IDEAS home Printed from https://ideas.repec.org/p/ehl/lserod/4425.html
   My bibliography  Save this paper

Testing for stochastic monotonicity

Author

Listed:
  • Lee, Sokbae
  • Linton, Oliver
  • Whang, Yoon-Jae

Abstract

We propose a test of the hypothesis of stochastic monotonicity. This hypothesis is of interest in many applications. Our test is based on the supremum of a rescaled U-statistic. We show that its asymptotic distribution is Gumbel. The proof is difficult because the approximating Gaussian stochastic process contains both a stationary and a nonstationary part and so we have to extend existing results that only apply to either one or the other case.

Suggested Citation

  • Lee, Sokbae & Linton, Oliver & Whang, Yoon-Jae, 2006. "Testing for stochastic monotonicity," LSE Research Online Documents on Economics 4425, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:4425
    as

    Download full text from publisher

    File URL: http://eprints.lse.ac.uk/4425/
    File Function: Open access version.
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dearden, Lorraine & Machin, Stephen & Reed, Howard, 1997. "Intergenerational Mobility in Britain," Economic Journal, Royal Economic Society, vol. 107(440), pages 47-66, January.
    2. Charles F. Manski, 1997. "Monotone Treatment Response," Econometrica, Econometric Society, vol. 65(6), pages 1311-1334, November.
    3. Pakes, Ariel & Ericson, Richard, 1998. "Empirical Implications of Alternative Models of Firm Dynamics," Journal of Economic Theory, Elsevier, vol. 79(1), pages 1-45, March.
    4. 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.
    5. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    6. Hopenhayn, Hugo A & Prescott, Edward C, 1992. "Stochastic Monotonicity and Stationary Distributions for Dynamic Economies," Econometrica, Econometric Society, vol. 60(6), pages 1387-1406, November.
    7. Einmahl, J.H.J. & Beirlant, J., 1996. "Maximal type test statistics based on conditional processes," Other publications TiSEM d031d073-2eea-4770-9bee-a, Tilburg University, School of Economics and Management.
    8. Gary Solon, 2002. "Cross-Country Differences in Intergenerational Earnings Mobility," Journal of Economic Perspectives, American Economic Association, vol. 16(3), pages 59-66, Summer.
    9. Solon, Gary, 1999. "Intergenerational mobility in the labor market," Handbook of Labor Economics, in: O. Ashenfelter & D. Card (ed.), Handbook of Labor Economics, edition 1, volume 3, chapter 29, pages 1761-1800, Elsevier.
    10. Phillips, Peter C. B., 1988. "Conditional and unconditional statistical independence," Journal of Econometrics, Elsevier, vol. 38(3), pages 341-348, July.
    11. Richard Blundell & Amanda Gosling & Hidehiko Ichimura & Costas Meghir, 2007. "Changes in the Distribution of Male and Female Wages Accounting for Employment Composition Using Bounds," Econometrica, Econometric Society, vol. 75(2), pages 323-363, March.
    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. Einmahl, J.H.J. & van Keilegom, I., 2004. "Goodness-of-fit Tests in Nonparametric Regression," Other publications TiSEM 44e08f75-b35d-424e-b33e-0, Tilburg University, School of Economics and Management.
    14. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
    15. 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.
    16. 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.
    17. 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.
    18. Horowitz, Joel L., 2001. "The Bootstrap," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 5, chapter 52, pages 3159-3228, Elsevier.
    19. Alexandra L. Minicozzi, 2003. "Estimation of sons' intergenerational earnings mobility in the presence of censoring," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 18(3), pages 291-314.
    20. repec:dau:papers:123456789/6486 is not listed on IDEAS
    Full references (including those not matched with items on IDEAS)

