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Conditional Rank-Rank Regression

Author

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  • Chernozhukov, Victor

    (MIT)

  • Fernández-Val, Iván

    (Boston University)

  • Meier, Jonas

    (Swiss National Bank)

  • van Vuuren, Aico

    (University of Groningen)

  • Vella, Francis

    (Georgetown University)

Abstract

Rank-rank regression is commonly employed in economic research as a way of capturing the relationship between two economic variables. It frequently features in studies of intergenerational mobility as the resulting coefficient, capturing the rank correlation between the variables, is easy to interpret and measures overall persistence. However, in many applications it is common practice to include other covariates to account for differences in persistence levels between groups defined by the values of these covariates. In these instances the resulting coefficients can be difficult to interpret. We propose the conditional rank-rank regression, which uses conditional ranks instead of unconditional ranks, to measure average within-group income persistence. The difference between conditional and unconditional rank-rank regression coefficients can then be interpreted as a measure of between-group persistence. We develop a flexible estimation approach using distribution regression and establish a theoretical framework for large sample inference. An empirical study on intergenerational income mobility in Switzerland demonstrates the advantages of this approach. The study reveals stronger intergenerational persistence between fathers and sons compared to fathers and daughters, with the within-group persistence explaining 62% of the overall income persistence for sons and 52% for daughters. Smaller families and those with highly educated fathers exhibit greater persistence in economic status.

Suggested Citation

  • Chernozhukov, Victor & Fernández-Val, Iván & Meier, Jonas & van Vuuren, Aico & Vella, Francis, 2025. "Conditional Rank-Rank Regression," IZA Discussion Papers 17591, Institute of Labor Economics (IZA).
  • Handle: RePEc:iza:izadps:dp17591
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    References listed on IDEAS

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    1. Victor Chernozhukov & Iván Fernández-Val, 2011. "Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 78(2), pages 559-589.
    2. Chun Li & Bryan E. Shepherd, 2012. "A new residual for ordinal outcomes," Biometrika, Biometrika Trust, vol. 99(2), pages 473-480.
    3. Ran Abramitzky & Leah Boustan & Elisa Jacome & Santiago Perez, 2021. "Intergenerational Mobility of Immigrants in the United States over Two Centuries," American Economic Review, American Economic Association, vol. 111(2), pages 580-608, February.
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