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Nonparametric analysis of intergenerational income mobility with application to the United States

  • Debopam Bhattacharya
  • Bhashkar Mazumder

This paper concerns the problem of inferring the effects of covariates on intergenerational income mobility, i.e. on the relationship between the incomes of parents and future earnings of their children. We focus on two different measures of mobility- (i) traditional transition probability of movement across income quantiles over generations and (ii) a new direct measure of upward mobility, viz. the probability that an adult child's relative position exceeds that of the parents. We estimate the effect of possibly continuously distributed covariates from data using nonparametric regression and average derivatives and derive the distribution theory for these measures. The analytical novelty in the derivation is that the dependent variables involve nonsmooth functions of estimated components- marginal quantiles for transition probabilities and relative ranks for upward mobility- thus necessitating nontrivial modifications of standard nonparametric regression theory. We use these methods on US data from the National Longitudinal Survey of Youth to study black-white differences in intergenerational mobility, a topic which has received scant attention in the literature. We document that whites experience greater intergenerational mobility than blacks. Estimates of conditional mobility using nonparametric regression reveal that most of the interracial mobility gap can be accounted for by differences in cognitive skills during adolescence. The methods developed here have wider applicability to estimation of nonparametric regression and average derivatives where the dependent variable either involves a preliminary finite-dimensional estimate in a nonsmooth way or is a nonsmooth functional of ranks of one or more random variables.

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Paper provided by Federal Reserve Bank of Chicago in its series Working Paper Series with number WP-07-12.

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Date of creation: 2007
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Handle: RePEc:fip:fedhwp:wp-07-12
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  1. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
  2. Derek A. Neal & William R. Johnson, 1995. "The Role of Pre-Market Factors in Black-White Wage Differences," NBER Working Papers 5124, National Bureau of Economic Research, Inc.
  3. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
  4. Zheng, Buhong, 2001. "Statistical inference for poverty measures with relative poverty lines," Journal of Econometrics, Elsevier, vol. 101(2), pages 337-356, April.
  5. Shorrocks, A F, 1978. "The Measurement of Mobility," Econometrica, Econometric Society, vol. 46(5), pages 1013-24, September.
  6. Pakes, Ariel & Pollard, David, 1989. "Simulation and the Asymptotics of Optimization Estimators," Econometrica, Econometric Society, vol. 57(5), pages 1027-57, September.
  7. Becker, Gary S & Tomes, Nigel, 1979. "An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1153-89, December.
  8. Formby, John P. & Smith, W. James & Zheng, Buhong, 2004. "Mobility measurement, transition matrices and statistical inference," Journal of Econometrics, Elsevier, vol. 120(1), pages 181-205, May.
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