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Nonparametric Identification and Estimation in a Generalized Roy Model

  • Patrick Bayer
  • Shakeeb Khan
  • Christopher Timmins

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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File URL: http://www.nber.org/papers/w13949.pdf
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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
Note: LS TWP
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  1. Khan, Shakeeb & Tamer, Elie, 2009. "Inference on endogenously censored regression models using conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 152(2), pages 104-119, October.
  2. Heckman, James J & Honore, Bo E, 1990. "The Empirical Content of the Roy Model," Econometrica, Econometric Society, vol. 58(5), pages 1121-49, September.
  3. Roback, Jennifer, 1982. "Wages, Rents, and the Quality of Life," Journal of Political Economy, University of Chicago Press, vol. 90(6), pages 1257-78, December.
  4. 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).
  5. Sokbae Lee, 2005. "Identification of a competing risks model with unknown transformations of latent failure times," CeMMAP working papers CWP17/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  6. Bayer, Patrick & Keohane, Nathaniel & Timmins, Christopher, 2009. "Migration and hedonic valuation: The case of air quality," Journal of Environmental Economics and Management, Elsevier, vol. 58(1), pages 1-14, July.
  7. George J. Borjas, 1987. "Self-Selection and the Earnings of Immigrants," NBER Working Papers 2248, National Bureau of Economic Research, Inc.
  8. Kennan,J. & Walker,J.R., 2003. "The effect of expected income on individual migration decisions," Working papers 7, Wisconsin Madison - Social Systems.
  9. Keisuke Hirano & Jack R. Porter, 2002. "Asymptotic Efficiency in Parametric Structural Models with Parameter-Dependent Support," Harvard Institute of Economic Research Working Papers 1988, Harvard - Institute of Economic Research.
  10. Ahn, Hyungtaik & Powell, James L., 1993. "Semiparametric estimation of censored selection models with a nonparametric selection mechanism," Journal of Econometrics, Elsevier, vol. 58(1-2), pages 3-29, July.
  11. 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, vol. 41(2), pages 337-360.
  12. Victor Chernozhukov & Han Hong, 2004. "Likelihood Estimation and Inference in a Class of Nonregular Econometric Models," Econometrica, Econometric Society, vol. 72(5), pages 1445-1480, 09.
  13. 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, vol. 28(2), pages 429-43, June.
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