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Nonparametric Identification and Estimation in a Generalized Roy Model

Author

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  • Patrick Bayer
  • Shakeeb Khan
  • Christopher Timmins

Abstract

This paper considers nonparametric identification and estimation of a generalized Roy model that includes a non-pecuniary component of utility associated with each choice alternative. Previous work has found that, without parametric restrictions or the availability of covariates, all of the useful content of a cross-sectional dataset is absorbed in a restrictive specification of Roy sorting behavior that imposes independence on wage draws. While this is true, we demonstrate that it is also possible to identify (under relatively innocuous assumptions and without the use of covariates) a common non-pecuniary component of utility associated with each choice alternative. We develop nonparametric estimators corresponding to two alternative assumptions under which we prove identification, derive asymptotic properties, and illustrate small sample properties with a series of Monte Carlo experiments. We demonstrate the usefulness of one of these estimators with an empirical application. Micro data from the 2000 Census are used to calculate the returns to a college education. If high-school and college graduates face different costs of migration, this would be reflected in different degrees of Roy-sorting-induced bias in their observed wage distributions. Correcting for this bias, the observed returns to a college degree are cut in half.

Suggested Citation

  • Patrick Bayer & Shakeeb Khan & Christopher Timmins, 2008. "Nonparametric Identification and Estimation in a Generalized Roy Model," NBER Working Papers 13949, National Bureau of Economic Research, Inc.
  • Handle: RePEc:nbr:nberwo:13949
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    7. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, vol. 72(5), pages 1445-1480, September.
    8. Gordon B. Dahl, 2002. "Mobility and the Return to Education: Testing a Roy Model with Multiple Markets," Econometrica, Econometric Society, vol. 70(6), pages 2367-2420, November.
    9. George J. Borjas, 2021. "Self-Selection and the Earnings of Immigrants," World Scientific Book Chapters, in: Foundational Essays in Immigration Economics, chapter 4, pages 69-91, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. D’Haultfoeuille, Xavier & Maurel, Arnaud, 2013. "Another Look At The Identification At Infinity Of Sample Selection Models," Econometric Theory, Cambridge University Press, vol. 29(1), pages 213-224, February.
    2. Bertoli, S. & Fernández-Huertas Moraga, J. & Ortega, F., 2013. "Crossing the border: Self-selection, earnings and individual migration decisions," Journal of Development Economics, Elsevier, vol. 101(C), pages 75-91.
    3. D'Haultfoeuille, Xavier & Maurel, Arnaud, 2009. "Inference on a Generalized Roy Model, with an Application to Schooling Decisions in France," IZA Discussion Papers 4606, Institute of Labor Economics (IZA).
    4. Thomas DeLeire & Shakeeb Khan & Christopher Timmins, 2013. "Roy Model Sorting And Nonrandom Selection In The Valuation Of A Statistical Life," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 54(1), pages 279-306, February.
    5. Marcel Fafchamps & Forhad Shilpi, 2013. "Determinants of the Choice of Migration Destination," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(3), pages 388-409, June.

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    More about this item

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • J24 - Labor and Demographic Economics - - Demand and Supply of Labor - - - Human Capital; Skills; Occupational Choice; Labor Productivity
    • J3 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs
    • J32 - Labor and Demographic Economics - - Wages, Compensation, and Labor Costs - - - Nonwage Labor Costs and Benefits; Retirement Plans; Private Pensions

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