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We introduce well-known microeconomics productivity measures in Solow models in discrete time or continuous time by adopting a Luenberger-type approach. In each framework, we derive the productivity indicators and the dynamical paths. Firstly, we show that the expression of the productivity indicators are similar to the well-known Solow residuals, allowing us to make ananalogy between a firm's behaviour in a microeconomic setting and a country's behaviour in a macroeconomic setting. Secondly, we demonstrate that the properties of the paths are similar in both frameworks Postprint

International audience; The purpose of this contribution is to provide an overview of developments in nonconvex production technologies and economic value functions, with special attention to the cost function. Apart from a somewhat selective review of theoretical issues, the emphasis is on whether the assumption of convexity makes a difference in practice. Anticipating our conclusion, we argue that traditional convex empirical results differ on average rather markedly from alternative nonconvex ones. This should make the discipline reconsider its traditional relationship with convexity in both theoretical and applied production analysis.

International audience; This paper extends to production theory some notions of compensated and equivalent variation analyzed in Luenberger (Econ Theory 7:445-462, 1996) in a consumer context. Along this line the Luenberger-Hicks-Moorsteen productivity indicator introduced in Briec and Kerstens (Econ Theory 23:925-939, 2004) is derived from these concepts for multi-output production technologies. The dual properties of this productivity indicator are analyzed and an aggregate indicator is introduced inspired from the resource function proposed in Luenberger (1996). A connection to a suitable Slutsky matrix is established.

International audience; From a theoretical point of view, -returns to scale is a relevant alternative to traditional DEA models for estimating production technologies under global returns to scale assumptions such as strictly increasing or strictly decreasing returns to scale. However, from a methodological and empirical point of view, a remaining question is the estimation of . This contribution proposes an effective methodology to estimate an optimal value of based upon a goodness-of-fit strategy. A global method using a grid search is presented first. Second, for generalised FDH technologies, a minimum extrapolation principle is developed to estimate directly the optimal -returns from a linear program. An illustration on 63 US industries over the period 1987-2012 shows the relevancy of our approach.

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. ispartof: Applied Economics vol:50 issue:27 pages:2938-2956 status: published

The concept of efficiency in groups postulates that a coalition of firms has to record a smaller distance toward the aggregate technology frontier compared with the sum of individual distances. Efficiency analysis (either allocative or technical) is defined with respect to cooperative firm game in order to provide operational distance functions, the so-called pseudo-distance functions. These pseudo-distances belong to the core interior of the allocative firm game, in other terms, any given firm coalition may always improve its allocative efficiency. We prove that such a result is impossible for technical efficiency, i.e., the technical efficiency cannot increase for all possible coalitions.

We introduce the special issue in memory of our late colleague Bernard Philippe of the University of Perpignan. We would like to acknowledge Bernard for the many things he gave us before leaving: scientific rigor, the importance of teaching, open-mindedness, and generosity.

In a recent paper Ramos and Silber (2005) used techniques developed in efficiency analysis to obtain estimates of human development obtained on the basis of Sen (1985) and Narayan et al. (2000) capability approach. In particular they propose to measure standard achievement and well being indexes using a distance function approach. In this paper, it is shown that the ratio based of well-being and standard achievement indexes form the Hicks–Moorsteen index introduced by Bjurek (1996). Along this line, an additive form of the standard achievement and well-being indexes is proposed. In particular, the paper focusses on the case of social inputs. Axiomatic and dual properties are established and some parametric and nonparametric models are proposed.

This paper analyses productivity growth and the nature of technical change in a sample of Portuguese hydroelectric generating plants over the period 2001 to 2008. In a first step, we employ the Luenberger productivity indicator to estimate and decompose productivity change. A Malmquist productivity index is also used for a comparative purpose. The results paint a picture of mixed productivity performance in the Portuguese energy sector. The first decomposition underlines that, in average, the productivity variation is explained by the technological change. Then, in a second step, we analyse the nature of this technical change by using the recent concept of parallel neutrality (Briec et al., 2006). We observe a global shift in the best practice frontier as well as in the evidence of input bias in technical change.

