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Specification Testing for Transformation Models with an Application to Generalized Accelerated Failure-time Models

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Listed:
  • Arthur Lewbel

    (Boston College)

  • Xun Lu

    (Hong Kong University of Science and Technology)

  • Liangjun Su

    (Singapore Management University)

Abstract

Consider a nonseparable model Y=R(X,U) where Y and X are observed, while U is unobserved and conditionally independent of X. This paper provides the first nonparametric test of whether R takes the form of a transformation model, meaning that Y is monotonic in the sum of a function of X plus a function of U. Transformation models of this form are commonly assumed in economics, including, e.g., standard specifications of duration models and hedonic pricing models. Our test statistic is asymptotically normal under local alternatives and consistent against nonparametric alternatives. Monte Carlo experiments show that our test performs well in finite samples. We apply our results to test for specifications of generalized accelerated failure-time (GAFT) models of the duration of strikes and of marriages.

Suggested Citation

  • Arthur Lewbel & Xun Lu & Liangjun Su, 2012. "Specification Testing for Transformation Models with an Application to Generalized Accelerated Failure-time Models," Boston College Working Papers in Economics 817, Boston College Department of Economics, revised 01 May 2013.
    • Handle: RePEc:boc:bocoec:817
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    Cited by:

    1. 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.
    2. Christoph Breunig & Stefan Hoderlein, 2018. "Specification testing in random coefficient models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1371-1417, November.
    3. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    4. Andrii Babii & Jean-Pierre Florens, 2017. "Are Unobservables Separable?," Papers 1705.01654, arXiv.org, revised Mar 2021.
    5. Huang, Liquan & Khalil, Umair & Yıldız, Neşe, 2019. "Identification and estimation of a triangular model with multiple endogenous variables and insufficiently many instrumental variables," Journal of Econometrics, Elsevier, vol. 208(2), pages 346-366.
    6. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    7. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    8. Khalil, Umair & Yıldız, Neşe, 2022. "A test of the selection on observables assumption using a discontinuously distributed covariate," Journal of Econometrics, Elsevier, vol. 226(2), pages 423-450.
    9. 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.
    10. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    11. 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.
    12. Christoph Breunig, 2016. "Specification Testing in Nonparametric Instrumental Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    13. 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.
    14. Li, Hongjun & Li, Qi & Liu, Ruixuan, 2016. "Consistent model specification tests based on k-nearest-neighbor estimation method," Journal of Econometrics, Elsevier, vol. 194(1), pages 187-202.
    15. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.

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    More about this item

    Keywords

    additivity; control variable; endogenous variable; monotonicity; nonparametric nonseparable model; hazard model; specification test; transformation model; unobserved heterogeneity;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General

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