关键词:
Economics
Spatial autoregressive model
Spatial error model
Spatial Durbin model
Estimation
Closed-form
APLE
GMM
Specification
Non-nested
Cox test
J test
QMLE
Bootstrap
Spatial
Consistency
Asymptotic refinement
Linear-quadratic form
摘要:
This dissertation consists of three chapters covering the following topics in spatial econometrics: estimation, specification and the bootstrap. In Chapter 1, we first generalize an approximate measure of spatial dependence, the APLE statistic (Li et al., 2007), to a spatial Durbin (SD) model. This generalized APLE takes into account exogenous variables directly and can be used to detect spatial dependence originating from either a spatial autoregressive (SAR), spatial error (SE) or SD process. However, that measure is not consistent. Secondly, by examining carefully the first order condition of the concentrated log likelihood of the SD (or SAR) model, whose first order approximation generates the APLE, we construct a moment equation quadratic in the autoregressive parameter that generalizes an original estimation approach in Ord (1975) and yields a closed-form consistent root estimator of the autoregressive parameter. With a specific moment equation constructed from an initial consistent estimator, the root estimator can be as efficient as the MLE under normality. Furthermore, when there is unknown heteroskedasticity in the disturbances, we derive a modified APLE and a root estimator which can be robust to unknown heteroskedasticity. The root estimators are computationally much simpler than the quasi-maximum likelihood estimators. In Chapter 2, we consider the Cox-type tests of non-nested hypotheses for spatial autoregressive (SAR) models with SAR disturbances. We formally derive the asymptotic distributions of the test statistics. In contrast to regression models, we show that the Cox-type and J-type tests for non-nested hypotheses in the framework of SAR models are not asymptotically equivalent under the null hypothesis. The Cox test in non-spatial setting has been found often to have large size distortion, which can be removed by the bootstrap. Cox-type tests for SAR models with SAR disturbances may also have large size distortion. We show that the bootstrap is