Estimating Production Uncertainty in Stochastic Frontier Production Function Models

One of the main purposes of the frontier literature is to estimate inefficiency. Given this objective, it is unfortunate that the issue of estimating firm-specific inefficiency in cross sectional context has not received much attention. To estimate firm-specific (technical) inefficiency, the standard procedure is to use the mean of the inefficiency term conditional on the entire composed error as suggested by Jondrow, Lovell, Materov and Schmidt (1982). This conditional mean could be viewed as the average loss of output (return). It is also quite natural to consider the conditional variance which could provide a measure of production uncertainty or risk. Once we have the conditional mean and variance, we can report standard errors and construct confidence intervals for firm level technical inefficiency. Moreover, we can also perform hypothesis tests. We postulate that when a firm attempts to move towards the frontier it not only increases its efficiency, but it also reduces its production uncertainty and this will lead to shorter confidence intervals. Analytical expressions for production uncertainty under different distributional assumptions are provided, and it is shown that the technical inefficiency as defined by Jondrow et al. (1982) and the production uncertainty are monotonic functions of the entire composed error term. It is very interesting to note that this monotonicity result is valid under different distributional assumptions of the inefficiency term. Furthermore, some alternative measures of production uncertainty are also proposed, and the concept of production uncertainty is generalized to the panel data models. Finally, our theoretical results are illustrated with an empirical example.     

Iterated bootstrap with applications to frontier models

The iterated bootstrap may be used to estimate errors which arise from a single pass of the bootstrap and thereby to correct for them. Here the iteration is employed to correct for coverage probability of confidence intervals obtained by a percentile method in the context of production frontier estimation with panel data. The parameter of interest is the maximum of the intercepts in a fixed firm effect model. The bootstrap distribution estimators are consistent if and only if there are no ties for this maximum. In the regular case (no ties), poor distribution estimators can result when the second largest intercept is close to the maximum. The iterated bootstrap is thus suggested to improve the accuracy of the obtained distributions. The result is illustrated in the analysis of labor efficiency of railway companies.This work was supported in part by grant No. 26 from the program Pôle d'attraction interuniversitaire-Deuxième phase to CORE and by the contract Projet d'Actions de Recherche Concertées of the Belgian governement (PARC) to the Institute of Statistics, Université Catholique de Louvain. The first author was partly financed by the Institut de Mathématiques Appliquées, Université Catholique de Louvain.     

Characterizing Managerial Skill and Technical Efficiency in a Fishery

Researchers have long recognized that entrepreneurial or managerial skill is a major determinant of productivity or reason why production among firms varies. Yet, except for a few studies, differences in productivity and output levels are usually attributed to plant configuration or scale. More important, there appears to have been few attempts to relate technical efficiency to managerial skill. Utilizing a stochastic production frontier, we examine the relationship between technical efficiency and characteristics of skill such as experience and education in a fishery. Although we can not determine threshold or essential levels of experience and education, substitution possibilities are found to exist between years of experience and education levels. Additional analysis of efficiency for two captains of the same background and experience reveals that additional characteristics need to be considered in the examination of skipper skill or the good-captain hypothesis.     

RAM: A Range Adjusted Measure of Inefficiency for Use with Additive Models,and Relations to Other Models and Measures in DEA

Generalized Efficiency Measures (GEMS) for use in DEA are developed and analyzed in a context of differing models where they might be employed. The additive model of DEA is accorded a central role and developed in association with a new measure of efficiency referred to as RAM (Range Adjusted Measure). The need for separately treating input oriented and output oriented approaches to efficient measurement is eliminated because additive models effect their evaluations by maximizing distance from the efficient frontier (in ₁, or weighted ₁, measure) and thereby simultaneously maximize outputs and minimize inputs. Contacts with other models and approaches are maintained with theorems and accompanying proofs to ensure the validity of the thus identified relations. New criteria are supplied, both managerial and mathematical, for evaluating proposed measures. The concept of approximating models is used to further extend these possibilities. The focus of the paper is on the physical aspects of performance involved in technical and mix inefficiencies. However, an Appendix shows how overall, allocative and technical inefficiencies may be incorporated in additive models.     

