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Fast estimation of matrix exponential spatial models

Author

Listed:
  • Ye Yang

    (Capital University of Economics and Business)

  • Osman Doğan

    (University of Illinois at Urbana-Champaign)

  • Süleyman Taşpınar

    (The City University of New York)

Abstract

The matrix exponential spatial specification (MESS) is an alternative to the spatial autoregressive-type (SAR-type) specifications with several attractive properties. The spatial dependence in the MESS-type models is formulated through a matrix exponential term, and the estimation of these models may require the computation of the matrix exponential terms many times in an estimation procedure. In the literature, it is well documented that the computation of the matrix exponential terms can pose challenges in terms of reliability, stability, accuracy, and efficiency. We propose a matrix-vector products approach based on the truncation of Taylor series expansion of the matrix exponential terms for the fast estimation of MESS-type models. We show how to efficiently implement this approach for a first-order MESS model, and provide extensive simulation evidence for its computational advantage over the default method utilized by a popular statistical software.

Suggested Citation

  • Ye Yang & Osman Doğan & Süleyman Taşpınar, 2021. "Fast estimation of matrix exponential spatial models," Journal of Spatial Econometrics, Springer, vol. 2(1), pages 1-50, December.
    • Handle: RePEc:spr:jospat:v:2:y:2021:i:1:d:10.1007_s43071-021-00015-2
    DOI: 10.1007/s43071-021-00015-2
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    References listed on IDEAS

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    1. 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.
    2. LeSage, James P. & Kelley Pace, R., 2007. "A matrix exponential spatial specification," Journal of Econometrics, Elsevier, vol. 140(1), pages 190-214, September.
    3. Debarsy, Nicolas & Jin, Fei & Lee, Lung-fei, 2015. "Large sample properties of the matrix exponential spatial specification with an application to FDI," Journal of Econometrics, Elsevier, vol. 188(1), pages 1-21.
    4. Süleyman Taşpınar & Osman Doğan & Wim P. M. Vijverberg, 2018. "GMM inference in spatial autoregressive models," Econometric Reviews, Taylor & Francis Journals, vol. 37(9), pages 931-954, October.
    5. Lung-Fei Lee, 2004. "Asymptotic Distributions of Quasi-Maximum Likelihood Estimators for Spatial Autoregressive Models," Econometrica, Econometric Society, vol. 72(6), pages 1899-1925, November.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Philipp Otto & Osman Dou{g}an & Suleyman Tac{s}p{i}nar & Wolfgang Schmid & Anil K. Bera, 2023. "Spatial and Spatiotemporal Volatility Models: A Review," Papers 2308.13061, arXiv.org.
    2. Ye Yang & Osman Dogan & Suleyman Taspinar & Fei Jin, 2023. "A Review of Cross-Sectional Matrix Exponential Spatial Models," Papers 2311.14813, arXiv.org.

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    More about this item

    Keywords

    Matrix exponential; MESS; QML; GMM; Bayesian; Inference; Impact measures;
    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
    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models

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