Inference for Inverse Stochastic Dominance
This note presents an innovative inference procedure for assessing if a pair of distributions can be ordered according to inverse stochastic dominance (ISD). At order 1 and 2, ISD coincides respectively with rank and generalized Lorenz dominance and it selects the preferred distribution by all social evaluation functions that are monotonic and display inequality aversion. At orders higher than the second, ISD is associated with dominance for classes of linear rank dependent evaluation functions. This paper focuses on the class of conditional single parameters Gini social evaluation functions and illustrates that these functions can be linearly decomposed into their empirically tractable influence functions. This approach gives estimators for ISD that are asymptotically normal with a variancecovariance structure which is robust to non-simple randomization sampling schemes, a common case in many surveys used in applied distribution analysis. One of these surveys, the French Labor Force Survey, is selected to test the robustness of Equality of Opportunity evaluations in France through ISD comparisons at order 3. The ISD tests proposed in this paper are operationalized through the user-written “isdtest” Stata routine.
|Date of creation:||Apr 2013|
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- Claudio Zoli, 2002. "Inverse stochastic dominance, inequality measurement and Gini indices," Journal of Economics, Springer, vol. 9(1), pages 119-161, December.
- Beach, Charles M & Davidson, Russell, 1983. "Distribution-Free Statistical Inference with Lorenz Curves and Income Shares," Review of Economic Studies, Wiley Blackwell, vol. 50(4), pages 723-35, October.
- Russell Davidson & Jean-Yves Duclos, 2000.
"Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality,"
Econometric Society, vol. 68(6), pages 1435-1464, November.
- Davidson, Russell & Duclos, Jean-Yves, 1998. "Statistical Inference for Stochastic Dominance and for the Measurement of Poverty and Inequality," Cahiers de recherche 9805, Université Laval - Département d'économique.
- 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.
- Buhong Zheng, 2002. "Testing Lorenz Curves with Non-Simple Random Samples," Econometrica, Econometric Society, vol. 70(3), pages 1235-1243, May.
- Rolf Aaberge, 2004.
"Ranking Intersecting Lorenz Curves,"
CEIS Research Paper
45, Tor Vergata University, CEIS.
- Aaberge, Rolf, 2008. "Ranking Intersecting Lorenz Curves," IZA Discussion Papers 3852, Institute for the Study of Labor (IZA).
- Rolf Aaberge, 2000. "Ranking Intersecting Lorenz Curves," Discussion Papers 271, Research Department of Statistics Norway.
- Rolf Aaberge, 2000. "Ranking intersectiong Lorenz Curves," ICER Working Papers 08-2000, ICER - International Centre for Economic Research.
- Fabio Maccheroni & Pietro Muliere & Claudio Zoli, 2005. "Inverse stochastic orders and generalized Gini functionals," Metron - International Journal of Statistics, Dipartimento di Statistica, Probabilità e Statistiche Applicate - University of Rome, vol. 0(3), pages 529-559.
- Arnaud LEFRANC, Nicolas PISTOLESI, Alain TRANNOY, 2009.
"Equality of opportunity and luck: De nitions and testable conditions, with an application to income in France,"
THEMA Working Papers
2009-01, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.
- 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.
- Muliere, Pietro & Scarsini, Marco, 1989. "A note on stochastic dominance and inequality measures," Journal of Economic Theory, Elsevier, vol. 49(2), pages 314-323, December.
- Foster, James & Greer, Joel & Thorbecke, Erik, 1984. "A Class of Decomposable Poverty Measures," Econometrica, Econometric Society, vol. 52(3), pages 761-66, May.
- Barrett, Garry F. & Donald, Stephen G., 2009. "Statistical Inference with Generalized Gini Indices of Inequality, Poverty, and Welfare," Journal of Business & Economic Statistics, American Statistical Association, vol. 27, pages 1-17.
- Rolf Aaberge, 2006.
"Gini’s Nuclear Family,"
491, Research Department of Statistics Norway.
- Fishburn, Peter C., 1976. "Continua of stochastic dominance relations for bounded probability distributions," Journal of Mathematical Economics, Elsevier, vol. 3(3), pages 295-311, December.
- Buhong Zheng, 1999. "Statistical Inferences for Testing Marginal Rank and (Generalized) Lorenz Dominances," Southern Economic Journal, Southern Economic Association, vol. 65(3), pages 557-570, January.
- Garry F. Barrett & Stephen G. Donald, 2003. "Consistent Tests for Stochastic Dominance," Econometrica, Econometric Society, vol. 71(1), pages 71-104, January.
- Fleurbaey, Marc, 2012.
"Fairness, Responsibility, and Welfare,"
Oxford University Press, number 9780199653591, March.
- DONALDSON, David & WEYMARK, John A., .
"Ethically flexible Gini indices for income distributions in the continuum,"
CORE Discussion Papers RP
-520, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- Donaldson, David & Weymark, John A., 1983. "Ethically flexible gini indices for income distributions in the continuum," Journal of Economic Theory, Elsevier, vol. 29(2), pages 353-358, April.
- Valentino Dardanoni & Antonio Forcina, 1999. "Inference for Lorenz curve orderings," Econometrics Journal, Royal Economic Society, vol. 2(1), pages 49-75.
- Shorrocks, Anthony F, 1983. "Ranking Income Distributions," Economica, London School of Economics and Political Science, vol. 50(197), pages 3-17, February.
- Davies, James & Hoy, Michael, 1995. "Making Inequality Comparisons When Lorenz Curves Intersect," American Economic Review, American Economic Association, vol. 85(4), pages 980-86, September.
- Yaari, Menahem E, 1987. "The Dual Theory of Choice under Risk," Econometrica, Econometric Society, vol. 55(1), pages 95-115, January.
- Claudio Zoli, 1999. "Intersecting generalized Lorenz curves and the Gini index," Social Choice and Welfare, Springer, vol. 16(2), pages 183-196.
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