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Estimating the Technology of Children's Skill Formation

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  • Francesco Agostinelli
  • Matthew Wiswall

Abstract

We develop a new estimator for the process of children's skill formation in which children's skills endogenously develop according to a dynamic latent factor structure. Rather than assuming skills are measured perfectly by a particular measure, we accommodate the variety of skills measures used in practice and allow latent skills to be measured with error using a system of arbitrarily located and scaled measures. For commonly estimated production technologies, which already have a known location and scale, we prove non-parametric identification of the primitive production function parameters. We treat the parameters of the measurement model as "nuisance" parameters and use transformations of moments of the measurement data to eliminate them, analogous to the data transformations used to eliminate fixed effects with panel data. We develop additional, empirically grounded, restrictions on the measurement process that allow identification of more general production technologies, including those exhibiting Hicks neutral total factor productivity (TFP) dynamics and non-constant returns to scale. We use our identification results to develop a sequential estimation algorithm for the joint dynamic process of investment and skill development, correcting for the biases due to measurement error in skills and investment. Using data for the United States, we estimate the technology of skill formation, the process of parental investments in children, and the adult distribution of completed schooling and earnings, allowing the production technology and investment process to freely vary as the child ages. Our estimates of high TFP and increasing returns to scale at early ages indicate that investments are particularly productive at these ages. We find that the marginal productivity of early investments is substantially higher for children with lower existing skills, suggesting the optimal targeting of interventions to disadvantaged children. Our estimates of the dynamic process of investment and skill development allow us to estimate heterogeneous treatment effects of policy interventions. We show that even a modest transfer of family income to families at ages 5-6 would substantially increase children's skills, completed schooling, and adult earnings, with the effects largest for low income families.

Suggested Citation

  • Francesco Agostinelli & Matthew Wiswall, 2016. "Estimating the Technology of Children's Skill Formation," NBER Working Papers 22442, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:22442
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    References listed on IDEAS

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    1. 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.
    2. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2015. "Estimating the Production Function for Human Capital: Results from a Randomized Control Trial in Colombia," Cowles Foundation Discussion Papers 1987, Cowles Foundation for Research in Economics, Yale University.
    3. Daniela Del Boca & Christopher Flinn & Matthew Wiswall, 2012. "Transfers to Households with Children and Child Development," Carlo Alberto Notebooks 273, Collegio Carlo Alberto.
    4. repec:bla:scandj:v:119:y:2017:i:1:p:102-147 is not listed on IDEAS
    5. James Heckman & Flavio Cunha, 2007. "The Technology of Skill Formation," American Economic Review, American Economic Association, vol. 97(2), pages 31-47, May.
    6. Pedro Carneiro & Karsten T. Hansen & James J. Heckman, 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College," NBER Working Papers 9546, National Bureau of Economic Research, Inc.
    7. Elizabeth M. Caucutt & Lance Lochner & Youngmin Park, 2017. "Correlation, Consumption, Confusion, or Constraints: Why Do Poor Children Perform so Poorly?," Scandinavian Journal of Economics, Wiley Blackwell, vol. 119(1), pages 102-147, January.
    8. Timothy N. Bond & Kevin Lang, 2013. "The Evolution of the Black-White Test Score Gap in Grades K–3: The Fragility of Results," The Review of Economics and Statistics, MIT Press, vol. 95(5), pages 1468-1479, December.
    9. Carneiro, Pedro & Hansen, Karsten T. & Heckman, James J., 2003. "Estimating Distributions of Treatment Effects with an Application to the Returns to Schooling and Measurement of the Effects of Uncertainty on College Choice," IZA Discussion Papers 767, Institute for the Study of Labor (IZA).
    10. Flavio Cunha & James J. Heckman, 2008. "Formulating, Identifying and Estimating the Technology of Cognitive and Noncognitive Skill Formation," Journal of Human Resources, University of Wisconsin Press, vol. 43(4).
    11. Flavio Cunha & James J. Heckman & Susanne M. Schennach, 2010. "Estimating the Technology of Cognitive and Noncognitive Skill Formation," Econometrica, Econometric Society, vol. 78(3), pages 883-931, May.
    12. Raquel Bernal, 2008. "The Effect Of Maternal Employment And Child Care On Children'S Cognitive Development," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 49(4), pages 1173-1209, November.
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    Citations

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    Cited by:

    1. Elizabeth M. Caucutt & Lance Lochner, 2012. "Early and Late Human Capital Investments, Borrowing Constraints, and the Family," NBER Working Papers 18493, National Bureau of Economic Research, Inc.
    2. Francesco Agostinelli & Matthew Wiswall, 2016. "Identification of Dynamic Latent Factor Models: The Implications of Re-Normalization in a Model of Child Development," NBER Working Papers 22441, National Bureau of Economic Research, Inc.
    3. Rauh, Christopher, 2017. "Voting, education, and the Great Gatsby Curve," Journal of Public Economics, Elsevier, vol. 146(C), pages 1-14.
    4. Jorge Luis García & James J. Heckman & Duncan Ermini Leaf & María José Prados, 2017. "Quantifying the Life-cycle Benefits of a Prototypical Early Childhood Program," NBER Working Papers 23479, National Bureau of Economic Research, Inc.
    5. Orazio Attanasio & Costas Meghir & Emily Nix, 2015. "Human Capital Development and Parental Investment in India," Cowles Foundation Discussion Papers 2026R, Cowles Foundation for Research in Economics, Yale University, revised Jul 2017.
    6. Jorge Rodriguez, 2017. "Understanding the Effects of Income and Child Care Subsidies on Children's Academic Achievement," 2017 Papers pro1077, Job Market Papers.
    7. Orazio Attanasio & Costas Meghir & Emily Nix & Francesca Salvati, 2017. "Human Capital Growth and Poverty: Evidence from Ethiopia and Peru," Review of Economic Dynamics, Elsevier for the Society for Economic Dynamics, vol. 25, pages 234-259, April.
    8. Francesco Agostinelli & Giuseppe Sorrenti, 2018. "Money vs. time: family income, maternal labor supply, and child development," ECON - Working Papers 273, Department of Economics - University of Zurich.

    More about this item

    JEL classification:

    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth

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