IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v184y2015i1p81-96.html

Specification testing for transformation models with an application to generalized accelerated failure-time models

Author

Listed:
  • Lewbel, Arthur
  • Lu, Xun
  • Su, Liangjun

Abstract

This paper provides a nonparametric test of the specification of a transformation model. Specifically, we test whether an observable outcome Y is monotonic in the sum of a function of observable covariates X plus an unobservable error 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 violating the implied restriction. 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.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:econom:v:184:y:2015:i:1:p:81-96
    DOI: 10.1016/j.jeconom.2014.09.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407614001936
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2014.09.008?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or

    for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Jacho-Chávez, David & Lewbel, Arthur & Linton, Oliver, 2010. "Identification and nonparametric estimation of a transformed additively separable model," Journal of Econometrics, Elsevier, vol. 156(2), pages 392-407, June.
    2. Mata, Jose & Portugal, Pedro, 1994. "Life Duration of New Firms," Journal of Industrial Economics, Wiley Blackwell, vol. 42(3), pages 227-245, September.
    3. Hansen, Bruce E., 2008. "Uniform Convergence Rates For Kernel Estimation With Dependent Data," Econometric Theory, Cambridge University Press, vol. 24(3), pages 726-748, June.
    4. Horowitz, Joel L. & Mammen, Enno, 2011. "Oracle-Efficient Nonparametric Estimation Of An Additive Model With An Unknown Link Function," Econometric Theory, Cambridge University Press, vol. 27(3), pages 582-608, June.
    5. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    6. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524131, January.
    7. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    8. Gorgens, Tue & Horowitz, Joel L., 1999. "Semiparametric estimation of a censored regression model with an unknown transformation of the dependent variable," Journal of Econometrics, Elsevier, vol. 90(2), pages 155-191, June.
    9. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    10. Ivar Ekeland & James J. Heckman & Lars Nesheim, 2004. "Identification and Estimation of Hedonic Models," Journal of Political Economy, University of Chicago Press, vol. 112(S1), pages 60-109, February.
    11. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818735, January.
    12. Li, Qi & Racine, Jeff, 2003. "Nonparametric estimation of distributions with categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 86(2), pages 266-292, August.
    13. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524124, January.
    14. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6a.
    15. Jaap Abbring & Pierre-André Chiappori & Tibor Zavadil, 2008. "Better Safe than Sorry? Ex Ante and Ex Post Moral Hazard in Dynamic Insurance Data," Tinbergen Institute Discussion Papers 08-075/3, Tinbergen Institute.
    16. Robert F. Engle, 2000. "The Econometrics of Ultra-High Frequency Data," Econometrica, Econometric Society, vol. 68(1), pages 1-22, January.
    17. Rosa L. Matzkin, 2003. "Nonparametric Estimation of Nonadditive Random Functions," Econometrica, Econometric Society, vol. 71(5), pages 1339-1375, September.
    18. Kiefer, Nicholas M, 1988. "Economic Duration Data and Hazard Functions," Journal of Economic Literature, American Economic Association, vol. 26(2), pages 646-679, June.
    19. Fan, Jianqing & Jiang, Jiancheng, 2005. "Nonparametric Inferences for Additive Models," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 890-907, September.
    20. Tibor Zavadil & Pierre-Andre Chiappori & Jaap H. Abbring, 2007. "Better Safe than Sorry? Ex Ante and Ex Post Moral Hazard in Dynamic Insurance," 2007 Meeting Papers 869, Society for Economic Dynamics.
    21. Geert Ridder, 1990. "The Non-Parametric Identification of Generalized Accelerated Failure-Time Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 167-181.
    22. Cameron,A. Colin & Trivedi,Pravin K., 2005. "Microeconometrics," Cambridge Books, Cambridge University Press, number 9780521848053, January.
    23. Richard W. Blundell & James L. Powell, 2004. "Endogeneity in Semiparametric Binary Response Models," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 71(3), pages 655-679.
    24. Stefan Hoderlein & Enno Mammen, 2007. "Identification of Marginal Effects in Nonseparable Models Without Monotonicity," Econometrica, Econometric Society, vol. 75(5), pages 1513-1518, September.
