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Intergenerational Income Mobility: Counterfactual Distributions with a Continuous Treatment


  • Brantly Callaway

    () (Department of Economics, Temple University)

  • Weige Huang

    () (Department of Economics, Temple University)


A vast literature in labor economics documents the correlation between parents' income and their child’s income. This paper develops new methods to study the entire distribution of child's income as a function of parents' income while (possibly) adjusting for differences in background characteristics (e.g. race or parents' education) across children whose parents had different incomes. The main challenge is that parents' income is a continuous variable and existing methods for generating counterfactual distributions consider the case with discrete groups. We develop new semiparametric estimators for counterfactual distributions with a continuous treatment variable that are simple to implement and compute quickly. We show that our estimators converge uniformly to Gaussian processes and that the empirical bootstrap can be used to conduct uniformly valid inference across a range of values of parents' income. Our main analysis focuses on parameters such as (i) the fraction of children below the poverty line, (ii) "local" intergenerational elasticities (LIGE), and (iii) the variance of child's income that are functions of the counterfactual distribution. We find variation in these parameters across parents' income levels. And, after documenting large differences in background characteristics across parents' income levels, we find that adjusting for differences in background characteristics tends to reduce (though not eliminate) the overall effect of parents' income on child's income as well as reduce differences in the LIGE and variance of child's income across parents' income levels.

Suggested Citation

  • Brantly Callaway & Weige Huang, 2018. "Intergenerational Income Mobility: Counterfactual Distributions with a Continuous Treatment," DETU Working Papers 1801, Department of Economics, Temple University.
  • Handle: RePEc:tem:wpaper:1801

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    References listed on IDEAS

    1. Rasmus Landersø & James J. Heckman, 2017. "The Scandinavian Fantasy: Sources of Intergenerational Mobility in Denmark and the US," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(1), pages 178-230, January.
    2. Gordon B. Dahl & Lance Lochner, 2012. "The Impact of Family Income on Child Achievement: Evidence from the Earned Income Tax Credit," American Economic Review, American Economic Association, vol. 102(5), pages 1927-1956, August.
    3. Foresi, S. & Paracchi, F., 1992. "The Conditional Distribution of Excess Returns: An Empirical Analysis," Working Papers 92-49, C.V. Starr Center for Applied Economics, New York University.
    4. Jeremiah Richey & Alicia Rosburg, 2017. "Changing Roles Of Ability And Education In U.S. Intergenerational Mobility," Economic Inquiry, Western Economic Association International, vol. 55(1), pages 187-201, January.
    5. Jeremiah Richey & Alicia Rosburg, 2018. "Decomposing economic mobility transition matrices," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 33(1), pages 91-108, January.
    6. Jantti, Markus & Bratsberg, Bernt & Roed, Knut & Raaum, Oddbjorn & Naylor, Robin & Osterbacka, Eva & Bjorklund, Anders & Eriksson, Tor, 2005. "American exceptionalism in a new light: a comparison of intergenerational earnings mobility in the Nordic countries, the United Kingdom and the United States," Economic Research Papers 269752, University of Warwick - Department of Economics.
    7. Bhashkar Mazumder, 2005. "Fortunate Sons: New Estimates of Intergenerational Mobility in the United States Using Social Security Earnings Data," The Review of Economics and Statistics, MIT Press, vol. 87(2), pages 235-255, May.
    8. Jonathan Davis & Bhashkar Mazumder, 2017. "The Decline in Intergenerational Mobility After 1980," Working Paper Series WP-2017-5, Federal Reserve Bank of Chicago, revised 16 Mar 2017.
    9. Bratberg, Espen & Nilsen, Øivind Anti & Vaage, Kjell, 2008. "Job losses and child outcomes," Labour Economics, Elsevier, vol. 15(4), pages 591-603, August.
    10. William J. Collins & Marianne H. Wanamaker, 2017. "African American Intergenerational Economic Mobility Since 1880," NBER Working Papers 23395, National Bureau of Economic Research, Inc.
    11. Raj Chetty & Nathaniel Hendren & Patrick Kline & Emmanuel Saez, 2014. "Where is the land of Opportunity? The Geography of Intergenerational Mobility in the United States," The Quarterly Journal of Economics, Oxford University Press, vol. 129(4), pages 1553-1623.
    12. repec:hrv:faseco:30750027 is not listed on IDEAS
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    More about this item


    Intergenerational Income Mobility; Counterfactual Distribution; Continuous Treatment; Treatment Effects; Distribution RegressionJoint Distribution of Potential Outcomes; Distribution of the Treatment Effect; Quantile of the Treatment Effect; Copula Stability Assumption; Panel Data; Job Displacement;

    JEL classification:

    • C21 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Cross-Sectional Models; Spatial Models; Treatment Effect Models
    • J62 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Job, Occupational and Intergenerational Mobility; Promotion


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