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Estimation of spatial autoregressive panel data models with xed e ¤ ects Lung -
| Content Provider | Semantic Scholar |
|---|---|
| Author | Lee, Fei |
| Copyright Year | 2008 |
| Abstract | This paper establishes asymptotic properties of quasi-maximum likelihood estimators for SAR panel data models with xed e¤ects and SAR disturbances, where the time periods T can be nite or large (and the number of spatial units n tends to in nity). A direct approach is to estimate all the parameters including the xed e¤ects. In the presence of xed e¤ects, because of the incidental parameter problem, some parameter estimates may be inconsistent or have asymptotic bias. We propose alternative estimation methods based on transformation. For the model with only individual e¤ects, the transformation approach yields consistent estimators for the common parameters even T is nite. The direct approach does not yield a consistent estimator of the variance parameter unless T is large, but the estimators for other common 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 common parameters regardless T is nite or 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 common parameters requires n to be large. JEL classi cation: C13; C23; R15 Keywords: Spatial autoregression, Panel data, Fixed e¤ects, Quasi-maximum likelihood estimation, Conditional likelihood We would like to thank participants of the seminars at Syracuse University and the University of Kentucky, and two anonymous referees for helpful comments. Lee acknowledges nancial support from NSF Grant No. SES-0519204. 1. Introduction Spatial econometrics consists of econometric techniques dealing with the interactions of economic units in space, which can be physical or economic characteristic. A sample may consist of cross sectional observations, where the spatial autoregressive (SAR) model by Cli¤ and Ord (1973) has received the most attention in economics1 . Panel data with spatial interaction is also of great interest as it enables researchers to take into account the dynamics but also control for the unobservable heterogeneity (e.g., Anselin 1988, Baltagi et al. 2003, 2007, Kapoor et al. 2007, Yu et al. 2007, 2008 and Yu and Lee 2007). Baltagi et al. (2003) consider the speci cation test for 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 and 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 models assumes xed e¤ects. The xed e¤ects speci cation has the advantage of robustness in that the xed e¤ects are allowed to correlate with included regressors in the model (Hausman, 1978). Yu et al. (2008, 2007) and Yu and Lee (2007) consider, respectively, the time and spatial lags in a panel data setting with stationarity, spatial cointegration, and unit roots in the time dimension. For panel data models with xed individual e¤ects, when the time dimension T is xed, we are likely to encounter the incidental parameter problem discussed in Neyman and Scott (1948). This is because the introduction of xed e¤ects increases the number of parameters to be estimated. For the linear panel regression model with xed e¤ects, the direct maximum likelihood (ML) approach will estimate jointly the common parameters of interest and xed e¤ects. The corresponding ML estimates (MLEs) of the regression coe¢ cients are known as the within estimates, which happen to be the conditional likelihood estimates conditional on the time means of the dependent variables. However, the MLE of the variance parameter is inconsistent when T is nite. The inconsistency of this variance parameter is exactly the one illustrated in Neyman and Scott (1948). For the SAR panel data models with individual e¤ects, similar ndings of the direct ML approach are found in this paper. The direct estimation approach will yield consistent estimates for the spatial and regression coe¢ cients except the variance of the disturbances when T is small (but n is large).2 For the SAR panel models with both individual and time e¤ects, the direct estimation approach will be inconsistent for the estimation of the common parameters unless n is large. Even when both n and T are large so that individual and time e¤ects can be consistently estimated, the estimates of the common 1Early development in estimation and testing for cross sectional data can be found in Anselin (1988), Cressie (1993), Kelejian and Robinson (1993), and Anselin and Bera (1998), among others. 2When a dynamic e¤ect is considered into the SAR panel data, we will have an initial conditionproblem which will cause the inconsistency of the direct likelihood estimates for all the parameters unless T is large (see Yu et al, 2007, 2008 and Yu and Lee (2007)). The initial value problem for the dynamic panel data model is well known (Nickell, 1981). |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | http://economics.ucr.edu/seminars_colloquia/2009/econometrics/Lee%20grad%20seminar%20paper%20for%204%2016%2009.pdf |
| Alternate Webpage(s) | http://econ.ucsb.edu/~doug/245a/Papers/Spatial%20Autoregressive%20Panel%20FE.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