    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. Markus Jäntti & Stephen P. Jenkins, 2013. "Income Mobility," SOEPpapers on Multidisciplinary Panel Data Research 607, DIW Berlin, The German Socio-Economic Panel (SOEP).
    2. Donal O’Neill & Olive Sweetman & Dirk Van de gaer, 2007. "The effects of measurement error and omitted variables when using transition matrices to measure intergenerational mobility," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 5(2), pages 159-178, August.
    3. Seo, Juwon, 2018. "Tests of stochastic monotonicity with improved power," Journal of Econometrics, Elsevier, vol. 207(1), pages 53-70.
    4. Maia Güell & José V. Rodríguez Mora & Christopher I. Telmer, 2014. "Intergenerational Mobility and the Informational Content of Surnames," Working Papers 2014-01, FEDEA.
    5. Arnaud Lefranc & Alain Trannoy, 2005. "Intergenerational earnings mobility in France: Is France more mobile than the U.S.?," Annals of Economics and Statistics, GENES, issue 78, pages 57-77.
    6. Güell, Maia & Rodríguez Mora, José V & Telmer, Chris, 2007. "Intergenerational Mobility and the Informative Content of Surnames," CEPR Discussion Papers 6316, C.E.P.R. Discussion Papers.
    7. Christian Dustmann, 2008. "Return Migration, Investment in Children, and Intergenerational Mobility: Comparing Sons of Foreign- and Native-Born Fathers," Journal of Human Resources, University of Wisconsin Press, vol. 43(2), pages 299-324.
    8. Markus Jäntti & Juho Saari & Juhana Vartiainen, 2006. "Growth and Equity in Finland," WIDER Working Paper Series DP2006-06, World Institute for Development Economic Research (UNU-WIDER).
    9. Michael Lechner & Blaise Melly, 2007. "Earnings Effects of Training Programs," University of St. Gallen Department of Economics working paper series 2007 2007-28, Department of Economics, University of St. Gallen.
    10. John Ermisch & Marco Francesconi & Thomas Siedler, 2004. "Intergenerational Economic Mobility and Assortative Mating," Discussion Papers of DIW Berlin 448, DIW Berlin, German Institute for Economic Research.
    11. John Hassler & José Rodríguez Mora & Joseph Zeira, 2007. "Inequality and mobility," Journal of Economic Growth, Springer, vol. 12(3), pages 235-259, September.
    12. Tsunao Okumura, 2011. "Nonparametric Estimation of Labor Supply and Demand Factors," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(1), pages 174-185, January.
    13. Robert Lucas & Sari Kerr, 2013. "Intergenerational income immobility in Finland: contrasting roles for parental earnings and family income," Journal of Population Economics, Springer;European Society for Population Economics, vol. 26(3), pages 1057-1094, July.
    14. Maia Güell & José V. Rodríguez Mora & Christopher I. Telmer, 2015. "The Informational Content of Surnames, the Evolution of Intergenerational Mobility, and Assortative Mating," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 82(2), pages 693-735.
    15. Bertha Rohenkohl, 2019. "Intergenerational Income Mobility in the UK:New evidence using the BHPS and Understanding Society," Working Papers 2019017, The University of Sheffield, Department of Economics.
    16. Monique de Haan, 2011. "The Effect of Parents' Schooling on Child's Schooling: A Nonparametric Bounds Analysis," Journal of Labor Economics, University of Chicago Press, vol. 29(4), pages 859-892.
    17. Grawe, Nathan D., 2006. "Lifecycle bias in estimates of intergenerational earnings persistence," Labour Economics, Elsevier, vol. 13(5), pages 551-570, October.
    18. Doruk, Ömer Tuğsal & Pastore, Francesco & Yavuz, Hasan Bilgehan, 2022. "Intergenerational mobility: An assessment for Latin American countries," Structural Change and Economic Dynamics, Elsevier, vol. 60(C), pages 141-157.
    19. Eisenhauer, Philipp & Pfeiffer, Friedhelm, 2008. "Assessing intergenerational earnings persistence among German workers," Zeitschrift für ArbeitsmarktForschung - Journal for Labour Market Research, Institut für Arbeitsmarkt- und Berufsforschung (IAB), Nürnberg [Institute for Employment Research, Nuremberg, Germany], vol. 41(2/3), pages 119-137.
    20. María Cervini-Plá, 2015. "Intergenerational Earnings and Income Mobility in Spain," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 61(4), pages 812-828, December.

    More about this item

    Keywords

    Distribution function; Extreme Value Theory; Gaussian Process; Monotonicity.;
    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:ehl:lserod:4425. 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: LSERO Manager (email available below). General contact details of provider: https://edirc.repec.org/data/lsepsuk.html .

    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.