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Nonparametric estimation in case of endogenous selection

Author

Listed:
  • Christoph Breunig
  • Enno Mammen
  • Anna Simoni

    (CREST - Centre de Recherche en Économie et Statistique - ENSAI - Ecole Nationale de la Statistique et de l'Analyse de l'Information [Bruz] - X - École polytechnique - ENSAE Paris - École Nationale de la Statistique et de l'Administration Économique - CNRS - Centre National de la Recherche Scientifique, CNRS - Centre National de la Recherche Scientifique)

Abstract

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 the exogenous and endogenous case, consistent two-step estimation procedures are proposed and their rates of convergence are derived. Pointwise asymptotic distribution of the estimators is established. In addition, bootstrap uniform confidence bands are obtained. Finite sample properties are illustrated in a Monte Carlo simulation study and an empirical illustration.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Christoph Breunig & Enno Mammen & Anna Simoni, 2018. "Nonparametric estimation in case of endogenous selection," Post-Print hal-03089885, HAL.
  • Handle: RePEc:hal:journl:hal-03089885
    DOI: 10.1016/j.jeconom.2017.11.002
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-03089885
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    1. Xiaohong Chen & Demian Pouzo, 2015. "Sieve Wald and QLR Inferences on Semi/Nonparametric Conditional Moment Models," Econometrica, Econometric Society, vol. 83(3), pages 1013-1079, May.
    2. Chen, Xiaohong & Reiss, Markus, 2011. "On Rate Optimality For Ill-Posed Inverse Problems In Econometrics," Econometric Theory, Cambridge University Press, vol. 27(3), pages 497-521, June.
    3. Breunig, Christoph & Huck, Steffen & Schmidt, Tobias & Weizsäcker, Georg, 2021. "The Standard Portfolio Choice Problem in Germany," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, pages 2413-2446.
    4. 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.
    5. Breunig, Christoph & Johannes, Jan, 2016. "Adaptive Estimation Of Functionals In Nonparametric Instrumental Regression," Econometric Theory, Cambridge University Press, vol. 32(3), pages 612-654, June.
    6. repec:hrv:faseco:34728615 is not listed on IDEAS
    7. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444606.
    8. S. Darolles & Y. Fan & J. P. Florens & E. Renault, 2011. "Nonparametric Instrumental Regression," Econometrica, Econometric Society, vol. 79(5), pages 1541-1565, September.
    9. Yingyao Hu & Susanne M. Schennach, 2008. "Instrumental Variable Treatment of Nonclassical Measurement Error Models," Econometrica, Econometric Society, vol. 76(1), pages 195-216, January.
    10. Horowitz, Joel L. & Lee, Sokbae, 2012. "Uniform confidence bands for functions estimated nonparametrically with instrumental variables," Journal of Econometrics, Elsevier, vol. 168(2), pages 175-188.
    11. Chen, Xiaohong & Christensen, Timothy M., 2015. "Optimal uniform convergence rates and asymptotic normality for series estimators under weak dependence and weak conditions," Journal of Econometrics, Elsevier, vol. 188(2), pages 447-465.
    12. Hoderlein, Stefan & Nesheim, Lars & Simoni, Anna, 2017. "Semiparametric Estimation Of Random Coefficients In Structural Economic Models," Econometric Theory, Cambridge University Press, vol. 33(6), pages 1265-1305, December.
    13. 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.
    14. Ai, Chunrong & Chen, Xiaohong, 2007. "Estimation of possibly misspecified semiparametric conditional moment restriction models with different conditioning variables," Journal of Econometrics, Elsevier, vol. 141(1), pages 5-43, November.
    15. 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.
    16. Newey, Whitney K., 1997. "Convergence rates and asymptotic normality for series estimators," Journal of Econometrics, Elsevier, vol. 79(1), pages 147-168, July.
    17. Sims,Christopher A. (ed.), 1994. "Advances in Econometrics," Cambridge Books, Cambridge University Press, number 9780521444590.
    18. Victor Chernozhukov & Sokbae Lee & Adam M. Rosen, 2013. "Intersection Bounds: Estimation and Inference," Econometrica, Econometric Society, vol. 81(2), pages 667-737, March.
    19. Lewbel, Arthur, 2007. "Endogenous selection or treatment model estimation," Journal of Econometrics, Elsevier, vol. 141(2), pages 777-806, December.
    20. Charles F. Manski, 1989. "Anatomy of the Selection Problem," Journal of Human Resources, University of Wisconsin Press, vol. 24(3), pages 343-360.
    21. 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.
    22. D’Haultfoeuille, Xavier, 2011. "On The Completeness Condition In Nonparametric Instrumental Problems," Econometric Theory, Cambridge University Press, vol. 27(3), pages 460-471, June.
    23. Chamberlain, Gary, 1986. "Asymptotic efficiency in semi-parametric models with censoring," Journal of Econometrics, Elsevier, vol. 32(2), pages 189-218, July.
    24. Marc Henry & Yuichi Kitamura & Bernard Salanié, 2014. "Partial identification of finite mixtures in econometric models," Quantitative Economics, Econometric Society, vol. 5, pages 123-144, March.
    25. D’Haultfoeuille, Xavier & Maurel, Arnaud, 2013. "Another Look At The Identification At Infinity Of Sample Selection Models," Econometric Theory, Cambridge University Press, vol. 29(1), pages 213-224, February.
    26. Chen, Xiaohong, 2007. "Large Sample Sieve Estimation of Semi-Nonparametric Models," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 76, Elsevier.
    27. Esmeralda A. Ramalho & Richard J. Smith, 2013. "Discrete Choice Non-Response," Review of Economic Studies, Oxford University Press, vol. 80(1), pages 343-364.
    28. Gong Tang, 2003. "Analysis of multivariate missing data with nonignorable nonresponse," Biometrika, Biometrika Trust, vol. 90(4), pages 747-764, December.
    29. Jiwei Zhao & Jun Shao, 2015. "Semiparametric Pseudo-Likelihoods in Generalized Linear Models With Nonignorable Missing Data," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1577-1590, December.
    30. Breunig, Christoph & Johannes, Jan, 2016. "Adaptive estimation of functionals in nonparametric instrumental regression," LIDAM Reprints ISBA 2016041, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    31. Heckman, James, 2013. "Sample selection bias as a specification error," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 31(3), pages 129-137.
    32. Jeffrey M Wooldridge, 2010. "Econometric Analysis of Cross Section and Panel Data," MIT Press Books, The MIT Press, edition 2, volume 1, number 0262232588.
    33. 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.
    34. Mitali Das & Whitney K. Newey & Francis Vella, 2003. "Nonparametric Estimation of Sample Selection Models," Review of Economic Studies, Oxford University Press, vol. 70(1), pages 33-58.
    35. 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.
    36. 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.
    37. Donald, Stephen G. & Imbens, Guido W. & Newey, Whitney K., 2003. "Empirical likelihood estimation and consistent tests with conditional moment restrictions," Journal of Econometrics, Elsevier, vol. 117(1), pages 55-93, November.
    38. Christoph Breunig, 2017. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2017-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    39. 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.
    40. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    41. Heckman, James J, 1974. "Shadow Prices, Market Wages, and Labor Supply," Econometrica, Econometric Society, vol. 42(4), pages 679-694, July.
    42. 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.
    43. Elie Tamer, 2010. "Partial Identification in Econometrics," Annual Review of Economics, Annual Reviews, vol. 2(1), pages 167-195, September.
    44. Whitney K. Newey & James L. Powell, 2003. "Instrumental Variable Estimation of Nonparametric Models," Econometrica, Econometric Society, vol. 71(5), pages 1565-1578, September.
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    Cited by:

