HAL (Le Centre pour la Communication Scientifique Directe), 2008
Successive CAP reforms have increased the exposure of European agriculture to market forces. As a... more 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.
This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios o... more 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-varianceskewness) 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 (
This paper considers an idempotent and symmetrical algebraic structure as well as some closely re... more This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the Hadamard matrix product and we give the algebraic form of a sequence of hyperplanes passing through a finite number of points. Thereby, some standard results arising for Max-Times systems with nonnegative entries appear as a special case. The case of two sided systems is also analyzed. In addition, a notion of eigenvalue in limit is considered. It is shown that one can construct a special semi-continuous regularized polynomial to find the eigenvalues of a matrix with nonnegative entries.
Mathematical Methods of Operations Research, Sep 1, 2004
Luenberger [8] introduced the so-called benefit function that converts preferences into a numeric... more Luenberger [8] introduced the so-called benefit function that converts preferences into a numerical function that has some cardinal meaning. This measure has a number of remarkable properties and is a powerful tool in analyzing welfare issues ([10], [12], [13], [14]). This paper studies the conditions for a general function to make it a relevant welfare measure. Therefore, we introduce a large class of measures, called generalized benefit functions. The generalized benefit function is derived from the minimization of a convex function over the complement of a convex set. We show this class encompases as a special case the benefit function and is suitable to provide an alternative characterization of preferences. We also make a connection to the expenditure function through Fenchel duality theory and derive a duality result from Lemaire [7] for reverse convex optimization. Finally, we study the relationship between our class of functions and Hicksian compensated demand and we establish a link to the Slutsky matrix.
This paper introduces in production theory a large class of efficiency measures that can be deriv... more 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.
Luenberger [3, 4] introduced a function he terms the benefit function,that converts preferences i... more Luenberger [3, 4] introduced a function he terms the benefit function,that converts preferences into a numerical function and has some cardinal meaning. In this paper, we show that the benefit function enjoys many interesting properties in a game theory context. We point out that the benefit function can be adapted to compare the mixed profiles of a game. Along this line, inspired from the Luenberger's approach, we propose a dual framework and establish a characterization of Nash equilibriums in terms of the benefit function. Moreover, some criterions are provided to identify the efficient mixed strategies of a game (which differ from the Pareto efficient strategies). Finally, we go a bit further proposing some issue in comparing profiles and equilibriums of a game. This we do using the so-called Σ-subdifferential of the benefit function.
International Journal of Production Economics, Apr 1, 2000
Following FaK re and Lovell (Journal of Economic Theory 19 (1978) 150}162), we introduce a graph-... more Following FaK re and Lovell (Journal of Economic Theory 19 (1978) 150}162), we introduce a graph-type extension of the Russell measure. Moreover, we show that our new measure can be computed by using linear programming. 2000 Elsevier Science B.V. All rights reserved.
We focus on a simple framework on wheat producer behaviour in a context of price output uncertain... more We focus on a simple framework on wheat producer behaviour in a context of price output uncertainty. More precisely, we establish a relationship between ex post output price level and allocative inefficiency that allows to characterize farmers' risk preferences. Given this analysis, the connection between risk aversion and other socioeconomic variables (such as degree of output specialisation, total asset, debts, farmer's age…) can furthermore empirically be explored. This relationship is empirically tested on an unbalanced panel including about 650 wheat producers located in the French Department of Meuse over 1992-2003.
We have two goals we wish to accomplish in this article. The first is the development of a framew... more We have two goals we wish to accomplish in this article. The first is the development of a framework for measuring efficiency in the full input-output space. This approach introduces a graph-type extension of the Farrell measure of technical efficiency. The second is the introduction of a weighting scheme for inputs and outputs, taking account of the particularity of the market summarized by input and output prices.
The purpose of this paper is to establish a topological relation between several classes of known... more The purpose of this paper is to establish a topological relation between several classes of known generalized convex models extending the approach proposed by Banker, Charnes and Cooper [6]. Using some basic algebraic convex structures proposed by Avriel [4] and Ben-Tal [9] we analyze the Painlevé-Kuratowski limit of the CES-CET and Alpha-returns to scale models. It is shown that their topological limits yield the B-convex and Cobb-Douglas production models. Along this line some semi-lattice production models satisfying an α-returns to scale assumption are proposed.
In a recent article, Briec, Kerstens and Vanden Eeckaut (2(t(t4) develop a series of nonparametri... more In a recent article, Briec, Kerstens and Vanden Eeckaut (2(t(t4) 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 a.nalytically 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.
This paper proposes a nonparametric efficiency measurement approach for the static portfolio sele... more This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-varianceskewness 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.
HAL (Le Centre pour la Communication Scientifique Directe), 2008
Successive CAP reforms have increased the exposure of European agriculture to market forces. As a... more 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.
