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

Author

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. Babii, Andrii & Florens, Jean-Pierre, 2017. "Distribution of residuals in the nonparametric IV model with application to separability testing," TSE Working Papers 17-802, Toulouse School of Economics (TSE).
    2. 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.
    3. Effraimidis, Georgios, 2016. "Nonparametric Identification of a Time-Varying Frailty Model," COHERE Working Paper 2016:6, University of Southern Denmark, COHERE - Centre of Health Economics Research.
    4. 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.
    5. Breunig, Christoph & Hoderlein, Stefan, 2018. "Specification Testing in Random Coefficient Models," Rationality and Competition Discussion Paper Series 77, CRC TRR 190 Rationality and Competition.
    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. Christoph Breunig, 2016. "Specification Testing in Nonparametric Instrumental Quantile Regression," SFB 649 Discussion Papers SFB649DP2016-032, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    8. 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.

    More about this item

    Keywords

    additivity; control variable; endogenous variable; monotonicity; nonparametric nonseparable model; hazard model; specification test; transformation model; unobserved heterogeneity;

    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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