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    2. Christoph Breunig, 2015. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2015-016, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    3. Breunig, Christoph & Haan, Peter, 2021. "Nonparametric regression with selectively missing covariates," Journal of Econometrics, Elsevier, vol. 223(1), pages 28-52.
    4. Christoph Breunig & Stephan Martin, 2020. "Nonclassical Measurement Error in the Outcome Variable," Papers 2009.12665, arXiv.org, revised May 2021.
    5. Breunig, Christoph & Kummer, Michael & Ohnemus, Jörg & Viete, Steffen, 2016. "IT outsourcing and firm productivity: Eliminating bias from selective missingness in the dependent variable," ZEW Discussion Papers 16-092, ZEW - Leibniz Centre for European Economic Research.
    6. Shengfang Tang & Zongwu Cai & Ying Fang & Ming Lin, 2019. "Testing Unconfoundedness Assumption Using Auxiliary Variables," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201905, University of Kansas, Department of Economics, revised Mar 2019.
    7. Breunig, Christoph, 2017. "Testing Missing At Random Using Instrumental Variables," Rationality and Competition Discussion Paper Series 59, CRC TRR 190 Rationality and Competition.
    8. Christoph Breunig & Peter Haan, 2018. "Nonparametric Regression with Selectively Missing Covariates," Papers 1810.00411, arXiv.org, revised Oct 2020.
    9. Lukáš Lafférs & Bernhard Schmidpeter, 2021. "Early child development and parents' labor supply," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 36(2), pages 190-208, March.
    10. Nir Billfeld & Moshe Kim, 2019. "Semiparametric correction for endogenous truncation bias with Vox Populi based participation decision," Papers 1902.06286, arXiv.org.
    11. Christoph Breunig, 2017. "Testing Missing at Random using Instrumental Variables," SFB 649 Discussion Papers SFB649DP2017-007, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

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    More about this item

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C26 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Instrumental Variables (IV) Estimation

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