Maximal asymptotic power and efficiency of two-sample tests based on generalized U-Statistics

In this article a systematic study is given of the asymptotic behavior of two-sample tests based on U-Statistics with arbitrary antisymmetric kernels . Besides the investigation under the hypothesis and under fixed alternatives we determine the local power as a function of as well as its maximizing value _opt. Moreover formulas for the asymptotic relative efficiency ARE(₂,₁) of the ₂-test with respect to the ₁-test are derived. It turns out that _opt also yields the most efficient test in the sense that ARE(_opt,)1 for all (admissible) kernels .     

Frontier production functions,technical efficiency and panel data: With application to paddy farmers in India

Frontier production functions are important for the prediction of technical efficiencies of individual firms in an industry. A stochastic frontier production function model for panel data is presented, for which the firm effects are an exponential function of time. The best predictor for the technical efficiency of an individual firm at a particular time period is presented for this time-varying model. An empirical example is presented using agricultural data for paddy farmers in a village in India.This article is a revision of the Invited Paper presented by the senior author in the Productivity and Efficiency Analysis sessions at the ORSA/TIMS 30th Joint National Meeting, Philadelphia, Pennsylvania, 29–31 October 1990. We have appreciated comments from Martin Beck, Phil Dawson, Knox Lovell and three anonymous referees. We gratefully acknowledge the International Crops Research Institute for the Semi-Arid Tropics (ICRISAT) for making available to us the data obtained from the Village Level Studies in India.     

Detecting Outliers in Frontier Models: A Simple Approach

In frontier analysis, most of the nonparametric approaches (DEA, FDH) are based on envelopment ideas which suppose that with probability one, all the observed units belong to the attainable set. In these deterministic frontier models, statistical theory is now mostly available (Simar and Wilson, 2000a). In the presence of super-efficient outliers, envelopment estimators could behave dramatically since they are very sensitive to extreme observations. Some recent results from Cazals et al. (2002) on robust nonparametric frontier estimators may be used in order to detect outliers by defining a new DEA/FDH deterministic type estimator which does not envelop all the data points and so is more robust to extreme data points. In this paper, we summarize the main results of Cazals et al. (2002) and we show how this tool can be used for detecting outliers when using the classical DEA/FDH estimators or any parametric techniques. We propose a methodology implementing the tool and we illustrate through some numerical examples with simulated and real data. The method should be used in a first step, as an exploratory data analysis, before using any frontier estimation.     

An Efficiency Comparison of European Banking Systems Operating under Different Environmental Conditions

The paper investigates the operating efficiency differences of a sample of commercial banks across 10 European countries. First, the paper analyzes the technical efficiency of each country sample following the basic Data Envelopment Analysis (DEA) model incorporating only banking variables. Then, a complete DEA model is introduced, incorporating environmental factors together with the banking variables of the basic model. The comparison between the two models shows that country-specific environmental conditions exercise a strong influence over the behavior of each country's banking industry.     

Bootstrapping Confidence Intervals for Linear Programming Efficiency Scores: With an Illustration Using Italian Banking Data

This article suggests a method for introducing a stochastic element into Farrell measures of technical efficiency as calculated via linear programming techniques. Specifically, a bootstrap of the original efficiency scores is performed to derive confidence intervals and a measure of bias for the scores. The bootstrap generates these measures of statistical precision for the nonstochastic efficiency measures by using computational power to derive empirical distributions for the efficiency measures.     

Effective participative decision making: A joint responsibility for success

Much of the current research on participative decision making focuses on the increasing need for broad-based decision-making systems, on the different outcomes associated with different forms of participation, or on the problems associated with poorly managed participative decision-making systems. This article considers the responsibilities of employees who participate in organizational decision making and the responsibilities of employers who expect to share decision-making tasks. A Bill of Responsibilities for Employees and a Bill of Responsibilities for Employers are presented. Pitfalls associated with neglecting these responsibilities are discussed.     

