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- Title
Efficiency Analysis for Multivariate Distributions.
- Authors
Levhari, David; Paroush, Jacob; Peleg, Bezalel
- Abstract
Necessary and sufficient efficiency conditions have recently been suggested and developed in the form of stochastic dominance rules by Quirk and Saposnik [8], Hadar and Russell [1, 2], Hanoch and Levy [3] and Rothschild and Stiglitz [9, 10]. All focus on cases where the random variable has a univariate distribution. Economic decisions are frequently taken in a multidimensional environment. In such a situation the random variable has a multivariate distribution function, F(x1, …, xn) and the individual has a multidimensional utility function u(x1, …, xn). The multivariate case has been treated in Tobin [11], Levy [4] and Levy and Paroush [5], but all these works assume either independence over time, where F(x1, …, xn) = ΠF(xi), or that the utility function is defined on terminal wealth, where u(x1, …, xn) = u(Πxi), or that the utility function is additive, where u(x1, …, xn) = Σu¹(xi). Such assumptions suppress multidimensionality and, in fact, degenerate it into a univariate case. To the best of our knowledge, the only attempt made at tackling the general problem is in Levy and Paroush [6]. However, in their work efficiency criteria have been found for the two-dimensional case only, and under certain restrictions on both the utility functions and the distribution.
- Subjects
UTILITY theory; ANALYSIS of variance; MULTIVARIATE analysis; DISTRIBUTION (Probability theory); MATHEMATICAL statistics; PROOF theory; STATISTICS; ECONOMICS
- Publication
Review of Economic Studies, 1975, Vol 42, Issue 1, p87
- ISSN
0034-6527
- Publication type
Article
- DOI
10.2307/2296822