Morey and Morey [1] have developed an approach for gauging portfolio efficiencies in the context of the Markowitz model. Following some recent contributions [2,3], this paper analyzes the axiomatic properties of distance functions extending an earlier approach proposed by Morey and Morey. The paper also focusses on the hyperbolic measure and the McFadden gauge function [4]. Among other things, overall, allocative and portfolio improvements possibilities (in term of return expansion or/and risk contraction) based upon the indirect mean-variance utility function are analyzed. Along this line, duality results are established in each case. This enables us to calculate the degree of risk aversion maximizing the investor indirect mean-variance utility function in either return expansion or risk contraction. An empirical illustration is provided and reveal ranking of preferred risks aversion for some “CAC40” assets.

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 Hicks-Moorsteen productivity indices. In a difierence perspective, the Luenberger and LuenbergerHicks-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 difierence-based counterpart) is well-deflned and satisfles the determinateness property, since the underlying distance functions are always feasible.

This contribution provides a way to define and compute a tangency notion of economic capacity based upon the relation between the various directional distance functions and the profit and cost functions using non-parametric technologies. A new result relating profit and cost function-based tangency capacity notions is established. ispartof: Economic Modelling vol:27 issue:5 pages:1156-1166 nrpages: 31 status: published

This paper proposes a procedure for analysing tourism productivity. The procedure is based on the Luenberger productivity indicator for estimating and decomposing productivity change into efficiency change and technological change. The authors expand the procedure and further decompose the process of technological change to study the sources of bias within it. Therefore, a clearer and more enlightening view emerges of the productivity of travel agencies. The Portuguese travel agency sector is used as an application. Some managerial implications are developed.

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 sufficient conditions for global optimality. It also forms a natural basis for developing tests on the influence of additional moments. Furthermore, a link is made with an approximation of an arbitrary order of a general indirect utility function. This non-parametric efficiency measurement framework permits to differentiate mainly between portfolio efficiency and allocative efficiency. Finally, information can, in principle, be inferred about the revealed risk aversion, prudence, temperance and other higher-order risk characteristics of investors.

This paper exams the concept of Pollution-generating Technologies (PgT). The main goal of this methodological contribution is to reveal any PgT in production processes compatible with a minimal set of assumptions. We model PgT using a congestion approach of the output set relaxing strong disposability assumption. To this end, we define the B-disposal assumption, that is a kind of limited strong disposability. The B-disposal assumption reflects cost disposability assumption with respect to the undesirable outputs. This disposability assumption leads to a new duality result between an output distance function and the revenue function with possibly negative shadow prices. A sample of 13 representative French airports is considered over the period 2007-2011, in order to implement the new B-disposal assumption on convex non-parametric technologies.

Cooperation between firms can never improve the technical efficiency of any coalition of firms. This standard result of the productivity measurement literature is based on the directional distance function computed on firm groups. Directional distance functions are usually defined on the standard sum of input/output vectors.In this paper, the aggregation of input/output vectors is generalized thanks to an isomorphism in order to capture three results: the cooperation improves technical efficiency ; the cooperation reduces technical efficiency ; and finally the cooperation between firms yields no variation of technical efficiency, i.e. , the distance function is quasi linear.The improvement of technical efficiency is shown to be compatible with semilattice technologies. In this case, the firms merge according to their inputs only because constraints are imposed on outputs, and conversely, they may merge according to the outputs they can produce because some limitations are imposed on the use of inputs.

This paper starts from Fukuyama and Weber's (2004) work on testing for inverse homotheticity to show that the equality of the output gain function and the Zieschang output gain function is not equivalent to inverse homotheticity. Hence, testing for the equality of these gain functions cannot prove that a technology is inverse homothetic. Moreover, it is established that the gain functions are equal if and only if the direct and indirect isoquant and the corresponding efficient set are equal, which does not depend on inverse homotheticity.

