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Estimation of Spatial Autoregressions with Stochastic Weight Matrices

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  • Gupta, A

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 and ordinary least squares 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 and suggests, like the theory, that spatial weights generated from distributions with ?smaller? moments yield better estimates. Our results are especially pertinent in situations where spatial weights are functions of stochastic economic variables.

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  • Gupta, A, 2015. "Estimation of Spatial Autoregressions with Stochastic Weight Matrices," Economics Discussion Papers 15617, University of Essex, Department of Economics.
    • Handle: RePEc:esx:essedp:15617
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    2. Federico Martellosio, 2020. "Non-Identifiability in Network Autoregressions," Papers 2011.11084, arXiv.org, revised Jun 2022.
    3. Badi H. Baltagi & Junjie Shu, 2024. "A Survey of Spatial Unit Roots," Mathematics, MDPI, vol. 12(7), pages 1-32, March.
    4. 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.
    5. Liu, Tuo & Xu, Xingbai & Lee, Lung-fei, 2022. "Consistency without compactness of the parameter space in spatial econometrics," Economics Letters, Elsevier, vol. 210(C).
    6. 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).

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