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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. 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.
  2. Gronau, Reuben, 1974. "Wage Comparisons-A Selectivity Bias," Journal of Political Economy, University of Chicago Press, vol. 82(6), pages 1119-43, Nov.-Dec..
  3. Belzil, Christian, 2006. "The Return to Schooling in Structural Dynamic Models: A Survey," IZA Discussion Papers 2370, Institute for the Study of Labor (IZA).
  4. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
  5. Belzil, Christian & Hansen, Jörgen, 2002. "A Structural Analysis of the Correlated Random Coefficient Wage Regression Model," IZA Discussion Papers 512, Institute for the Study of Labor (IZA).
  6. Michael P. Keane & Kenneth I. Wolpin, 1995. "The career decisions of young men," Working Papers 559, Federal Reserve Bank of Minneapolis.
  7. 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.
  8. Card, David, 2001. "Estimating the Return to Schooling: Progress on Some Persistent Econometric Problems," Econometrica, Econometric Society, vol. 69(5), pages 1127-60, September.
  9. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
  10. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Working Papers 11259, National Bureau of Economic Research, Inc.
  11. Griliches, Zvi, 1977. "Estimating the Returns to Schooling: Some Econometric Problems," Econometrica, Econometric Society, vol. 45(1), pages 1-22, January.
  12. 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-.
  13. Belzil, Christian & Hansen, Jörgen, 2002. "Unobserved Ability and the Return to Schooling," IZA Discussion Papers 508, Institute for the Study of Labor (IZA).
  14. 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.
  15. 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.
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Cited by:
  1. 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.
  2. John K. Dagsvik & Zhiyang Jia & Tom Kornstad & Thor Olav Thoresen, 2012. "Theoretical and Practical Arguments for Modeling Labor Supply as a Choice among Latent Jobs," CESifo Working Paper Series 3708, CESifo Group Munich.
  3. 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).

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