IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v207y2018i1p53-70.html
   My bibliography  Save this article

Tests of stochastic monotonicity with improved power

Author

Listed:
  • Seo, Juwon

Abstract

We develop improved statistical procedures for testing stochastic monotonicity. While existing tests use a fixed critical value to set the limiting rejection rate equal to nominal size at the least favorable case, we use a bootstrap procedure to raise the limiting rejection rate to nominal size over much of the null. This improves power against relevant local alternatives. To show the validity of our approach we draw on recent results on the directional differentiability of the least concave majorant operator, and on bootstrap inference when smoothness conditions sufficient to apply the functional delta method for the bootstrap are not satisfied.

Suggested Citation

  • Seo, Juwon, 2018. "Tests of stochastic monotonicity with improved power," Journal of Econometrics, Elsevier, vol. 207(1), pages 53-70.
    • Handle: RePEc:eee:econom:v:207:y:2018:i:1:p:53-70
    DOI: 10.1016/j.jeconom.2018.04.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407618301179
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2018.04.004?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. Linton, Oliver & Song, Kyungchul & Whang, Yoon-Jae, 2010. "An improved bootstrap test of stochastic dominance," Journal of Econometrics, Elsevier, vol. 154(2), pages 186-202, February.
    2. Gary S. Becker, 1981. "A Treatise on the Family," NBER Books, National Bureau of Economic Research, Inc, number beck81-1, March.
    3. Brendan K. Beare & Lawrence D. W. Schmidt, 2016. "An Empirical Test of Pricing Kernel Monotonicity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 31(2), pages 338-356, March.
    4. 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.
    5. Giacomini, Raffaella & Politis, Dimitris N. & White, Halbert, 2013. "A Warp-Speed Method For Conducting Monte Carlo Experiments Involving Bootstrap Estimators," Econometric Theory, Cambridge University Press, vol. 29(3), pages 567-589, June.
    6. Gary S. Becker & Nigel Tomes, 1994. "Human Capital and the Rise and Fall of Families," NBER Chapters, in: Human Capital: A Theoretical and Empirical Analysis with Special Reference to Education, Third Edition, pages 257-298, National Bureau of Economic Research, Inc.
    7. Diego Restuccia & Carlos Urrutia, 2004. "Intergenerational Persistence of Earnings: The Role of Early and College Education," American Economic Review, American Economic Association, vol. 94(5), pages 1354-1378, December.
    8. Raquel Fernández & Richard Rogerson, 2001. "Sorting and Long-Run Inequality," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 116(4), pages 1305-1341.
    9. Jeremy Greenwood & Nezih Guner & Georgi Kocharkov & Cezar Santos, 2014. "Marry Your Like: Assortative Mating and Income Inequality," American Economic Review, American Economic Association, vol. 104(5), pages 348-353, May.
    10. Casey B. Mulligan, 1999. "Galton versus the Human Capital Approach to Inheritance," Journal of Political Economy, University of Chicago Press, vol. 107(S6), pages 184-224, December.
    11. Christine Schwartz & Robert Mare, 2005. "Trends in educational assortative marriage from 1940 to 2003," Demography, Springer;Population Association of America (PAA), vol. 42(4), pages 621-646, November.
    12. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    13. Bücher, Axel & Dette, Holger, 2010. "A note on bootstrap approximations for the empirical copula process," Statistics & Probability Letters, Elsevier, vol. 80(23-24), pages 1925-1932, December.
    14. Rémillard, Bruno & Scaillet, Olivier, 2009. "Testing for equality between two copulas," Journal of Multivariate Analysis, Elsevier, vol. 100(3), pages 377-386, March.
    15. 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.
    16. Segers, Johan, 2012. "Asymptotics of empirical copula processes under non-restrictive smoothness assumptions," LIDAM Reprints ISBA 2012009, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Delgado, Miguel A. & Escanciano, Juan Carlos, 2012. "Distribution-free tests of stochastic monotonicity," Journal of Econometrics, Elsevier, vol. 170(1), pages 68-75.
    18. Christopher A. Carolan & Joshua M. Tebbs, 2005. "Nonparametric tests for and against likelihood ratio ordering in the two-sample problem," Biometrika, Biometrika Trust, vol. 92(1), pages 159-171, March.
    19. Beare, Brendan K. & Moon, Jong-Myun, 2015. "Nonparametric Tests Of Density Ratio Ordering," Econometric Theory, Cambridge University Press, vol. 31(3), pages 471-492, June.
    20. 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.
    21. Anderson, Gordon & Linton, Oliver & Whang, Yoon-Jae, 2012. "Nonparametric estimation and inference about the overlap of two distributions," Journal of Econometrics, Elsevier, vol. 171(1), pages 1-23.
    22. 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.
    23. Han, Song & Mulligan, Casey B, 2001. "Human Capital, Heterogeneity and Estimated Degrees of Intergenerational Mobility," Economic Journal, Royal Economic Society, vol. 111(470), pages 207-243, April.
    24. Olivier Scaillet, 2005. "A Kolmogorov-Smirnov Type Test for Positive Quadrant Dependence," FAME Research Paper Series rp128, International Center for Financial Asset Management and Engineering.
    25. Gary Solon, 2002. "Cross-Country Differences in Intergenerational Earnings Mobility," Journal of Economic Perspectives, American Economic Association, vol. 16(3), pages 59-66, Summer.
    26. Christian Genest & Johanna Nešlehová & Jean-François Quessy, 2012. "Tests of symmetry for bivariate copulas," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(4), pages 811-834, August.
    27. Solon, Gary, 1992. "Intergenerational Income Mobility in the United States," American Economic Review, American Economic Association, vol. 82(3), pages 393-408, June.
    28. Becker, Gary S & Tomes, Nigel, 1979. "An Equilibrium Theory of the Distribution of Income and Intergenerational Mobility," Journal of Political Economy, University of Chicago Press, vol. 87(6), pages 1153-1189, December.
    29. Paul Doukhan & Jean-David Fermanian & Gabriel Lang, 2009. "An empirical central limit theorem with applications to copulas under weak dependence," Statistical Inference for Stochastic Processes, Springer, vol. 12(1), pages 65-87, 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. Hongyi Jiang & Zhenting Sun & Shiyun Hu, 2023. "A Nonparametric Test of $m$th-degree Inverse Stochastic Dominance," Papers 2306.12271, arXiv.org, revised Jul 2023.
    2. 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.
    3. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    4. Zheng Fang, 2021. "A Unifying Framework for Testing Shape Restrictions," Papers 2107.12494, arXiv.org, revised Aug 2021.
    5. Sungwon Lee, 2021. "Partial Identification and Inference for Conditional Distributions of Treatment Effects," Papers 2108.00723, arXiv.org, revised Nov 2023.
    6. Brendan K. Beare & Jackson D. Clarke, 2022. "Modified Wilcoxon-Mann-Whitney tests of stochastic dominance," Papers 2210.08892, arXiv.org.
    7. Sungwon Lee, 2024. "Partial identification and inference for conditional distributions of treatment effects," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 39(1), pages 107-127, January.

