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Generalized Spatial Two Stage Least Squares Estimation of Spatial Autoregressive Models with Autoregressive Disturbances in the Presence of Endogenous Regressors and Many Instruments

Author

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  • Fei Jin

    (School of Economics, Shanghai University of Finance and Economics, Shanghai 200433, China)

  • Lung-fei Lee

    (Department of Economics, The Ohio State University, Columbus, OH 43210, USA)

Abstract

This paper studies the generalized spatial two stage least squares (GS2SLS) estimation of spatial autoregressive models with autoregressive disturbances when there are endogenous regressors with many valid instruments. Using many instruments may improve the efficiency of estimators asymptotically, but the bias might be large in finite samples, making the inference inaccurate. We consider the case that the number of instruments K increases with, but at a rate slower than, the sample size, and derive the approximate mean square errors (MSE) that account for the trade-offs between the bias and variance, for both the GS2SLS estimator and a bias-corrected GS2SLS estimator. A criterion function for the optimal K selection can be based on the approximate MSEs. Monte Carlo experiments are provided to show the performance of our procedure of choosing K.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jecnmx:v:1:y:2013:i:1:p:71-114:d:26028
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    References listed on IDEAS

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    3. 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.
    4. 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.
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    9. 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.
    10. 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.
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