Input, Output and Graph Technical Efficiency Measures on Non-Convex FDH Models with Various Scaling Laws: An Integrated Approach Based upon Implicit Enumeration Algorithms

In a recent article, Briec, Kerstens and Vanden Eeckaut (2004) develop a series of nonparametric, deterministic non-convex technologies integrating traditional returns to scale assumptions into the non-convex FDH model. They show, among other things, how the traditional technical input efficiency measure can be analytically derived for these technology specifications. In this paper, we develop a similar approach to calculate output and graph measures of technical efficiency and indicate the general advantage of such solution strategy via enumeration. Furthermore, several analytical formulas are established and some algorithms are proposed relating the three measurement orientations to one another.Data Envelopment Analysis, Free Disposal Hull, technical efficiency

The Luenberger Productivity Indicator: An Economic Specifcation Leading to Infeasibilities.

This contribution points out a minor problem in the specifcation of technology when computing the Luenberger productivity indicator that has been hitherto ignored in the literature. The solution of this problem increases the likelihood that the directional distance functions underlying this productivity indicator are ill-defined.Luenberger productivity indicator, infeasibility

Portfolio Selection in Multidimensional General and Partial Moment Space.

This paper develops a general approach for the single period portfolio optimization problem in a multidimensional general and partial moment space. A shortage function is defined that looks for possible increases in odd moments and decreases in even moments. A main result is that this shortage function ensures suffcient conditions for global optimality. It also forms a natural basis for developing tests on the infuence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirectutility function. This nonparametric effciency measurement framework permits to dfferentiate mainly between portfolio effciency and allocative effciency. Finally, information can,in principle, be inferred about the revealed risk aversion, prudence, temperance and otherhigher-order risk characteristics of investors.shortage function, efficient frontier, K-moment portfolios

The Hicks-Moorsteen Productivity Index Satisfies the Determinateness Axiom.

There are two total factor productivity indices available in the literature based on a primal notion of the technology. In a ratio tradition, these are the Malmquist and the HicksMoorsteen productivity indices. In a difference perspective, the Luenberger and Luenberger-Hicks-Moorsteen productivity indicators are based upon a sightly different concept. The purpose of this note is to establish that -in contrast to the Malmquist index- the Hicks-Moorsteen type of productivity index (as well as its difference-based counterpart) is well-defined and satisfies the determinateness property, since the underlying distance functions are always feasible.Malmquist productivity index, Hicks-Moorsteen productivity index, determinateness

Infeasibility and Directional Distance Functions with Application to the Determinateness of the Luenberger Productivity Indicator

The purpose of this contribution is to highlight an underexplored property of the directional distance function, a recently introduced generalization of the Shephard distance function. It diagnoses in detail the economic conditions under which infeasibilities may occur for the case of directional distance functions and explores whether there exist any solutions that remedy the problem in an economically meaningful way. This discussion is linked to determinateness as a property in index theory and illustrated by analyzing the Luenberger total factor productivity indicator, based upon directional distance functions. This indicator turns out to be impossible to compute under certain weak conditions. A fortiori, the same problems can also occur for less general productivity indicators and indexes.Directional distance function, Shortage function, Well-definedness, Infeasibility, Determinateness

Incentive Regulation and the Role of Convexity in Benchmarking Electricity Distribution: Economists versus Engineers

This note illustrates the potential impact of the specification of a convex production technology on establishing minimal costs compared to the use of a non-convex technology when benchmarking electricity distributors. This methodological reflection is mainly motivated by recent engineering literature providing evidence for non-convexities in electricity distribution. An empirical illustration using non-parametric specifications of technology illustrates this main point using a sample of Spanish electricity distribution firms earlier analysed in Grifell-Tatjé and Lovell (2003).Convexity, incentive regulation, benchmarking, engineering

Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach

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, non-convex 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

Tangency Capacity Notions Based upon the Pro?t and Cost Functions: A Non-Parametric Approach and a Comparison

This contribution provides a way to de?ne and compute a tangency notion of economic capacity based upon the relation between the various directional distance functions and the pro?t and cost functions using non-parametric technologies. A new result relating pro?t and cost function-based tangency capacity notions is established.economic capacity, pro?t function, cost function, directional distance function, tangency

Comparing Efficiency Across Markets: An Extension and Critique of the Zhang and Bartels (1998) Methodology

The use of non-parametric frontier methods for the evaluation of product market efficiency in heterogeneous markets seems to have gained some popularity recently. However, the statistical properties of these frontier estimators have been largely ignored. The main point is that nonparametric frontier estimators are biased and that the degree of bias depends on specific sample properties, most importantly sample size and number of dimensions of the model. To investigate the effect of this bias on comparing market efficiency, this contribution estimates the efficiency for several datasets for two main product categories. Following Zhang and Bartels (1998), these results comprise re-estimates for the larger samples limiting their size to that of the smaller samples when the model dimensions for different samples are identical. Furthermore, sample sizes are adjusted to mitigate the eventual differences in dimensions in specification. This allows comparing market efficiency for different markets on a more equal footing, since it reduces the bias effect to a minimum making the comparison of market efficiency possible. However, the article also points out the critical limitations of this Zhang and Bartels (1998) approach in certain respects. Apart from reporting these negative results, we also offer some suggestions for future work.Market Efficiency, Heterogeneous Product Markets, Bias, Monte-Carlo Simulation