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A Note on the Importance of Normalizations in Dynamic Latent Factor Models of Skill Formation

Author

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  • Del Bono, Emilia

    (ISER, University of Essex)

  • Kinsler, Josh

    (University of Georgia)

  • Pavan, Ronni

    (University of Rochester)

Abstract

In this paper we highlight an important property of the translog production function for the identification of treatment effects in a model of latent skill formation. We show that when using a translog specification of the skill technology, properly anchored treatment effect estimates are invariant to any location and scale normalizations of the underlying measures. By contrast, when researchers assume a CES production function and impose standard location and scale normalizations, the resulting treatment effect estimates are biased. Interestingly, the CES technology with standard normalizations yields biased treatment effect estimates even when age-invariant measures of the skills are available. We theoretically prove the normalization invariance of the translog production function and then produce several simulations illustrating the effects of location and scale normalizations for different technologies and types of skills measures.

Suggested Citation

  • Del Bono, Emilia & Kinsler, Josh & Pavan, Ronni, 2020. "A Note on the Importance of Normalizations in Dynamic Latent Factor Models of Skill Formation," IZA Discussion Papers 13714, Institute of Labor Economics (IZA).
    • Handle: RePEc:iza:izadps:dp13714
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    References listed on IDEAS

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    1. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    2. 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.
    3. 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.
    4. Esteban Aucejo & Jonathan James, 2021. "The Path to College Education: The Role of Math and Verbal Skills," Journal of Political Economy, University of Chicago Press, vol. 129(10), pages 2905-2946.
    5. Christensen, Laurits R & Jorgenson, Dale W & Lau, Lawrence J, 1973. "Transcendental Logarithmic Production Frontiers," The Review of Economics and Statistics, MIT Press, vol. 55(1), pages 28-45, February.
    6. 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.
    7. Del Bono, Emilia & Kinsler, Josh & Pavan, Ronni, 2020. "Skill Formation and the Trouble with Child Non-Cognitive Skill Measures," IZA Discussion Papers 13713, Institute of Labor Economics (IZA).
    8. 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).
    9. 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.
    10. Christensen, Laurits R & Greene, William H, 1976. "Economies of Scale in U.S. Electric Power Generation," Journal of Political Economy, University of Chicago Press, vol. 84(4), pages 655-676, August.
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    Cited by:

    1. Nirav Mehta, 2022. "A Partial Identification Approach to Identifying the Determinants of Human Capital Accumulation: An Application to Teachers," University of Western Ontario, Departmental Research Report Series 20221, University of Western Ontario, Department of Economics.
    2. Matthew Harding & Carlos Lamarche & Chris Muris, 2022. "Estimation of a Factor-Augmented Linear Model with Applications Using Student Achievement Data," Papers 2203.03051, arXiv.org.
    3. Joachim Freyberger, 2021. "Normalizations and misspecification in skill formation models," Papers 2104.00473, arXiv.org, revised Jul 2022.
    4. Del Bono, Emilia & Kinsler, Josh & Pavan, Ronni, 2020. "Skill Formation and the Trouble with Child Non-Cognitive Skill Measures," IZA Discussion Papers 13713, Institute of Labor Economics (IZA).

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    More about this item

    Keywords

    dynamic factor analysis; human capital; children; measurement; policy;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • I38 - Health, Education, and Welfare - - Welfare, Well-Being, and Poverty - - - Government Programs; Provision and Effects of Welfare Programs
    • J13 - Labor and Demographic Economics - - Demographic Economics - - - Fertility; Family Planning; Child Care; Children; Youth
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity

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