A numerical representation of semiorders on a countable set

Let be a semiorder on a countable setX and letx⁰ y if and only if either there existsx withxxy or there existsx withxxy. Then ⁰ is a preference relation with transitive indifference, which can be represented by a utility functionf of the usual sort. It is well known that is represented by a pair of real-valued functionsu, v, in the sense thatxy if and only ifu(x)>v(y). We prove that there exists a pair of functionsu, v, representing , such thatu+v is the utility function which represents in the usual sense. Moreover it is easily seen that, for such a pair of functionsu, v, we havex⁰ y if and only if eitheru(x)>u(y) or (u(x)=u(y) andv(x)>v(y)).

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Sommario Consideriamo unsemiordine su un insiemeX numerabile e poniamox⁰ y se e solo se esistex tale chexxy, oppure esistex tale chexxy. In questo caso ⁰ è unordine debole, che può essere rappresentato da una funzione di utilitàf nel senso usuale. D'altra parte è rappresentato da una coppia di funzioniu, v, nel senso chexy se e solo seu(x)>v(y). In questo lavoro si prova che ammette una rappresentazioneu, v tale chex⁰ y se e solo seu(x)+v(x)>u(y)+v(y). Si dimostra altresì che, con riguardo ad una siffatta rappresentazioneu, v di , riescex⁰ y se e solo seu(x)>u(y) oppure (u(x)=u(y) ed anchev(x)>v(y)).

     

ICT Investment, Productivity and Efficiency: Evidence at Firm Level Using a Stochastic Frontier Approach

We analyze the determinants of ICT investment and the impact of information technology on productivity and efficiency on a representative sample of small and medium sized Italian firms. In order to test the most relevant theoretical predictions from the ICT literature we evaluate the impact of investment in software, hardware and telecommunications of these firms on a series of intermediate variables and on productivity. Among intermediate variables we consider the demand for skilled workers, the introduction of new products and processes and the rate of capacity utilization. Among productivity measures we include total factor productivity, the productivity of labor, and the distance from the best practice by using a stochastic frontier approach. Our results show that the effect of ICT investment on firm efficiency can be more clearly detected at firm level data by decomposing it into software and telecommunications investment. We find that telecommunications investment positively affects the creation of new products and processes, while software investment increases the demand for skilled workers, average labor productivity and proximity to the optimal production frontier. We interpret these results by arguing that ICT investment modifies the trade-off between scale and scope economies. While software investment increases the scale of firm operations, telecommunications investment creates a flexibility option easing the switch from a Fordist to a flexible network productive model in which products and processes are more frequently adapted to satisfy consumers taste for variety.     

A dual approach for matrix-derivatives

Summary A dual approach for matrix by matrix derivatives is proposed, based on the work ofBalestra and the idea ofDwyer/MacPhail. The two derivative concepts are calledB-type derivative for the form B/A = (b _kl /A), because it was studied fully inBalestra, andA-type derivative for the form B/ /A = (B/a _ij ). Both derivative concepts are linked by permutation matrices, which also reveil the duality aspect more clearly, and can be transformed to each other very easily. The derivatives are applied to least squares estimates and posterior means in the general regression model and the seemingly unrelated regression (SUR)-system, introduced byZellner. The derivatives with respect to the covariance matrix is related to the local sensitivity concept ofLeamer [1978], while the derivatives with respect to the data-matrix, also called local resistance, is linked with the robustness concept ofTukey. The newly definedB-derivative enables an easier interpretation of the results.     

One-Step and Two-Step Estimation of the Effects of Exogenous Variables on Technical Efficiency Levels

Consider a stochastic frontier model with one-sided inefficiency u, and suppose that the scale of u depends on some variables (firm characteristics) z. A one-step model specifies both the stochastic frontier and the way in which u depends on z, and can be estimated in a single step, for example by maximum likelihood. This is in contrast to a two-step procedure, where the first step is to estimate a standard stochastic frontier model, and the second step is to estimate the relationship between (estimated) u and z.In this paper we propose a class of one-step models based on the scaling property that u equals a function of z times a one-sided error u ^* whose distribution does not depend on z. We explain theoretically why two-step procedures are biased, and we present Monte Carlo evidence showing that the bias can be very severe. This evidence argues strongly for one-step models whenever one is interested in the effects of firm characteristics on efficiency levels.     

