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Estimation Of Spatial Autoregressions With Stochastic Weight Matrices

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  • Gupta, Abhimanyu

Abstract

We examine a higher-order spatial autoregressive model with stochastic, but exogenous, spatial weight matrices. Allowing a general spatial linear process form for the disturbances that permits many common types of error specifications as well as potential ‘long memory’, we provide sufficient conditions for consistency and asymptotic normality of instrumental variables, ordinary least squares, and pseudo maximum likelihood estimates. The implications of popular weight matrix normalizations and structures for our theoretical conditions are discussed. A set of Monte Carlo simulations examines the behaviour of the estimates in a variety of situations. Our results are especially pertinent in situations where spatial weights are functions of stochastic economic variables, and this type of setting is also studied in our simulations.

Suggested Citation

  • Gupta, Abhimanyu, 2019. "Estimation Of Spatial Autoregressions With Stochastic Weight Matrices," Econometric Theory, Cambridge University Press, vol. 35(2), pages 417-463, April.
    • Handle: RePEc:cup:etheor:v:35:y:2019:i:02:p:417-463_00
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    Cited by:

    1. Federico Martellosio, 2020. "Non-Identifiability in Network Autoregressions," Papers 2011.11084, arXiv.org, revised Jun 2022.
    2. Liu, Tuo & Xu, Xingbai & Lee, Lung-fei, 2022. "Consistency without compactness of the parameter space in spatial econometrics," Economics Letters, Elsevier, vol. 210(C).
    3. Luo, Guowang & Wu, Mixia & Xu, Liwen, 2021. "IPW-based robust estimation of the SAR model with missing data," Statistics & Probability Letters, Elsevier, vol. 172(C).
    4. Michaelides, Alexander & Kokas, Sotirios & Gupta, Abhimanyu, 2017. "Credit Market Spillovers: Evidence from a Syndicated Loan Market Network," CEPR Discussion Papers 12424, C.E.P.R. Discussion Papers.
    5. Gupta, Abhimanyu & Kokas, Sotirios & Michaelides, Alexander & Minetti, Raoul, 2025. "Networks and information in credit markets," Journal of Corporate Finance, Elsevier, vol. 94(C).
    6. Badi H. Baltagi & Junjie Shu, 2024. "A Survey of Spatial Unit Roots," Mathematics, MDPI, vol. 12(7), pages 1-32, March.
    7. J. Paul Elhorst & Ioanna Tziolas & Chang Tan & Petros Milionis, 2024. "The distance decay effect and spatial reach of spillovers," Journal of Geographical Systems, Springer, vol. 26(2), pages 265-289, April.
    8. Lu, Fang & Pan, Hao & Yang, Jing, 2025. "GMM estimation and variable selection of semiparametric model with increasing dimension and high-order spatial dependence," Computational Statistics & Data Analysis, Elsevier, vol. 205(C).

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