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Higher-Order Least Squares Inference for Spatial Autoregressions

Author

Listed:
  • Francesca Rossi

    (Department of Economics (University of Verona))

  • Peter M. Robinson

    (London School of Economics)

Abstract

We develop refined inference for spatial regression models with predetermined regressors. The ordinary least squares estimate of the spatial parameter is neither consistent, nor asymptotically normal, unless the elements of the spatial weight matrix uniformly vanish as sample size diverges. We develop refined testing of the hypothesis of no spatial dependence, without requiring negligibility of spatial weights, by formal Edgeworth expansions. We also develop higher-order expansions for both an unstudentized and a studentized transformed estimator, where the studentized one can be used to provide refined interval estimates. A Monte Carlo study of finite sample performance is included.

Suggested Citation

  • Francesca Rossi & Peter M. Robinson, 2020. "Higher-Order Least Squares Inference for Spatial Autoregressions," Working Papers 04/2020, University of Verona, Department of Economics.
    • Handle: RePEc:ver:wpaper:04/2020
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    References listed on IDEAS

    as
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    6. Kelejian, Harry H & Prucha, Ingmar R, 1998. "A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances," The Journal of Real Estate Finance and Economics, Springer, vol. 17(1), pages 99-121, July.
    7. Kelejian, Harry H. & Prucha, Ingmar R., 2010. "Specification and estimation of spatial autoregressive models with autoregressive and heteroskedastic disturbances," Journal of Econometrics, Elsevier, vol. 157(1), pages 53-67, July.
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    12. Badi H. Baltagi & Zhenlin Yang, 2013. "Standardized LM tests for spatial error dependence in linear or panel regressions," Econometrics Journal, Royal Economic Society, vol. 16(1), pages 103-134, February.
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    16. Martellosio, Federico, 2008. "Testing for spatial autocorrelation: the regressors that make the power disappear," MPRA Paper 10542, University Library of Munich, Germany.
    17. Robinson, Peter M. & Rossi, Francesca, 2015. "Refined Tests For Spatial Correlation," Econometric Theory, Cambridge University Press, vol. 31(6), pages 1249-1280, December.
    18. Liu, Shew Fan & Yang, Zhenlin, 2015. "Improved inferences for spatial regression models," Regional Science and Urban Economics, Elsevier, vol. 55(C), pages 55-67.
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    21. Robinson, Peter, 2008. "Correlation testing in time series, spatial and cross-sectional data," LSE Research Online Documents on Economics 25470, London School of Economics and Political Science, LSE Library.
    22. Robinson, P.M., 2008. "Correlation testing in time series, spatial and cross-sectional data," Journal of Econometrics, Elsevier, vol. 147(1), pages 5-16, November.
    23. Maekawa, Koichi, 1985. "Edgeworth Expansion for the OLS Estimator in a Time Series Regression Model," Econometric Theory, Cambridge University Press, vol. 1(2), pages 223-239, August.
    24. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
    25. Maria Kyriacou & Peter C. B. Phillips & Francesca Rossi, 2017. "Indirect inference in spatial autoregression," Econometrics Journal, Royal Economic Society, vol. 20(2), pages 168-189, June.
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    Full references (including those not matched with items on IDEAS)

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    More about this item

    Keywords

    Spatial autoregression; least squares estimation; higher-order inference; Edgeworth expansion; testing spatial independence.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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