The shortage function, an important tool in production theory, measures potential increases in outputs and decreases in inputs for a given direction g at a given date. To develop a temporal version of technical efficiency measurement, we introduce the concept of a temporal shortage function. This temporal efficiency measure is easily computed using linear programming. We also establish a duality result stating that the temporal profit function and the temporal shortage function are dual to one another. This result has two consequences. First, one can derive a shadow price path via the shadow prices of the temporal shortage function. Second, transposing the classic Farrell inefficiency decomposition, temporal profit efficiency is decomposed into temporal technical and temporal allocative efficiency components. Finally, in line with the recent literature on aggregation over firms, this contribution treats the possibilities and limits of the aggregation of efficiency measures over time.

International audience; This empirical application investigates the eventual presence of credit constraints using a panel of French farmers. The credit-constrained profit maximization model proposed by Fare, 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.; A l'instar de Fare, Grosskopf, et Lee (1990), cet article a pour objet de révéler l'existence de contraintes de financement et d'en évaluer l'impact sur les performances économiques d'exploitations agricoles. Nous prolongeons néanmoins leurs travaux sur plusieurs points. Dans un premier temps, nous reformulons leur modèle en termes de fonctions de distance directionnelle qui permet la dualité avec la fonction de profit. Dans un deuxième temps, nous modélisons les contraintes financières de court terme et de long terme. Enfin, nous considérons les contraintes financières retardées d'une période afin de prendre en compte le décalage qui existe entre les décisions en termes de production et les récoltes effectives. Nos résultats montrent l'importance des contraintes de crédit et d'investissement sur le profit dans un échantillon d'agriculteurs français au cours des années 1994 à 2001. De plus, nous montrons que les exploitations non contraintes financièrement sont de plus grande taille, plus efficace et semblent tirer parti d'un cercle vertueux où l'accès aux marchés financiers permet de réaliser de meilleurs choix productifs.

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.

CNRS 3, FNEGE 3, HCERES B; International audience; The shortage function has recently been introduced in portfolio selection theory for measuring efficiency. In this paper we focuss on the case of shortselling. We show that, in such a case, the shortage function can be computed in closed form. Some issues concerning duality are also analyzed. We also analyze the case of a riskless asset.

The purpose of this short article is to simplify goodness-of-fit methods to obtain qualitative information about returns to scale for individual observations. Traditional and new goodness-of-fit methods developed for estimating returns to scale on nonparametric deterministic reference technologies are reviewed. Using composition rules for technologies with specific returns to scale assumptions, we show how these goodness-of-fit methods can be simplified in the case of convex technologies (Data Envelopment Analysis (DEA) models).

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. A numerical example illustrates this algorithm.

Cecchetti et al. (2006) develop a method for allocating macroeconomic performance changes among the structure of the economy, variability of supply shocks and monetary policy. We propose a dual approach of their method by borrowing well-known tools from production theory, namely the Farrell measure and the Malmquist index. Following Färe et al (1994) we propose a decomposition of the efficiency of monetary policy. It is shown that the global efficiency changes can be rewritten as the product of the changes in macroeconomic performance, minimum quadratic loss, and efficiency frontier.

Production frontiers for the manufacturing sector are estimated to determine a 'country specific' catching-up process of Total Factor Productivity (TFP). TFP gains were aimed at assessing the manufacturing industry's productive performances for 14 Organization for Economic Cooperation and Development (OECD) countries over the period 1970 to 2001. Our TFP measure does not assume technical or allocative efficiency which are inherent drawbacks of usual TFP indices. We show that catching-up processes can be very different between sub-periods and across countries. A significant catching-up process was in progress in the manufacturing sector between 1970 and 1986, then it overturned over the period 1987 to 2001. During the first sub-period, the speed of technological catching-up of the Eurozone countries was definitely higher than those of the other European or OECD nations, whereas the divergence noted in the second sub-period had the same order of magnitude amongst the three groups.

