and contextual effects in student academic achievement, even after controlling for school-grade fixed effects. The result indicates that students benefit from the presence of high quality peers, and that associating with peers living with both parents helps improve a student's GPA, while associating with peers whose mothers receive welfare has a negative effect. Chapter 3 considers GMM estimation of spatial autoregressive (SAR) models with unknown heteroskedasticity. In the presence of heteroskedastic disturbances, the maximum likelihood estimator (MLE) for the SAR models without taking into account the heteroskedasticity is generally inconsistent. In contrast, GMM estimators obtained from certain moment conditions can be robust against unknown heteroskedasticity. Asymptotically valid inferences can be drawn with consistently estimated covariance matrices. Furthermore, efficiency can be improved by constructing the optimal weighted GMM estimation. Tests for heteroskedasticity are investigated. Monte Carlo experiments are designed to study the finite sample properties of the GMM and other estimators such as MLE and 2SLSE, and the test statistics. The Monte Carlo results show that even though 2SLS estimates shall be consistent in the presence of unknown heteroskedasticity, they can have large variances and biases in finite samples for cases where regressors do not have strong effects. The robust GMM estimator has desirable properties while the biases associated with MLE and non-robust GMME may remain in large sample, especially, for the spatial effect coefficient and the intercept term. However, the magnitudes of biases are only moderate. With moderate large sample sizes, those biases may be statistically insignificant. The various approaches are applied to the study of county teenage pregnancy rates. The empirical results show a strong spatial convergence among county teenage pregnancy rates with a significant spatial effect.