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Quasi Maximum Likelihood Estimation of Spatial Models with Heterogeneous Coefficients

Author

Listed:
  • Michele Aquaro
  • Natalia Bailey
  • M. Hashem Pesaran
Abstract
This paper considers spatial autoregressive panel data models and extends their analysis to the case where the spatial coefficients differ across the spatial units. It derives conditions under which the spatial coefficients are identified and develops a quasi maximum likelihood (QML) estimation procedure. Under certain regularity conditions, it is shown that the QML estimators of individual spatial coefficients are consistent and asymptotically normally distributed when both the time and cross section dimensions of the panel are large. It derives the asymptotic covariance matrix of the QML estimators allowing for the possibility of non-Gaussian error processes. Small sample properties of the proposed estimators are investigated by Monte Carlo simulations for Gaussian and non-Gaussian errors, and with spatial weight matrices of differing degree of sparseness. The simulation results are in line with the paper’s key theoretical findings and show that the QML estimators have satisfactory small sample properties for panels with moderate time dimensions and irrespective of the number of cross section units in the panel, under certain sparsity conditions on the spatial weight matrix.

Suggested Citation

  • Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2015. "Quasi Maximum Likelihood Estimation of Spatial Models with Heterogeneous Coefficients," CESifo Working Paper Series 5428, CESifo.
    • Handle: RePEc:ces:ceswps:_5428
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    References listed on IDEAS

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    Cited by:

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    2. Ciccarelli, Carlo & Elhorst, J.Paul, 2018. "A dynamic spatial econometric diffusion model with common factors: The rise and spread of cigarette consumption in Italy," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 131-142.
    3. Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2021. "Estimation and inference for spatial models with heterogeneous coefficients: An application to US house prices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(1), pages 18-44, January.
    4. Cynthia Fan Yang, 2021. "Common factors and spatial dependence: an application to US house prices," Econometric Reviews, Taylor & Francis Journals, vol. 40(1), pages 14-50, January.
    5. Xu, Yuhong & Yang, Zhenlin, 2020. "Specification Tests for Temporal Heterogeneity in Spatial Panel Data Models with Fixed Effects," Regional Science and Urban Economics, Elsevier, vol. 81(C).
    6. Margaretic, Paula & Cifuentes, Rodrigo & Carreño, José Gabriel, 2021. "Banks’ interconnections and peer effects: Evidence from Chile," Research in International Business and Finance, Elsevier, vol. 58(C).
    7. Elhorst, J. Paul & Gross, Marco & Tereanu, Eugen, 2018. "Spillovers in space and time: where spatial econometrics and Global VAR models meet," Working Paper Series 2134, European Central Bank.
    8. Corinne Autant-Bernard & James P. LeSage, 2019. "A heterogeneous coefficient approach to the knowledge production function," Spatial Economic Analysis, Taylor & Francis Journals, vol. 14(2), pages 196-218, April.
    9. Hou, Zhezhi & Jin, Man & Kumbhakar, Subal C., 2020. "Productivity spillovers and human capital: A semiparametric varying coefficient approach," European Journal of Operational Research, Elsevier, vol. 287(1), pages 317-330.
    10. Sebastian Langer, 2019. "Expenditure interactions between municipalities and the role of agglomeration forces: a spatial analysis for North Rhine-Westphalia," The Annals of Regional Science, Springer;Western Regional Science Association, vol. 62(3), pages 497-527, June.
    11. Debarsy, Nicolas & Dossougoin, Cyrille & Ertur, Cem & Gnabo, Jean-Yves, 2018. "Measuring sovereign risk spillovers and assessing the role of transmission channels: A spatial econometrics approach," Journal of Economic Dynamics and Control, Elsevier, vol. 87(C), pages 21-45.
    12. LeSage, James P. & Chih, Yao-Yu, 2016. "Interpreting heterogeneous coefficient spatial autoregressive panel models," Economics Letters, Elsevier, vol. 142(C), pages 1-5.
    13. Alberto Gude & Inmaculada Álvarez & Luis Orea, 2018. "Heterogeneous spillovers among Spanish provinces: a generalized spatial stochastic frontier model," Journal of Productivity Analysis, Springer, vol. 50(3), pages 155-173, December.
    14. LeSage, James P. & Vance, Colin & Chih, Yao-Yu, 2017. "A Bayesian heterogeneous coefficients spatial autoregressive panel data model of retail fuel duopoly pricing," Regional Science and Urban Economics, Elsevier, vol. 62(C), pages 46-55.
    15. Lesage, James P. & Vance, Colin & Chih, Yao-Yu, 2016. "A Bayesian heterogeneous coefficients spatial autoregressive panel data model of retail fuel price rivalry," Ruhr Economic Papers 617, RWI - Leibniz-Institut für Wirtschaftsforschung, Ruhr-University Bochum, TU Dortmund University, University of Duisburg-Essen.
    16. Niko Hauzenberger & Michael Pfarrhofer, 2021. "Bayesian State‐Space Modeling for Analyzing Heterogeneous Network Effects of US Monetary Policy," Scandinavian Journal of Economics, Wiley Blackwell, vol. 123(4), pages 1261-1291, October.
    17. LeSage, James P. & Chih, Yao-Yu, 2018. "A Bayesian spatial panel model with heterogeneous coefficients," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 58-73.
    18. Edoardo Otranto & Massimo Mucciardi, 2019. "Clustering space-time series: FSTAR as a flexible STAR approach," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 13(1), pages 175-199, March.
    19. Debarsy, Nicolas & Yang, Zhenlin, 2018. "Editorial for the special issue entitled: New advances in spatial econometrics: Interactions matter," Regional Science and Urban Economics, Elsevier, vol. 72(C), pages 1-5.
    20. Cornwall, Gary J. & Parent, Olivier, 2017. "Embracing heterogeneity: the spatial autoregressive mixture model," Regional Science and Urban Economics, Elsevier, vol. 64(C), pages 148-161.
    21. Su, Liangjun & Wang, Wuyi & Xu, Xingbai, 2023. "Identifying latent group structures in spatial dynamic panels," Journal of Econometrics, Elsevier, vol. 235(2), pages 1955-1980.
    22. E. Otranto & M. Mucciardi, 2017. "Clustering Space-Time Series: A Flexible STAR Approach," Working Paper CRENoS 201707, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.

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    More about this item

    Keywords

    spatial panel data models; heterogeneous spatial lag; coefficients; identification; quasi maximum likelihood (QML) estimators; non-Gaussian errors;
    All these keywords.

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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