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Two-Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments

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  • Xiaodong Liu
  • Lung-Fei Lee

Abstract

This paper considers the IV estimation of spatial autoregressive models with endogenous regressors in the presence of many instruments. To improve asymptotic efficiency, it may be desirable to use many valid instruments. However, finite sample properties of IV estimators can be sensitive to the number of instruments. For a spatial model with endogenous regressors, this paper derives the asymptotic distribution of the two-stage least squares (2SLS) estimator when the number of instruments grows with the sample size, and suggests a bias-correction procedure based on the leading-order many-instrument bias. The paper also gives the Nagar-type approximate mean square errors (MSEs) of the 2SLS estimator and the bias-corrected 2SLS estimator, which can be minimized to choose instruments as in Donald and Newey (2001). A limited Monte Carlo experiment is carried out to study the finite sample performance of the instrument selection procedure.

Suggested Citation

  • Xiaodong Liu & Lung-Fei Lee, 2013. "Two-Stage Least Squares Estimation of Spatial Autoregressive Models with Endogenous Regressors and Many Instruments," Econometric Reviews, Taylor & Francis Journals, vol. 32(5-6), pages 734-753, August.
    • Handle: RePEc:taf:emetrv:v:32:y:2013:i:5-6:p:734-753
    DOI: 10.1080/07474938.2013.741018
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    Cited by:

    1. Simplice A. Asongu & Samba Diop, 2021. "Human development and governance in Africa: do good fences make good neighbours?," Working Papers 21/051, European Xtramile Centre of African Studies (EXCAS).
    2. Tadao Hoshino, 2018. "Semiparametric Spatial Autoregressive Models With Endogenous Regressors: With an Application to Crime Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 36(1), pages 160-172, January.
    3. Maite Alguacil & Luisa Alamá-Sabater, 2021. "Migration in Spain: The Role of Cultural Diversity Revisited," Politics and Governance, Cogitatio Press, vol. 9(4), pages 118-132.
    4. Hoshino, Tadao, 2022. "Sieve IV estimation of cross-sectional interaction models with nonparametric endogenous effect," Journal of Econometrics, Elsevier, vol. 229(2), pages 263-275.
    5. Guy Tchuente, 2016. "Estimation of social interaction models using regularization," Studies in Economics 1607, School of Economics, University of Kent.
    6. 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.
    7. Liu, Xiaodong & Saraiva, Paulo, 2015. "GMM estimation of SAR models with endogenous regressors," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 68-79.
    8. You, Jing & Huang, Yongfu, 2013. "Green-to-Grey China: Determinants and Forecasts of its Green Growth," MPRA Paper 57468, University Library of Munich, Germany, revised 16 Jul 2014.
    9. Luisa Alamá-Sabater & Teresa Fernández-Núñez & Miguel Ángel Márquez & Javier Salinas-Jimenez, 2020. "Do Countries with Similar Levels of Corruption Compete to Attract Foreign Investment? Evidence Using World Panel Data," Sustainability, MDPI, vol. 12(15), pages 1-15, July.
    10. Fei Jin & Lung-fei Lee, 2013. "Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments," Econometrics, MDPI, vol. 1(1), pages 1-44, May.
    11. Jean‐Claude Kouladoum, 2023. "Technology and control of corruption in Africa," Journal of International Development, John Wiley & Sons, Ltd., vol. 35(6), pages 1163-1180, August.
    12. Povilas Lastauskas & Eirini Tatsi, 2013. "Spatial Nexus in Crime and unemployment in Times of crisis: Evidence from Germany," Cambridge Working Papers in Economics 1359, Faculty of Economics, University of Cambridge.
    13. Jin, Fei & Lee, Lung-fei, 2018. "Irregular N2SLS and LASSO estimation of the matrix exponential spatial specification model," Journal of Econometrics, Elsevier, vol. 206(2), pages 336-358.
    14. Malabika Koley & Anil K. Bera, 2022. "Testing for spatial dependence in a spatial autoregressive (SAR) model in the presence of endogenous regressors," Journal of Spatial Econometrics, Springer, vol. 3(1), pages 1-46, December.
    15. Sylvain Barde & Rowan Cherodian & Guy Tchuente, 2024. "Moran's I 2-Stage Lasso: for Models with Spatial Correlation and Endogenous Variables," Papers 2404.02584, arXiv.org.
    16. Bernard Fingleton, 2023. "Estimating dynamic spatial panel data models with endogenous regressors using synthetic instruments," Journal of Geographical Systems, Springer, vol. 25(1), pages 121-152, January.
    17. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.
    18. Nestor Garza & Colin Lizieri, 2019. "An empirical approach to urban land monopoly: A case study of the city of Barranquilla, Colombia," Urban Studies, Urban Studies Journal Limited, vol. 56(10), pages 1931-1950, August.

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