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 (Fama and French, 1996, 1997) using US monthly data from January 1931 to August 2007. © 2009 Elsevier B.V. ispartof: JOURNAL OF BANKING & FINANCE vol:34 issue:8 pages:1899-1910 status: published

This article extends the analysis of multi-horizon mean-variance portfolio analysis in the Morey and Morey [Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking. Omega 1999;27:241–58] article in several ways. First, instead of either proportionally contracting risk dimensions or proportionally expanding return dimensions, a more general efficiency measure simultaneously attempts to reduce risk and to expand return over all time periods. Second, a duality relation is established between this generalized multi-horizon efficiency measure and an indirect mean-variance utility function, underscoring the natural interpretation of this generalized efficiency measure in terms of investor's preferences. Furthermore, the need to properly apply time discounting in multi-horizon mean-variance portfolio problems is argued for. An empirical illustration based on the original mutual fund data set in Morey and Morey [Mutual fund performance appraisals: a multi-horizon perspective with endogenous benchmarking. Omega 1999;27:241–58] is added to contrast the new and the original approaches.

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.

International audience; This study re-examines the catching-up hypothesis at the industry level across the main OECD countries, using panel data econometric models involving technological gap indicators calculated with a nonparametric distance function suggested by Färe et al. [Färe, R.S., Grosskopf, M.N., Norris, M., Xhang, Z., 1994. Productivity growth, technical progress, and efficiency change in industrialized countries. American Economic Review 84, 66–83]. The results show that there is statistical evidence of a catching-up process at the industry level. Moreover, both tradables and nontradables sectors exhibit catching-up effects and technology adoption from abroad. This result complements the findings by Bernard and Jones [Bernard, A.B., Jones, C.I., 1996a. Comparing apples to oranges: productivity convergence and measurement across industries and countries. American Economic Review 86(5), 1216–1238., Bernard, A.B., Jones, C.I., 1996b. Productivity across industries and countries: Time series theory and evidence. Review Of Economics and Statistics 78, 135–146], Gouyette and Perelman [Gouyette, C., Perelman, S., 1997. Productivity convergence in OECD services industries. Structural Change and Economic Dynamics 8, 279–295] and Hansson and Henrekson [Hansson, P., Henrekson, M., 1997. Catching up, social capability, government size and economic growth, in V. Bergström, eds, Government and Growth, Oxford: Clarendon Press, 61–126] that there is no (or even a slow) catching-up effect in the manufacturing sector. Moreover, social capability indicators evaluated for each country show that “Non-European” and “Central European” tradables sectors have a rather similar degree of inefficiency while “North European” countries are less efficient for both tradables and non-tradables. Lastly, both the cross country and the cross sectors dispersions of inefficiency levels are smaller for tradables sectors than for non-tradables.

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.

http://www.blackwell-synergy.com/toc/boer/55/4; International audience; This contribution establishes, from a theoretical viewpoint, the relations between the Malmquist productivity indices, that measure in either input or output orientations, and the Luenberger productivity indices, that can simultaneously contract inputs and expand outputs, but that can also measure in either input or output orientations. The main result is that a Malmquist productivity index overestimates productivity changes, since it provides productivity measures that are nearly twice those given by the Luenberger productivity index looking for simultaneous contractions of inputs and expansions of outputs. This relationship is empirically illustrated using data from 20 OECD countries over the 1974–97 period.

This paper aims at developing a new method for measuring efficiency with respect to a suitable frontier in portfolio management, based on a stochastic-frontier approach. This yields an index of performance of the managed portfolio with respect to the efficient frontier. The method provides a suitable endogenous benchmark for both diversified stock portfolios or investment funds.