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Estimation of fixed effects panel regression models with separable and nonseparable space–time filters

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  • Lee, Lung-fei
  • Yu, Jihai

Abstract

This paper considers a quasi-maximum likelihood estimation for a linear panel data model with time and individual fixed effects, where the disturbances have dynamic and spatial correlations which might be spatially stable or unstable. We first consider both separable and nonseparable space–time filters for the stable model. The separable space–time filter is subject to a parametric restriction which results in relative computational simplicity. In contrast to the spatial econometrics literature, we expose economic restrictions imposed by the separable space–time filter model and explore computational tractability of the nonseparable filter model. Throughout this paper, the effect of initial observations is taken into account, which results in an exact likelihood function for estimation. This is important when the span of time periods is short. We then investigate spatial unstable cases, where we propose to apply a “spatial differencing” to all variables in the regression equation as a data transformation, which may eliminate unstable or explosive spatial components in order to achieve a robust estimator. For estimates of the parameters in both the regression part and the disturbance process, they are nT-consistent and asymptotically centered normal regardless of whether T is large or not and whether the process is stable or not.

Suggested Citation

  • Lee, Lung-fei & Yu, Jihai, 2015. "Estimation of fixed effects panel regression models with separable and nonseparable space–time filters," Journal of Econometrics, Elsevier, vol. 184(1), pages 174-192.
  • Handle: RePEc:eee:econom:v:184:y:2015:i:1:p:174-192
    DOI: 10.1016/j.jeconom.2014.08.006
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    1. James P. LeSage & R. Kelley Pace, 2004. "Models for Spatially Dependent Missing Data," The Journal of Real Estate Finance and Economics, Springer, vol. 29(2), pages 233-254, September.
    2. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2008. "Quasi-maximum likelihood estimators for spatial dynamic panel data with fixed effects when both n and T are large," Journal of Econometrics, Elsevier, vol. 146(1), pages 118-134, September.
    3. Elhorst, J. Paul, 2010. "Dynamic panels with endogenous interaction effects when T is small," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 272-282, September.
    4. 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.
    5. Su, Liangjun & Ullah, Aman, 2007. "More efficient estimation of nonparametric panel data models with random effects," Economics Letters, Elsevier, vol. 96(3), pages 375-380, September.
    6. Franzese, Robert J. & Hays, Jude C., 2007. "Spatial Econometric Models of Cross-Sectional Interdependence in Political Science Panel and Time-Series-Cross-Section Data," Political Analysis, Cambridge University Press, vol. 15(02), pages 140-164, March.
    7. Baltagi, Badi H. & Heun Song, Seuck & Cheol Jung, Byoung & Koh, Won, 2007. "Testing for serial correlation, spatial autocorrelation and random effects using panel data," Journal of Econometrics, Elsevier, vol. 140(1), pages 5-51, September.
    8. Baltagi, Badi H. & Bresson, Georges & Pirotte, Alain, 2012. "Forecasting with spatial panel data," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3381-3397.
    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. Holly, Sean & Hashem Pesaran, M. & Yamagata, Takashi, 2011. "The spatial and temporal diffusion of house prices in the UK," Journal of Urban Economics, Elsevier, vol. 69(1), pages 2-23, January.
    11. Wang, Wei & Lee, Lung-fei, 2013. "Estimation of spatial panel data models with randomly missing data in the dependent variable," Regional Science and Urban Economics, Elsevier, vol. 43(3), pages 521-538.
    12. Lin, Xu & Lee, Lung-fei, 2010. "GMM estimation of spatial autoregressive models with unknown heteroskedasticity," Journal of Econometrics, Elsevier, vol. 157(1), pages 34-52, July.
    13. Harry Kelejian & Ingmar Prucha, 2010. "Spatial models with spatially lagged dependent variables and incomplete data," Journal of Geographical Systems, Springer, vol. 12(3), pages 241-257, September.
    14. Mohl, P. & Hagen, T., 2010. "Do EU structural funds promote regional growth? New evidence from various panel data approaches," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 353-365, September.
    15. Su, Liangjun & Yang, Zhenlin, 2015. "QML estimation of dynamic panel data models with spatial errors," Journal of Econometrics, Elsevier, vol. 185(1), pages 230-258.
    16. Keller, Wolfgang & Shiue, Carol H., 2007. "The origin of spatial interaction," Journal of Econometrics, Elsevier, vol. 140(1), pages 304-332, September.
    17. Badi Baltagi & Seuck Song, 2006. "Unbalanced panel data: A survey," Statistical Papers, Springer, vol. 47(4), pages 493-523, October.
    18. Lottmann, Franziska, 2012. "Spatial dependencies in German matching functions," Regional Science and Urban Economics, Elsevier, vol. 42(1-2), pages 27-41.
    19. Badi H. Baltagi & Bernard Fingleton & Alain Pirotte, 2014. "Estimating and Forecasting with a Dynamic Spatial Panel Data Model," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(1), pages 112-138, February.
