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

  • Xavier d'Haultfoeuille


  • Arnaud Maurel


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 Centre de Recherche en Economie et Statistique in its series Working Papers with number 2010-11.

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Length: 51
Date of creation: 2010
Date of revision:
Handle: RePEc:crs:wpaper:2010-11
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  1. Piero Cipollone & Alfonso Rosolia, 2006. "Social Interactions in High School: Lessons from an Earthquake," Temi di discussione (Economic working papers) 596, Bank of Italy, Economic Research and International Relations Area.
  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. 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.
  4. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
  5. 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.
  6. 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.
  7. Ichimura, H., 1991. "Semiparametric Least Squares (sls) and Weighted SLS Estimation of Single- Index Models," Papers 264, Minnesota - Center for Economic Research.
  8. Cattaneo, Alejandra & Lalive, Rafael, 2006. "Social Interactions and Schooling Decisions," CEPR Discussion Papers 5816, C.E.P.R. Discussion Papers.
  9. Xavier d'Haultfoeuille, 2008. "A New Instrumental Method for Dealing with Endogenous Selection," Working Papers 2008-23, Centre de Recherche en Economie et Statistique.
  10. J.P. Florensy & J. J. Heckmanz & C. Meghirx & E. Vytlacil, 2008. "Identification of Treatment Effects Using Control Functions in Models with Continuous, Endogenous Treatment and Heterogeneous Effects," Working Papers 200832, Geary Institute, University College Dublin.
  11. Carneiro, Pedro & Lee, Sokbae, 2009. "Estimating distributions of potential outcomes using local instrumental variables with an application to changes in college enrollment and wage inequality," Journal of Econometrics, Elsevier, vol. 149(2), pages 191-208, April.
  12. Burhanettin Kuruscu, 2006. "Training and Lifetime Income," American Economic Review, American Economic Association, vol. 96(3), pages 832-846, June.
  13. 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.
  14. Robert J. Willis & Sherwin Rosen, 1978. "Education and Self-Selection," NBER Working Papers 0249, National Bureau of Economic Research, Inc.
  15. Orley Ashenfelter & David Card, 1984. "Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs," NBER Working Papers 1489, National Bureau of Economic Research, Inc.
  16. Dustmann, Christian & van Soest, Arthur, 1998. "Public and private sector wages of male workers in Germany," European Economic Review, Elsevier, vol. 42(8), pages 1417-1441, September.
  17. 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.
  18. 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.
  19. Klein, Roger W & Spady, Richard H, 1993. "An Efficient Semiparametric Estimator for Binary Response Models," Econometrica, Econometric Society, vol. 61(2), pages 387-421, March.
  20. Whitney Newey, 1999. "Two Step Series Estimation of Sample Selection Models," Working papers 99-04, Massachusetts Institute of Technology (MIT), Department of Economics.
  21. James J. Heckman & Salvador Navarro, 2005. "Dynamic Discrete Choice and Dynamic Treatment Effects," NBER Technical Working Papers 0316, National Bureau of Economic Research, Inc.
  22. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Working Papers 11259, National Bureau of Economic Research, Inc.
  23. 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.
  24. 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.
  25. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-94, July.
  26. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September.
  27. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
  28. 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.
  29. 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.
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