Testing for Cross-Sectional Dependence in a RandomEffects Model
ABSTRACT
This paper extends and generalizes the works of [1,2] to allow for cross-sectional dependence in the context of a two-way error components model and consequently develops LM test. The cross-sectional dependence follows the first order spatial autoregressive error (SAE) process and is imposed on the remainder disturbances. It is important to note that this paper does not consider alternative forms of spatial lag dependence other than SAE. It also does not allow for endogeneity of the regressors and requires the normality assumption to derive the LM test.
This paper extends and generalizes the works of [1,2] to allow for cross-sectional dependence in the context of a two-way error components model and consequently develops LM test. The cross-sectional dependence follows the first order spatial autoregressive error (SAE) process and is imposed on the remainder disturbances. It is important to note that this paper does not consider alternative forms of spatial lag dependence other than SAE. It also does not allow for endogeneity of the regressors and requires the normality assumption to derive the LM test.
Cite this paper
A. Salisu, S. Olofin and E. Kouassi, "Testing for Cross-Sectional Dependence in a RandomEffects Model," Open Journal of Statistics, Vol. 2 No. 1, 2012, pp. 88-97. doi: 10.4236/ojs.2012.21009.
A. Salisu, S. Olofin and E. Kouassi, "Testing for Cross-Sectional Dependence in a RandomEffects Model," Open Journal of Statistics, Vol. 2 No. 1, 2012, pp. 88-97. doi: 10.4236/ojs.2012.21009.
References
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Anselin, “Some Robust Approaches to Testing and Estimation in Spatial Econometrics,” Regional Science and Urban Economics, Vol. 20, No. 2, 1990, pp. 1-17. doi:10.1016/0166-0462(90)90001-J [21] H. Kelejian and I. R. Prucha, “A Generalized Spatial Two Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances,” Journal of Real Estate Finance and Economics, Vol. 17, No. 1, 1998, pp. 99-121. doi:10.1023/A:1007707430416 [22] B. H. Baltagi, S. H. Song, B. C. Jung and W. Koh, “Testing for Serial Correlation, Spatial Autocorrelation and Random Effects Using Panel Data,” Journal of Econometrics, Vol. 140, No. 1, 2007, pp. 5-51. doi:10.1016/j.jeconom.2006.09.001 [23] B. H. Baltagi, S. H. Song and J. H. Kwon, “Testing for Heteroscedasticity and Spatial Correlation in a Random Effects Panel Data Model,” Computational Statistics and Data Analysis, Vol. 53, No. 8, 2009, pp. 2897-2922. doi:10.1016/j.csda.2008.06.009 [24] T. J. Wansbeek and A. Kapteyn, “A Simple Way to Obtain the Spectral Decomposition of Variance Components Models for Balanced Data,” Communications in Statistics, Vol. 11, No. 18, 1982, pp. 2105-2112. doi:10.1080/03610928208828373 [25] J. R. Magnus, “Multivariate Error Components Analysis of Linear and Nonlinear Regression Models by Maximum Likelihood,” Journal of Econometrics, Vol. 19, No. 2-3, 1982, pp. 239-285. doi:10.1016/0304-4076(82)90005-7 [26] J. R. Magnus and H. Neudecker, “Matrix Differential Calculus with Applications in Statistics and Econometrics,” Wiley Series in Probability and Statistics, Chichester, 1988. [27] D. A. Harville, “Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems,” Journal of the American Statistical Association, Vol. 72, No. 358, 1977, pp. 320-338. doi:10.2307/2286796
[1] B. H. Baltagi, S. H. Song and W. Koh, “Testing Panel Data Regression Models with Spatial Error Correlation,” Journal of Econometrics, Vol. 117, No. 1, 2003, pp. 123- 150. doi:10.1016/S0304-4076(03)00120-9 [2] L. Anselin, “Rao’s Score Tests in Spatial Econometrics,” Journal of Statistical Planning and Inference, Vol. 97, No. 1, 2001, pp. 113-139. doi:10.1016/S0378-3758(00)00349-9 [3] B. H. Baltagi, “Econometric Analysis of Panel Data,” 6th Edition, Wiley, Chichester, 2008. [4] L. Anselin, “Spatial Econometrics: Methods and Model,” Kluwer Academic Publishers, Dordrecht, 1988. [5] L. Anselin and S. Rey, “Properties of Tests for Spatial Dependence in Linear Regression Models,” Geographical Analysis, Vol. 23, No. 2, 1991, pp. 112-131. doi:10.1111/j.1538-4632.1991.tb00228.x [6] J. Ord, “Estimation Methods for Models of Spatial Interaction,” Journal of the American Statistical Association, Vol. 70, No. 349, 1975, pp. 120-126. doi:10.2307/2285387 [7] A. Brandsma and R. Ketellapper, “Further Evidence on Alternative Procedures for Testing of Spatial Autocorrelation among