.ISSN (e) 1759-7331
(print) 1759-7323
Quantitative Economics
An open-access journal in quantitative economics
Journal of the
Econometric Society
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Quantitative Economics, Volume 2, Issue 3 (November 2011)

A nonparametric analysis of black–white differences in intergenerational income mobility in the United States

Debopam Bhattacharya, Bhashkar Mazumder


Lower intergenerational income mobility for blacks is a likely cause behind the
persistent interracial gap in economic status in the United States. However, few
studies have analyzed black–white differences in intergenerational income mobil-
ity and the factors that determine these differences. This is largely due to the ab-
sence of appropriate methodological tools. We develop nonparametric methods
to estimate the effects of covariates on two measures of mobility. We first consider
the traditional transition probability of movement across income quantiles. We
then introduce a new measure of upward mobility which is the probability that an
adult child’s relative position exceeds that of the parents. Conducting statistical in-
ference on these mobility measures and the effects of covariates on them requires
nontrivial modifications of standard nonparametric regression theory since the
dependent variables are nonsmooth functions of marginal quantiles or relative
ranks. Using National Longitudinal Survey of Youth data, we document that blacks
experience much less upward mobility across generations than whites. Applying
our new methodological tools, we find that most of this gap can be accounted for
by differences in cognitive skills during adolescence.
Keywords. Intergenerational mobility, upward mobility, nonparametric regres-
sion, Hadamard differentiability, black–white mobility gap.
JEL classification. C14, D31.

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