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Instrumental values

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  • Chesher, Andrew

Abstract

This paper studies the identification of partial differences of nonseparable structural functions. The paper considers triangular structures with no more stochastic unobservables than observable outcomes, that exhibit a degree of monotonicity with respect to variation in certain stochastic unobservables. It is shown that, the existence of a set of instrumental values of covariates, over which the stochastic unobservables exhibit local quantile invariance and over which a local order condition holds, defines a model which identifies certain partial differences of structural functions. This result is useful when covariates exhibit discrete variation. The paper also considers the identification of partial derivatives in smooth structures when covariates exhibit continuous variation.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 139 (2007)
Issue (Month): 1 (July)
Pages: 15-34

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Handle: RePEc:eee:econom:v:139:y:2007:i:1:p:15-34

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Web page: http://www.elsevier.com/locate/jeconom

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References

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  1. Alberto Abadie & Joshua Angrist & Guido Imbens, 2002. "Instrumental Variables Estimates of the Effect of Subsidized Training on the Quantiles of Trainee Earnings," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 91-117, January.
  2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, Econometric Society, vol. 46(1), pages 33-50, January.
  3. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, Econometric Society, vol. 71(5), pages 1339-1375, 09.
  4. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, Econometric Society, vol. 39(3), pages 577-91, May.
  5. DAROLLES, Serge & FLORENS, Jean-Pierre & RENAULT, Éric, 2002. "Nonparametric Instrumental Regression," Cahiers de recherche, Universite de Montreal, Departement de sciences economiques 2002-05, Universite de Montreal, Departement de sciences economiques.
  6. Joshua D. Angrist & Guido W. Imbens & Alan Krueger, 1995. "Jackknife Instrumental Variables Estimation," NBER Technical Working Papers 0172, National Bureau of Economic Research, Inc.
  7. Roehrig, Charles S, 1988. "Conditions for Identification in Nonparametric and Parametic Models," Econometrica, Econometric Society, Econometric Society, vol. 56(2), pages 433-47, March.
  8. Serge Darolles & Jean-Pierre Florens & Eric Renault, 2000. "Nonparametric Instrumental Regression," Working Papers 2000-17, Centre de Recherche en Economie et Statistique.
  9. Joseph G. Altonji & Rosa L. Matzkin, 2001. "Panel Data Estimators for Nonseparable Models with Endogenous Regressors," NBER Technical Working Papers 0267, National Bureau of Economic Research, Inc.
  10. Newey, Whitney K. & Powell, James L., 1990. "Efficient Estimation of Linear and Type I Censored Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 6(03), pages 295-317, September.
  11. Whitney Newey & James Powell & Francis Vella, 1998. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Working papers 98-16, Massachusetts Institute of Technology (MIT), Department of Economics.
  12. Powell, James L, 1983. "The Asymptotic Normality of Two-Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, Econometric Society, vol. 51(5), pages 1569-75, September.
  13. repec:cup:etheor:v:6:y:1990:i:3:p:295-317 is not listed on IDEAS
  14. James J. Heckman & Edward Vytlacil, 2005. "Structural Equations, Treatment Effects and Econometric Policy Evaluation," NBER Working Papers 11259, National Bureau of Economic Research, Inc.
  15. Angrist, Joshua D & Krueger, Alan B, 1991. "Does Compulsory School Attendance Affect Schooling and Earnings?," The Quarterly Journal of Economics, MIT Press, MIT Press, vol. 106(4), pages 979-1014, November.
  16. Andrew Chesher, 2001. "Exogenous impact and conditional quantile functions," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP01/01, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  17. Khan, Shakeeb, 2001. "Two-stage rank estimation of quantile index models," Journal of Econometrics, Elsevier, Elsevier, vol. 100(2), pages 319-355, February.
  18. Brown, Bryan W, 1983. "The Identification Problem in Systems Nonlinear in the Variables," Econometrica, Econometric Society, Econometric Society, vol. 51(1), pages 175-96, January.
  19. Andrew Chesher, 2002. "Instrumental Values," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP17/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  20. Andrew Chesher, 2003. "Identification in Nonseparable Models," Econometrica, Econometric Society, Econometric Society, vol. 71(5), pages 1405-1441, 09.
  21. Amemiya, Takeshi, 1982. "Two Stage Least Absolute Deviations Estimators," Econometrica, Econometric Society, Econometric Society, vol. 50(3), pages 689-711, May.
  22. Joshua D. Angrist & Guido W. Imbens, 1995. "Identification and Estimation of Local Average Treatment Effects," NBER Technical Working Papers 0118, National Bureau of Economic Research, Inc.
  23. Lee, Sokbae, 2003. "Efficient Semiparametric Estimation Of A Partially Linear Quantile Regression Model," Econometric Theory, Cambridge University Press, vol. 19(01), pages 1-31, February.
  24. Mitali Das, 2000. "Instrumental Variables Estimation of Nonparametric Models with Discrete Endogenous Regressors," Econometric Society World Congress 2000 Contributed Papers 1008, Econometric Society.
  25. Heckman, James J, 1990. "Varieties of Selection Bias," American Economic Review, American Economic Association, vol. 80(2), pages 313-18, May.
  26. Andrew Chesher, 2005. "Nonparametric Identification under Discrete Variation," Econometrica, Econometric Society, Econometric Society, vol. 73(5), pages 1525-1550, 09.
  27. Edward Vytlacil, 2002. "Independence, Monotonicity, and Latent Index Models: An Equivalence Result," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 331-341, January.
  28. Heckman, James J & Smith, Jeffrey, 1997. "Making the Most Out of Programme Evaluations and Social Experiments: Accounting for Heterogeneity in Programme Impacts," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 64(4), pages 487-535, October.
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Citations

