Portfolio performance gauging in discrete time using a Luenberger productivity indicator

This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios over time. Integrating the shortage function (Luenberger, 1995) into a Luenberger portfolio productivity indicator (Chambers, 2002), this study estimates the changes in the relative positions of portfolios with respect to the traditional Markowitz mean-variance efficient frontier, as well as the eventual shifts of this frontier over time. Based on the analysis of local changes relative to these mean-variance and higher moment (in casu, mean-variance-skewness and mean-variance-skewness-kurtosis) frontiers, this methodology allows to neatly separate between on the one hand performance changes due to portfolio strategies and on the other hand performance changes due to the market evolution. This methodology is empirically illustrated using a mimicking portfolio approach (22 and 23) using US monthly data from January 1931 to August 2007.     

An extension of the multi-output state-contingent production model

This paper presents new developments on the state-contingent theory of production under uncertainty with stochastic prices. Our main purpose is to generalize the usual finite discrete state-contingent production model to infinite dimensional, possibly uncountable spaces which look like a more realistic framework. Usual duality results are established in this general context, shedding some light on the links between risk-neutral probabilities and shadow prices. A direct generalized production risk premium is defined and is shown to be independent of the inputs level when the technology is output translation homothetic. In such a case, the technology exhibits constant absolute riskiness. We thank Bob Chambers for his helpful comments.     

Parallel Neutrality

This paper develops the notion of parallel-neutral technical change for inputs and outputs. It is shown that parallel-neutral technical change generalizes existing radial notions of neutral technical change. A taxonomy of the structural consequences of parallel-neutral technical change is developed.     

Non-convex Technologies and Cost Functions: Definitions,Duality and Nonparametric Tests of Convexity

This contribution is the first systematic attempt to develop a series of nonparametric, deterministic technologies and cost functions without maintaining convexity. Specifically, we introduce returns to scale assumptions into an existing non-convex technology and, dual to these technologies, define non-convex cost functions that are never lower than their convex counterparts. Both non-convex technologies and cost functions (total, ray-average and marginal) are characterized by closed form expressions. Furthermore, a local duality result is established between a local cost function and the input distance function. Finally, nonparametric goodness-of-fit tests for convexity are developed as a first step towards making it a statistically testable hypothesis. An erratum to this article is available at .     

Hypercongestion in production correspondences: an empirical exploration

This empirical contribution reviews the rather limited existing literature measuring congestion in production. It first compares current ways to measure congestion using nonparametric specifications of technologies. In particular, it focuses on the magnitude and incidence of the congestion detected in empirical studies using traditional radial efficiency measures. Thereafter, it shows the limitations of this radial measurement and how alternative measurement schemes may reveal higher amounts of congestion. Then, the new, more general methodology of measuring S-congestion is presented. In particular, we first present a numerical example to illustrate the way the S-disposable technologies allow to capture more extreme forms of congestion by setting empirically determined upper bounds to the wasting of inputs. Then, an empirical illustration is presented based on an existing sample of data. A final section concludes.     

Returns to Scale on Nonparametric Deterministic Technologies: Simplifying Goodness-of-Fit Methods Using Operations on Technologies

Thepurpose of this short article is to simplify goodness-of-fitmethods to obtain qualitative information about returns to scalefor individual observations. Traditional and new goodness-of-fitmethods developed for estimating returns to scale on nonparametricdeterministic reference technologies are reviewed. Using compositionrules for technologies with specific returns to scale assumptions,we show how these goodness-of-fit methods can be simplified inthe case of convex technologies (Data Envelopment Analysis (DEA)models).     

Dual Representations of Non-Parametric Technologies and Measurement of Technical Efficiency

This paper extends the recent work by Frei and Harker on projections onto efficient frontiers (1999) in three ways. First, we provide a formal definition of the production set as the intersection of a finite number of closed halfspaces. We emphasize the necessity of a complete enumeration of the supporting hyperplanes to define the production set properly. We focus on the problem of exhaustive enumeration of the supporting hyperplanes to characterize the production set. Second, we consider the problem of an arbitrary-norm projection on the boundary of the production set. We use the concept of the Hölder distance function and we derive the necessary mathematics to calculate distances and projections of inefficient DMUs onto the efficient frontier. Third, we introduce a relevant weighting scheme for inputs and outputs so that the Hölder distance function respects the commensurability axiom defined by Russell (1988). Finally, we present an illustration using the same data set as Frei and Harker (1999) to highlight some of the extensions proposed in the paper.     

A DEA estimation of a lower bound for firms’ allocative efficiency without information on price data

In this paper, we estimate a lower bound for the sum of firms’ allocative efficiencies in the absence of information on prices. For this purpose, we only estimate technical efficiency at both the firm and the industry level using a directional distance function and choosing a relevant direction. Our result relies on the decomposition of overall inefficiency into technical and allocative inefficiency at both the firm and the industry level. The convexity of a technology induces a transfer from both total technical inefficiency and part of allocative inefficiency at the firm level to technical inefficiency solely at the industry level. The remaining firms’ allocative inefficiency could be counted at the industry level. Hence, the difference between technical inefficiencies at both levels can be interpreted as a lower bound for the sum of allocative inefficiency in the industry. We show how to implement this bound in a DEA framework.