IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v190y2016i1p100-114.html
   My bibliography  Save this article

Testing for monotonicity under endogeneity

Author

Listed:
  • Gutknecht, Daniel

Abstract

This paper develops a test for monotonicity of nonparametric regression models under endogeneity, which in its generality is novel in the literature. The test statistic, which is built upon a second order U-process, introduces ‘correction terms’ based on control functions that purge the endogeneity. The test has a non-standard asymptotic distribution from which asymptotic critical values can directly be derived. Furthermore, the test statistic is extended to accommodate multivariate (exogenous) regressors. Consistency against general alternatives is proved and the finite sample properties of the test are examined in a Monte Carlo experiment. The test is used to formally assess the monotonicity of the reservation wage as a declining function of elapsed unemployment duration, which has implications for underlying job search models. This relationship is difficult to measure due to the simultaneity of both variables. Results for UK data indicate that reservation wage functions do in fact not decline monotonically thereby contradicting some partial equilibrium job search models.

Suggested Citation

  • Gutknecht, Daniel, 2016. "Testing for monotonicity under endogeneity," Journal of Econometrics, Elsevier, vol. 190(1), pages 100-114.
    • Handle: RePEc:eee:econom:v:190:y:2016:i:1:p:100-114
    DOI: 10.1016/j.jeconom.2015.09.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407615002341
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2015.09.002?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 search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Kiefer, Nicholas M & Neumann, George R, 1979. "An Empirical Job-Search Model, with a Test of the Constant Reservation-Wage Hypothesis," Journal of Political Economy, University of Chicago Press, vol. 87(1), pages 89-107, February.
    3. Fermanian, Jean-David & Salanié, Bernard, 2004. "A Nonparametric Simulated Maximum Likelihood Estimation Method," Econometric Theory, Cambridge University Press, vol. 20(4), pages 701-734, August.
    4. Addison, John T. & Centeno, Mario & Portugal, Pedro, 2004. "Reservation Wages, Search Duration, and Accepted Wages in Europe," IZA Discussion Papers 1252, Institute of Labor Economics (IZA).
    5. Lavergne, Pascal & Vuong, Quang H, 1996. "Nonparametric Selection of Regressors: The Nonnested Case," Econometrica, Econometric Society, vol. 64(1), pages 207-219, January.
    6. Escanciano, Juan Carlos & Jacho-Chávez, David T. & Lewbel, Arthur, 2014. "Uniform convergence of weighted sums of non and semiparametric residuals for estimation and testing," Journal of Econometrics, Elsevier, vol. 178(P3), pages 426-443.
    7. Rothe, Christoph, 2009. "Semiparametric estimation of binary response models with endogenous regressors," Journal of Econometrics, Elsevier, vol. 153(1), pages 51-64, November.
    8. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    9. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    10. Gerard J. van den Berg, 1990. "Nonstationarity in Job Search Theory," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(2), pages 255-277.
    11. Lancaster, Tony, 1985. "Simultaneous equations models in applied search theory," Journal of Econometrics, Elsevier, vol. 28(1), pages 113-126, April.
    12. P. Lavergne & Q.H. Vuong, 1996. "Nonparametric selection of regressors : the nonnested case [[Sélection non paramétrique de régresseurs : le cas de régressions non emboîtées]]," Post-Print hal-02689500, HAL.
    13. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    14. Glenn Ellison & Sara Fisher Ellison, 2011. "Strategic Entry Deterrence and the Behavior of Pharmaceutical Incumbents Prior to Patent Expiration," American Economic Journal: Microeconomics, American Economic Association, vol. 3(1), pages 1-36, February.
    15. Richard Blundell & Luigi Pistaferri & Ian Preston, 2008. "Consumption Inequality and Partial Insurance," American Economic Review, American Economic Association, vol. 98(5), pages 1887-1921, December.
    16. Whitney K. Newey & James L. Powell & Francis Vella, 1999. "Nonparametric Estimation of Triangular Simultaneous Equations Models," Econometrica, Econometric Society, vol. 67(3), pages 565-604, May.
    17. Brown, Sarah & Taylor, Karl, 2013. "Reservation wages, expected wages and unemployment," Economics Letters, Elsevier, vol. 119(3), pages 276-279.
    18. Jennifer C. Smith, 2011. "The Ins and Outs of UK Unemployment," Economic Journal, Royal Economic Society, vol. 121(552), pages 402-444, May.
    19. Garen, John, 1984. "The Returns to Schooling: A Selectivity Bias Approach with a Continuous Choice Variable," Econometrica, Econometric Society, vol. 52(5), pages 1199-1218, September.
    20. Richard Blundell & Rosa L. Matzkin, 2014. "Control functions in nonseparable simultaneous equations models," Quantitative Economics, Econometric Society, vol. 5, pages 271-295, July.
    21. Melanie Birke & Natalie Neumeyer, 2013. "Testing Monotonicity of Regression Functions – An Empirical Process Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 40(3), pages 438-454, September.
    22. Gillian Paull, 2002. "Biases in the reporting of labour market dynamics," IFS Working Papers W02/10, Institute for Fiscal Studies.
    23. Vella, Francis, 1993. "Nonwage Benefits in a Simultaneous Model of Wages and Hours: Labor Supply Functions of Young Females," Journal of Labor Economics, University of Chicago Press, vol. 11(4), pages 704-723, October.
    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. Yusuke Matsuki, 2016. "A Distribution-Free Test of Monotonicity with an Application to Auctions," Working Papers e110, Tokyo Center for Economic Research.
    2. Zheng Fang & Juwon Seo, 2021. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Econometrica, Econometric Society, vol. 89(5), pages 2439-2458, September.
    3. Yu Zhu, 2020. "Inference in nonparametric/semiparametric moment equality models with shape restrictions," Quantitative Economics, Econometric Society, vol. 11(2), pages 609-636, May.
    4. Elia Lapenta, 2022. "A Bootstrap Specification Test for Semiparametric Models with Generated Regressors," Papers 2212.11112, arXiv.org, revised Oct 2023.
    5. Zheng Fang & Juwon Seo, 2019. "A Projection Framework for Testing Shape Restrictions That Form Convex Cones," Papers 1910.07689, arXiv.org, revised Sep 2021.

