Approximated likelihood and root estimators for spatial interaction in spatial autoregressive models
AbstractIn this paper, 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Regional Science and Urban Economics.
Volume (Year): 42 (2012)
Issue (Month): 3 ()
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Web page: http://www.elsevier.com/locate/regec
Spatial autoregressive model; Spatial error model; Spatial Durbin model; APLE; GMM;
Find related papers by JEL classification:
- C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
- R15 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Econometric and Input-Output Models; Other Methods
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