    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. Berghaus, Betina & Bücher, Axel, 2014. "Nonparametric tests for tail monotonicity," Journal of Econometrics, Elsevier, vol. 180(2), pages 117-126.
    2. Anna Christina D'Addio, 2007. "Intergenerational Transmission of Disadvantage: Mobility or Immobility Across Generations?," OECD Social, Employment and Migration Working Papers 52, OECD Publishing.
    3. Beare, Brendan K. & Shi, Xiaoxia, 2019. "An improved bootstrap test of density ratio ordering," Econometrics and Statistics, Elsevier, vol. 10(C), pages 9-26.
    4. Markus Jäntti & Stephen P. Jenkins, 2013. "Income Mobility," SOEPpapers on Multidisciplinary Panel Data Research 607, DIW Berlin, The German Socio-Economic Panel (SOEP).
    5. Bernt Bratsberg & Knut Røed & Oddbjørn Raaum & Robin Naylor & Markus Ja¨ntti & Tor Eriksson & Eva O¨sterbacka, 2007. "Nonlinearities in Intergenerational Earnings Mobility: Consequences for Cross-Country Comparisons," Economic Journal, Royal Economic Society, vol. 117(519), pages 72-92, 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. Corak, Miles & Piraino, Patrizio, 2010. "Intergenerational Earnings Mobility and the Inheritance of Employers," IZA Discussion Papers 4876, Institute of Labor Economics (IZA).
    8. 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.
    9. Ermisch, John & Francesconi, Marco, 2002. "Intergenerational Social Mobility and Assortative Mating in Britain," IZA Discussion Papers 465, Institute of Labor Economics (IZA).
    10. Sokbae Lee & Oliver Linton & Yoon-Jae Whang, 2009. "Testing for Stochastic Monotonicity," Econometrica, Econometric Society, vol. 77(2), pages 585-602, March.
    11. Levine, David I. & Jellema, Jon R., 2005. "Growth, Industrialization, and the Intergenerational Correlation of Advantage," Institute for Research on Labor and Employment, Working Paper Series qt2q74s1tg, Institute of Industrial Relations, UC Berkeley.
    12. B. Ben Halima & N. Chusseau & J. Hellier, 2013. "Skill Premia and Intergenerational Skill Transmission: The French Case," Working Papers 285, ECINEQ, Society for the Study of Economic Inequality.
    13. 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.
    14. María Cervini-Plá, 2013. "Exploring the Sources of Earnings Transmission in Spain," Hacienda Pública Española / Review of Public Economics, IEF, vol. 204(1), pages 45-66, March.
    15. Pekkarinen, Tuomas & Pekkala, Sari & Uusitalo, Roope, 2006. "Educational policy and intergenerational income mobility: evidence from the Finnish comprehensive school reform," Working Paper Series 2006:13, IFAU - Institute for Evaluation of Labour Market and Education Policy.
    16. Vera Tolstova, 2021. "Marital Sorting and Cross-Country Differences in Intergenerational Earnings Persistence," CERGE-EI Working Papers wp680, The Center for Economic Research and Graduate Education - Economics Institute, Prague.
    17. Miguel A. Delgado & Juan Carlos Escanciano, 2013. "Conditional Stochastic Dominance Testing," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(1), pages 16-28, January.
    18. Guell, Maia & Rodriguez Mora, Jose V. & Telmer, Chris, 2007. "Intergenerational mobility and the informative content of surnames," LSE Research Online Documents on Economics 19701, London School of Economics and Political Science, LSE Library.
    19. Nathan D. Grawe & Casey B. Mulligan, 2002. "Economic Interpretations of Intergenerational Correlations," Journal of Economic Perspectives, American Economic Association, vol. 16(3), pages 45-58, Summer.
    20. Maribel Jiménez, 2011. "Un Análisis Empírico de las No Linealidades en la Movilidad Intergeneracional del Ingreso. El caso de la Argentina," CEDLAS, Working Papers 0114, CEDLAS, Universidad Nacional de La Plata.

    More about this item

    Keywords

    Stochastic monotonicity; Copula; Least concave majorant; Hadamard differentiability; Hadamard directional differentiability;
    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:207:y:2018:i:1:p:53-70. 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.