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On the bootstrap for Moran’s I test for spatial dependence

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  • Jin, Fei
  • Lee, Lung-fei

Abstract

This paper is concerned with the use of the bootstrap for statistics in spatial econometric models, with a focus on the test statistic for Moran’s I test for spatial dependence. We show that, for many statistics in spatial econometric models, the bootstrap can be studied based on linear–quadratic (LQ) forms of disturbances. By proving the uniform convergence of the cumulative distribution function for LQ forms to that of a normal distribution, we show that the bootstrap is generally consistent for test statistics that can be approximated by LQ forms, including Moran’s I. Possible asymptotic refinements of the bootstrap are most commonly studied using Edgeworth expansions. For spatial econometric models, we may establish asymptotic refinements of the bootstrap based on asymptotic expansions of LQ forms. When the disturbances are normal, we prove the existence of the usual Edgeworth expansions for LQ forms; when the disturbances are not normal, we establish an asymptotic expansion of LQ forms based on martingales. These results are applied to show the second order correctness of the bootstrap for Moran’s I test.

Suggested Citation

  • Jin, Fei & Lee, Lung-fei, 2015. "On the bootstrap for Moran’s I test for spatial dependence," Journal of Econometrics, Elsevier, vol. 184(2), pages 295-314.
    • Handle: RePEc:eee:econom:v:184:y:2015:i:2:p:295-314
    DOI: 10.1016/j.jeconom.2014.09.005
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    References listed on IDEAS

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    Cited by:

    1. Zhenlin Yang, 2018. "Bootstrap LM tests for higher-order spatial effects in spatial linear regression models," Empirical Economics, Springer, vol. 55(1), pages 35-68, August.
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    3. Sun, Yiguo & Malikov, Emir, 2018. "Estimation and inference in functional-coefficient spatial autoregressive panel data models with fixed effects," Journal of Econometrics, Elsevier, vol. 203(2), pages 359-378.
    4. Jin, Fei & Lee, Lung-fei, 2019. "GEL estimation and tests of spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 208(2), pages 585-612.
    5. Ou Bianling & Long Zhihe & Li Wenqian, 2019. "Bootstrap LM Tests for Spatial Dependence in Panel Data Models with Fixed Effects," Journal of Systems Science and Information, De Gruyter, vol. 7(4), pages 330-343, August.

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    More about this item

    Keywords

    Bootstrap; Spatial; Moran’s I; Consistency; Asymptotic refinement; Linear–quadratic form;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • R15 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Econometric and Input-Output Models; Other Methods

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