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Nonparametric identification and estimation of transformation models

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  • Chiappori, Pierre-André
  • Komunjer, Ivana
  • Kristensen, Dennis

Abstract

This paper derives sufficient conditions for nonparametric transformation models to be identified and develops estimators of the identified components. Our nonparametric identification result is global, and allows for endogenous regressors. In particular, we show that a completeness assumption combined with conditional independence with respect to one of the regressors suffices for the model to be nonparametrically identified. The identification result is also constructive in the sense that it yields explicit expressions of the functions of interest. We show how natural estimators can be developed from these expressions, and analyze their theoretical properties. Importantly, it is demonstrated that different normalizations of the model lead to different asymptotic properties of the estimators with one normalization in particular resulting in an estimator for the unknown transformation function that converges at a parametric rate. A test for whether a candidate regressor satisfies the conditional independence assumption required for identification is developed. A Monte Carlo experiment illustrates the performance of our method in the context of a duration model with endogenous regressors.

Suggested Citation

  • Chiappori, Pierre-André & Komunjer, Ivana & Kristensen, Dennis, 2015. "Nonparametric identification and estimation of transformation models," Journal of Econometrics, Elsevier, vol. 188(1), pages 22-39.
  • Handle: RePEc:eee:econom:v:188:y:2015:i:1:p:22-39
    DOI: 10.1016/j.jeconom.2015.01.001
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    Cited by:

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    5. Ruixuan Liu, 2020. "A competing risks model with time‐varying heterogeneity and simultaneous failure," Quantitative Economics, Econometric Society, vol. 11(2), pages 535-577, May.
    6. Liyu Dou & Jakub Kastl & John Lazarev, 2020. "Quantifying Delay Externalities in Airline Networks," Working Papers 2020-65, Princeton University. Economics Department..
    7. Áureo de Paula & Imran Rasul & Pedro CL Souza, 2019. "Identifying network ties from panel data: theory and an application to tax competition," CeMMAP working papers CWP55/19, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Andrew Chesher & Adam M. Rosen & Konrad Smolinski, 2013. "An instrumental variable model of multiple discrete choice," Quantitative Economics, Econometric Society, vol. 4(2), pages 157-196, July.
    9. Bonev, Petyo, 2020. "Nonparametric identification in nonseparable duration models with unobserved heterogeneity," Economics Working Paper Series 2005, University of St. Gallen, School of Economics and Political Science.
    10. Christoph Breunig, 2016. "Specification Testing in Nonparametric Instrumental Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    11. Lewbel, Arthur & Lu, Xun & Su, Liangjun, 2015. "Specification testing for transformation models with an application to generalized accelerated failure-time models," Journal of Econometrics, Elsevier, vol. 184(1), pages 81-96.
    12. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.
    13. Irene Botosaru & Chris Muris & Krishna Pendakur, 2020. "Identification of Time-Varying Transformation Models with Fixed Effects, with an Application to Unobserved Heterogeneity in Resource Shares," Papers 2008.05507, arXiv.org, revised Apr 2021.
    14. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    15. Krief, Jerome M., 2017. "Direct instrumental nonparametric estimation of inverse regression functions," Journal of Econometrics, Elsevier, vol. 201(1), pages 95-107.
    16. Gouriéroux, Christian & Monfort, Alain & Zakoian, Jean-Michel, 2017. "Pseudo-Maximum Likelihood and Lie Groups of Linear Transformations," MPRA Paper 79623, University Library of Munich, Germany.
    17. Irene Botosaru & Chris Muris, 2017. "Binarization for panel models with fixed effects," CeMMAP working papers CWP31/17, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    18. Effraimidis, Georgios, 2016. "Nonparametric Identification of a Time-Varying Frailty Model," DaCHE discussion papers 2016:6, University of Southern Denmark, Dache - Danish Centre for Health Economics.
    19. Christoph Breunig & Stephan Martin, 2020. "Nonclassical Measurement Error in the Outcome Variable," Papers 2009.12665, arXiv.org, revised May 2021.
    20. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," LSE Research Online Documents on Economics 103830, London School of Economics and Political Science, LSE Library.
    21. Joachim Freyberger, 2021. "Normalizations and misspecification in skill formation models," Papers 2104.00473, arXiv.org, revised Jul 2022.
    22. Irene Botosaru & Chris Muris & Senay Sokullu, 2022. "Time-Varying Linear Transformation Models with Fixed Effects and Endogeneity for Short Panels," Department of Economics Working Papers 2022-01, McMaster University.
    23. Nick Kloodt & Natalie Neumeyer & Ingrid Keilegom, 2021. "Specification testing in semi-parametric transformation models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 980-1003, December.
    24. Irene Botosaru & Chris Muris & Krishna Pendakur, 2020. "Intertemporal Collective Household Models: Identification in Short Panels with Unobserved Heterogeneity in Resource Shares," CeMMAP working papers CWP26/20, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.

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    More about this item

    Keywords

    Nonparametric identification; Transformation models; Endogeneity; Special regressor; Kernel estimation;
    All these keywords.

    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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