Abstract
Incomplete orderings of distributions are nowadays used routinely in the analysis of uncertainty, inequality, welfare and poverty. The popularity of these orderings - of which stochastic dominance and Lorenz dominance are the best known examples - is due to the fact that they distinguish those distributional rankings which are widely accepted from those which depend on personal value judgements, and are therefore less clear cut. In this respect, the use of incomplete orderings may be viewed as an attempt to mark the boundary between positive and normative economics.
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References
Aczel, J.: Lectures on Functional Equations and their Applications. New York: Academic Press, 1966.
Arnold, B. G: Majorization and the Lorenz Order: A Brief Introduction, Lecture Notes in Statistics, Vol. 43. Berlin: Springer Verlag, 1987.
Arnold, B. G: ‘The Lorenz Order and the Effects of Taxation Policies’, Bulletin of Economic Research, 42 (1990), pp 249–264.
Arnold, B. C. and Villaseñor, J. A.: ‘Inequality Preserving and Inequality Attenuating Transformations’, mimeo, 1985.
Eichhorn, W., W. Funke and W. F. Richter: Tax Progression and Inequality of Income Distribution’, Journal of Mathematical Economics, 13 (1984), pp 127–131.
Fellman, J.: The Effect of Transformations on Lorenz Curves’, Econometrica, 44 (1976), pp 823–824.
Fishburn, P. C.: ‘Stochastic Dominance and Moments of Distributions’, Mathematics of Operations Research, 5 (1980), pp 94–100.
Fishburn, P. C. and R. G. Vickson: ‘Theoretical Foundations of Stochastic Dominance’ in G. A. Whitmore and M. C. Findlay (eds.), Stochastic Dominance. Lexington: D. C. Heath and Co., 1978.
Foster, J. E. and A. F. Shorrocks: ‘Poverty Orderings and Welfare Dominance’, Social Choice and Welfare, 5 (1988), pp 179–198. Reprinted in W. Gaertner and P. K. Pattanaik (eds.), Distributive Justice and Inequality, Berlin: Springer Verlag, 1988.
Hardy, G. H., J. E. Littlewood and G. Polya: Inequalities. Second Edition. Cambridge: Cambridge University Press, 1952.
Jakobsson, U.: ‘On the Measurement of the Degree of Progression’, Journal of Public Economics, 5 (1976), pp 161–168.
Kakwani, N.: ‘Applications of Lorenz Curves in Economic Analysis’, Econometrica, 45 (1977), pp 719–727.
Lambert, P. J.: The Distribution and Redistribution of Income: A Mathematical Analysis. Oxford: Basil Blackwell, 1989.
Marshall, A. W. and I. Olkin: Inequalities: Theory of Majorization and its Applications. New York: Academic Press, 1979.
Moyes, P.: ‘Some Classes of Functions that Preserve the Inequality and Welfare Orderings of Income Distributions’, Journal of Economic Theory, 49 (1989), pp 347–359.
Rudin, W.: Principles of Mathematical Analysis.. Second Edition. New York: McGraw Hill, 1964.
Shorrocks, A. F.: ‘Ranking Income Distributions’, Economica, 50 (1983), pp 3–17.
Shorrocks, A. F. and J. E. Foster: ‘Transfer Sensitive Inequality Measures’, Review of Economic Studies, 54 (1987), pp 485–497.
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© 1994 Springer-Verlag Berlin · Heidelberg
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Moyes, P., Shorrocks, A. (1994). Transformations of Stochastic Orderings. In: Eichhorn, W. (eds) Models and Measurement of Welfare and Inequality. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-79037-9_9
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DOI: https://doi.org/10.1007/978-3-642-79037-9_9
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