IDEAS home Printed from https://ideas.repec.org/p/sur/surrec/1205.html
   My bibliography  Save this paper

A nonparametric test of stochastic dominance in multivariate distributions

Author

Listed:
  • Ian Crawford

    (University of Surrey and cemmap, Institute for Fiscal Studies)

Abstract

The literature on statistical test of stochastic dominance has thus far been concerned with univariate distributions. This paper presents nonparametric statistical tests for multivariate distributions. This allows a nonparametric treatment of multiple welfare indicators. These test are applied to a time series of cross-section datasets on household level total expenditure and non labour market time in the UK. This contrasts the welfare inferences which might be drawn from looking at univariate (marginal) distributions with those which consider the joint distribution.

Suggested Citation

  • Ian Crawford, 2005. "A nonparametric test of stochastic dominance in multivariate distributions," School of Economics Discussion Papers 1205, School of Economics, University of Surrey.
    • Handle: RePEc:sur:surrec:1205
    as

    Download full text from publisher

    File URL: https://repec.som.surrey.ac.uk/2005/DP12-05.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
    2. Neary, J. P. & Roberts, K. W. S., 1980. "The theory of household behaviour under rationing," European Economic Review, Elsevier, vol. 13(1), pages 25-42, January.
    3. Russell Davidson & Jean-Yves Duclos, 2000. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Econometrica, Econometric Society, vol. 68(6), pages 1435-1464, November.
    4. Levy, Haim & Paroush, Jacob, 1974. "Toward multivariate efficiency criteria," Journal of Economic Theory, Elsevier, vol. 7(2), pages 129-142, February.
    5. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63(4), pages 309-309.
    6. A. B. Atkinson & F. Bourguignon, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 49(2), pages 183-201.
    7. E. Rothbarth, 1941. "The Measurement of Changes in Real Income under Conditions of Rationing," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 8(2), pages 100-107.
    8. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
    9. Ulph, David, 1978. "On labour supply and the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 19(2), pages 492-512, December.
    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. Schumann, Keith D., 2011. "Semi-nonparametric test of second degree stochastic dominance with respect to a function," Journal of Econometrics, Elsevier, vol. 162(1), pages 71-78, May.
    2. Nicolas Gravel & Abhiroop Mukhopadhyay, 2010. "Is India better off today than 15 years ago? A robust multidimensional answer," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 8(2), pages 173-195, June.
    3. Arndt, Channing & Distante, Roberta & Hussain, M. Azhar & Østerdal, Lars Peter & Huong, Pham Lan & Ibraimo, Maimuna, 2012. "Ordinal Welfare Comparisons with Multiple Discrete Indicators: A First Order Dominance Approach and Application to Child Poverty," World Development, Elsevier, vol. 40(11), pages 2290-2301.
    4. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series wp-2013-097, World Institute for Development Economic Research (UNU-WIDER).
    5. M. Azhar Hussain & Nikolaj Siersbæk & Lars Peter Østerdal, 2020. "Multidimensional welfare comparisons of EU member states before, during, and after the financial crisis: a dominance approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 645-686, December.
    6. Gaston Yalonetzky, 2013. "Stochastic Dominance with Ordinal Variables: Conditions and a Test," Econometric Reviews, Taylor & Francis Journals, vol. 32(1), pages 126-163, January.
    7. Sonne-Schmidt, Christoffer & Tarp, Finn & Peter, Lars, 2011. "Ordinal multidimensional inequality: theory and application to the 2x2 case," MPRA Paper 72838, University Library of Munich, Germany.
    8. Gaston Yalonetzky, 2014. "Conditions for the most robust multidimensional poverty comparisons using counting measures and ordinal variables," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 43(4), pages 773-807, December.
    9. Nicolas Gravel & Patrick Moyes, 2006. "Ethically Robust Comparisons of Distributions of Two Individual Attributes," IDEP Working Papers 0605, Institut d'economie publique (IDEP), Marseille, France, revised Aug 2006.
    10. Sonne-Schmidt, Christoffer & Tarp, Finn & Østerdal, Lars Peter, 2013. "Ordinal Multidimensional Inequality," WIDER Working Paper Series 097, World Institute for Development Economic Research (UNU-WIDER).
    11. Nicolas Gravel & Patrick Moyes & Benoît Tarroux, 2009. "Robust International Comparisons of Distributions of Disposable Income and Regional Public Goods," Economica, London School of Economics and Political Science, vol. 76(303), pages 432-461, July.
    12. Millimet Daniel L & Wang Le, 2006. "A Distributional Analysis of the Gender Earnings Gap in Urban China," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 5(1), pages 1-50, February.
    13. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2008. "Ordinal Comparison of Multidimensional Deprivation: theory and application," Discussion Papers 08-33, University of Copenhagen. Department of Economics.
    14. Gaston Yalonetzky, 2011. "Conditions for the Most Robust Poverty Comparisons Using the Alkire-Foster Family of Measures," OPHI Working Papers ophiwp044b, Queen Elizabeth House, University of Oxford.
    15. Christoffer Sonne-Schmidt & Finn Tarp & Lars Peter Østerdal, 2016. "Ordinal Bivariate Inequality: Concepts and Application to Child Deprivation in Mozambique," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 62(3), pages 559-573, September.
    16. Arndt, Channing & Distante, Roberta & Hussain, M. Azhar & Østerdal, Lars Peter & Huong, Pham Lan & Ibraimo, Maimuna, 2012. "Ordinal Welfare Comparisons with Multiple Discrete Indicators: A First Order Dominance Approach and Application to Child Poverty," World Development, Elsevier, vol. 40(11), pages 2290-2301.
    17. Brian McCaig & Adonis Yatchew, 2007. "International welfare comparisons and nonparametric testing of multivariate stochastic dominance," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 22(5), pages 951-969.

