IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v170y2012i1p68-75.html
   My bibliography  Save this article

Distribution-free tests of stochastic monotonicity

Author

Listed:
  • Delgado, Miguel A.
  • Escanciano, Juan Carlos

Abstract

This article proposes a nonparametric test of monotonicity for conditional distributions and its moments. Unlike previous proposals, our method does not require smooth estimation of the derivatives of nonparametric curves. Distinguishing features of our approach are that critical values are pivotal under the null in finite samples and that the test is invariant to any monotonic continuous transformation of the explanatory variable. The test statistic is the sup-norm of the difference between the empirical copula function and its least concave majorant with respect to the explanatory variable coordinate. The resulting test is able to detect local alternatives converging to the null at the parametric rate n−1/2, with n the sample size. The finite sample performance of the test is examined by means of a Monte Carlo experiment and an application to testing intergenerational income mobility.

Suggested Citation

  • Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    • Handle: RePEc:eee:econom:v:170:y:2012:i:1:p:68-75
    DOI: 10.1016/j.jeconom.2012.02.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407612000723
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2012.02.005?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. Jacob Boudoukh & Matthew Richardson & Tom Smith & Robert F. Whitelaw, 1999. "Ex Ante Bond Returns and the Liquidity Preference Hypothesis," Journal of Finance, American Finance Association, vol. 54(3), pages 1153-1167, June.
    2. Banerjee, Moulinath & Mukherjee, Debasri & Mishra, Santosh, 2009. "Semiparametric binary regression models under shape constraints with an application to Indian schooling data," Journal of Econometrics, Elsevier, vol. 149(2), pages 101-117, April.
    3. Arthur Lewbel & Oliver Linton, 2007. "Nonparametric Matching and Efficient Estimators of Homothetically Separable Functions," Econometrica, Econometric Society, vol. 75(4), pages 1209-1227, July.
    4. Aguirregabiria, Victor, 2010. "Another Look at the Identification of Dynamic Discrete Decision Processes: An Application to Retirement Behavior," Journal of Business & Economic Statistics, American Statistical Association, vol. 28(2), pages 201-218.
    5. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    6. Valentino Dardanoni & Mario Fiorini & Antonio Forcina, 2012. "Stochastic monotonicity in intergenerational mobility tables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(1), pages 85-107, January.
    7. Escanciano, Juan Carlos & Jacho-Chávez, David T., 2012. "n-uniformly consistent density estimation in nonparametric regression models," Journal of Econometrics, Elsevier, vol. 167(2), pages 305-316.
    8. Durot, Cécile, 2003. "A Kolmogorov-type test for monotonicity of regression," Statistics & Probability Letters, Elsevier, vol. 63(4), pages 425-433, July.
    9. Richard Ericson & Ariel Pakes, 1995. "Markov-Perfect Industry Dynamics: A Framework for Empirical Work," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 62(1), pages 53-82.
    10. Pakes, Ariel S, 1986. "Patents as Options: Some Estimates of the Value of Holding European Patent Stocks," Econometrica, Econometric Society, vol. 54(4), pages 755-784, July.
    11. Charles F. Manski & John V. Pepper, 2000. "Monotone Instrumental Variables, with an Application to the Returns to Schooling," Econometrica, Econometric Society, vol. 68(4), pages 997-1012, July.
    12. Olley, G Steven & Pakes, Ariel, 1996. "The Dynamics of Productivity in the Telecommunications Equipment Industry," Econometrica, Econometric Society, vol. 64(6), pages 1263-1297, November.
    13. Paul R. Milgrom, 1981. "Good News and Bad News: Representation Theorems and Applications," Bell Journal of Economics, The RAND Corporation, vol. 12(2), pages 380-391, Autumn.
    14. Gordon Bril & Richard Dykstra & Carolyn Pillers & Tim Robertson, 1984. "Isotonic Regression in Two Independent Variables," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 33(3), pages 352-357, November.
    15. Matthew Richardson & Paul Richardson & Tom Smith, "undated". "The Monotonicity of the Term Premium: Another Look (Reprint 026)," Rodney L. White Center for Financial Research Working Papers 3-92, Wharton School Rodney L. White Center for Financial Research.
