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Estimation and inference for spatial models with heterogeneous coefficients: an application to U.S. house prices

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  • Michele Aquaro
  • Natalia Bailey
  • M. Hashem Pesaran

Abstract

This paper considers the problem of identification, estimation and inference in the case of spatial panel data models with heterogeneous spatial lag coefficients, with and without (weakly) exogenous regressors, and subject to heteroskedastic errors. A quasi maximum likelihood (QML) estimation procedure is developed and the conditions for identification of spatial coefficients are derived. Regularity conditions are established for the QML estimators of individual spatial coefficients, as well as their means (the mean group estimators), to be consistent and asymptotically normal. 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 degrees of sparsity. The simulation results are in line with the paper's key theoretical findings even for panels with moderate time dimensions, irrespective of the number of cross section units. An empirical application to U.S. house price changes during the 1975-2014 period shows a significant degree of heterogeneity in spill-over effects over the 338 Metropolitan Statistical Areas considered.

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  • Michele Aquaro & Natalia Bailey & M. Hashem Pesaran, 2019. "Estimation and inference for spatial models with heterogeneous coefficients: an application to U.S. house prices," CESifo Working Paper Series 7542, CESifo.
    • Handle: RePEc:ces:ceswps:_7542
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    17. Jin Seo Cho & Matthew Greenwood‐Nimmo & Yongcheol Shin, 2023. "Recent developments of the autoregressive distributed lag modelling framework," Journal of Economic Surveys, Wiley Blackwell, vol. 37(1), pages 7-32, February.
    18. Tiia‐Maria Pasanen & Miikka Voutilainen & Jouni Helske & Harri Högmander, 2022. "A Bayesian spatio‐temporal analysis of markets during the Finnish 1860s famine," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1282-1302, November.
    19. Chen, Jia & Shin, Yongcheol & Zheng, Chaowen, 2022. "Estimation and inference in heterogeneous spatial panels with a multifactor error structure," Journal of Econometrics, Elsevier, vol. 229(1), pages 55-79.
    20. Guo, Juncong & Qu, Xi, 2020. "Fixed effects spatial panel data models with time-varying spatial dependence," Economics Letters, Elsevier, vol. 196(C).
    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. Ye Yang & Osman Doğan & Süleyman Taşpınar, 2023. "Observed-data DIC for spatial panel data models," Empirical Economics, Springer, vol. 64(3), pages 1281-1314, March.
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    25. F. Blasques & P. Gorgi & S. J. Koopman & J. Sampi, 2023. "Does trade integration imply growth in Latin America? Evidence from a dynamic spatial spillover model," Tinbergen Institute Discussion Papers 23-007/IVI, Tinbergen Institute.

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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; house price changes; Metropolitan Statistical Areas;
    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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