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Ranking Alternative Non-Combinable Prospects: A Stochastic Dominance Based Route to the Second Best Solution

Listed author(s):
  • Gordon Anderson
  • Teng Wah Leo

The problem considered here is that of dealing with the "incompleteness" property of Stochastic Dominance Orderings by quantifying the extent to which distributions differ when there is no dominant distribution at a given order. For example consider a policymaker's choice problem when facing a set of distinct, non-combinable policy options. When policies are not combinable, the classic comparative static or first best solution to the choice problem is not available. The approach proposed here is an elaboration of a technique employed in the optimal statistical testing literature. It is supposed that policies could be combined so that the ideal first best "stochastically dominant" optimal envelope policy outcome is constructed under the policymaker's given imperative. Then the second best policy whose outcome most closely approximates this ideal is selected by employing a statistic that measures proximity of alternative policies to that ideal. The statistic is shown to obey an Independence of Irrelevant Alternatives proposition. The paper concludes with 3 illustrative examples of its use.

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Paper provided by University of Toronto, Department of Economics in its series Working Papers with number tecipa-520.

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Length: Unknown pages
Date of creation: 20 Oct 2014
Handle: RePEc:tor:tecipa:tecipa-520
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  1. John Knight & Stephen Satchell, 2008. "Testing for infinite order stochastic dominance with applications to finance, risk and income inequality," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 32(1), pages 35-46, January.
  2. Oliver Linton & Esfandiar Maasoumi & Yoon-Jae Whang, 2005. "Consistent Testing for Stochastic Dominance under General Sampling Schemes," Review of Economic Studies, Oxford University Press, vol. 72(3), pages 735-765.
  3. Atkinson, A B, 1987. "On the Measurement of Poverty," Econometrica, Econometric Society, vol. 55(4), pages 749-764, July.
  4. Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
  5. Foster, James E. & Shorrocks, Anthony F., 1988. "Inequality and poverty orderings," European Economic Review, Elsevier, vol. 32(2-3), pages 654-661, March.
  6. R. G. Lipsey & Kelvin Lancaster, 1956. "The General Theory of Second Best," Review of Economic Studies, Oxford University Press, vol. 24(1), pages 11-32.
  7. Arnaud Lefranc & Nicolas Pistolesi & Alain Trannoy, 2008. "Inequality Of Opportunities Vs. Inequality Of Outcomes: Are Western Societies All Alike?," Review of Income and Wealth, International Association for Research in Income and Wealth, vol. 54(4), pages 513-546, December.
  8. Juhl, Ted & Xiao, Zhijie, 2003. "Power Functions And Envelopes For Unit Root Tests," Econometric Theory, Cambridge University Press, vol. 19(02), pages 240-253, April.
  9. Lefranc, Arnaud & Pistolesi, Nicolas & Trannoy, Alain, 2009. "Equality of opportunity and luck: Definitions and testable conditions, with an application to income in France," Journal of Public Economics, Elsevier, vol. 93(11-12), pages 1189-1207, December.
  10. 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.
  11. Gordon Anderson & Oliver Linton & Teng Leo, 2012. "A polarization-cohesion perspective on cross-country convergence," Journal of Economic Growth, Springer, vol. 17(1), pages 49-69, March.
  12. Anderson, Gordon & Crawford, Ian & Leicester, Andrew, 2011. "Welfare rankings from multivariate data, a nonparametric approach," Journal of Public Economics, Elsevier, vol. 95(3), pages 247-252.
  13. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
  14. Foster, James E & Shorrocks, Anthony F, 1988. "Poverty Orderings," Econometrica, Econometric Society, vol. 56(1), pages 173-177, January.
  15. Anderson, Gordon, 1996. "Nonparametric Tests of Stochastic Dominance in Income Distributions," Econometrica, Econometric Society, vol. 64(5), pages 1183-1193, September.
  16. Anderson, Gordon, 2004. "Toward an empirical analysis of polarization," Journal of Econometrics, Elsevier, vol. 122(1), pages 1-26, September.
  17. Rothschild, Michael & Stiglitz, Joseph E., 1970. "Increasing risk: I. A definition," Journal of Economic Theory, Elsevier, vol. 2(3), pages 225-243, September.
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