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Theoretical foundations for spatial econometric research

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  • Xu, Xingbai
  • Lee, Lung-fei

Abstract

This paper reviews the development of large sample theories for spatial econometric models. These theories form important parts on statistical foundations for spatial econometrics. Another important component is the theoretical economics foundation for spatial econometric model specifications. We discuss how spatial econometric models can be regarded as the Nash equilibrium of some complete information games. Moran's I test for spatial dependence is based on a statistic with a linear-quadratic form. Scores of the ML and moments for 2SLS and GMM are also in linear-quadratic form. A statistic with a linear-quadratic form can be characterized as a sum of martingale differences, so the central limit theorem for martingale difference arrays is crucial for asymptotic distributions of such statistics. For linear spatial models, statistics on linear-quadratic forms are the basis of spatial econometrics. For nonlinear spatial models, near-epoch dependent random fields play a crucial role. We summarize some important properties of near-epoch dependent random fields and illustrate how they are used in studying nonlinear spatial models such as spatial Tobit and spatial binary choice models.

Suggested Citation

  • Xu, Xingbai & Lee, Lung-fei, 2019. "Theoretical foundations for spatial econometric research," Regional Science and Urban Economics, Elsevier, vol. 76(C), pages 2-12.
    • Handle: RePEc:eee:regeco:v:76:y:2019:i:c:p:2-12
    DOI: 10.1016/j.regsciurbeco.2018.04.002
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    Citations

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    Cited by:

    1. Ruonan Xu & Jeffrey M. Wooldridge, 2022. "A Design-Based Approach to Spatial Correlation," Papers 2211.14354, arXiv.org.
    2. Yu, Danlin & Murakami, Daisuke & Zhang, Yaojun & Wu, Xiwei & Li, Ding & Wang, Xiaoxi & Li, Guangdong, 2020. "Investigating high-speed rail construction's support to county level regional development in China: An eigenvector based spatial filtering panel data analysis," Transportation Research Part B: Methodological, Elsevier, vol. 133(C), pages 21-37.
    3. J. Paul Elhorst, 2022. "The dynamic general nesting spatial econometric model for spatial panels with common factors: Further raising the bar," Review of Regional Research: Jahrbuch für Regionalwissenschaft, Springer;Gesellschaft für Regionalforschung (GfR), vol. 42(3), pages 249-267, December.

    More about this item

    Keywords

    Spatial autoregressive model; GMM; MLE; Linear-quadratic form; Martingale CLT; Spatial near-epoch dependence;
    All these keywords.

    JEL classification:

    • 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
    • C24 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Truncated and Censored Models; Switching Regression Models; Threshold Regression Models
    • C57 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Econometrics of Games and Auctions

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