    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. Daniel Gutknecht, 2013. "Testing for Monotonicity under Endogeneity An Application to the Reservation Wage Function," Economics Series Working Papers 673, University of Oxford, Department of Economics.
    2. Gutknecht, Daniel, 2012. "Do Reservation Wages Decline Monotonically? A Novel Statistical Test," Economic Research Papers 270635, University of Warwick - Department of Economics.
    3. repec:wrk:warwec:991 is not listed on IDEAS
    4. Juan Carlos Escanciano & Telmo P'erez-Izquierdo, 2023. "Automatic Locally Robust Estimation with Generated Regressors," Papers 2301.10643, arXiv.org, revised Nov 2023.
    5. 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.
    6. John T. Addison & José A. F. Machado & Pedro Portugal, 2013. "The Reservation Wage Unemployment Duration Nexus," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 75(6), pages 980-987, December.
    7. Ying-Ying Lee, 2018. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Papers 1811.00157, arXiv.org.
    8. Matthew A. Masten & Alexandre Poirier, 2018. "Interpreting Quantile Independence," Papers 1804.10957, arXiv.org.
    9. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    10. Ying-Ying Lee, 2014. "Partial Mean Processes with Generated Regressors: Continuous Treatment Effects and Nonseparable Models," Economics Series Working Papers 706, University of Oxford, Department of Economics.
    11. Matzkin, Rosa L., 2016. "On independence conditions in nonseparable models: Observable and unobservable instruments," Journal of Econometrics, Elsevier, vol. 191(2), pages 302-311.
    12. Chernozhukov, Victor & Fernández-Val, Iván & Kowalski, Amanda E., 2015. "Quantile regression with censoring and endogeneity," Journal of Econometrics, Elsevier, vol. 186(1), pages 201-221.
    13. Elia Lapenta, 2022. "A Bootstrap Specification Test for Semiparametric Models with Generated Regressors," Papers 2212.11112, arXiv.org, revised Oct 2023.
    14. Chetverikov, Denis & Wilhelm, Daniel & Kim, Dongwoo, 2021. "An Adaptive Test Of Stochastic Monotonicity," Econometric Theory, Cambridge University Press, vol. 37(3), pages 495-536, June.
    15. Centorrino, Samuele & Florens, Jean-Pierre, 2021. "Nonparametric Instrumental Variable Estimation of Binary Response Models with Continuous Endogenous Regressors," Econometrics and Statistics, Elsevier, vol. 17(C), pages 35-63.
    16. Carlson, Alyssa, 2023. "Relaxing conditional independence in an endogenous binary response model," Journal of Econometrics, Elsevier, vol. 232(2), pages 490-500.
    17. Caetano, Carolina & Rothe, Christoph & Yıldız, Neşe, 2016. "A discontinuity test for identification in triangular nonseparable models," Journal of Econometrics, Elsevier, vol. 193(1), pages 113-122.
    18. Lapenta, Elia & Lavergne, Pascal, 2022. "Encompassing Tests for Nonparametric Regressions," TSE Working Papers 22-1332, Toulouse School of Economics (TSE).
    19. Denis Chetverikov & Daniel Wilhelm, 2016. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 48/16, Institute for Fiscal Studies.
    20. Denis Chetverikov & Daniel Wilhelm, 2015. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 39/15, Institute for Fiscal Studies.
    21. Roland A. Amann & Tobias J. Klein, 2012. "Returns to type or tenure?," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 175(1), pages 153-166, January.

    More about this item

    Keywords

    Control function; Endogeneity; Reservation wages; Test for monotonicity;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C36 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Instrumental Variables (IV) Estimation
    • C54 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Quantitative Policy Modeling
    • J64 - Labor and Demographic Economics - - Mobility, Unemployment, Vacancies, and Immigrant Workers - - - Unemployment: Models, Duration, Incidence, and Job Search

    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:190:y:2016:i:1:p:100-114. 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.