This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-variance-skewness space. A shortage function is defined that looks for possible increases in return and skewness and decreases in variance. Global optimality is guaranteed for the resulting optimal portfolios. We also establish a link to a proper indirect mean-variance-skewness utility function. For computational reasons, the optimal portfolios resulting from this dual approach are only locally optimal. This framework permits to differentiate between portfolio efficiency and allocative efficiency, and a convexity efficiency component related to the difference between the primal, nonconvex approach and the dual, convex approach. Furthermore, in principle, information can be retrieved about the revealed risk aversion and prudence of investors. An empirical section on a small sample of assets serves as an illustration.shortage function, efficient frontier, mean-variance-skewness portfolios, risk aversion, prudence

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This empirical application investigates the eventual presence of credit constraints using a panel of French farmers. The credit-constrained profit maximization model proposed by F�re, Grosskopf, and Lee is extended in three ways. First, we rephrase the model in terms of directional distance functions to allow duality with the profit function. Second, we model credit constraints in the short-run and investment constraints in the long-run using short- and long-run profit functions. Third, we lag the expenditure constraint one year to account for the separation between planning and production. We find empirical evidence of credit and investment constraints. Financially unconstrained farmers are larger, perform better, and seem to benefit from a virtuous circle where access to financial markets allows better productive choices. Copyright 2006, Oxford University Press.

Introducing a new difference-based Luenberger-Hicks-Moorsteen productivity indicator, this contribution establishes theoretically its relations with some existing ratio- and difference-based productivity indexes and indicators. The first main result is an approximation proposition stating that the logarithm of the Hicks-Moorsteen productivity index is about equal to the Luenberger-Hicks-Moorsteen productivity indicator. Secondly, we also establish the specific conditions under which the Luenberger-Hicks-Moorsteen indicator equals the recently introduced Luenberger indicator and compare these to the conditions governing the relations between ratio-based Hicks-Moorsteen and Malmquist indices. Copyright Springer-Verlag Berlin/Heidelberg 2004Malmquist productivity index, Hicks-Moorsteen productivity index, Luenberger productivity indicator, Luenberger-Hicks-Moorsteen productivity indicator.,