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EC3SLS Estimator for a Simultaneous System of Spatial Autoregressive Equations with Random Effects

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  • Badi H. Baltagi
  • Ying Deng

Abstract

This article derives a 3SLS estimator for a simultaneous system of spatial autoregressive equations with random effects which can therefore handle endoegeneity, spatial lag dependence, heterogeneity as well as cross equation correlation. This is done by utilizing the Kelejian and Prucha (1998) and Lee (2003) type instruments from the cross-section spatial autoregressive literature and marrying them to the error components 3SLS estimator derived by Baltagi (1981) for a system of simultaneous panel data equations. Our Monte Carlo experiments indicate that, for the single equation spatial error components 2SLS estimators, there is a slight gain in efficiency when Lee (2003) type rather than Kelejian and Prucha (1998) instruments are used. However, there is not much difference in efficiency between these instruments for spatial error components 3SLS estimators.

Suggested Citation

  • Badi H. Baltagi & Ying Deng, 2015. "EC3SLS Estimator for a Simultaneous System of Spatial Autoregressive Equations with Random Effects," Econometric Reviews, Taylor & Francis Journals, vol. 34(6-10), pages 659-694, December.
    • Handle: RePEc:taf:emetrv:v:34:y:2015:i:6-10:p:659-694
    DOI: 10.1080/07474938.2014.956030
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    1. László Mátyás & Patrick Sevestre (ed.), 2008. "The Econometrics of Panel Data," Advanced Studies in Theoretical and Applied Econometrics, Springer, number 978-3-540-75892-1, July-Dece.
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    1. Torben Dall Schmidt & Aki Kangasharju & Timo Mitze & Daniel Rauhut, 2014. "The impact of aging on regional employment: Linking spatial econometrics and population projections for a scenario analysis of future labor market outcomes in Nordic regions," Economics and Business Letters, Oviedo University Press, vol. 3(4), pages 232-246.
    2. Peter H. Egger & Ingmar R. Prucha, 2023. "Refined GMM estimators for simultaneous equations models with network interactions," Empirical Economics, Springer, vol. 64(6), pages 2535-2542, June.
    3. J. Paul Elhorst & Marco Gross & Eugen Tereanu, 2021. "Cross‐Sectional Dependence And Spillovers In Space And Time: Where Spatial Econometrics And Global Var Models Meet," Journal of Economic Surveys, Wiley Blackwell, vol. 35(1), pages 192-226, February.
    4. Heather D. Gibson & Stephen G. Hall & Deborah Gefang & Pavlos Petroulas & George S. Tavlas, 2020. "Did the absence of a central bank backstop in the sovereign bond markets exacerbate spillovers during the euro-area crisis?," Working Papers 281, Bank of Greece.
    5. Harrison, Jane L. & Montgomery, Claire A. & Jeanty, P. Wilner, 2019. "A spatial, simultaneous model of social capital and poverty," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 78(C), pages 183-192.
    6. Wang, Luya & Li, Kunpeng & Wang, Zhengwei, 2014. "Quasi maximum likelihood estimation for simultaneous spatial autoregressive models," MPRA Paper 59901, University Library of Munich, Germany.
    7. Badi H. Baltagi & Peter H. Egger & Michaela Kesina, 2022. "Bayesian estimation of multivariate panel probits with higher‐order network interdependence and an application to firms' global market participation in Guangdong," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(7), pages 1356-1378, November.
    8. Ahmed A. Elamer & Collins G. Ntim & Hussein A. Abdou & Alaa Mansour Zalata & Mohamed Elmagrhi, 2019. "The impact of multi-layer governance on bank risk disclosure in emerging markets: the case of Middle East and North Africa," Accounting Forum, Taylor & Francis Journals, vol. 43(2), pages 246-281, April.
