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Nonparametric and Semiparametric Estimation of Upward Rank Mobility Curves

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  • Tsung-Chih Lai
  • Jia-Han Shih
  • Yi-Hau Chen

Abstract

We introduce the upward rank mobility curve as a new measure of intergenerational mobility that captures upward movements across the entire parental income distribution. Our approach extends Bhattacharya and Mazumder (2011) by conditioning on a single parental income rank, thereby eliminating aggregation bias. We show that the measure can be characterized solely by the copula of parent and child income, and we propose a nonparametric copula-based estimator with better properties than kernel-based alternatives. For a conditional version of the measure without such a representation, we develop a two-step semiparametric estimator based on distribution regression and establish its asymptotic properties. An application to U.S. data reveals that whites exhibit significant upward mobility dominance over blacks among lower-middle-income families.

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  • Tsung-Chih Lai & Jia-Han Shih & Yi-Hau Chen, 2025. "Nonparametric and Semiparametric Estimation of Upward Rank Mobility Curves," Papers 2509.23174, arXiv.org.
    • Handle: RePEc:arx:papers:2509.23174
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    References listed on IDEAS

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    1. Michele Bavaro & Federico Tullio, 2023. "Intergenerational mobility measurement with latent transition matrices," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 21(1), pages 25-45, March.
    2. Black, Sandra E. & Devereux, Paul J., 2011. "Recent Developments in Intergenerational Mobility," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 4, chapter 16, pages 1487-1541, Elsevier.
    3. Daniel L. Millimet & Hao Li & Punarjit Roychowdhury, 2020. "Partial Identification of Economic Mobility: With an Application to the United States," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(4), pages 732-753, October.
    4. Sancetta, Alessio & Satchell, Stephen, 2004. "The Bernstein Copula And Its Applications To Modeling And Approximations Of Multivariate Distributions," Econometric Theory, Cambridge University Press, vol. 20(3), pages 535-562, June.
    5. William J. Collins & Marianne H. Wanamaker, 2022. "African American Intergenerational Economic Mobility since 1880," American Economic Journal: Applied Economics, American Economic Association, vol. 14(3), pages 84-117, July.
    6. Debopam Bhattacharya & Bhashkar Mazumder, 2011. "A nonparametric analysis of black–white differences in intergenerational income mobility in the United States," Quantitative Economics, Econometric Society, vol. 2(3), pages 335-379, November.
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