Kristiaan Kerstens

Cost efficiency of Belgian local governments: A comparative analysis of FDH, DEA, and econometric approaches

The purpose of this paper is to analyze the efficiency of local governments in Belgium using a broad variety of non-parametric and parametric reference technologies. Specifically, we calculate indices of cost efficiency for five different reference technologies, two non-parametric ones (Free Disposal Hull (FDH) and variable returns to scale Data Envelopment Analysis (DEA)) and three parametric frontiers (one deterministic and two stochastic). We first compare the various alternatives in terms of the efficiency-inefficiency dichotomy, we look at the distributions of the different measures, and we consider the differences in ranking. In a final stage we examine the degree to which the calculated inefficiencies can be explained by a common set of explanatory variables.

Public transit performance: What does one learn from frontier studies?

This paper provides a comprehensive survey of the literature on production and cost frontiers for public transit operators, and it evaluates the contributions of frontier analysis to the understanding of the performance of the public transport sector. The authors first succinctly contrast best practice (or frontier) and average practice specifications of technology. They also review relevant performance indicators and the methods to measure them. Next, the existing frontier studies measuring urban transit performance are systematically summarized and critically assessed. It is shown that the organization of the market, contract design, the degree and nature of the regulatory regime, and the characteristics of the network being served are all important determinants of inefficiency. However, although the frontier literature has substantially contributed to the knowledge of urban transit technologies and the determinants of performance, it is found that many important issues remain unresolved.

Explaining differences in productive efficiency: An application to Belgian municipalities

The purpose of this paper is to measure and explain variations in productive efficiency of municipal governments in Belgium. Technical efficiency is evaluated using a non-parametric method based on the Free Disposal Hull (FDH) reference technology. We first calculate input, output, and graph Farrell efficiency measures for a cross-section of all 589 Belgian municipalities. In a second stage of the analysis we explain the calculated differences in efficiency in terms of variables related to the structural characteristics of municipalities and to the institutional environment.

Technical efficiency measurement and explanation of French urban transit companies

The performance of a sample of French urban transit companies is evaluated using a broad selection of nonparametric reference technologies for two specifications of the production process. In particular, the variable returns to scale Data Envelopment Analysis (DEA) models with either strong or weak disposability in both inputs and outputs, and the Free Disposal Hull (FDH) are applied. An extensive comparison of the resulting radial output efficiency measures yields the following major methodological conclusions. First, the location of the efficiency distributions differs substantially depending on the methodology and especially on the output specification considered. The latter differences vanish if the impact of outliers is eliminated. Second, convexity has a stronger influence on the efficient-inefficient dichotomy than allowing for congestion by means of a weakly disposable DEA model. For policy purposes, these efficiency distributions are explained using a Tobit model. The findings corroborate results reported elsewhere: the relevance of ownership, the use of risk-sharing incentives in contracting, the harmful impact of subsidies, etc. Furthermore, the network structure seems to account for some differences in performance. Finally, a novelty in the urban transit context is the indirect monitoring effect of the French earmarked transportation tax.

Mean-Variance-Skewness Portfolio Performance Gauging: A General Shortage Function and Dual Approach

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.

Luenberger and Malmquist Productivity Indices: Theoretical Comparisons and Empirical Illustration

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.

Estimating returns to scale using non-parametric deterministic technologies: A new method based on goodness-of-fit

The purpose of this note is to define a new and more general method to obtain qualitative information about returns to scale for individual observations. In a second section the traditional methods developed for estimating returns to scale on nonparametric deterministic reference technologies (Data Envelopment Analysis (DEA) models) are reviewed. Section 3 provides a new and more general method that is suitable for all reference technologies. Its usefulness is illustrated by considering variations on an existing non-convex production model, known as the Free Disposal Hull (FDH). When different returns to scale assumptions are introduced into the FDH, then previous methods for determining returns to scale do no longer apply.

Short- and Long-Run Credit Constraints in French Agriculture: A Directional Distance Function Framework Using Expenditure-Constrained Profit Functions

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.

Radial and nonradial measures of technical efficiency: An empirical illustration for Belgian local governments using an FDH reference technology

This paper serves two purposes. First, we argue that radial efficiency measures are inappropriate for the Free Disposal Hull (FDH) technology, and we provide a comparative analysis of alternative nonradial measures. In particular, using information on Belgian local government expenditures and output indicators we implement various radial and nonradial measures on the FDH reference technology, and we investigate to which extent these efficiency measures imply different distributions and rankings. Second, we analyze the patterns of measured technical efficiency implied by the various indices. Specifically, we investigate whether different measures make any substantial difference for the explanation of the calculated inefficiencies. The empirical results suggest that more important differences in rankings exist between radial and nonradial measures than between different nonradial alternatives; moreover, the radial and the nonradial efficiency measures do yield a somewhat different pattern of explanation.

Negative Data in Dea: A Simple Proportional Distance Function Approach

The need to adapt Data Envelopment Analysis (DEA) and other frontier models in the context of negative data has been a rather neglected issue in the literature. A recent article in this journal proposed a variation on the directional distance function, a very general distance function that is dual to the profit function, to accommodate the occurrence of negative data. In this contribution, we define and recommend a generalised Farrell proportional distance function that can do the same job and that maintains a proportional interpretation under mild conditions.