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Testing for Serial Correlation, Spatial Autocorrelation and Random Effects

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  • Won Koh
  • Badi H. Baltagi
  • Seuck Heun Song

Abstract

This paper considers a spatial panel data regression model with serial correlation on each spatial unit over time as well as spatial dependence between the spatial units at each point in time. In addition, the model allows for heterogeneity across the spatial units using random effects. The paper then derives several Lagrange Multiplier tests for this panel data regression model including a joint test for serial correlation, spatial autocorrelation and random effects. These tests draw upon two strands of earlier work. The first is the LM tests for the spatial error correlation model discussed in Anselin and Bera (1998) and in the panel data context by Baltagi, Song and Koh (2003). The second is the LM tests for the error component panel data model with serial correlation derived by Baltagi and Li (1995). Hence the joint LM test derived in this paper encompasses those derived in both strands of earlier works. In fact, in the context of our general model, the earlier LM tests become marginal LM tests that ignore either serial correlation over time or spatial error correlation. The paper then derives conditional LM and LR tests that do not ignore these correlations and contrast them with their marginal LM and LR counterparts. The small sample performance of these tests is investigated using Monte Carlo experiments. As expected, ignoring any correlation when it is significant can lead to misleading inference.

Suggested Citation

  • Won Koh & Badi H. Baltagi & Seuck Heun Song, 2004. "Testing for Serial Correlation, Spatial Autocorrelation and Random Effects," Econometric Society 2004 Far Eastern Meetings 415, Econometric Society.
    • Handle: RePEc:ecm:feam04:415
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    References listed on IDEAS

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    1. Kelejian, Harry H & Prucha, Ingmar R, 1999. "A Generalized Moments Estimator for the Autoregressive Parameter in a Spatial Model," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 40(2), pages 509-533, May.
    2. Breusch, T S, 1978. "Testing for Autocorrelation in Dynamic Linear Models," Australian Economic Papers, Wiley Blackwell, vol. 17(31), pages 334-355, December.
    3. Kathleen P. Bell & Nancy E. Bockstael, 2000. "Applying the Generalized-Moments Estimation Approach to Spatial Problems Involving Microlevel Data," The Review of Economics and Statistics, MIT Press, vol. 82(1), pages 72-82, February.
    4. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    5. Baltagi, Badi H. & Song, Seuck Heun & Koh, Won, 2003. "Testing panel data regression models with spatial error correlation," Journal of Econometrics, Elsevier, vol. 117(1), pages 123-150, November.
    6. Luc Anselin & Raymond J. G. M. Florax, 1995. "Small Sample Properties of Tests for Spatial Dependence in Regression Models: Some Further Results," Advances in Spatial Science, in: Luc Anselin & Raymond J. G. M. Florax (ed.), New Directions in Spatial Econometrics, chapter 2, pages 21-74, Springer.
    7. Baltagi, Badi H. & Li, Qi, 1995. "Testing AR(1) against MA(1) disturbances in an error component model," Journal of Econometrics, Elsevier, vol. 68(1), pages 133-151, July.
    8. Nerlove, Marc, 1971. "Further Evidence on the Estimation of Dynamic Economic Relations from a Time Series of Cross Sections," Econometrica, Econometric Society, vol. 39(2), pages 359-382, March.
    9. H. Kelejian, Harry & Prucha, Ingmar R., 2001. "On the asymptotic distribution of the Moran I test statistic with applications," Journal of Econometrics, Elsevier, vol. 104(2), pages 219-257, September.
    10. Magnus, Jan R., 1982. "Multivariate error components analysis of linear and nonlinear regression models by maximum likelihood," Journal of Econometrics, Elsevier, vol. 19(2-3), pages 239-285, August.
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    14. Kelejian, Harry H. & Robinson, Dennis P., 1992. "Spatial autocorrelation : A new computationally simple test with an application to per capita county police expenditures," Regional Science and Urban Economics, Elsevier, vol. 22(3), pages 317-331, September.
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    Cited by:

    1. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
    2. Xiaodong Du & David A. Hennessy & William M. Edwards, 2007. "Determinants of Iowa Cropland Cash Rental Rates: Testing Ricardian Rent Theory," Center for Agricultural and Rural Development (CARD) Publications 07-wp454, Center for Agricultural and Rural Development (CARD) at Iowa State University.
    3. Caporin Massimiliano & Paruolo Paolo, 2005. "Multivariate ARCH with spatial effects for stock sector and size," Economics and Quantitative Methods qf0509, Department of Economics, University of Insubria.
    4. Caporin Massimiliano & Paruolo Paolo, 2005. "Spatial effects in multivariate ARCH," Economics and Quantitative Methods qf0501, Department of Economics, University of Insubria.

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    More about this item

    Keywords

    panel data; spatial correlation;

    JEL classification:

    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General

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