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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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    Cited by:

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    3. Marcelo C. Medeiros & Eduardo F. Mendes, 2015. "l1-Regularization of High-Dimensional Time-Series Models with Flexible Innovations," Textos para discussão 636, Department of Economics PUC-Rio (Brazil).
    4. 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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    More about this item

    Keywords

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

    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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