This paper proposes a pragmatic, discrete time indicator to gauge the performance of portfolios o... more 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-varianceskewness) 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 (
This paper considers an idempotent and symmetrical algebraic structure as well as some closely re... more This paper considers an idempotent and symmetrical algebraic structure as well as some closely related concept. A special notion of determinant is introduced and a Cramer formula is derived for a class of limit systems derived from the Hadamard matrix product and we give the algebraic form of a sequence of hyperplanes passing through a finite number of points. Thereby, some standard results arising for Max-Times systems with nonnegative entries appear as a special case. The case of two sided systems is also analyzed. In addition, a notion of eigenvalue in limit is considered. It is shown that one can construct a special semi-continuous regularized polynomial to find the eigenvalues of a matrix with nonnegative entries.
Mathematical Methods of Operations Research, Sep 1, 2004
Luenberger [8] introduced the so-called benefit function that converts preferences into a numeric... more Luenberger [8] introduced the so-called benefit function that converts preferences into a numerical function that has some cardinal meaning. This measure has a number of remarkable properties and is a powerful tool in analyzing welfare issues ([10], [12], [13], [14]). This paper studies the conditions for a general function to make it a relevant welfare measure. Therefore, we introduce a large class of measures, called generalized benefit functions. The generalized benefit function is derived from the minimization of a convex function over the complement of a convex set. We show this class encompases as a special case the benefit function and is suitable to provide an alternative characterization of preferences. We also make a connection to the expenditure function through Fenchel duality theory and derive a duality result from Lemaire [7] for reverse convex optimization. Finally, we study the relationship between our class of functions and Hicksian compensated demand and we establish a link to the Slutsky matrix.
This paper introduces in production theory a large class of efficiency measures that can be deriv... more 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.
Luenberger [3, 4] introduced a function he terms the benefit function,that converts preferences i... more Luenberger [3, 4] introduced a function he terms the benefit function,that converts preferences into a numerical function and has some cardinal meaning. In this paper, we show that the benefit function enjoys many interesting properties in a game theory context. We point out that the benefit function can be adapted to compare the mixed profiles of a game. Along this line, inspired from the Luenberger's approach, we propose a dual framework and establish a characterization of Nash equilibriums in terms of the benefit function. Moreover, some criterions are provided to identify the efficient mixed strategies of a game (which differ from the Pareto efficient strategies). Finally, we go a bit further proposing some issue in comparing profiles and equilibriums of a game. This we do using the so-called Σ-subdifferential of the benefit function.
International Journal of Production Economics, Apr 1, 2000
Following FaK re and Lovell (Journal of Economic Theory 19 (1978) 150}162), we introduce a graph-... more Following FaK re and Lovell (Journal of Economic Theory 19 (1978) 150}162), we introduce a graph-type extension of the Russell measure. Moreover, we show that our new measure can be computed by using linear programming. 2000 Elsevier Science B.V. All rights reserved.
We focus on a simple framework on wheat producer behaviour in a context of price output uncertain... more We focus on a simple framework on wheat producer behaviour in a context of price output uncertainty. More precisely, we establish a relationship between ex post output price level and allocative inefficiency that allows to characterize farmers' risk preferences. Given this analysis, the connection between risk aversion and other socioeconomic variables (such as degree of output specialisation, total asset, debts, farmer's age…) can furthermore empirically be explored. This relationship is empirically tested on an unbalanced panel including about 650 wheat producers located in the French Department of Meuse over 1992-2003.
We have two goals we wish to accomplish in this article. The first is the development of a framew... more We have two goals we wish to accomplish in this article. The first is the development of a framework for measuring efficiency in the full input-output space. This approach introduces a graph-type extension of the Farrell measure of technical efficiency. The second is the introduction of a weighting scheme for inputs and outputs, taking account of the particularity of the market summarized by input and output prices.
The purpose of this paper is to establish a topological relation between several classes of known... more The purpose of this paper is to establish a topological relation between several classes of known generalized convex models extending the approach proposed by Banker, Charnes and Cooper [6]. Using some basic algebraic convex structures proposed by Avriel [4] and Ben-Tal [9] we analyze the Painlevé-Kuratowski limit of the CES-CET and Alpha-returns to scale models. It is shown that their topological limits yield the B-convex and Cobb-Douglas production models. Along this line some semi-lattice production models satisfying an α-returns to scale assumption are proposed.
In a recent article, Briec, Kerstens and Vanden Eeckaut (2(t(t4) develop a series of nonparametri... more In a recent article, Briec, Kerstens and Vanden Eeckaut (2(t(t4) 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 a.nalytically 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.
This paper proposes a nonparametric efficiency measurement approach for the static portfolio sele... more This paper proposes a nonparametric efficiency measurement approach for the static portfolio selection problem in mean-varianceskewness 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.
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Papers by Walter Briec