Spatial Autoregressive Panel FE

Spatial Autoregressive Panel FE - Estimation of spatial...

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Unformatted text preview: Estimation of spatial autoregressive panel data models with &xed e/ects Lung-fei Lee & Department of Economics Ohio State University l¡[email protected] Jihai Yu Department of Economics University of Kentucky [email protected] March 4, 2008 Abstract This paper establishes asymptotic properties of quasi-maximum likelihood estimators for &xed e/ects SAR panel data models with SAR disturbances where the time periods T and¢or the number of spatial units n can be &nite or large in all combinations except that both T and n are &nite. A direct approach is to estimate all the parameters including &xed e/ects. We propose alternative estimation methods based on transformation. For the model with only individual e/ects, the transformation approach yields consistent estimators for all the parameters when either n or T are large, while the direct approach does not yield a consistent estimator of the variance of disturbances unless T is large, although the estimators for other parameters are the same as those of the transformation approach. For the model with both individual and time e/ects, the transformation approach yields consistent estimators of all the parameters when either n or T are large. When we estimate both individual and time e/ects directly, consistency of the variance parameter requires both n and T to be large and consistency of other parameters requires n to be large. JEL classi&cation: C13; C23; R15 Keywords: Spatial autoregression, Panel data, Fixed e/ects, Time e/ects, Quasi-maximum likelihood estimation, Conditional likelihood & Lee acknowledges &nancial support for his research from NSF under Grant No. SES-0519204 1 Introduction Spatial econometrics deals with the spatial interactions of economic units in cross-section and/or panel data. To capture correlation among cross-sectional units, the spatial autoregressive (SAR) model by Cli¡and Ord (1973) has received the most attention in economics. It extends autocorrelation in times series to spatial dimensions and captures interactions or competition among spatial units. Early development in estimation and testing is summarized in Anselin (1988), Cressie (1993), Kelejian and Robinson (1993), and Anselin and Bera (1998), among others. The spatial correlation can be extended to panel data models (Anselin, 1988). Baltagi et al. (2003) consider the speci&cation test of the spatial correlation in a panel regression with error component and SAR disturbances. Kapoor et al. (2007) provide a rigorous theoretical analysis of a panel model with SAR disturbances which incorporate error components. Baltagi et al. (2007) generalize Baltagi et al. (2003) by allowing for spatial correlations in both individual and error components such that they might have di¡erent spatial autoregressive parameters, which encompasses the spatial correlation speci&cations in Baltagi et al. (2003) and Kapoor et al. (2007). Instead of random e¡ect error components, an alternative speci&cation for panel data model assumes &xed e¡ects. The &xed e¡ects speci&cation has the advantage ofspeci&cation for panel data model assumes &xed e¡ects....
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Spatial Autoregressive Panel FE - Estimation of spatial...

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