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This paper proposes to estimate the returns-to-scale of a production set by considering the individual return of each observed firm. Each individual returns-to-scale is estimated from the goodness of fit approach proposed by Boussemart et al. (2019). The global technology is then constructed as the intersection of all the individual technologies. We propose an axiomatic foundation by introducing the notion of $\Lambda$-returns to scale that encompasses as a special case the standard definition of $\alpha$-returns to scale (Boussemart et al., 2009). Along this line it is shown that many production models involving variable, non-increasing and non-decreasing returns-to-scale appear to be special cases of models satisfying a $\Lambda$-returns to scale assumption., Comment: 27 pages, 8 figures

This paper proposes to estimate the returns-to-scale of a production set by considering the individual return of each observed firm. Each individual returns-to-scale is estimated from the goodness of fit approach proposed by Boussemart et al. (2019). The global technology is then constructed as the intersection of all the individual technologies. We propose an axiomatic foundation by introducing the notion of $Λ$-returns to scale that encompasses as a special case the standard definition of $α$-returns to scale (Boussemart et al., 2009). Along this line it is shown that many production models involving variable, non-increasing and non-decreasing returns-to-scale appear to be special cases of models satisfying a $Λ$-returns to scale assumption., 27 pages, 8 figures

International audience; The magnitude of short run variations in unemployment induced by output shocks is influenced, interalia, by a variety of supply-side characteristics of the economy in question. This paper argues that one important element of those characteristics is a coun- try’s ‘distance’ from the technological frontier. Using both, a panel interaction model and a panel threshold model, we show that the value of the coefficient linking short run vari- ations in unemployment to output changes (often known as the Okun’s Law Coefficient) is influenced by the technological distance of a country to the world efficiency frontier. Specifically, the larger the distance to the frontier, the larger the impact of real GDP movements on unemployment rate variations. Moreover, the magnitude of this impact is both considerable and exhibits wide variation between countries; decomposition of the total derivatives of unemployment with respect to GDP shows that the technology-induced share of this derivative is around 20% for Norway and Denmark countries (close to the frontier) and around 40% for Greece (which has the largest technological gap). Traditional growth enhancing demand side policies should thus go in hand with adequate supply side policies in order to stabilise or reduce the unemployment rate in technologically advanced countries.; Nous utilisons deux techniques de modélisation complémentaires pour analyser l’influence de la distance technologique des pays sur la force de la relation entre les fluctuations de court terme de l’activité et celles du taux de chômage dans la Loi d’Okun. Il apparait que le coefficient d’Okun est positivement corrélé avec la distance technologique des pays. Plus la distance technologique d’un pays par rapport à la frontière mondiale est grande, plus l’impact des variations de court terme du PIB sur les mouvements conjoncturels du taux de chômage est important. La décomposition de cet impact pour chaque pays de l’échantillon montre que l’effet de l’écart technologique sur corrélation entre les mouvements du PIB réel et de ceux du taux de chômage varie entre les différents pays. Cet effet est par exemple proche de 20% pour le Danemark et la Norvège mais plutôt de l’ordre de 40% pour la Grèce.

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.

This paper introduces in production theory a large class of efficiency measures that can be derived from the notion of utility function. This article also establishes a relation between these distance functions and Stone-Geary utility functions. More specifically, the paper focusses on new distance function that generalizes several existing efficiency measures. The new distance function is inspired from the Atkinson inequality index and maximizes the sum of the netput expansions required to reach an efficient point. A generalized duality theorem is proved and a duality result linking the new distance functions and the profit function is obtained. For all feasible production vectors, it includes as special cases most of the dual correspondences previously established in the literature. Finally, we identify a large class of measures for which these duality results can be obtained without convexity.

