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Detection and estimation of block structure in spatial weight matrix

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  • Lam, Clifford
  • Souza, Pedro C.L.

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 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 paper 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 US Senate voting data and correctly identified blocks based on party affiliations. Simulations also show that the method performs well.

Suggested Citation

  • Lam, Clifford & Souza, Pedro C.L., 2015. "Detection and estimation of block structure in spatial weight matrix," LSE Research Online Documents on Economics 59898, London School of Economics and Political Science, LSE Library.
  • Handle: RePEc:ehl:lserod:59898
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    File URL: http://eprints.lse.ac.uk/59898/
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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(04), pages 456-487, September.
    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. James P. Lesage, 2008. "An Introduction to Spatial Econometrics," Revue d'économie industrielle, De Boeck Université, vol. 0(3), pages 19-44.
    5. 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.
    6. 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.
    7. Joris Pinkse & Margaret E. Slade & Craig Brett, 2002. "Spatial Price Competition: A Semiparametric Approach," Econometrica, Econometric Society, vol. 70(3), pages 1111-1153, May.
    8. Joris Pinkse & Margaret E. Slade, 2010. "The Future Of Spatial Econometrics," Journal of Regional Science, Wiley Blackwell, vol. 50(1), pages 103-117.
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    More about this item

    Keywords

    spatial weight matrix; LASSO penalization; zero-block consistency; spatial lag/error model; Nagaev-type inequality;

    JEL classification:

    • C31 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions; Social Interaction Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models

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