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Inference on a Generalized Roy Model, with an Application to Schooling Decisions in France

  • d'Haultfoeuille, Xavier

    ()

    (CREST-INSEE)

  • Maurel, Arnaud

    ()

    (Duke University)

This paper considers the identification and estimation of an extension of Roy's model (1951) of occupational choice, which includes a non-pecuniary component in the decision equation and allows for uncertainty on the potential outcomes. This framework is well suited to various economic contexts, including educational and sectoral choices, or migration decisions. We focus in particular on the identification of the non-pecuniary component under the condition that at least one variable affects the selection probability only through potential earnings, that is under the opposite of the usual exclusion restrictions used to identify switching regressions models and treatment effects. Point identification is achieved if such variables are continuous, while bounds are obtained otherwise. As a result, the distribution of the ex ante treatment effects can be point or set identified without any usual instruments. We propose a three-stages semiparametric estimation procedure for this model, which yields root-n consistent and asymptotically normal estimators. We apply our results to the educational context, by providing new evidence from French data that non-pecuniary factors are a key determinant of higher education attendance decisions.

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Paper provided by Institute for the Study of Labor (IZA) in its series IZA Discussion Papers with number 4606.

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Length: 51 pages
Date of creation: Dec 2009
Date of revision:
Publication status: published as 'Inference on an Extended Roy Model, with an Application to Schooling Decisions in France' in: Journal of Econometrics, 2013, 174 (2), 95–106
Handle: RePEc:iza:izadps:dp4606
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  1. Rafael Lalive & Alejandra Cattaneo, 2006. "Social Interactions and Schooling Decisions," IEW - Working Papers 298, Institute for Empirical Research in Economics - University of Zurich.
  2. Dolton, P J & Makepeace, G H & Van Der Klaauw, W, 1989. "Occupational Choice and Earnings Determination: The Role of Sample Selection and Non-pecuniary Factors," Oxford Economic Papers, Oxford University Press, vol. 41(3), pages 573-94, July.
  3. Coppejans, Mark, 2001. "Estimation of the binary response model using a mixture of distributions estimator (MOD)," Journal of Econometrics, Elsevier, vol. 102(2), pages 231-269, June.
  4. Carneiro, Pedro & Hansen, Karsten & Heckman, James, 2003. "Estimating distributions of treatment effects with an application to the returns to schooling and measurement of the effects of uncertainty on college choice," Working Paper Series 2003:9, IFAU - Institute for Evaluation of Labour Market and Education Policy.
  5. Piero Cipollone & Alfonso Rosolia, 2007. "Social Interactions in High School: Lessons from an Earthquake," American Economic Review, American Economic Association, vol. 97(3), pages 948-965, June.
  6. Willis, Robert J & Rosen, Sherwin, 1979. "Education and Self-Selection," Journal of Political Economy, University of Chicago Press, vol. 87(5), pages S7-36, October.
  7. Whitney Newey, 1999. "Two Step Series Estimation of Sample Selection Models," Working papers 99-04, Massachusetts Institute of Technology (MIT), Department of Economics.
  8. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects, and Econometric Policy Evaluation," Econometrica, Econometric Society, vol. 73(3), pages 669-738, 05.
  9. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
  10. Arnaud Maurel & Xavier D'Haultfoeuille, 2011. "Another Look at the Identification at Infinity of Sample Selection Models," Working Papers 11-11, Duke University, Department of Economics.
  11. Dustmann, C. & van Soest, A., 1997. "Public and Private Sector Wages of Male Workers in Germany," Economics Working Papers eco97/13, European University Institute.
  12. Jean-Pierre Florens & James J. Heckman & Costas Meghir & Edward J. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects," NBER Working Papers 14002, National Bureau of Economic Research, Inc.
  13. d'Haultfoeuille, Xavier, 2010. "A new instrumental method for dealing with endogenous selection," Journal of Econometrics, Elsevier, vol. 154(1), pages 1-15, January.
  14. Pedro Carneiro & Sokbae 'Simon' Lee, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," CeMMAP working papers CWP01/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  15. Burhanettin Kuruscu, 2006. "Training and Lifetime Income," American Economic Review, American Economic Association, vol. 96(3), pages 832-846, June.
  16. Klein, R.W. & Spady, R.H., 1991. "An Efficient Semiparametric Estimator for Binary Response Models," Papers 70, Bell Communications - Economic Research Group.
  17. Heckman, James J. & Navarro, Salvador, 2005. "Dynamic Discrete Choice and Dynamic Treatment Effects," IZA Discussion Papers 1790, Institute for the Study of Labor (IZA).
  18. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
  19. Charles F. Manski & Elie Tamer, 2002. "Inference on Regressions with Interval Data on a Regressor or Outcome," Econometrica, Econometric Society, vol. 70(2), pages 519-546, March.
  20. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September.
  21. van den Berg, Gerard J., 1997. "Association measures for durations in bivariate hazard rate models," Journal of Econometrics, Elsevier, vol. 79(2), pages 221-245, August.
  22. Orley Ashenfelter & David Card, 1984. "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs," Working Papers 554, Princeton University, Department of Economics, Industrial Relations Section..
  23. Robinson, Chris & Tomes, Nigel, 1984. "Union Wage Differentials in the Public and Private Sectors: A Simultaneous Equations Specification," Journal of Labor Economics, University of Chicago Press, vol. 2(1), pages 106-27, January.
  24. 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.
  25. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
  26. Ham, John C & LaLonde, Robert J, 1996. "The Effect of Sample Selection and Initial Conditions in Duration Models: Evidence from Experimental Data on Training," Econometrica, Econometric Society, vol. 64(1), pages 175-205, January.
  27. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
  28. Jaap H. Abbring & Gerard J. van den Berg, 2003. "The identifiability of the mixed proportional hazards competing risks model," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 65(3), pages 701-710.
  29. Cunha, Flavio & Heckman, James J., 2007. "Identifying and Estimating the Distributions of Ex Post and Ex Ante Returns to Schooling," Labour Economics, Elsevier, vol. 14(6), pages 870-893, December.
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