The magnitude of short run variations in unemployment induced by output shocks is influenced, inter alia, by a variety of supply-side characteristics of the economy in question. This paper argues that one important element of those characteristics is a country’s ‘distance ’ from the technological frontier. Using both, a panel interaction model and a panel threshold model, we show that the value of the coefficient linking short run variations in unemployment to output changes (often known as the Okun’s Law Coefficient) is influenced by the technological distance of a country to the world efficiency frontier. Specifically, the larger the distance to the frontier, the larger the impact of real GDP movements on unemployment rate variations. Moreover, the magnitude of this impact is both considerable and exhibits wide variation between countries; decomposition of the total derivatives of unemployment with respect to GDP shows that the technology-induced share of this derivative is around 20% for Norway and Denmark countries (close to the frontier) and around 40% for Greece (which has the largest technological gap). Traditional growth enhancing demand side policies should thus go in hand with adequate supply side policies in order to stabilise or reduce the unemployment rate in technologically advanced countries.

Cooperation between firms can never improve the technical efficiency of any firm coalition. The directional distance function, by virtue of its additive nature, is a useful tool that outlines this impossibility. In this paper, the additive aggregation scheme of input/output vectors is generalized according to an aggregator. Accordingly, cooperation between firms may increase the technical efficiency of the firm group. This improvement is shown to be compatible with nonjoint semilattice technologies that bring out either output or input (weak) complementarity. Firm games are investigated to show that firms may merge on the basis of their inputs due to constraints imposed on outputs. Conversely, they may merge with respect to the outputs they can produce because of limitations imposed on inputs.

International audience; The software available to implement and carry out efficiency analysis is crucial for the diffusion of efficiency frontier techniques among applied researchers and policy makers. The implementation of up-to-date productivity and efficiency analysis is indeed important to advance our knowledge in many fields, ranging from the public and regulated sectors to the private ones. This contributionfillsagapintheexistingliteratureandsurveysthecurrentlyavailableoptionstoestimate a variety of frontier methodologies using either general or dedicated programs. We outline directions for future research.

International audience

International audience

International audience

International audience

How does technical change influence the size of the Okun’s Law coefficient? Using a nonlinear version of Okun’s Law augmented with technical change and technological distance, we show that the impact of output movements on unemployment variations is influenced by the imitation or innovation origins of technical change

The main aim of this contribution is to compare existing and newly developed techniques for geometrically representing mean-variance-skewness portfolio frontiers based on the rather widely adapted methodology of polynomial goal programming (PGP) on the one hand and the more recent approach based on the shortage function on the other hand. Moreover, we explain the working of these different methodologies in detail and provide graphical illustrations. Inspired by these illustrations, we prove a generalization of the well-known two fund separation theorem from traditional mean-variance portfolio theory.

This note shows how the linear programs needed to compute cost and revenue functions under constant returns to scale and a single output or input, respectively, can be replaced with a more efficient enumeration algorithm. An empirical illustration shows the gain in computer time one can obtain.

nrpages: 33 status: published

A function $u: X\to\mathbb{R}$ defined on a partially ordered set is quasi-Leontief if, if for all $x\in X$, the upper level set $\{x^\prime\in X: u(x^\prime)\geqslant u(x)\} $ has a smallest element. A function $u: \prod_{j=1}^nX_j\to\mathbb{R}$ whose partial functions obtained by freezing $n-1$ of the variables are all quasi-Leontief is an individually quasi-Leontief function; a point $x$ of the product space is an efficient point for $u$ if it is a minimal element of $\{x^\prime\in X: u(x^\prime)\geqslant u(x)\} $. Part I deals with the maximisation of quasi-Leontief functions and the existence of efficient maximizers. Part II is concerned with the existence of efficient Nash equilibria for abstract games whose payoff functions are individually quasi-Leontief. Order theoretical and algebraic arguments are dominant in the first part while, in the second part, topology is heavily involved. In the framework and the language of tropical algebras, our quasi-Leontief functions are the additive functions defined on a semimodule with values in the semiring of scalars.

