Hervé Leleu

A LINEAR PROGRAMMING FRAMEWORK FOR FREE DISPOSAL HULL TECHNOLOGIES AND COST FUNCTIONS: PRIMAL AND DUAL MODELS

Abstract The free disposal hull (FDH) model, introduced by Deprins et al. [The Performance of Public Enterprises Concepts and Measurements, Elsevier, 1984], is based on a representation of the production technology given by observed production plans, imposing strong disposability of inputs and outputs but without the convexity assumption. In its traditional form, the FDH model assumes implicitly variable returns to scale (VRS) and the model was solved by a mixed integer linear program (MILP). The MILP structure is often used to compare the FDH model to data envelopment analysis (DEA) models although an equivalent FDH LP model exists (see Agrell and Tind [Journal of Productivity Analysis 16 (2) (2001) 129]). More recently, specific returns to scale (RTS) assumptions have been introduced in FDH models by Kerstens and Vanden Eeckaut [European Journal of Operational Research 113 (1999) 206], including non-increasing, non-decreasing, or constant returns to scale (NIRS, NDRS, and CRS, respectively). Podinovski [European Journal of Operational Research 152 (2004) 800] showed that the related technical efficiency measures can be computed by mixed integer linear programs. In this paper, the modeling proposed here goes one step further by introducing a complete LP framework to deal with all previous FDH models.

Shadow pricing of undesirable outputs in nonparametric analysis

For three decades a growing interest in the modeling of desirable and undesirable outputs has led to a theoretical and methodological debate in the nonparametric literature on production technology and efficiency. The first main discussion is about the way of modeling ‘bad/undesirables’ as inputs or outputs, or by transformation functions. The second debate concerns the implications of the weak disposability assumption in the modeling of bad outputs, in particular the possibility of assigning unexpected signs to shadow prices of bad outputs. In addition, we point out a current error in the modeling of weak disposability under a variable returns to scale technology. In this paper we introduce a hybrid model to ensure the economically meaningful jointness of good and bad outputs while constraining shadow prices of bad outputs to their expected sign. We argue that it is a sound compromise to model undesirable outputs with a meaningful primal/dual economic interpretation. Finally we propose an extension to define shadow prices for undesirable outputs following the Law of One Price (LoOP) rule.

Comparing French and US hospital technologies: a directional input distance function approach

French and US hospital technologies are compared using directional input distance functions. The aggregation properties of the directional distance function allow comparison of hospital industry-level performance as well as standard firm-level performance with regard to productive efficiency. In addition, the underlying constituents of efficiency – in the short run, congestion and technical inefficiency, and in the long run, scale inefficiency – are analysed by decomposing the overall measure. By virtue of using the directional distance function, it is also possible to obtain an estimate of a lower bound on allocative inefficiency. It is found that French and US hospitals use quite different technologies. Long run scale inefficiencies cause most of the French hospitals’ inefficiency, while short run technical inefficiency is the main source of overall productive inefficiency in the US hospitals.

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.

Mixing DEA and FDH models together

New formulations of data envelopment analysis (DEA) and free disposal hull (FDH) models in a unified linear framework are proposed. One of the main objectives of this paper is to derive meaningful economic interpretations of the dual models in the price space. In particular, we introduce a new formulation of the returns to scale assumption with a straightforward economic interpretation. This framework allows for mixing DEA and FDH models together in a more general framework.

Economic value of greenhouse gases and nitrogen surpluses: Society vs farmers’ valuation

Livestock supply must challenge the growth of final demand in the developing countries. This challenge has to take into account its ecological effects since the dairy and livestock sectors are clearly pointed out as human activities which contribute significantly to environmental deterioration. Therefore, livestock activity models have to include desirable and undesirable outputs simultaneously. Using this perspective, we implement a Data Envelopment Analysis model to evaluate shadow prices of outputs under contradictory objectives between the society and the farmers. We show that farmers are able to reduce pollution significantly if society accepts to balance farmers’ opportunity cost. Finally, we observe that initial levels of the CO2 tax implemented in European countries are in line with farmers’ valuation while the current level of the CO2 tax tends to reach the value of pollution targeted by the society.

Measuring potential gains from specialization under non-convex technologies

In this paper, the Free Coordination Hull (FCH) approach developed by Green and Cook (2004) is combined with the Free Disposal Hull (FDH) model to detect potential gains from specialization. As a non-convex approach that allows both directly observed and summed Decision Making Units to define the production technology, FCH is the relevant model for analysing optimal reallocation of activity among smaller and more specialized units. Indeed in more traditional Data Envelopment Analysis models the convexity assumption precludes the possibility of detecting potential gains from specialization and can only reveal economies of scope. Therefore non-convex technologies are required to model diseconomies of scope. On the basis of FDH and FCH technologies, an overall efficiency measure is decomposed into three components, namely: technical, size and specialization efficiencies. A 2003 database of French farms is used as an illustration. Results indicate that input inefficiency in the agricultural sector is mainly driven by a lack of specialization, which represents approximately 50% of the overall inefficiency.

The Optimality of Hospital Financing System: The Role of Physician-Manager Interactions

The ability of a prospective payment system to ensure an optimal level of both quality and cost reducing activities in the hospital industry has been stressed by Ma (Ma, J Econ Manage Strategy 8(2):93–112, 1994) whose analysis assumes that decisions about quality and costs are made by a single agent. This paper examines whether this result holds when the main decisions made within the hospital are shared between physicians (quality of treatment) and hospital managers (cost reduction). Ma’s conclusions appear to be relevant in the US context (where the hospital managers pay the whole cost of treatment). Nonetheless, when physicians partly reimburse hospitals for the treatment cost as it is the case in many European countries, we show that the ability of a prospective payment system to achieve both objectives is sensitive to the type of interaction (simultaneous, sequential or joint decision-making) between the agents. Our analysis suggests that regulation policies in the hospital sector should not be exclusively focused on the financing system but should also take the interaction between physicians and hospital managers into account.

Efficiency of purchasing and selling agents in markets with quality uncertainty: The case of illicit drug transactions

Since Akerlof’s theory of lemons, economists have viewed quality uncertainty as an informational advantage for sellers. Drawing on frontier techniques, we propose in this paper a simple method for measuring inefficiency of both sellers and buyers in markets for goods with different levels of quality. We apply a non-parametric robust double-frontier framework to the case of illicit substance markets, which suffer from imperfect information about drug quality for purchasers and to a lesser extent for sellers. We use unique data on cannabis and cocaine transactions collected in France that include information about price, quantity exchanged and purity. We find that transactional inefficiency does not really benefit either dealers or purchasers. Furthermore, information influences the performance of agents during market transactions.