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Estimating the Returns to Schooling: A Likelihood Approach Based on Normal Mixtures

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  • John K. Dagsvik
  • Torbjørn Hægeland
  • Arvid Raknerud

    ()
    (Statistics Norway)

Abstract

In this paper we develop likelihood based methods for statistical inference in a joint system of equations for the choice of length of schooling and earnings. The model for schooling choice is assumed to be an ordered probit model, whereas the earnings equation contains variables that are flexible transformations of schooling and experience, with corresponding coefficients that are allowed to be heterogeneous across individuals. Under the assumption that the distribution of the random terms of the model can be expressed as a particular finite mixture of multinormal distributions, we show that the joint probability distribution for schooling and earnings can be expressed on closed form. In an application of our method on Norwegian data, we find that the mixed Gaussian model offers a substantial improvement in fit to the (heavy-tailed) empirical distribution of log-earnings compared to a multinormal benchmark model.

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Bibliographic Info

Paper provided by Research Department of Statistics Norway in its series Discussion Papers with number 567.

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Date of creation: Dec 2008
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Handle: RePEc:ssb:dispap:567

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Keywords: Schooling choice; earnings equation; normal mixtures; treatment effects; self-selection; random coefficients; full information maximum likelihood;

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References

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  1. Christian Belzil, 2006. "The Return to Schooling in Structural Dynamic Models: A Survey," Working Papers 0609, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  2. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January.
  3. Christian Belzil & Jörgen Hansen, 2004. "A Structural Analysis of the Correlated Random Coefficient Wage Regression Model," Working Papers 0405, Groupe d'Analyse et de Théorie Economique (GATE), Centre national de la recherche scientifique (CNRS), Université Lyon 2, Ecole Normale Supérieure.
  4. Stephen V. Cameron & James J. Heckman, 1998. "Life Cycle Schooling and Dynamic Selection Bias: Models and Evidence for Five Cohorts of American Males," Journal of Political Economy, University of Chicago Press, vol. 106(2), pages 262-333, April.
  5. Haegeland, T. & Klette, T.J. & Salvanes, K.G., 1999. "Declining Returns to Education in NOrway? Comparing Estimates Across Cohorts, Sectors and Over Time," Papers 14/99, Norwegian School of Economics and Business Administration-.
  6. Christian Belzil & J�rgen Hansen, 2002. "Unobserved Ability and the Return to Schooling," Econometrica, Econometric Society, vol. 70(5), pages 2075-2091, September.
  7. David Card, 2000. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," NBER Working Papers 7769, National Bureau of Economic Research, Inc.
  8. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Working Papers 11259, National Bureau of Economic Research, Inc.
  9. Garen, John, 1984. "The Returns to Schooling: A Selectivity Bias Approach with a Continuous Choice Variable," Econometrica, Econometric Society, vol. 52(5), pages 1199-1218, September.
  10. Heckman, James J, 1979. "Sample Selection Bias as a Specification Error," Econometrica, Econometric Society, vol. 47(1), pages 153-61, January.
  11. 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.
  12. Wooldridge, Jeffrey M., 1997. "On two stage least squares estimation of the average treatment effect in a random coefficient model," Economics Letters, Elsevier, vol. 56(2), pages 129-133, October.
  13. Keane, Michael P & Wolpin, Kenneth I, 1997. "The Career Decisions of Young Men," Journal of Political Economy, University of Chicago Press, vol. 105(3), pages 473-522, June.
  14. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-43, Nov.-Dec..
  15. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
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Cited by:
  1. John K. Dagsvik & Zhiyang Jia & Tom Kornstad & Thor O. Thoresen, 2012. "Theoretical and practical arguments for modeling labor supply as a choice among latent jobs," Discussion Papers 692, Research Department of Statistics Norway.
  2. Bratsberg, Bernt & Raaum, Oddbjørn & Røed, Knut, 2011. "Educating Children of Immigrants: Closing the Gap in Norwegian Schools," IZA Discussion Papers 6138, Institute for the Study of Labor (IZA).
  3. Ådne Cappelen & Arvid Raknerud & Marina Rybalka, 2008. "The effects of R&D tax credits on patenting and innovations," Discussion Papers 565, Research Department of Statistics Norway.

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