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Nonparametric Identification and Estimation in a Generalized Roy Model

Author

Listed:
  • 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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    References listed on IDEAS

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    1. John Kennan & James R. Walker, 2011. "The Effect of Expected Income on Individual Migration Decisions," Econometrica, Econometric Society, vol. 79(1), pages 211-251, January.
    2. Roback, Jennifer, 1982. "Wages, Rents, and the Quality of Life," Journal of Political Economy, University of Chicago Press, vol. 90(6), pages 1257-1278, December.
    3. Falaris, Evangelos M, 1987. "A Nested Logit Migration Model with Selectivity," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 429-443, June.
    4. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-1149, September.
    5. Bayer, Patrick & Keohane, Nathaniel & Timmins, Christopher, 2009. "Migration and hedonic valuation: The case of air quality," Journal of Environmental Economics and Management, Elsevier, vol. 58(1), pages 1-14, July.
    6. Paul S. Davies & Michael J. Greenwood & Haizheng Li, 2001. "A Conditional Logit Approach to U.S. State-to-State Migration," Journal of Regional Science, Wiley Blackwell, vol. 41(2), pages 337-360.
    7. Keisuke Hirano & Jack R. Porter, 2003. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Econometrica, Econometric Society, vol. 71(5), pages 1307-1338, September.
    8. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
    9. Sokbae Lee, 2006. "Identification of a competing risks model with unknown transformations of latent failure times," Biometrika, Biometrika Trust, vol. 93(4), pages 996-1002, December.
    10. Borjas, George J, 1987. "Self-Selection and the Earnings of Immigrants," American Economic Review, American Economic Association, vol. 77(4), pages 531-553, September.
    11. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
    12. 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.
    13. A. D. Roy, 1951. "Some Thoughts On The Distribution Of Earnings," Oxford Economic Papers, Oxford University Press, vol. 3(2), pages 135-146.
    14. 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.
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    Citations

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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(01), 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 for the Study of Labor (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.
    6. Fafchamps, Marcel & Shilpi, Forhad, 2008. "Determinants of choice of migration destination," Policy Research Working Paper Series 4728, The World Bank.

    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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