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Testing for Bivariate Stochastic Dominance Using Inequality Restrictions

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  • Thanasis Stengos

    ()

    (Department of Economics, University of Guelph)

  • Brennan S. Thompson

    ()

    (Department of Economics, Ryerson University, Toronto)

Abstract

In this paper, we propose of a test of bivariate stochastic dominance using a generalized framework for testing inequality constraints. Unlike existing tests, this test has the advantage of utilizing the covariance structure of the estimates of the joint distribution functions. The performance of our proposed test is examined by way of a Monte Carlo experiment. We also consider an empirical example which utilizes household survey data on income and health status.

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Paper provided by The Rimini Centre for Economic Analysis in its series Working Paper Series with number 32_11.

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Date of creation: Jul 2011
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Handle: RePEc:rim:rimwps:32_11
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Keywords: Stochastic dominance; inequality restrictions; multidimensional welfare;

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Find related papers by JEL classification:
  • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
  • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
  • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement

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  1. Charles M. Beach & Russell Davidson, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Oxford University Press, vol. 50(4), pages 723-735.
  2. Russell Davidson, 2007. "Testing For Restricted Stochastic Dominances: Some Further Results," Departmental Working Papers 2007-15, McGill University, Department of Economics.
  3. Davidson, R. & Duclos, J.-Y., 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," G.R.E.Q.A.M. 98a14, Universite Aix-Marseille III.
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  7. Kuan Xu & L. Osberg, 1998. "A distribution-free test for deprivation dominance," Econometric Reviews, Taylor & Francis Journals, vol. 17(4), pages 415-429.
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  9. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Poverty Comparisons with Discrete Indicators of Well-being," Cahiers de recherche 0628, CIRPEE.
  10. Gordon Anderson, 2008. "The empirical assessment of multidimensional welfare, inequality and poverty: Sample weighted multivariate generalizations of the Kolmogorov–Smirnov two sample tests for stochastic dominance," Journal of Economic Inequality, Springer, vol. 6(1), pages 73-87, March.
  11. Kodde, David A & Palm, Franz C, 1986. "Wald Criteria for Jointly Testing Equality and Inequality Restriction s," Econometrica, Econometric Society, vol. 54(5), pages 1243-48, September.
  12. Wolak, Frank A., 1989. "Local and Global Testing of Linear and Nonlinear Inequality Constraints in Nonlinear Econometric Models," Econometric Theory, Cambridge University Press, vol. 5(01), pages 1-35, April.
  13. Jean-Yves Duclos & David Sahn & Stephen D. Younger, 2006. "Robust Multidimensional Spatial Poverty Comparisons in Ghana, Madagascar, and Uganda," World Bank Economic Review, World Bank Group, vol. 20(1), pages 91-113.
  14. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, June.
  15. Fisher, Gordon & Willson, Douglas & Xu, Kuan, 1998. "An empirical analysis of term premiums using significance tests for stochastic dominance," Economics Letters, Elsevier, vol. 60(2), pages 195-203, August.
  16. 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.
  17. Heshmati, Almas & Maasoumi, Esfandiar, 1998. "Stochastic Dominance Amongst Swedish Income Distributions," SSE/EFI Working Paper Series in Economics and Finance 279, Stockholm School of Economics.
  18. Kaur, Amarjot & Prakasa Rao, B.L.S. & Singh, Harshinder, 1994. "Testing for Second-Order Stochastic Dominance of Two Distributions," Econometric Theory, Cambridge University Press, vol. 10(05), pages 849-866, December.
  19. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  20. W Furlong & D Feeny & G Torrance & C Goldsmith & S DePauw & Z Zhu & M Denton & M Boyle, 1998. "Multiplicative Multi-Attribute Utility Function for the Health Utilities Index Mark 3 (HUI3) System: A Technical Report," Centre for Health Economics and Policy Analysis Working Paper Series 1998-11, Centre for Health Economics and Policy Analysis (CHEPA), McMaster University, Hamilton, Canada.
  21. Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
  22. Horvath, Lajos & Kokoszka, Piotr & Zitikis, Ricardas, 2006. "Testing for stochastic dominance using the weighted McFadden-type statistic," Journal of Econometrics, Elsevier, vol. 133(1), pages 191-205, July.
  23. Beach, Charles M & Richmond, James, 1985. "Joint Confidence Intervals for Income Shares and Lorenz Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 26(2), pages 439-50, June.
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