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GMM estimation of spatial autoregressive models in a system of simultaneous equations with heteroskedasticity

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  • Xiaodong Liu
  • Paulo Saraiva

Abstract

This paper proposes a GMM estimation framework for the SAR model in a system of simultaneous equations with heteroskedastic disturbances. Besides linear moment conditions, the proposed GMM estimator also utilizes quadratic moment conditions based on the covariance structure of model disturbances within and across equations. Compared with the QML approach, the GMM estimator is easier to implement and robust under heteroskedasticity of unknown form. We derive the heteroskedasticity-robust standard error for the GMM estimator. Monte Carlo experiments show that the proposed GMM estimator performs well in finite samples.

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  • Xiaodong Liu & Paulo Saraiva, 2019. "GMM estimation of spatial autoregressive models in a system of simultaneous equations with heteroskedasticity," Econometric Reviews, Taylor & Francis Journals, vol. 38(4), pages 359-385, April.
    • Handle: RePEc:taf:emetrv:v:38:y:2019:i:4:p:359-385
    DOI: 10.1080/07474938.2017.1308087
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    Citations

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    Cited by:

    1. Xiaodong Liu, 2020. "GMM identification and estimation of peer effects in a system of simultaneous equations," Journal of Spatial Econometrics, Springer, vol. 1(1), pages 1-27, December.
    2. Stephen G. Hall & George S. Tavlas & Deborah Gefang, 2023. "A test to select between spatial weighting matrices," Journal of Spatial Econometrics, Springer, vol. 4(1), pages 1-10, December.
    3. 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.
    4. Deborah Gefang & Stephen G. Hall & George S. Tavlas, 2022. "Fast Two-Stage Variational Bayesian Approach to Estimating Panel Spatial Autoregressive Models with Unrestricted Spatial Weights Matrices," Papers 2205.15420, arXiv.org, revised Aug 2023.
    5. 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.
    6. Marius C. O. Amba, 2021. "Simultaneous Equations with Three Way Error Components," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 19(3), pages 583-596, September.
    7. 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).
    8. 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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