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Near Unit Root in the Spatial Autoregressive Model


  • Lung-Fei Lee
  • Jihai Yu


This paper studies the spatial autoregressive (SAR) model for cross-sectional data when the coefficient of the spatial lag of the dependent variable is near unity. We decompose the data generating process into an unstable component and a stable one, and establish asymptotic properties of QMLE, 2SLSE and linearized QMLE of the parameters. The estimator for the spatial effect has a higher rate of convergence, and the estimators for other parameters have the regular rate. The higher rate of convergence reflects how fast the spatial root converges to unity. In contrast to near unit root in time series, the estimators are all asymptotically normal. Similarly to the regular SAR model, QMLE and linearized QMLE are more efficient than 2SLSE.

Suggested Citation

  • Lung-Fei Lee & Jihai Yu, 2013. "Near Unit Root in the Spatial Autoregressive Model," Spatial Economic Analysis, Taylor & Francis Journals, vol. 8(3), pages 314-351, September.
  • Handle: RePEc:taf:specan:v:8:y:2013:i:3:p:314-351
    DOI: 10.1080/17421772.2012.760134

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    References listed on IDEAS

    1. Ruud, Paul A., 2000. "An Introduction to Classical Econometric Theory," OUP Catalogue, Oxford University Press, number 9780195111644.
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    Cited by:

    1. Baltagi, Badi H. & Fingleton, Bernard & Pirotte, Alain, 2014. "Spatial lag models with nested random effects: An instrumental variable procedure with an application to English house prices," Journal of Urban Economics, Elsevier, vol. 80(C), pages 76-86.
    2. Liu, Long, 2015. "A note on 2SLS estimation of the mixed regressive spatial autoregressive model," Economics Letters, Elsevier, vol. 134(C), pages 49-52.
    3. 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.
    4. Dou, Baojun & Parrella, Maria Lucia & Yao, Qiwei, 2016. "Generalized Yule–Walker estimation for spatio-temporal models with unknown diagonal coefficients," Journal of Econometrics, Elsevier, vol. 194(2), pages 369-382.
    5. Dou, Baojun & Parrella, Maria Lucia & Yao, Qiwei, 2016. "Generalized Yule–Walker estimation for spatio-temporal models with unknown diagonal coefficients," LSE Research Online Documents on Economics 67151, London School of Economics and Political Science, LSE Library.

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