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Mahalanobis Metric Based Clustering for Fixed Effects Model

Author

Listed:
  • Chihwa Kao

    (University of Connecticut)

  • Min Seong Kim

    (University of Connecticut)

  • Zhonghui Zhang

    (University of Connecticut)

Abstract

In this paper, we propose a Mahalanobis metric based k-means algorithm (KMM) for group membership estimation in linear panel data models with time-varying grouped fixed-effects by Bonhomme and Manresa (Econometrica 83, 1147–1184, 2015). The proposed method improves the accuracy of estimates by taking serial correlation and heteroscedasticity into account. We also derive the optimal β for group membership estimation and show that it may be different from the true coefficient parameter. Since the optimal β is not feasible in practice, we propose the data driven selection method for its implementation.

Suggested Citation

  • Chihwa Kao & Min Seong Kim & Zhonghui Zhang, 2021. "Mahalanobis Metric Based Clustering for Fixed Effects Model," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 83(2), pages 493-506, November.
    • Handle: RePEc:spr:sankhb:v:83:y:2021:i:2:d:10.1007_s13571-019-00211-z
    DOI: 10.1007/s13571-019-00211-z
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    References listed on IDEAS

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    1. Jianqing Fan & Yuan Liao & Martina Mincheva, 2013. "Large covariance estimation by thresholding principal orthogonal complements," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(4), pages 603-680, September.
    2. Stéphane Bonhomme & Elena Manresa, 2015. "Grouped Patterns of Heterogeneity in Panel Data," Econometrica, Econometric Society, vol. 83(3), pages 1147-1184, May.
    3. Arellano, M, 1987. "Computing Robust Standard Errors for Within-Groups Estimators," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 49(4), pages 431-434, November.
    4. Bester, C. Alan & Hansen, Christian B., 2016. "Grouped effects estimators in fixed effects models," Journal of Econometrics, Elsevier, vol. 190(1), pages 197-208.
    5. Brock, Guy & Pihur, Vasyl & Datta, Susmita & Datta, Somnath, 2008. "clValid: An R Package for Cluster Validation," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 25(i04).
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