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


  • Xiaodong Liu
  • Lung-Fei Lee


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. Xiaodong Liu, 2020. "GMM identification and estimation of peer effects in a system of simultaneous equations," Journal in Spatial Econometrics, Springer, vol. 1(1), pages 1-27, December.
    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. Guy Tchuente, 2016. "Estimation of social interaction models using regularization," Studies in Economics 1607, School of Economics, University of Kent.
    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.
    5. 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.
    6. Solmaria Halleck Vega & J. Paul Elhorst, 2015. "The Slx Model," Journal of Regional Science, Wiley Blackwell, vol. 55(3), pages 339-363, June.

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