    9. William C. Horrace & Hyunseok Jung & Shane Sanders, 2022. "Network Competition and Team Chemistry in the NBA," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(1), pages 35-49, January.
    10. Lin Guo, 2017. "Income Inequality, Household Consumption And Co2 Emissions In China," The Singapore Economic Review (SER), World Scientific Publishing Co. Pte. Ltd., vol. 62(02), pages 531-553, June.
    11. Lina Lu, 2017. "Simultaneous Spatial Panel Data Models with Common Shocks," Supervisory Research and Analysis Working Papers RPA 17-3, Federal Reserve Bank of Boston.
    12. AMBA OYON, Claude Marius & Mbratana, Taoufiki, 2017. "Simultaneous equation models with spatially autocorrelated error components," MPRA Paper 82395, University Library of Munich, Germany.
    13. Zhu, Xuening & Huang, Danyang & Pan, Rui & Wang, Hansheng, 2020. "Multivariate spatial autoregressive model for large scale social networks," Journal of Econometrics, Elsevier, vol. 215(2), pages 591-606.
    14. cyrine hannafi & Christophe Muller, 2016. "The Poverty-Economic Growth-Health Triangle," EcoMod2016 9587, EcoMod.
    15. Yang, Kai & Lee, Lung-fei, 2017. "Identification and QML estimation of multivariate and simultaneous equations spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 196(1), pages 196-214.
    16. Wang, Wei & Lee, Lung-Fei & Bao, Yan, 2018. "GMM estimation of the spatial autoregressive model in a system of interrelated networks," Regional Science and Urban Economics, Elsevier, vol. 69(C), pages 167-198.
    17. AMBA OYON, Claude Marius & Mbratana, Taoufiki, 2018. "Simultaneous Generalized Method of Moments Estimator for Panel Data Models with Spatially Correlated Error Components," MPRA Paper 84746, University Library of Munich, Germany.
    18. Baltagi, Badi H. & Egger, Peter H. & Kesina, Michaela, 2017. "Determinants of firm-level domestic sales and exports with spillovers: Evidence from China," Journal of Econometrics, Elsevier, vol. 199(2), pages 184-201.
    19. Heather D Gibson & Stephen G Hall & Deborah GeFang & Pavlos Petroulas & George S Tavlas, 2021. "Cross-country spillovers of national financial markets and the effectiveness of ECB policies during the euro-area crisis," Oxford Economic Papers, Oxford University Press, vol. 73(4), pages 1454-1470.
    20. Elhorst, J. Paul & Emili, Silvia, 2022. "A spatial econometric multivariate model of Okun's law," Regional Science and Urban Economics, Elsevier, vol. 93(C).
    21. Fernando A. López & Pedro J. Martínez-Ortiz & Juan-Gabriel Cegarra-Navarro, 2017. "Spatial spillovers in public expenditure on a municipal level in Spain," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 58(1), pages 39-65, January.
    22. Yang, Kai & Lee, Lung-fei, 2021. "Estimation of dynamic panel spatial vector autoregression: Stability and spatial multivariate cointegration," Journal of Econometrics, Elsevier, vol. 221(2), pages 337-367.
    23. Gibson, Heather D. & Hall, Stephen G. & Petroulas, Pavlos & Tavlas, George S., 2022. "An investigation into feedback and spatial relationships between banks’ share prices and sovereign bond spreads during the euro crisis," Journal of Financial Stability, Elsevier, vol. 63(C).
    24. Xiaoning Zhang & Mei Qu, 2020. "Impact of Environmental Regulation on Scientific and Technological Competitiveness of Resource-Based Cities in China—Based on Panel Data of 33 Resource-Based Cities," IJERPH, MDPI, vol. 17(24), pages 1-16, December.
    25. Marius C. O. Amba & Taoufiki Mbratana & Julie Gallo, 2023. "Spatial panel simultaneous equations models with error components," Empirical Economics, Springer, vol. 65(3), pages 1149-1196, September.

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    More about this item

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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