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Cited by:
  1. Andrew Chesher, 2002. "Instrumental Values," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP17/02, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  2. Chesher, Andrew, 2009. "Excess heterogeneity, endogeneity and index restrictions," Journal of Econometrics, Elsevier, Elsevier, vol. 152(1), pages 37-45, September.
  3. Andrew Chesher, 2003. "Nonparametric identification under discrete variation," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP19/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  4. Jinhyun Lee, . "Sharp Bounds on Heterogeneous Individual Treatment Responses," Discussion Paper Series, Department of Economics 201310, Department of Economics, University of St. Andrews.
  5. Kasey Buckles & Daniel M. Hungerman, 2008. "Season of Birth and Later Outcomes: Old Questions, New Answers," NBER Working Papers 14573, National Bureau of Economic Research, Inc.
  6. Andrew Chesher, 2003. "Nonparametric identification with discrete endogenous variables," CeMMAP working papers, Centre for Microdata Methods and Practice, Institute for Fiscal Studies CWP06/03, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  7. Andrew Chesher, 2004. "Identification of sensitivity to variation in endogenous variables," Econometric Society 2004 Australasian Meetings 353, Econometric Society.
  8. Brunello, Giorgio & Fort, Margherita & Weber, Guglielmo, 2007. "“For One More Year with You”: Changes in Compulsory Schooling, Education and the Distribution of Wages in Europe," IZA Discussion Papers 3102, Institute for the Study of Labor (IZA).
  9. Limor Golan & George-Levi Gayle, 2008. "Estimating a Dynamic Adverse-Selection Model: Labor-Force Experience and the Changing Gender Earnings Gap 1968-93," 2008 Meeting Papers 301, Society for Economic Dynamics.
  10. Xavier d'Haultfoeuille & Philippe Février, 2011. "Identification of Nonseparable Modes with Endogeneity and Discrete Instruments," Working Papers 2011-28, Centre de Recherche en Economie et Statistique.
  11. Horowitz, Joel L. & Lee, Sokbae, 2009. "Testing a parametric quantile-regression model with an endogenous explanatory variable against a nonparametric alternative," Journal of Econometrics, Elsevier, Elsevier, vol. 152(2), pages 141-152, October.
  12. Santos, Andres, 2011. "Instrumental variable methods for recovering continuous linear functionals," Journal of Econometrics, Elsevier, Elsevier, vol. 161(2), pages 129-146, April.

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