Laurens Cherchye

The law of one price in data envelopment analysis: restricting weight flexibility across firms

The Law of One Price (LoOP) states that all firms face the same prices for their inputs and outputs in the competitive market equilibrium. This law has powerful implications for productive efficiency analysis, which have remained unexploited thus far. This paper shows how LoOP-based weight restrictions can be incorporated in Data Envelopment Analysis (DEA). Utilizing the relation between the industry level and the firm level cost efficiency measures, we propose to apply a set of input prices that is common for all firms and that maximizes cost efficiency of the industry. Our framework allows for firm-specific output weights and variable returns-to-scale, and preserves the linear programming structure of the standard DEA. We apply the proposed methodology for evaluating research efficiency of economics departments of Dutch Universities. This application shows that the methodology is computationally tractable for practical efficiency analysis, and that it helps in deepening the DEA analysis.

What Is the Economic Meaning of FDH? A Reply to Thrall

In a recent issue of the Journal of Productivity Analysis, Thrall (1999) called for abandoning the Free Disposable Hull (FDH, Deprins et al. (1984)) approximation of production possibilities as economically meaningless in comparison to the Convex Monotone Hull (CMH; Banker et al. (1984)) approximation. This strong conclusion was solely based on Thralls Principal Theorem, which essentially demonstrates that FDH can give a technically efficient classification to output-input vectors that are inefficient in terms of profit maximisation, i.e. at all non-negative price vectors there exists an alternative output-input vector that yields higher profit. In this short communication, we argue that the economic meaning of the competing empirical production sets cannot be inferred from this theorem. Specifically, we demonstrate that both empirical production sets are economically equally meaningful under the economic conditions that underlie Thralls theorem. In addition, we demonstrate that FDH can be economically more meaningful than CMH under non-trivial alternative economic conditions.

Methodological Advances in DEA: A survey and an application for the Dutch electricity sector

We survey the methodological advances in DEA over the last 25 years and discuss the necessary conditions for a sound empirical application. We hope this survey will contribute to the further dissemination of DEA, the knowledge of its relative strengths and weaknesses, and the tools currently available for exploiting its full potential. Our main points are illustrated by the case of the DEA study used by the regulatory office of the Dutch electricity sector (Dienst Toezicht Elektriciteitswet; Dte) for setting price caps.

FDH Directional Distance Functions with an Application to European Commercial Banks

Weextend Free Disposable Hull (FDH) efficiency analysis towardsthe general directional distance function framework. The profitinterpretation of directional distance functions is extendedto the non-convex FDH technologies. In addition, we derive anefficient enumerative algorithm for computing distance measuresin Free Disposable Hull (FDH) technologies, which applies tothe entire (infinitely large) family of directional distancefunctions. A simple numerical example and an application to Europeancommercial banks illustrate the algorithm.

Firm and industry level profit efficiency analysis using absolute and uniform shadow prices

We discuss the nonparametric approach to profit efficiency analysis at the firm and industry levels in the absence of complete price information. Two new insights are developed. First, we measure profit inefficiency in monetary terms using absolute shadow prices. Second, we evaluate all firms using the same input-output prices. This allows us to aggregate firm-level profit inefficiencies to the overall industry inefficiency. Besides the measurement of profit losses, the presented approach enables one to recover absolute price information from quantity data. We conduct a series of Monte Carlo simulations to study the performance of the proposed approach in controlled production environments.

Nonparametric Efficiency Estimation In Stochastic Environments

This paper develops a new nonparametric model for efficiency estimation. In contrast to Data Envelopment Analysis (DEA), it does not impose debatable production assumptions like free disposability and convexity, and it does not assume that the data are measured without error. The estimators are asymptotically unbiased and have an asymptotic variance that is comparable to that of stochastic frontier estimators (provided the latter use a correct specification of the functional form for the production relationships). In addition, the estimators can be computed using a simple enumeration algorithm.

Non-Radial Efficiency as Semi-Radial Efficiency

Existing non-radial efficiency measures have focused on solving the slack problem associated with the Debreu-Farrell notion of efficiency, sometimes at the expense of the underlying economic intuition as regards their eventual projection. In this paper we take another perspective. Building on the idea that any reference point can be obtained using a semi-radial method, we start by imposing some (desirable) properties on the reference. Specifically, we require the projection to be as close as possible to the radial one while still belonging to the efficient subset of the production technology. In a second step efficiency scores are then computed by reference to the obtained projection. These scores can be decomposed in a Debreu-Farrell component and a factor that captures the divergence between reference and evaluated input-output mixes. This second component can also be interpreted as measuring the extent to which the radial projection deviates from the closest Pareto-Koopmans efficient feasible point. This new way of measuring non-radial efficiency allows to maintain the attractive interpretation of radial measures while avoiding the slack problem.

Learning from input-output mixes in DEA: A proportional measure for slack-based efficient projections

Several Data Envelopment Analysis (DEA) models use a radial distance measure that is based on the Debreu-Farrell notion of (in)efficiency. While this measure has an attractive interpretation, its use may be problematic if slacks or zeros are present in the data. The additive DEA model can perfectly deal with these problems, but the meaning of its associated scores is less intuitive than the one attached to the radial measures. We introduce an alternative efficiency measure, based on the results of the additive model, that can be decomposed in a Debreu-Farrell component and a factor that captures differences in input-output mixes with respect to those of the best practice reference observation. On an aggregate level, this second component can be considered as an indicator of the dispersion between radial efficiency measurement and results based on the Pareto-Koopmans efficiency notion. On the individual level, the measure allows us to regard relative inefficiency as resulting from (i) a divergence of implicit cost price vectors, and (ii) a cost level that is too high, even after adjustment for the implicit cost prices. Copyright