    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. Ian Crawford, 1999. "Nonparametric tests of stochastic dominance in bivariate distributions, with an application to UK data," IFS Working Papers W99/28, Institute for Fiscal Studies.
    2. David Lander & David Gunawan & William Griffiths & Duangkamon Chotikapanich, 2020. "Bayesian assessment of Lorenz and stochastic dominance," Canadian Journal of Economics/Revue canadienne d'économique, John Wiley & Sons, vol. 53(2), pages 767-799, May.
    3. M. Azhar Hussain & Nikolaj Siersbæk & Lars Peter Østerdal, 2020. "Multidimensional welfare comparisons of EU member states before, during, and after the financial crisis: a dominance approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(4), pages 645-686, December.
    4. David Lander & David Gunawan & William E. Griffiths & Duangkamon Chotikapanich, 2016. "Bayesian Assessment of Lorenz and Stochastic Dominance Using a Mixture of Gamma Densities," Department of Economics - Working Papers Series 2023, The University of Melbourne.
    5. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
    6. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Wang, 2002. "Consistent testing for stochastic dominance: a subsampling approach," CeMMAP working papers 03/02, Institute for Fiscal Studies.
    7. Hooi Hooi Lean & Michael McAleer & Wing-Keung Wong, 2013. "Risk-averse and Risk-seeking Investor Preferences for Oil Spot and Futures," Documentos de Trabajo del ICAE 2013-31, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico, revised Aug 2013.
    8. Jesus Gonzalo & Jose Olmo, 2014. "Conditional Stochastic Dominance Tests In Dynamic Settings," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 55(3), pages 819-838, August.
    9. Maasoumi, Esfandiar & Almas Heshmati, 2003. "Evaluating Dominance Ranking of PSID Incomes by various Household Attributes," Departmental Working Papers 0509, Southern Methodist University, Department of Economics.
    10. Lean, Hooi Hooi & McAleer, Michael & Wong, Wing-Keung, 2015. "Preferences of risk-averse and risk-seeking investors for oil spot and futures before, during and after the Global Financial Crisis," International Review of Economics & Finance, Elsevier, vol. 40(C), pages 204-216.
    11. Tsang, Chun-Kei & Wong, Wing-Keung & Horowitz, Ira, 2016. "A stochastic-dominance approach to determining the optimal home-size purchase: The case of Hong Kong," MPRA Paper 69175, University Library of Munich, Germany.
    12. Grönqvist, Charlotta, 2009. "Empirical studies on the private value of Finnish patents," Bank of Finland Scientific Monographs, Bank of Finland, volume 0, number sm2009_041.
    13. 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.
    14. Wong, Wing-Keung & Phoon, Kok Fai & Lean, Hooi Hooi, 2008. "Stochastic dominance analysis of Asian hedge funds," Pacific-Basin Finance Journal, Elsevier, vol. 16(3), pages 204-223, June.
    15. Wen-Hao Chen & Jean-Yves Duclos, 2011. "Testing for poverty dominance: an application to Canada," Canadian Journal of Economics, Canadian Economics Association, vol. 44(3), pages 781-803, August.
    16. Lee, Kyungho & Linton, Oliver & Whang, Yoon-Jae, 2023. "Testing for time stochastic dominance," Journal of Econometrics, Elsevier, vol. 235(2), pages 352-371.
    17. Khaled, Mohamad A. & Makdissi, Paul & Yazbeck, Myra, 2018. "Income-related health transfers principles and orderings of joint distributions of income and health," Journal of Health Economics, Elsevier, vol. 57(C), pages 315-331.
    18. Lean, Hooi Hooi & McAleer, Michael & Wong, Wing-Keung, 2010. "Market efficiency of oil spot and futures: A mean-variance and stochastic dominance approach," Energy Economics, Elsevier, vol. 32(5), pages 979-986, September.
    19. Andrews, Donald W.K. & Shi, Xiaoxia, 2017. "Inference based on many conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 196(2), pages 275-287.
    20. Mehmet Pinar & Thanasis Stengos & M. Ege Yazgan, 2012. "Is there an Optimal Forecast Combination? A Stochastic Dominance Approach to Forecast Combination Puzzle," Working Paper series 17_12, Rimini Centre for Economic Analysis.

    More about this item

    Keywords

    Social welfare; stochastic dominance; nonparametric statistical methods;
    All these keywords.

    JEL classification:

    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • D30 - Microeconomics - - Distribution - - - General

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:sur:surrec:1205. 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: Ioannis Lazopoulos (email available below). General contact details of provider: https://edirc.repec.org/data/desuruk.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.