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A nonparametric test of stochastic dominance in multivariate distributions

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  • 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.

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File URL: http://www.fahs.surrey.ac.uk/economics/discussion_papers/2005/DP12-05.pdf
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Bibliographic Info

Paper provided by School of Economics, University of Surrey in its series School of Economics Discussion Papers with number 1205.

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Length: 39 pages
Date of creation: Jun 2005
Date of revision:
Handle: RePEc:sur:surrec:1205

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Keywords: Social welfare; stochastic dominance; nonparametric statistical methods;

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References

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  1. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-93, September.
  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. Ulph, David, 1978. "On labour supply and the measurement of inequality," Journal of Economic Theory, Elsevier, vol. 19(2), pages 492-512, December.
  5. John C. Harsanyi, 1955. "Cardinal Welfare, Individualistic Ethics, and Interpersonal Comparisons of Utility," Journal of Political Economy, University of Chicago Press, vol. 63, pages 309.
  6. Atkinson, Anthony B & Bourguignon, Francois, 1982. "The Comparison of Multi-Dimensioned Distributions of Economic Status," Review of Economic Studies, Wiley Blackwell, vol. 49(2), pages 183-201, April.
  7. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  8. Levy, Haim & Paroush, Jacob, 1974. "Toward multivariate efficiency criteria," Journal of Economic Theory, Elsevier, vol. 7(2), pages 129-142, February.
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Cited by:
  1. Gaston Yalonetzky, 2012. "Conditions for the most robust multidimensional poverty comparisons using counting measures and ordinal variables," Working Papers 257, ECINEQ, Society for the Study of Economic Inequality.
  2. Sonne-Schmidt, Christoffer & Tarp, Finn & Osterdal, Lars Peter, 2013. "Ordinal multidimensional inequality," Working Paper Series UNU-WIDER Research Paper , World Institute for Development Economic Research (UNU-WIDER).
  3. 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.
  4. Nicolas Gravel, 2007. "Is India Better off Today Than 15 Years Ago? A Robust Multidimensional Answer," Working Papers id:1056, eSocialSciences.
  5. 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.
  6. 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.
  7. 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.
  8. 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.
  9. 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.

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