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Unobserved Grouped Heteroskedasticity and Fixed Effects

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  • Jorge A. Rivero

Abstract

This paper extends the linear grouped fixed effects (GFE) panel model to allow for heteroskedasticity from a discrete latent group variable. Key features of GFE are preserved, such as individuals belonging to one of a finite number of groups and group membership is unrestricted and estimated. Ignoring group heteroskedasticity may lead to poor classification, which is detrimental to finite sample bias and standard errors of estimators. I introduce the "weighted grouped fixed effects" (WGFE) estimator that minimizes a weighted average of group sum of squared residuals. I establish $\sqrt{NT}$-consistency and normality under a concept of group separation based on second moments. A test of group homoskedasticity is discussed. A fast computation procedure is provided. Simulations show that WGFE outperforms alternatives that exclude second moment information. I demonstrate this approach by considering the link between income and democracy and the effect of unionization on earnings.

Suggested Citation

  • Jorge A. Rivero, 2023. "Unobserved Grouped Heteroskedasticity and Fixed Effects," Papers 2310.14068, arXiv.org, revised Oct 2023.
    • Handle: RePEc:arx:papers:2310.14068
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    References listed on IDEAS

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    1. Jushan Bai & Serena Ng, 2002. "Determining the Number of Factors in Approximate Factor Models," Econometrica, Econometric Society, vol. 70(1), pages 191-221, January.
    2. Stéphane Bonhomme & Elena Manresa, 2015. "Grouped Patterns of Heterogeneity in Panel Data," Econometrica, Econometric Society, vol. 83(3), pages 1147-1184, May.
    3. Boyuan Zhang, 2020. "Forecasting with Bayesian Grouped Random Effects in Panel Data," Papers 2007.02435, arXiv.org, revised Oct 2020.
    4. Xun Lu & Liangjun Su, 2017. "Determining the number of groups in latent panel structures with an application to income and democracy," Quantitative Economics, Econometric Society, vol. 8(3), pages 729-760, November.
    5. Liangjun Su & Zhentao Shi & Peter C. B. Phillips, 2016. "Identifying Latent Structures in Panel Data," Econometrica, Econometric Society, vol. 84, pages 2215-2264, November.
    6. Deb Partha & Trivedi Pravin K., 2013. "Finite Mixture for Panels with Fixed Effects," Journal of Econometric Methods, De Gruyter, vol. 2(1), pages 35-51, July.
    7. Tomohiro Ando & Jushan Bai, 2016. "Panel Data Models with Grouped Factor Structure Under Unknown Group Membership," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(1), pages 163-191, January.
    8. Card, David, 1996. "The Effect of Unions on the Structure of Wages: A Longitudinal Analysis," Econometrica, Econometric Society, vol. 64(4), pages 957-979, July.
    9. Jushan Bai, 2009. "Panel Data Models With Interactive Fixed Effects," Econometrica, Econometric Society, vol. 77(4), pages 1229-1279, July.
    10. Hiroyuki Kasahara & Katsumi Shimotsu, 2009. "Nonparametric Identification of Finite Mixture Models of Dynamic Discrete Choices," Econometrica, Econometric Society, vol. 77(1), pages 135-175, January.
    11. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588, December.
    12. Bester, C. Alan & Hansen, Christian B., 2016. "Grouped effects estimators in fixed effects models," Journal of Econometrics, Elsevier, vol. 190(1), pages 197-208.
    13. Jaeho Kim & Le Wang, 2019. "Hidden group patterns in democracy developments: Bayesian inference for grouped heterogeneity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 34(6), pages 1016-1028, September.
    14. Lin Chang-Ching & Ng Serena, 2012. "Estimation of Panel Data Models with Parameter Heterogeneity when Group Membership is Unknown," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 42-55, August.
    15. John S. Ahlquist & Erik Wibbels, 2012. "Riding the Wave: World Trade and Factor‐Based Models of Democratization," American Journal of Political Science, John Wiley & Sons, vol. 56(2), pages 447-464, April.
    16. Sun, Yixiao X, 2005. "Estimation and Inference in Panel Structure Models," University of California at San Diego, Economics Working Paper Series qt5tf1231k, Department of Economics, UC San Diego.
    17. Michael Brusco & Douglas Steinley, 2007. "A Comparison of Heuristic Procedures for Minimum Within-Cluster Sums of Squares Partitioning," Psychometrika, Springer;The Psychometric Society, vol. 72(4), pages 583-600, December.
    18. Su, Liangjun & Ju, Gaosheng, 2018. "Identifying latent grouped patterns in panel data models with interactive fixed effects," Journal of Econometrics, Elsevier, vol. 206(2), pages 554-573.
    19. Pacheco, Joaquin & Valencia, Olga, 2003. "Design of hybrids for the minimum sum-of-squares clustering problem," Computational Statistics & Data Analysis, Elsevier, vol. 43(2), pages 235-248, June.
    20. Stock J.H. & Watson M.W., 2002. "Forecasting Using Principal Components From a Large Number of Predictors," Journal of the American Statistical Association, American Statistical Association, vol. 97, pages 1167-1179, December.
    21. Michael Brusco, 2006. "A Repetitive Branch-and-Bound Procedure for Minimum Within-Cluster Sums of Squares Partitioning," Psychometrika, Springer;The Psychometric Society, vol. 71(2), pages 347-363, June.
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