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Estimation and Selection of Spatial Weight Matrix in a Spatial Lag Model

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  • Clifford Lam
  • Pedro C.L. Souza

Abstract

Spatial econometric models allow for interactions among variables through the specification of a spatial weight matrix. Practitioners often face the risk of misspecification of such a matrix. In many problems a number of potential specifications exist, such as geographic distances, or various economic quantities among variables. We propose estimating the best linear combination of these specifications, added with a potentially sparse adjustment matrix. The coefficients in the linear combination, together with the sparse adjustment matrix, are subjected to variable selection through the adaptive least absolute shrinkage and selection operator (LASSO). As a special case, if no spatial weight matrices are specified, the sparse adjustment matrix becomes a sparse spatial weight matrix estimator of our model. Our method can therefore, be seen as a unified framework for the estimation and selection of a spatial weight matrix. The rate of convergence of all proposed estimators are determined when the number of time series variables can grow faster than the number of time points for data, while oracle properties for all penalized estimators are presented. Simulations and an application to stocks data confirms the good performance of our procedure.

Suggested Citation

  • Clifford Lam & Pedro C.L. Souza, 2020. "Estimation and Selection of Spatial Weight Matrix in a Spatial Lag Model," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(3), pages 693-710, July.
    • Handle: RePEc:taf:jnlbes:v:38:y:2020:i:3:p:693-710
    DOI: 10.1080/07350015.2019.1569526
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    Cited by:

    1. Khambai Khamjalas, 2024. "Exploring the Spatial Dynamics of FEW Nexus Policies and Their Impact on Income Inequality Using Spatial Econometric Models: Evidence from Southeast Asian Countries," International Journal of Economics and Financial Issues, Econjournals, vol. 14(2), pages 152-167, March.
    2. Koji Murayama & Jun Nagayasu & Lamia Bazzaoui, 2022. "Spatial Dependence, Social Networks, and Economic Structures in Japanese Regional Labor Migration," Sustainability, MDPI, vol. 14(3), pages 1-31, February.
    3. Dean Fantazzini & Julia Pushchelenko & Alexey Mironenkov & Alexey Kurbatskii, 2021. "Forecasting Internal Migration in Russia Using Google Trends: Evidence from Moscow and Saint Petersburg," Forecasting, MDPI, vol. 3(4), pages 1-30, October.
    4. Wu, Yujia & Lan, Wei & Fan, Xinyan & Fang, Kuangnan, 2024. "Bipartite network influence analysis of a two-mode network," Journal of Econometrics, Elsevier, vol. 239(2).
    5. Tatjana Dahlhaus & Julia Schaumburg & Tatevik Sekhposyan, 2021. "Networking the Yield Curve: Implications for Monetary Policy," Staff Working Papers 21-4, Bank of Canada.
    6. Gupta, Abhimanyu & Kokas, Sotirios & Michaelides, Alexander & Minetti, Raoul, 2023. "Networks and Information in Credit Markets," Working Papers 2023-1, Michigan State University, Department of Economics.
    7. Rossi, Francesca & Lieberman, Offer, 2023. "Spatial autoregressions with an extended parameter space and similarity-based weights," Journal of Econometrics, Elsevier, vol. 235(2), pages 1770-1798.
    8. Christian Glocker & Matteo Iacopini & Tam'as Krisztin & Philipp Piribauer, 2023. "A Bayesian Markov-switching SAR model for time-varying cross-price spillovers," Papers 2310.19557, arXiv.org.
    9. Piribauer, Philipp & Glocker, Christian & Krisztin, Tamás, 2023. "Beyond distance: The spatial relationships of European regional economic growth," Journal of Economic Dynamics and Control, Elsevier, vol. 155(C).
    10. Bao, Yong, 2024. "Estimating spatial autoregressions under heteroskedasticity without searching for instruments," Regional Science and Urban Economics, Elsevier, vol. 106(C).
    11. Xiangyang Cao & Yishao Shi & Liangliang Zhou & Tianhui Tao & Qianqian Yang, 2021. "Analysis of Factors Influencing the Urban Carrying Capacity of the Shanghai Metropolis Based on a Multiscale Geographically Weighted Regression (MGWR) Model," Land, MDPI, vol. 10(6), pages 1-19, May.
    12. Jungyoon Lee & Peter C.B. Phillips & Francesca Rossi, 2020. "Consistent Misspecification Testing in Spatial Autoregressive Models," Cowles Foundation Discussion Papers 2256, Cowles Foundation for Research in Economics, Yale University.
    13. Deborah Gefang & Stephen G. Hall & George S. Tavlas, 2023. "Identifying spatial interdependence in panel data with large N and small T," Papers 2309.03740, arXiv.org.
    14. Keqiang Dong & Liao Guo, 2021. "Research on the Spatial Correlation and Spatial Lag of COVID-19 Infection Based on Spatial Analysis," Sustainability, MDPI, vol. 13(21), pages 1-16, October.
    15. Yu Hao & Shang Gao & Yunxia Guo & Zhiqiang Gai & Haitao Wu, 2021. "Measuring the nexus between economic development and environmental quality based on environmental Kuznets curve: a comparative study between China and Germany for the period of 2000–2017," Environment, Development and Sustainability: A Multidisciplinary Approach to the Theory and Practice of Sustainable Development, Springer, vol. 23(11), pages 16848-16873, November.
    16. P. S. Morawakage & G. Earl & B. Liu & E. Roca & A. Omura, 2023. "Housing Risk and Returns in Submarkets with Spatial Dependence and Heterogeneity," The Journal of Real Estate Finance and Economics, Springer, vol. 67(4), pages 695-734, November.

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