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Nonparametric Estimation in case of Endogenous Selection

Listed author(s):
  • Christoph Breunig
  • Enno Mammen
  • Anna Simoni

This paper addresses the problem of estimation of a nonparametric regression function from selectively observed data when selection is endogenous. Our approach relies on independence between covariates and selection conditionally on potential outcomes. Endogeneity of regressors is also allowed for. In both cases, consistent two-step estimation procedures are proposed and their rates of convergence are derived. Also pointwise asymptotic distribution of the estimators is established. In addition, we propose a nonparametric specification test to check the validity of our independence assumption. Finite sample properties are illustrated in a Monte Carlo simulation study and an empirical illustration.

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File URL: http://sfb649.wiwi.hu-berlin.de/papers/pdf/SFB649DP2015-050.pdf
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Paper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2015-050.

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Length: 40 pages
Date of creation:
Handle: RePEc:hum:wpaper:sfb649dp2015-050
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  1. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
  2. Xiaohong Chen & Demian Pouzo, 2013. "Sieve Quasi Likelihood Ratio Inference on Semi/nonparametric Conditional Moment Models," Cowles Foundation Discussion Papers 1897, Cowles Foundation for Research in Economics, Yale University.
  3. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Kato, Kengo, 2015. "Some new asymptotic theory for least squares series: Pointwise and uniform results," Journal of Econometrics, Elsevier, vol. 186(2), pages 345-366.
  4. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
  5. 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.
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  7. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 31(3), pages 129-137.
  8. D’Haultfoeuille, Xavier & Maurel, Arnaud, 2013. "Another Look At The Identification At Infinity Of Sample Selection Models," Econometric Theory, Cambridge University Press, vol. 29(01), pages 213-224, February.
  9. Yingyao Hu & Susanne M. Schennach, 2006. "Identification and estimation of nonclassical nonlinear errors-in-variables models with continuous distributions using instruments," CeMMAP working papers CWP17/06, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  10. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
  11. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
  12. Breunig, Christoph, 2015. "Goodness-of-fit tests based on series estimators in nonparametric instrumental regression," Journal of Econometrics, Elsevier, vol. 184(2), pages 328-346.
  13. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 343-364.
  14. Stefan Hoderlein & Lars Nesheim & Anna Simoni, 2012. "Semiparametric estimation of random coefficients in structural economic models," CeMMAP working papers CWP09/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
  15. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
  16. Richard Blundell & Xiaohong Chen & Dennis Kristensen, 2007. "Semi-Nonparametric IV Estimation of Shape-Invariant Engel Curves," Econometrica, Econometric Society, vol. 75(6), pages 1613-1669, November.
  17. Chunrong Ai & Xiaohong Chen, 2003. "Efficient Estimation of Models with Conditional Moment Restrictions Containing Unknown Functions," Econometrica, Econometric Society, vol. 71(6), pages 1795-1843, November.
  18. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
  19. Xiaohong Chen & Demian Pouzo, 2012. "Estimation of Nonparametric Conditional Moment Models With Possibly Nonsmooth Generalized Residuals," Econometrica, Econometric Society, vol. 80(1), pages 277-321, January.
  20. Xiaohong Chen & Han Hong & Denis Nekipelov, 2011. "Nonlinear Models of Measurement Errors," Journal of Economic Literature, American Economic Association, vol. 49(4), pages 901-937, December.
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