This contribution compares existing and newly developed techniques for geometrically representing mean-variances-kewness portfolio frontiers based on the rather widely adapted methodology of polynomial goal programming (PGP) on the one hand and the more recent approach based on the shortage function on the other hand. Moreover, we explain the working of these different methodologies in detail and provide graphical illustrations. Inspired by these illustrations, we prove a generalization of the well-known two fund separation theorem from traditionalmean-variance portfolio theory.

This contribution compares existing and newly developed techniques for geometrically representing mean-variances-kewness portfolio frontiers based on the rather widely adapted methodology of polynomial goal programming (PGP) on the one hand and the more recent approach based on the shortage function on the other hand. Moreover, we explain the working of these different methodologies in detail and provide graphical illustrations. Inspired by these illustrations, we prove a generalization of the well-known two fund separation theorem from traditionalmean-variance portfolio theory.

We prove that, under appropriate conditions, an abstract game with quasi-Leontief payoff functions $u_i : \prod_{j=1}^nX_j\to\mathbb{R}$ has a Nash equilibria. When all the payoff functions are globally quasi-Leontief, the existence and the characterization of efficient Nash equilibria mainly follows from the analysis carried out in part I. When the payoff functions are individually quasi-Leontief functions the matter is somewhat more complicated. We assume that all the strategy spaces are compact topological semilattices, and under appropriate continuity conditions on the payoff functions, we show that there exists an efficient Nash equilibria using the Eilenberg-Montgomery Fixed Point Theorem for acyclic valued upper semicontinuous maps defined on an absolute retract and some non trivial properties of topological semilattices. The map in question is defined on the set of Nash equilibria and its fixed points are exactly the efficient Nash equilibria.

Plural form tends to be the most popular organization form in retail and service networks compared to purely franchisedor purely company-owned systems. In the first part, this paper exposes the evolution of researchers' state of mind from theway of thinking which considers franchising and ownership as substitutable organizational forms to theories which analyzethe utilization of both franchise and company arrangements. The paper describes the main attempts to explain theoretically thesuperiority of plural forms. In the second part, the paper discusses the hypothesis which says that there is a relationship betweenthe organizational form of the chain and its efficiency score. It is demonstrated through the application of a data envelopmentanalysis method on French hotel chains that plural form networks are in average more efficient than strictly franchised andwholly owned chains. The Kruskal–Wallis test which is a distribution-free rank-order statistic is used to statistically verify thisrelationship. The result does not permit the rejection of the null hypothesis regarding whether an organizational form is moreefficient than another one. Hence, this paper opens prospects for researches aiming at testing the organizational form effect ondifferent samples and with other methods.

This paper proposes a pragmatic, discrete time indicator to gauge the performance of port-folios 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 e±- cient 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) 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 (Fama and French 1996; 1997) using US monthly data from January 1931 to August 2007.

Successive CAP reforms have increased the exposure of European agriculture to market forces. As a result, farmers have become preoccupied with their competitiveness and have progressively adopted best practices. However, these long-run technological adjustments could be slowed down by eventual short-run financial constraints. This contribution measures the role of these financial constraints on the catching-up component of total factor productivity for a panel of French farmers in Nord-Pas-de-Calais region during 1994-2001. For TFP estimates based on non-parametric distance functions, the second stage econometric results indicate that the technological adaptation is significantly conditioned by financial constraints.

Markowitz portfolio theory (1952) has induced research into the efficiency of portfolio management. This paper studies existing nonparametric efficiency measurement approaches for single period portfolio selection from a theoretical perspective and generalises currently used efficiency measures into the full mean-variance space. Therefore, we introduce the efficiency improvement possibility function (a variation on the shortage function), study its axiomatic properties in the context of Markowitz efficient frontier, and establish a link to the indirect mean-variance utility function. This framework allows distinguishing between portfolio efficiency and allocative efficiency. Furthermore, it permits retrieving information about the revealed risk aversion of investors. The efficiency improvement possibility function thus provides a more general framework for gauging the efficiency of portfolio management using nonparametric frontier envelopment methods based on quadratic optimisation.