Decomposing Joint Distributions via Reweighting Functions: An Application to Intergenerational Economic Mobility

Richey, Jeremiah and Rosburg, Alicia (2016): Decomposing Joint Distributions via Reweighting Functions: An Application to Intergenerational Economic Mobility.

Abstract

We propose a decomposition method that extends the traditional Oaxaca-Blinder decomposition to a continuous group membership setting that can be applied to any distributional measure of interest. This is achieved by reframing the problem as a decomposition of joint distributions: we decompose the difference between an empirical and a (hypothetical) independent joint distribution of membership index and an outcome of interest. Differences are divided into a composition effect and a structure effect. The method is based on the estimation of a counterfactual joint distribution via reweighting functions that can be caste into various distributional measures to investigate the drivers of the empirical relationship. We apply the method to U.S. intergenerational economic mobility and investigate multiple versions of the intergenerational elasticity of income (IGE): the traditional linear IGE, quantile regression counterparts, and a nonparametric IGE. Quantile results reveal a U-shaped effect which is primarily compositional in nature; nonparametric results indicate the composition effect is the main driver of the mean parental-offspring link at low levels of parental income while the structural effect is the main driver at high levels of parental income. Both of these effects are masked by the traditional IGE which implies an even 50-50 split between the composition and structure effect.

• Item Type: MPRA Paper
• Language: English
• Keywords: intergenerational mobility, decomposition methods
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C20 - General; J - Labor and Demographic Economics > J3 - Wages, Compensation, and Labor Costs > J31 - Wage Level and Structure ; Wage Differentials; J - Labor and Demographic Economics > J6 - Mobility, Unemployment, Vacancies, and Immigrant Workers > J62 - Job, Occupational, and Intergenerational Mobility

References

Altonji J, Bharadwaj P, Lange F. 2012. Changes in the characteristics of american youth: implications for adult outcomes. Journal of Labor Economics 4: 783-828.

Becker G, Tomes N. 1979. An equilibrium theory of the distribution of income and intergenerational mobility. Journal of Political Economy 87: 1153-1189.

Becker G, Tomes N. 1986. Human capital and the rise and fall of families. Journal of Labor Economics 4(3):S1-S39.

Bhattacharya D, Mazumder B. 2011. A nonparametric analysis of black-white differences in intergenerational income mobility in the United States. Quantitative Economics 43(1): 139-172.

Bjorklund A, Lindahl M, Plug E. 2006. The origins of intergenerational associations: lessons from Swedish adoption data. Quarterly Journal of Economics 121(3): 999-1028.

Blanden J, Gregg P, Macmillan L. 2007. Accounting for intergenerational income persistance: noncognitive skills, ability and education. The Economic Journal 117:C43-C60.

Blinder A. 1973. Wage discrimination: reduced form and structural estimates. Journal of Human Resources 8:436-455.

Bohlmark A, Lindquist M. 2006. Life-cycle variations in the association between current and lifetime income: replication and extension for Sweden. Journal of Labor Economics 24(4): 879-896.

Bowles S, Gintis H. 2002. The inheritance of inequality. Journal of Economic Perspectives 16(3): 3-30.

Bratsberg B, Roed K, Raaum O, Naylor R, Jantti M, Eriksson T, Osterbacka E. 2007. Nonlinearities in intergenerational earnings mobility: consequences for cross-country comparisons. The Economic Journal 117 C72-C92.

Bureau of Labor Statistics (BLS). 2015. NLSY79 appendix 21: attitudinal scales. Bureau of Labor Statistics - National Longitudinal Survey of Youth 1979. Accessed June 29, 2015.

Cardak B, Johnston D, Martin V. 2013. Intergenerational income mobility: a new decomposition of investment and endowment effects. Labour Economics 24: 39-47.

Chernozhukov V, Fernandez-Val I, Melly B. 2013. Inference on counterfactual distributions. Econometrica 81: 2205-2268.

Corak M, Heisz A. 1999. The intergenerational earnings and income mobility of Canadian men: evidence from longitudinal income tax data. The Journal of Human Resources 34: 504-533.

Deng H, Wickham, H. 2011. Density estimation in R. Unpublished Manuscript

DiNardo J, Fortin N, Lemieux T. 1996. Labor market institutions and the distribution of wages, 1973-1992: a semiparametric approach. Econometrica 64: 1001-1044.

Eide, E, Showalter, M. 1999. Factors affecting the transmission of earnings across generations: a quantile regression approach. The Journal of Human Resources 34(2): 253-267.

Firpo, S, Fortin, N, Lemieux, T. 2007. Decomposing wage distributions using recentered influence function regressions. Mimeo, University of British Columbia.

Foresi S, Peracchi F. 1995. The conditional distribution of excess returns: an empirical analysis. Journal of the American Statistical Association 90: 451-466.

Fortin N, Lemieux T, Firpo S. 2011. Decomposition methods in economics. Chapter 1 in O. Ashenfelter, R. Layard, and D. Card (eds.), Handbook of Labor Economics. Volume 4(A): 1 - 102. New Holland.

Grawe, Nathan. 2004. Reconsidering the use of nonlinearities in intergenerational earnings mobility as a test for credit constraints. Journal of Human Resources 39 813-827.

Haider S, Solon G. 2006. Life-cycle variation in the association betwen current and lifetime earnings. American Economic Review 96(4): 1308-1320.

Koenker R, Bassett G. 1978. Regression quantiles. Econometrica 46: 33-50.

Lefgren L, Lindquist M, Sims D. 2012. Rich dad, smart dad: decomposing the intergenerational transmission of income. Journal of Political Economy 120: 268-303.

Liu H, Zeng J. 2009. Genetic ability and intergenerational income mobility. Journal of Population Economics 22: 75-95.

Machado J, Mata J. 2005. Counterfactual decomposition of changes in wage distributions using quantile regression. Journal of Applied Econometrics 20: 445-465.

Mayer S, Lopoo L. 2008. Government spending and intergenerational mobility. Journal of Public Economics 92: 139-158.

Mincer J. 1974. Schooling, Experience and Earnings. New York: National Bureau of Economic Research.

Nopo, H. 2008. An extension of the Blinder-Oaxaca decomposition to a continuum of comparison groups. Economics Letters 100: 292-296.

Nybom M, Stuhler J. 2015. Biases in standard measures of intergenerational income dependence. Working Paper.

Oaxaca R. 1973. Male-female wage differentials in urban labor markets. International Economic Review 14: 693-709.

Regan T, Oaxaca R. 2009. Work experience as a source of specification error in earnings models: implications for gender wage decompositions. Journal of Population Economics 22: 463-499.

Richey J, Rosburg A. 2016a. Changing roles of ability and education in U.S. intergenerational mobility. Economic Inquiry, forthcoming.

Richey J, Rosburg A. 2016b. Decomposing economic mobility transition matrices. Working paper

Richey J, Rosburg A. 2016c. Understanding intergenerational economic mobility by decomposing joint distributions. Working paper

Rothe C. 2015. Decomposing the composition effect: the role of covariates in determining between-group differences in economic outcomes. Journal of Business and Economic Statistics 33(3): 323-337.

Shea J. 2000. Does parents' money matter? Journal of Public Economics 111(3): 358-368.

Ulrick S. 2012. The Oaxaca decomposition generalized to a continuous group variable. Economics Letters 115(1): 35-37.