    25. 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.
    26. Fan, Jianqing & Yao, Qiwei & Tong, Howell, 1996. "Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems," LSE Research Online Documents on Economics 6704, London School of Economics and Political Science, LSE Library.
    27. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    28. J.J. Heckman & E.E. Leamer (ed.), 2007. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 6, number 6b.
    29. Lu, Xun & White, Halbert, 2014. "Testing for separability in structural equations," Journal of Econometrics, Elsevier, vol. 182(1), pages 14-26.
    30. Halbert White & Xun Lu, 2011. "Causal Diagrams for Treatment Effect Estimation with Application to Efficient Covariate Selection," The Review of Economics and Statistics, MIT Press, vol. 93(4), pages 1453-1459, November.
    31. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818728, January.
    32. Kennan, John, 1985. "The duration of contract strikes in U.S. manufacturing," Journal of Econometrics, Elsevier, vol. 28(1), pages 5-28, April.
    33. Guido W. Imbens & Whitney K. Newey, 2009. "Identification and Estimation of Triangular Simultaneous Equations Models Without Additivity," Econometrica, Econometric Society, vol. 77(5), pages 1481-1512, September.
    34. Joseph G. Altonji & Rosa L. Matzkin, 2005. "Cross Section and Panel Data Estimators for Nonseparable Models with Endogenous Regressors," Econometrica, Econometric Society, vol. 73(4), pages 1053-1102, July.
    35. Lewbel, Arthur, 1995. "Consistent nonparametric hypothesis tests with an application to Slutsky symmetry," Journal of Econometrics, Elsevier, vol. 67(2), pages 379-401, June.
    36. Joel L. Horowitz, 2012. "Nonparametric additive models," CeMMAP working papers CWP20/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    37. Horowitz, Joel L, 2001. "Nonparametric Estimation of a Generalized Additive Model with an Unknown Link Function," Econometrica, Econometric Society, vol. 69(2), pages 499-513, March.
    38. Elias Masry, 1996. "Multivariate Local Polynomial Regression For Time Series:Uniform Strong Consistency And Rates," Journal of Time Series Analysis, Wiley Blackwell, vol. 17(6), pages 571-599, November.
    39. Racine, Jeffrey & Su, Liangjun & Ullah, Aman, 2014. "The Oxford Handbook of Applied Nonparametric and Semiparametric Econometrics and Statistics," OUP Catalogue, Oxford University Press, number 9780199857944.
    40. repec:dau:papers:123456789/6486 is not listed on IDEAS
    41. J.J. Heckman & E.E. Leamer (ed.), 2001. "Handbook of Econometrics," Handbook of Econometrics, Elsevier, edition 1, volume 5, number 5.
    42. Van den Berg, Gerard J., 2001. "Duration models: specification, identification and multiple durations," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 55, pages 3381-3460, Elsevier.
    43. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    44. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521818742, January.
    45. Horowitz, Joel L. & Lee, Sokbae, 2005. "Nonparametric Estimation of an Additive Quantile Regression Model," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1238-1249, December.
    46. Horowitz, Joel L, 1996. "Semiparametric Estimation of a Regression Model with an Unknown Transformation of the Dependent Variable," Econometrica, Econometric Society, vol. 64(1), pages 103-137, January.
    47. Dewatripont,Mathias & Hansen,Lars Peter & Turnovsky,Stephen J. (ed.), 2003. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521524117, January.
    48. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. 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.
    2. Christoph Breunig & Stefan Hoderlein, 2018. "Specification testing in random coefficient models," Quantitative Economics, Econometric Society, vol. 9(3), pages 1371-1417, November.
    3. 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.
    4. repec:hum:wpaper:sfb649dp2016-032 is not listed on IDEAS
    5. Lin, Yingqian & Tu, Yundong, 2025. "Identification and inference for semiparametric single index transformation models," Journal of Econometrics, Elsevier, vol. 251(C).
    6. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.
    7. Lin, Yingqian & Tu, Yundong & Yao, Qiwei, 2020. "Estimation for double-nonlinear cointegration," Journal of Econometrics, Elsevier, vol. 216(1), pages 175-191.
    8. 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.
    9. 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.
    10. Su, Liangjun & Ura, Takuya & Zhang, Yichong, 2019. "Non-separable models with high-dimensional data," Journal of Econometrics, Elsevier, vol. 212(2), pages 646-677.