    16. Matthew Richardson & Paul Richardson & Tom Smith, "undated". "The Monotonicity of the Term Premium: Another Look (Reprint 026)," Rodney L. White Center for Financial Research Working Papers 03-92, Wharton School Rodney L. White Center for Financial Research.
    17. G. W. Cran, 1980. "Amalgamation of Means in the Case of Simple Ordering," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 29(2), pages 209-211, June.
    18. Richardson, Matthew & Richardson, Paul & Smith, Tom, 1992. "The monotonicity of the term premium *1: Another look," Journal of Financial Economics, Elsevier, vol. 31(1), pages 97-105.
    19. George Akerlof, 1976. "The Economics of Caste and of the Rat Race and Other Woeful Tales," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 90(4), pages 599-617.
    20. George A. Akerlof, 1970. "The Market for "Lemons": Quality Uncertainty and the Market Mechanism," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 84(3), pages 488-500.
    21. Michael Spence, 1973. "Job Market Signaling," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 87(3), pages 355-374.
    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. Ismaël Mourifié & Marc Henry & Romuald Méango, 2020. "Sharp Bounds and Testability of a Roy Model of STEM Major Choices," Journal of Political Economy, University of Chicago Press, vol. 128(8), pages 3220-3283.
    2. Matthew A. Masten & Alexandre Poirier, 2018. "Interpreting Quantile Independence," Papers 1804.10957, arXiv.org.
    3. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2018. "Testing For A General Class Of Functional Inequalities," Econometric Theory, Cambridge University Press, vol. 34(5), pages 1018-1064, October.
    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. Lee, Tae-Hwy & Tu, Yundong & Ullah, Aman, 2014. "Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting," Journal of Econometrics, Elsevier, vol. 182(1), pages 196-210.
    6. Gutknecht, Daniel, 2016. "Testing for monotonicity under endogeneity," Journal of Econometrics, Elsevier, vol. 190(1), pages 100-114.
    7. Henry, Marc & Méango, Romuald & Mourifié, Ismaël, 2024. "Role models and revealed gender-specific costs of STEM in an extended Roy model of major choice," Journal of Econometrics, Elsevier, vol. 238(2).
    8. Denis Chetverikov & Daniel Wilhelm, 2016. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 48/16, Institute for Fiscal Studies.
    9. Denis Chetverikov & Daniel Wilhelm, 2017. "Nonparametric Instrumental Variable Estimation Under Monotonicity," Econometrica, Econometric Society, vol. 85, pages 1303-1320, July.
    10. 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.
    11. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    12. José Romeo & Nelson Tanaka & Antonio Pedroso-de-Lima & Victor Salinas-Torres, 2013. "Large sample properties for a class of copulas in bivariate survival analysis," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(8), pages 997-1015, November.
    13. Lee, Sokbae & Song, Kyungchul & Whang, Yoon-Jae, 2013. "Testing functional inequalities," Journal of Econometrics, Elsevier, vol. 172(1), pages 14-32.
    14. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.
    15. Liu, Nianqing & Vuong, Quang & Xu, Haiqing, 2017. "Rationalization and identification of binary games with correlated types," Journal of Econometrics, Elsevier, vol. 201(2), pages 249-268.
    16. 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.
    17. repec:cte:werepe:we1138 is not listed on IDEAS
    18. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    19. repec:wrk:warwec:991 is not listed on IDEAS
    20. Denis Chetverikov & Daniel Wilhelm, 2015. "Nonparametric instrumental variable estimation under monotonicity," CeMMAP working papers 39/15, Institute for Fiscal Studies.
    21. Gutknecht, Daniel, 2012. "Do Reservation Wages Decline Monotonically? A Novel Statistical Test," Economic Research Papers 270635, University of Warwick - Department of Economics.
    22. Colubi, Ana & Domínguez-Menchero, J. Santos & González-Rodríguez, Gil, 2014. "Testing constancy in monotone response models," Computational Statistics & Data Analysis, Elsevier, vol. 72(C), pages 45-56.
    23. Toru Kitagawa & Martin Nybom & Jan Stuhler, 2018. "Measurement error and rank correlations," CeMMAP working papers CWP28/18, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    24. Seo, Juwon, 2018. "Tests of stochastic monotonicity with improved power," Journal of Econometrics, Elsevier, vol. 207(1), pages 53-70.

