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Bivariate Distribution Regression; Theory, Estimation and an Application to Intergenerational Mobility

Author

Listed:
  • Chernozhukov, Victor

    (MIT)

  • Fernández-Val, Iván

    (Boston University)

  • Meier, Jonas

    (Swiss National Bank)

  • van Vuuren, Aico

    (University of Groningen)

  • Vella, Francis

    (Georgetown University)

Abstract

We employ distribution regression to estimate the joint distribution of two outcome variables conditional on covariates. Bivariate Distribution Regression (BDR) is particularly valuable when some dependence between the outcomes persists after accounting for the impact of the covariates. Our analysis relies on Chernozhukov et al. (2018) which shows that any conditional joint distribution has a local Gaussian representation. We describe how BDR can be implemented and present some functionals of interest. As modeling the unexplained dependence is a key feature of BDR, we focus on functionals related to this dependence. We decompose the difference between the joint distributions for different groups into composition, marginal and sorting effects. We provide a similar decomposition for the transition matrices which describe how location in the distribution of one outcome is associated with location in the other. Our theoretical contributions are the derivation of the properties of these estimated functionals and appropriate procedures for inference. Our empirical illustration focuses on intergenerational mobility. Using the Panel Survey of Income Dynamics data, we model the joint distribution of parents’ and children’s earnings.

Suggested Citation

  • Chernozhukov, Victor & Fernández-Val, Iván & Meier, Jonas & van Vuuren, Aico & Vella, Francis, 2025. "Bivariate Distribution Regression; Theory, Estimation and an Application to Intergenerational Mobility," IZA Discussion Papers 18091, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp18091
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    References listed on IDEAS

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    1. Adrian Adermon & Mikael Lindahl & Daniel Waldenström, 2018. "Intergenerational Wealth Mobility and the Role of Inheritance: Evidence from Multiple Generations," Economic Journal, Royal Economic Society, vol. 128(612), pages 482-513, July.
    2. Victor Chernozhukov & Iván Fernández‐Val & Whitney Newey & Sami Stouli & Francis Vella, 2020. "Semiparametric estimation of structural functions in nonseparable triangular models," Quantitative Economics, Econometric Society, vol. 11(2), pages 503-533, May.
    3. Victor Chernozhukov & Iv'an Fern'andez-Val & Jonas Meier & Aico van Vuuren & Francis Vella, 2024. "Conditional Rank-Rank Regression," Papers 2407.06387, arXiv.org, revised Oct 2025.
    4. Iv'an Fern'andez-Val & Aico van Vuuren & Francis Vella, 2023. "Marital Sorting, Household Inequality and Selection," Papers 2310.07839, arXiv.org.
    5. 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.
    6. Victor Chernozhukov & Iv'an Fern'andez-Val & Siyi Luo, 2018. "Distribution Regression with Sample Selection, with an Application to Wage Decompositions in the UK," Papers 1811.11603, arXiv.org, revised Dec 2023.
    7. Jonas Meier, 2020. "Multivariate Distribution Regression," Diskussionsschriften dp2023, Universitaet Bern, Departement Volkswirtschaft.
    Full references (including those not matched with items on IDEAS)

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    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models

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