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Detection and Estimation of Block Structure in Spatial Weight Matrix

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  • Clifford Lam
  • Pedro C. L. Souza

Abstract

In many economic applications, it is often of interest to categorize, classify, or label individuals by groups based on similarity of observed behavior. We propose a method that captures group affiliation or, equivalently, estimates the block structure of a neighboring matrix embedded in a Spatial Econometric model. The main results of the Least Absolute Shrinkage and Selection Operator (Lasso) estimator shows that off-diagonal block elements are estimated as zeros with high probability, property defined as “zero-block consistency.” Furthermore, we present and prove zero-block consistency for the estimated spatial weight matrix even under a thin margin of interaction between groups. The tool developed in this article can be used as a verification of block structure by applied researchers, or as an exploration tool for estimating unknown block structures. We analyzed the U.S. Senate voting data and correctly identified blocks based on party affiliations. Simulations also show that the method performs well.

Suggested Citation

  • Clifford Lam & Pedro C. L. Souza, 2016. "Detection and Estimation of Block Structure in Spatial Weight Matrix," Econometric Reviews, Taylor & Francis Journals, vol. 35(8-10), pages 1347-1376, December.
    • Handle: RePEc:taf:emetrv:v:35:y:2016:i:8-10:p:1347-1376
    DOI: 10.1080/07474938.2015.1085775
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    References listed on IDEAS

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    1. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Fowler, James H., 2006. "Connecting the Congress: A Study of Cosponsorship Networks," Political Analysis, Cambridge University Press, vol. 14(4), pages 456-487, October.
    3. Bhattacharjee, Arnab & Jensen-Butler, Chris, 2013. "Estimation of the spatial weights matrix under structural constraints," Regional Science and Urban Economics, Elsevier, vol. 43(4), pages 617-634.
    4. Hansheng Wang & Bo Li & Chenlei Leng, 2009. "Shrinkage tuning parameter selection with a diverging number of parameters," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(3), pages 671-683, June.
    5. Giuseppe Arbia & Bernard Fingleton, 2008. "New spatial econometric techniques and applications in regional science," Papers in Regional Science, Wiley Blackwell, vol. 87(3), pages 311-317, August.
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    Cited by:

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    6. Arnab Bhattacharjee & Sudipto Roy, 2019. "Abnormal Returns or Mismeasured Risk? Network Effects and Risk Spillover in Stock Returns," JRFM, MDPI, vol. 12(2), pages 1-13, March.

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