Regression Disturbances,” In: C. Bartels and R. Ketellapper, Eds., Exploratory and Explanatory Analysis in Spatial Data, Martinus Nijhoff, Boston, 1979, pp. 11-36. doi:10.1007/978-94-009-9233-7_5 [8] H. Bloommestein, “Specification and Estimation of Spatial Econometric Models: A Discussion of Alternative Strategies for Spatial Economic Modeling,” Regional Science and Urban Economics, Vol. 13, No. 2, 1985, pp. 251-270. doi:10.1016/0166-0462(83)90016-9 [9] H. Kelejian and I.R. Prucha, A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model,” International Economic Review, Vol. 40, No. 2, 1999, pp. 509-533. doi:10.1111/1468-2354.00027 [10] H. H. Kelejian, I. R. Prucha and E. Yusefovich, “Instrumental Variable Estimation of A Spatial Autoregressive Model with Autoregressive Disturbances: Large and Small Sample Results,” In: J. LeSage and R. K. Pace, Eds., Spatial and Spatiotemporal Econometrics (Advances in Econometrics), Vol. 18, Elsevier, New York, 2004, pp. 163-198. doi:10.1016/S0731-9053(04)18005-5 [11] R. Haining, “Spatial Data Analysis in the Social and Environmental Sciences,” Cambridge University Press, Cambridge, 1988. [12] L. Anselin and A. K. Bera, “Spatial Dependence in Linear Regression Models with an Introduction to Spatial Econometrics,” In: A. Ullah and D. E. A. Giles, Eds., Handbook of Applied Economic Statistics, Marcel Dekker, New York, 1998. [13] P. Burridge, “On the Cliff-Ord Test for Spatial Autocorrelation,” Journal of the Royal Statistical Society, Vol. 42, 1980, pp. 107-108. [14] J. S. Huang, “The Autoregressive Moving Average Model for Spatial Analysis,” Australian Journal of Statistics, Vol. 26, No. 2, 1988, pp. 169-178. doi:10.1111/j.1467-842X.1984.tb01231.x [15] A. Case, “Spatial Patterns in Household Demand.” Econometrica, Vol. 59, No. 4, 1991, pp. 953-965. doi:10.2307/2938168 [16] K. V. Mardia and R. J. Marshall, “Maximum Likelihood Estimation of Models for Residual Covariance in Spatial Regression,” Biomerika, Vol. 71, No. 1, 1984, pp. 135- 146. doi:10.1093/biomet/71.1.135 [17] K. V. Mardia, “Maximum Likelihood Estimation for Spatial Models,” In: D. A. Griffith, Ed., Spatial Statistics: Past, Present and Future, Institute of Mathematical Geography, Ann Arbor, 1990, pp. 203-251. [18] H. Kelejian and D. P. Robinson, “Spatial Correlation: A Suggested Alternative to the Autoregressive Model,” In: L. Anselin and R. Florax, Eds., New Directions in Spatial Econometrics, Springer-Verlag, Berlin, 1995, pp. 75-95. doi:10.1007/978-3-642-79877-1_3 [19] L. Anselin and R. Moreno, “Properties of Tests for Spatial Error Components,” Regional Science and Urban Economics, Vol. 33, No. 5, 2003, pp. 595-618. doi:10.1016/S0166-0462(03)00008-5 [20] L. Anselin, “Some Robust Approaches to Testing and Estimation in Spatial Econometrics,” Regional Science and Urban Economics, Vol. 20, No. 2, 1990, pp. 1-17. doi:10.1016/0166-0462(90)90001-J [21] H. Kelejian and I. R. Prucha, “A Generalized Spatial Two Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances,” Journal of Real Estate Finance and Economics, Vol. 17, No. 1, 1998, pp. 99-121. doi:10.1023/A:1007707430416 [22] B. H. Baltagi, S. H. Song, B. C. Jung and W. Koh, “Testing for Serial Correlation, Spatial Autocorrelation and Random Effects Using Panel Data,” Journal of Econometrics, Vol. 140, No. 1, 2007, pp. 5-51. doi:10.1016/j.jeconom.2006.09.001 [23] B. H. Baltagi, S. H. Song and J. H. Kwon, “Testing for Heteroscedasticity and Spatial Correlation in a Random Effects Panel Data Model,” Computational Statistics and Data Analysis, Vol. 53, No. 8, 2009, pp. 2897-2922. doi:10.1016/j.csda.2008.06.009 [24] T. J. Wansbeek and A. Kapteyn, “A Simple Way to Obtain the Spectral Decomposition of Variance Components Models for Balanced Data,” Communications in Statistics, Vol. 11, No. 18, 1982, pp. 2105-2112. doi:10.1080/03610928208828373 [25] J. R. Magnus, “Multivariate Error Components Analysis of Linear and Nonlinear Regression Models by Maximum Likelihood,” Journal of Econometrics, Vol. 19, No. 2-3, 1982, pp. 239-285. doi:10.1016/0304-4076(82)90005-7 [26] J. R. Magnus and H. Neudecker, “Matrix Differential Calculus with Applications in Statistics and Econometrics,” Wiley Series in Probability and Statistics, Chichester, 1988. [27] D. A. Harville, “Maximum Likelihood Approaches to Variance Component Estimation and to Related Problems,” Journal of the American Statistical Association, Vol. 72, No. 358, 1977, pp. 320-338. doi:10.2307/2286796