    20. Lung-fei Lee & Jihai Yu, 2012. "QML Estimation of Spatial Dynamic Panel Data Models with Time Varying Spatial Weights Matrices," Spatial Economic Analysis, Taylor & Francis Journals, vol. 7(1), pages 31-74, March.
    21. Elhorst, J. Paul, 2008. "Serial and spatial error correlation," Economics Letters, Elsevier, vol. 100(3), pages 422-424, September.
    22. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    23. Korniotis, George M., 2010. "Estimating Panel Models With Internal and External Habit Formation," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(1), pages 145-158.
    24. Cem Ertur & Wilfried Koch, 2007. "Growth, technological interdependence and spatial externalities: theory and evidence," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(6), pages 1033-1062.
    25. Giacomini, Raffaella & Granger, Clive W. J., 2004. "Aggregation of space-time processes," Journal of Econometrics, Elsevier, vol. 118(1-2), pages 7-26.
    26. Yu, Jihai & de Jong, Robert & Lee, Lung-fei, 2012. "Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration," Journal of Econometrics, Elsevier, vol. 167(1), pages 16-37.
    27. Lee, Lung-fei & Yu, Jihai, 2010. "Estimation of spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 154(2), pages 165-185, February.
    28. Federico Revelli, 2001. "Spatial patterns in local taxation: tax mimicking or error mimicking?," Applied Economics, Taylor & Francis Journals, vol. 33(9), pages 1101-1107.
    29. Parent, Olivier & LeSage, James P., 2011. "A space-time filter for panel data models containing random effects," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 475-490, January.
    30. Lung‐fei Lee & Jihai Yu, 2012. "Spatial Panels: Random Components Versus Fixed Effects," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 53(4), pages 1369-1412, November.
    31. J. Elhorst, 2012. "Dynamic spatial panels: models, methods, and inferences," Journal of Geographical Systems, Springer, vol. 14(1), pages 5-28, January.
    32. Lancaster, Tony, 2000. "The incidental parameter problem since 1948," Journal of Econometrics, Elsevier, vol. 95(2), pages 391-413, April.
    33. Hsiao, Cheng & Hashem Pesaran, M. & Kamil Tahmiscioglu, A., 2002. "Maximum likelihood estimation of fixed effects dynamic panel data models covering short time periods," Journal of Econometrics, Elsevier, vol. 109(1), pages 107-150, July.
    34. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    35. Badi H. Baltagi & Chihwa Kao & Long Liu, 2008. "Asymptotic properties of estimators for the linear panel regression model with random individual effects and serially correlated errors: the case of stationary and non-stationary regressors and residu," Econometrics Journal, Royal Economic Society, vol. 11(3), pages 554-572, November.
    36. Wei Wang & Lung‐Fei Lee, 2013. "Estimation of spatial autoregressive models with randomly missing data in the dependent variable," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 73-102, February.
    37. Simonetta Longhi & Peter Nijkamp, 2007. "Forecasting Regional Labor Market Developments under Spatial Autocorrelation," International Regional Science Review, , vol. 30(2), pages 100-119, April.
    38. Parent, Olivier & LeSage, James P., 2012. "Spatial dynamic panel data models with random effects," Regional Science and Urban Economics, Elsevier, vol. 42(4), pages 727-738.
    39. Kapoor, Mudit & Kelejian, Harry H. & Prucha, Ingmar R., 2007. "Panel data models with spatially correlated error components," Journal of Econometrics, Elsevier, vol. 140(1), pages 97-130, September.
    40. Liu, Xiaodong & Lee, Lung-fei & Bollinger, Christopher R., 2010. "An efficient GMM estimator of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 159(2), pages 303-319, December.
    41. Lee, Lung-fei, 2007. "GMM and 2SLS estimation of mixed regressive, spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 137(2), pages 489-514, April.
    42. Lee, Lung-fei & Yu, Jihai, 2010. "Some recent developments in spatial panel data models," Regional Science and Urban Economics, Elsevier, vol. 40(5), pages 255-271, September.
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    Cited by:

    1. repec:eee:regeco:v:65:y:2017:i:c:p:65-88 is not listed on IDEAS
    2. Jiti Gao & Kai Xia, 2017. "Heterogeneous panel data models with cross-sectional dependence," Monash Econometrics and Business Statistics Working Papers 16/17, Monash University, Department of Econometrics and Business Statistics.
    3. Shi, Wei & Lee, Lung-fei, 2017. "Spatial dynamic panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 197(2), pages 323-347.
    4. Taspinar, Suleyman & Dogan, Osman & Bera, Anil K., 2017. "GMM Gradient Tests for Spatial Dynamic Panel Data Models," MPRA Paper 82830, University Library of Munich, Germany.
    5. Li, Kunpeng, 2017. "Fixed-effects dynamic spatial panel data models and impulse response analysis," Journal of Econometrics, Elsevier, vol. 198(1), pages 102-121.

    More about this item

    Keywords

    Spatial autoregression; Space–time filter; Panel data; Spatial cointegration; Explosive roots; Fixed effects; Time effects; Quasi-maximum likelihood estimation; Exact likelihood function;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • R15 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Econometric and Input-Output Models; Other Methods

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