Estimation of spatial autoregressive panel data models with xed e¤ects

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