Continuous representations of interval orders based on induced preorders

Conditions are given for the existence of a pair of continuous real valued functions (u, v) representing an interval order on a topological space (X, ), in the sense that [xy if and only ifu(x)].I am deeply indepted to Professor Alain Chateauneuf for many valuable suggestions.     

Theorems on the decomposition of a large nonlinear convex separable economic system in the dual direction

Large mathematical programming problems often arise as the result of the economic planning process. When such a problem is not only large, but nonlinear as well, there is a need to make it more manageable by breaking it down into several smaller and more easily handled subproblems. The subproblems are solved separately with the coordination activity carried out by a master problem. A decomposition method can be seen as a dialogue between the master problem and the subproblems, where the flow of information back and forth between the former and the latters results in a series of approximations converging to the solution of the overall problem. Such a decomposition method was elaborated by Benders [1] for linear programmes and generalized to nonlinear convex separable programmes by Kronsjö [4] and by Geoffrion [3]. After considering our basic nonlinear programming problem from a two-stage minimization point of view, we review the Kronsjö nonlinear decomposition algorithm. Then we establish some properties of a function related to this algorithm.I am grateful to Professor T.O.M. Kronsjö for inspiring this work and giving valuable help.     

Marginal Rates and Two-dimensional Level Curves in DEA

Of great importance to management, the computation of trade-offs presents particular difficulties within DEA since the piecewise linear nature of the envelopment surfaces does not allow for unique derivatives at every point. We present a comprehensive framework for analyzing marginal rates, and directional derivatives in general, on DEA frontiers. A useful characterization of these derivatives at given points can be provided in terms of the ranges they can take; equivalently, the bounds of these ranges correspond to derivatives to the rightand to the left at these points. We present two approaches for their computation: first, the dual equivalents calculation of minimum and maximum multiplier ratios / finite differences, and then a modified simplex tableau method. The simplex tableau method provides a more general application of the method introduced by Hackman et al. (1994) to generate any two-dimensional section of the isoquant and is a practical tool to generate level plots of the frontier. By giving a complete picture of trade-offs and allowing a better visualization of high dimensional production possibility sets, these tools can be very useful for managerial applications.     

Projections Onto Efficient Frontiers: Theoretical and Computational Extensions to DEA

Data Envelopment Analysis (DEA) has been widely studied in the literature since its inception in 1978. The methodology behind the classical DEA, the oriented method, is to hold inputs (outputs) constant and to determine how much of an improvement in the output (input) dimensions is necessary in order to become efficient. This paper extends this methodology in two substantive ways. First, a method is developed that determines the least-norm projection from an inefficient DMU to the efficient frontier in both the input and output space simultaneously, and second, introduces the notion of the observable frontier and its subsequent projection. The observable frontier is the portion of the frontier that has been experienced by other DMUs (or convex combinations of such) and thus, the projection onto this portion of the frontier guarantees a recommendation that has already been demonstrated by an existing DMU or a convex combination of existing DMUs. A numerical example is used to illustrate the importance of these two methodological extensions.     

Wrongful termination: Balancing employer and employee rights—A summary with recommendations

The employer's right to terminate for any cause has been seriously constrained. Recent court rulings and discrimination legislation make employee termination a hazardous undertaking. The prevailing logic is based on the concept of just cause. This concept attempts to balance employer, employee, and society's rights and fit action to the situation. Recommended management action involves little more than careful management of human resources as practiced by well managed firms for many years.     

Hypocrisy pay

Emotional labor—putting on an act asrequired explicitly orimplicitly in work situations-is very often psychologically, emotionally, and mentally damaging to most employees. As for soldiers in wartime who receive combat pay, it is suggested that such employees be specially compensated for their emotional labor with hypocrisy pay. Another solution is to select only those who are immune to such stress for jobs involving emotional labor—an ideal that probably cannot be achieved in all cases. Another assessment is that such special compensation is unwarranted.