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Nonparametric Identification and Estimation in a Generalized Roy Model

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  • 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.

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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Working Papers with number 13949.

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Date of creation: Apr 2008
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Handle: RePEc:nbr:nberwo:13949

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  1. Patrick Bayer & Nathaniel Keohane & Christopher Timmins, 2006. "Migration and Hedonic Valuation: The Case of Air Quality," NBER Working Papers 12106, National Bureau of Economic Research, Inc.
  2. Keisuke Hirano & Jack R. Porter, 2002. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Harvard Institute of Economic Research Working Papers, Harvard - Institute of Economic Research 1988, Harvard - Institute of Economic Research.
  3. Borjas, George J, 1987. "Self-Selection and the Earnings of Immigrants," American Economic Review, American Economic Association, American Economic Association, vol. 77(4), pages 531-53, September.
  4. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, Econometric Society, vol. 58(5), pages 1121-49, September.
  5. Gordon B. Dahl, 2002. "Mobility and the Return to Education: Testing a Roy Model with Multiple Markets," RCER Working Papers 488, University of Rochester - Center for Economic Research (RCER).
  6. John Kennan & James R. Walker, 2011. "The Effect of Expected Income on Individual Migration Decisions," Econometrica, Econometric Society, Econometric Society, vol. 79(1), pages 211-251, 01.
  7. 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, Wiley Blackwell, vol. 41(2), pages 337-360.
  8. Sokbae Lee, 2006. "Identification of a competing risks model with unknown transformations of latent failure times," Biometrika, Biometrika Trust, Biometrika Trust, vol. 93(4), pages 996-1002, December.
  9. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 28(2), pages 429-43, June.
  10. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, Elsevier, vol. 152(2), pages 104-119, October.
  11. Roback, Jennifer, 1982. "Wages, Rents, and the Quality of Life," Journal of Political Economy, University of Chicago Press, University of Chicago Press, vol. 90(6), pages 1257-78, December.
  12. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, Elsevier, vol. 58(1-2), pages 3-29, July.
  13. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, Econometric Society, vol. 72(5), pages 1445-1480, 09.
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Cited by:
  1. Fafchamps, Marcel & Shilpi, Forhad, 2008. "Determinants of choice of migration destination," Policy Research Working Paper Series 4728, The World Bank.
  2. d'Haultfoeuille, Xavier & Maurel, Arnaud, 2009. "Another Look at the Identification at Infinity of Sample Selection Models," IZA Discussion Papers 4334, Institute for the Study of Labor (IZA).
  3. Marcel Fafchamps & Forhad Shilpi, 2009. "Determinants of the Choice of Migration Destination," Economics Series Working Papers, University of Oxford, Department of Economics CSAE WPS/2009-09, University of Oxford, Department of Economics.
  4. Bertoli, S. & Fernández-Huertas Moraga, J. & Ortega, F., 2013. "Crossing the border: Self-selection, earnings and individual migration decisions," Journal of Development Economics, Elsevier, Elsevier, vol. 101(C), pages 75-91.
  5. Thomas DeLeire & Christopher Timmins, 2008. "Roy Model Sorting and Non-Random Selection in the Valuation of a Statistical Life," NBER Working Papers 14364, National Bureau of Economic Research, Inc.
  6. Xavier d'Haultfoeuille & Arnaud Maurel, 2010. "Inference on a Generalized Roy Model, with an Application to Schooling Decisions in France," Working Papers, Centre de Recherche en Economie et Statistique 2010-11, Centre de Recherche en Economie et Statistique.

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