    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. 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.
    2. Le-Yu Chen & Jerzy Szroeter, 2009. "Hypothesis testing of multiple inequalities: the method of constraint chaining," CeMMAP working papers CWP13/09, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    3. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    4. Panagiotis T. Konstantinou, 2005. "The Expectations Hypothesis of the Term Structure : A Look at the Polish Interbank Market," Emerging Markets Finance and Trade, Taylor & Francis Journals, vol. 41(3), pages 70-91, May.
    5. Ornelas, Jose Renato Haas & Silva Jr., Antonio Francisco de Almeida, 2015. "Testing the liquidity preference hypothesis using survey forecasts," Emerging Markets Review, Elsevier, vol. 23(C), pages 173-185.
    6. Drakos, Konstantinos, 2001. "Fixed income excess returns and time to maturity," International Review of Financial Analysis, Elsevier, vol. 10(4), pages 431-442.
    7. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    8. Patton, Andrew J. & Timmermann, Allan, 2010. "Monotonicity in asset returns: New tests with applications to the term structure, the CAPM, and portfolio sorts," Journal of Financial Economics, Elsevier, vol. 98(3), pages 605-625, December.
    9. Konstantinou, Panagiotis, 2004. "Term Structure Dynamics: A Daily View from the Hungarian Foreign Currency Deposits Markets," Economia Internazionale / International Economics, Camera di Commercio Industria Artigianato Agricoltura di Genova, vol. 57(3), pages 315-331.
    10. Ostdiek, Barbara, 1998. "The world ex ante risk premium: an empirical investigation," Journal of International Money and Finance, Elsevier, vol. 17(6), pages 967-999, December.
    11. Dato, Simon & Grunewald, Andreas & Kräkel, Matthias & Müller, Daniel, 2016. "Asymmetric employer information, promotions, and the wage policy of firms," Games and Economic Behavior, Elsevier, vol. 100(C), pages 273-300.
    12. Hooker, Mark A., 1999. "The maturity structure of term premia with time-varying expected returns," The Quarterly Review of Economics and Finance, Elsevier, vol. 39(3), pages 391-407.
    13. repec:cte:werepe:we1138 is not listed on IDEAS
    14. Tzavalis, Elias & Wickens, Michael R, 1997. "Explaining the Failures of the Term Spread Models of the Rational Expectations Hypothesis of the Term Structure," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(3), pages 364-380, August.
    15. Ariel Pakes, 2003. "Common Sense and Simplicity in Empirical Industrial Organization," Review of Industrial Organization, Springer;The Industrial Organization Society, vol. 23(3), pages 193-215, December.
    16. Nuria Rodriguez-Planas, 2003. "Signaling in The Labor Market: New Evidence On Layoffs, and Plant Closings," William Davidson Institute Working Papers Series 2003-610, William Davidson Institute at the University of Michigan.
    17. repec:eee:labchp:v:2:y:1986:i:c:p:789-848 is not listed on IDEAS
    18. Klaus Friesenbichler & George Clarke & Michael Wong, 2014. "Price competition and market transparency: evidence from a random response technique," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(1), pages 5-21, February.
    19. Victor Aguirregabiria & Margaret Slade, 2017. "Empirical models of firms and industries," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 50(5), pages 1445-1488, December.
    20. Hu, Maggie Rong & Li, Xiaoyang & Shi, Yang, 2019. "Adverse Selection and Credit Certificates: Evidence from a P2P Platform," ADBI Working Papers 942, Asian Development Bank Institute.
    21. Robin S. Lee, 2013. "Vertical Integration and Exclusivity in Platform and Two-Sided Markets," American Economic Review, American Economic Association, vol. 103(7), pages 2960-3000, December.
    22. Stefano Ficco, 2004. "Information Overload in Monopsony Markets," Tinbergen Institute Discussion Papers 04-082/1, Tinbergen Institute.

    More about this item

    Keywords

    Stochastic monotonicity; Conditional moments; Least concave majorant; Copula process; Distribution-free in finite samples; Tests invariant to monotone transforms;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation 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:170:y:2012:i:1:p:68-75. 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.