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Determining the number of groups in latent panel structures with an application to income and democracy

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  • Xun Lu
  • Liangjun Su

Abstract

We consider a latent group panel structure as recently studied by Su, Shi, and Phillips (2016), where the number of groups is unknown and has to be determined empirically. We propose a testing procedure to determine the number of groups. Our test is a residual‐based Lagrange multiplier‐type test. We show that after being appropriately standardized, our test is asymptotically normally distributed under the null hypothesis of a given number of groups and has the power to detect deviations from the null. Monte Carlo simulations show that our test performs remarkably well in finite samples. We apply our method to study the effect of income on democracy and find strong evidence of heterogeneity in the slope coefficients. Our testing procedure determines three latent groups among 74 countries.

Suggested Citation

  • 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.
    • Handle: RePEc:wly:quante:v:8:y:2017:i:3:p:729-760
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    Cited by:

    1. Wang, Yiren & Phillips, Peter C.B. & Su, Liangjun, 2024. "Panel data models with time-varying latent group structures," Journal of Econometrics, Elsevier, vol. 240(1).
    2. Jorge A. Rivero, 2023. "Unobserved Grouped Heteroskedasticity and Fixed Effects," Papers 2310.14068, arXiv.org, revised Oct 2023.
    3. Custodio João, Igor & Lucas, André & Schaumburg, Julia & Schwaab, Bernd, 2023. "Dynamic clustering of multivariate panel data," Journal of Econometrics, Elsevier, vol. 237(2).
    4. Andreas Dzemski & Ryo Okui, 2024. "Confidence set for group membership," Quantitative Economics, Econometric Society, vol. 15(2), pages 245-277, May.
    5. Bruce E. Hansen & Seojeong Jay Lee, 2018. "Inference for Iterated GMM Under Misspecification and Clustering," Discussion Papers 2018-07, School of Economics, The University of New South Wales.
    6. Liu, Ruiqi & Shang, Zuofeng & Zhang, Yonghui & Zhou, Qiankun, 2020. "Identification and estimation in panel models with overspecified number of groups," Journal of Econometrics, Elsevier, vol. 215(2), pages 574-590.
    7. Yanbo Liu & Peter C. B. Phillips & Jun Yu, 2023. "A Panel Clustering Approach To Analyzing Bubble Behavior," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 64(4), pages 1347-1395, November.
    8. Huang, Wenxin & Jin, Sainan & Phillips, Peter C.B. & Su, Liangjun, 2021. "Nonstationary panel models with latent group structures and cross-section dependence," Journal of Econometrics, Elsevier, vol. 221(1), pages 198-222.
    9. Wang, Wuyi & Phillips, Peter C.B. & Su, Liangjun, 2019. "The heterogeneous effects of the minimum wage on employment across states," Economics Letters, Elsevier, vol. 174(C), pages 179-185.
    10. Miao, Ke & Su, Liangjun & Wang, Wendun, 2020. "Panel threshold regressions with latent group structures," Journal of Econometrics, Elsevier, vol. 214(2), pages 451-481.
    11. Yao Luo & Hidenori Takahashi, 2022. "Bidding for Contracts under Uncertain Demand: Skewed Bidding and Risk Sharing," Working Papers tecipa-732, University of Toronto, Department of Economics.
    12. Saptorshee Kanto Chakraborty & Massimiliano Mazzanti, 2021. "Revisiting the literature on the dynamic Environmental Kuznets Curves using a latent structure approach," Economia Politica: Journal of Analytical and Institutional Economics, Springer;Fondazione Edison, vol. 38(3), pages 923-941, October.
    13. Wang, Wuyi & Su, Liangjun, 2021. "Identifying latent group structures in nonlinear panels," Journal of Econometrics, Elsevier, vol. 220(2), pages 272-295.
    14. Bruce E. Hansen & Seojeong Lee, 2021. "Inference for Iterated GMM Under Misspecification," Econometrica, Econometric Society, vol. 89(3), pages 1419-1447, May.
    15. Francesco Fallucchi & Andrea Mercatanti & Jan Niederreiter, 2021. "Identifying types in contest experiments," International Journal of Game Theory, Springer;Game Theory Society, vol. 50(1), pages 39-61, March.
    16. Zhan Gao & Zhentao Shi, 2021. "Implementing Convex Optimization in R: Two Econometric Examples," Computational Economics, Springer;Society for Computational Economics, vol. 58(4), pages 1127-1135, December.
    17. Yu Hao & Hiroyuki Kasahara, 2022. "Testing the Number of Components in Finite Mixture Normal Regression Model with Panel Data," Papers 2210.02824, arXiv.org, revised Jun 2023.
    18. Mehrabani, Ali, 2023. "Estimation and identification of latent group structures in panel data," Journal of Econometrics, Elsevier, vol. 235(2), pages 1464-1482.
    19. Okui, Ryo & Wang, Wendun, 2021. "Heterogeneous structural breaks in panel data models," Journal of Econometrics, Elsevier, vol. 220(2), pages 447-473.
    20. Dzemski, Andreas & Okui, Ryo, 2018. "Confidence Set for Group Membership," Working Papers in Economics 727, University of Gothenburg, Department of Economics.
    21. Su, Liangjun & Wang, Wuyi & Xu, Xingbai, 2023. "Identifying latent group structures in spatial dynamic panels," Journal of Econometrics, Elsevier, vol. 235(2), pages 1955-1980.
    22. Jan Niederreiter, 2023. "Broadening Economics in the Era of Artificial Intelligence and Experimental Evidence," Italian Economic Journal: A Continuation of Rivista Italiana degli Economisti and Giornale degli Economisti, Springer;Società Italiana degli Economisti (Italian Economic Association), vol. 9(1), pages 265-294, March.

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