    11. Christoph Breunig & Stefan Hoderlein, 2016. "Nonparametric Specification Testing in Random Parameter Models," Boston College Working Papers in Economics 897, Boston College Department of Economics.
    12. Breunig, Christoph, 2016. "Specification testing in nonparametric instrumental quantile regression," SFB 649 Discussion Papers 2016-032, Humboldt University Berlin, Collaborative Research Center 649: Economic Risk.
    13. Babii, Andrii & Florens, Jean-Pierre, 2025. "Are Unobservables Separable?," Econometric Theory, Cambridge University Press, vol. 41(3), pages 551-583, June.
    14. 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.
    15. 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.
    16. 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.
    17. 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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Vanhems, Anne & Van Keilegom, Ingrid, 2011. "Semiparametric transformation model with endogeneity: a control function approach," LIDAM Discussion Papers ISBA 2011011, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    2. Van Keilegom, Ingrid & Vanhems, Anne, 2011. "Semiparametric transformation model with endogeneity: a control function approach," TSE Working Papers 11-243, Toulouse School of Economics (TSE).
    3. Vanhems, Anne & Van Keilegom, Ingrid, 2013. "Semiparametric transformation model with endogeneity: a control function approach," LIDAM Discussion Papers ISBA 2013018, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    4. Lu, Xun & White, Habert, 2015. "Testing For Treatment Dependence Of Effects Of A Continuous Treatment," Econometric Theory, Cambridge University Press, vol. 31(5), pages 1016-1053, October.
    5. James J. Heckman & Rodrigo Pinto, 2022. "Causality and Econometrics," NBER Working Papers 29787, National Bureau of Economic Research, Inc.
    6. Arthur Lewbel & Krishna Pendakur, 2017. "Unobserved Preference Heterogeneity in Demand Using Generalized Random Coefficients," Journal of Political Economy, University of Chicago Press, vol. 125(4), pages 1100-1148.
    7. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    8. James J. Heckman, 2008. "The Principles Underlying Evaluation Estimators with an Application to Matching," Annals of Economics and Statistics, GENES, issue 91-92, pages 9-73.
    9. Luke Taylor & Taisuke Otsu, 2019. "Estimation of nonseparable models with censored dependent variables and endogenous regressors," Econometric Reviews, Taylor & Francis Journals, vol. 38(1), pages 4-24, January.
    10. Heckman, James J., 2010. "The Assumptions Underlying Evaluation Estimators," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 30(2), December.
    11. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    12. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Viewpoint: Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics, Canadian Economics Association, vol. 45(3), pages 809-829, August.
    13. 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.
    14. Arthur Lewbel & Yingying Dong & Thomas Tao Yang, 2012. "Comparing features of convenient estimators for binary choice models with endogenous regressors," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 45(3), pages 809-829, August.
    15. 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.
    16. repec:cep:stiecm:/2014/575 is not listed on IDEAS
    17. Suqin Ge & João Macieira, 2024. "Unobserved Worker Quality and Inter‐Industry Wage Differentials," Journal of Industrial Economics, Wiley Blackwell, vol. 72(1), pages 459-515, March.
    18. Frédérique Fève & Jean-Pierre Florens, 2010. "The practice of non-parametric estimation by solving inverse problems: the example of transformation models," Econometrics Journal, Royal Economic Society, vol. 13(3), pages 1-27, October.
    19. James L. Powell, 2017. "Identification and Asymptotic Approximations: Three Examples of Progress in Econometric Theory," Journal of Economic Perspectives, American Economic Association, vol. 31(2), pages 107-124, Spring.
    20. Stefan Hoderlein & Yuya Sasaki, 2011. "On the role of time in nonseparable panel data models," CeMMAP working papers CWP15/11, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    21. Xiaohong Chen & Timothy Christensen, 2013. "Optimal Uniform Convergence Rates for Sieve Nonparametric Instrumental Variables Regression," Cowles Foundation Discussion Papers 1923, Cowles Foundation for Research in Economics, Yale University.

    More about this item

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:184:y:2015:i:1:p:81-96. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.