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A multidimensional spatial lag panel data model with spatial moving average nested random effects errors

Author

Listed:
  • Bernard Fingleton

    (Department of Land Economy - University of Cambridge)

  • Julie Le Gallo

    (CESAER - Centre d'Economie et de Sociologie Rurales Appliquées à l'Agriculture et aux Espaces Ruraux - INRA - Institut National de la Recherche Agronomique - AgroSup Dijon - Institut National Supérieur des Sciences Agronomiques, de l'Alimentation et de l'Environnement)

  • Alain Pirotte
Abstract
This paper focuses on a three-dimensional model that combines two different types of spatial interaction effects, i.e. endogenous interaction effects via a spatial lag on the dependent variable and interaction effects among the disturbances via a spatial moving average (SMA) nested random effects errors. A three-stage procedure is proposed to estimate the parameters. In a first stage, the spatial lag panel data model is estimated using an instrumental variable (IV) estimator. In a second stage, a generalized moments (GM) approach is developed to estimate the SMA parameter and the variance components of the disturbance process using IV residuals from the first stage. In a third stage, to purge the equation of the specific structure of the disturbances a Cochrane–Orcutt-type transformation is applied combined with the IV principle. This leads to the GM spatial IV estimator and the regression parameter estimates. Monte Carlo simulations show that our estimators are not very different in terms of root mean square error from those produced by maximum likelihood. The approach is applied to European Union regional employment data for regions nested within countries.

Suggested Citation

  • Bernard Fingleton & Julie Le Gallo & Alain Pirotte, 2018. "A multidimensional spatial lag panel data model with spatial moving average nested random effects errors," Post-Print hal-01868535, HAL.
    • Handle: RePEc:hal:journl:hal-01868535
    DOI: 10.1007/s00181-017-1410-7
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    References listed on IDEAS

    as
    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. Bernard Fingleton, 2008. "A Generalized Method of Moments Estimator for a Spatial Panel Model with an Endogenous Spatial Lag and Spatial Moving Average Errors," Spatial Economic Analysis, Taylor & Francis Journals, vol. 3(1), pages 27-44.
    3. 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.
    4. H. Baltagi, Badi & Heun Song, Seuck & Cheol Jung, Byoung, 2001. "The unbalanced nested error component regression model," Journal of Econometrics, Elsevier, vol. 101(2), pages 357-381, April.
    5. Wolfang Polasek & Carlos Llano & Richard Sellner, 2010. "Bayesian Methods for Completing Data in Spatial Models," Review of Economic Analysis, Digital Initiatives at the University of Waterloo Library, vol. 2(2), pages 194-214, June.
    6. Baltagi, Badi H. & Fingleton, Bernard & Pirotte, Alain, 2014. "Spatial lag models with nested random effects: An instrumental variable procedure with an application to English house prices," Journal of Urban Economics, Elsevier, vol. 80(C), pages 76-86.
    7. 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.
    8. Bernard Fingleton & Harry Garretsen & Ron Martin, 2015. "Shocking aspects of monetary union: the vulnerability of regions in Euroland," Journal of Economic Geography, Oxford University Press, vol. 15(5), pages 907-934.
    9. Chow, Gregory C & Lin, An-loh, 1971. "Best Linear Unbiased Interpolation, Distribution, and Extrapolation of Time Series by Related Series," The Review of Economics and Statistics, MIT Press, vol. 53(4), pages 372-375, November.
    10. 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.
    11. Antweiler, Werner, 2001. "Nested random effects estimation in unbalanced panel data," Journal of Econometrics, Elsevier, vol. 101(2), pages 295-313, April.
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    Cited by:

    1. Bernard Fingleton & Franz Fuerst & Nikodem Szumilo, 2019. "Housing affordability: Is new local supply the key?," Environment and Planning A, , vol. 51(1), pages 25-50, February.
    2. Carsten Ochsen, 2021. "Age cohort effects on unemployment in the USA: Evidence from the regional level," Papers in Regional Science, Wiley Blackwell, vol. 100(4), pages 1025-1053, August.
    3. Fingleton, Bernard & Szumilo, Nikodem, 2019. "Simulating the impact of transport infrastructure investment on wages: A dynamic spatial panel model approach," Regional Science and Urban Economics, Elsevier, vol. 75(C), pages 148-164.
    4. Bernard Fingleton, 2020. "Exploring Brexit with dynamic spatial panel models: some possible outcomes for employment across the EU regions," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 64(2), pages 455-491, April.
    5. Bernard Fingleton & Daniel Olner & Gwilym Pryce, 2020. "Estimating the local employment impacts of immigration: A dynamic spatial panel model," Urban Studies, Urban Studies Journal Limited, vol. 57(13), pages 2646-2662, October.
    6. Huijun Ji & Arber Hoti, 2022. "Green economy based perspective of low-carbon agriculture growth for total factor energy efficiency improvement," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 13(1), pages 353-363, March.
    7. Bernard Fingleton, 2020. "Italexit, is it another Brexit?," Journal of Geographical Systems, Springer, vol. 22(1), pages 77-104, January.
    8. Liu, Yunqiang & Zhu, Jialing & Li, Eldon Y. & Meng, Zhiyi & Song, Yan, 2020. "Environmental regulation, green technological innovation, and eco-efficiency: The case of Yangtze river economic belt in China," Technological Forecasting and Social Change, Elsevier, vol. 155(C).

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    More about this item

    Keywords

    Multidimensional; Spatial moving average nested random effects; Generalized moments; Instrumental variables; Maximum likelihood; Panel data;
    All these keywords.

    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

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