Trade restrictiveness and efficiency*

This article proposes a trade restrictiveness quantity index (TRQI) to measure the welfare impact of trade restrictions based on a distance functions approach. The TRQI embodies two Farrell measures of efficiency—respectively for producers and consumers—that can be computed using standard efficiency measurement techniques. The TRQI can also be decomposed into a trade distortion and domestic distortion component. In the context of the debate on the interlinkages between openness and economic performance, the TRQI offers a means to disentangle economic inefficiencies induced by trade restrictions alone, from otherwise not directly trade‐related economic inefficiencies induced by domestic distortions.     

Technical efficiency of European railways: a distance function approach

This study has two principal objectives. The first objective is to measure and compare the performance of European railways. The second objective is to illustrate the usefulness of econometric distance functions in the analysis of production in multioutput industries, where behavioural assumptions such as cost minimization or profit maximization, are unlikely to be applicable. Using annual data on 17 railways companies during 1988–1993, multioutput distance functions are estimated using corrected ordinary least squares (COLS). The resulting technical efficiency estimates range from 0.980 for the Netherlands to 0.784 for Italy, with a mean of 0.863. The distance function results are also compared with those obtained from single-output production functions, where aggregate output measures are formed using either total revenue or a Tornqvist index. The results obtained indicate substantial differences in parameter estimates and technical efficiency rankings, casting significant doubt upon the reliability of these single-output models, particularly when a total revenue measure is used to proxy aggregate output.     

Off-farm labour and the structure of US agriculture: the case of corn/soybean farms

While the growing importance of off-farm earnings suggests large benefits accrue to farmers from efforts to expand off-farm income opportunities, economic well being also depends on greater efficiency. To comprehensively gauge the economic health of farm operator households' off-farm income is interpreted as an output along with corn, soybeans, livestock and other crops. To accomplish this task two related methodologies were used. First, using 2000 data, a multi-activity cost function was set up to analyse labour allocation decisions within the farm operator household and also to estimate returns to scale and scope. Second, using 1996–2000 data, an input distance function approach was followed to estimate returns to scale, cost economies and technical efficiency – and the relative performance of farm operator households with and without off-farm wages and salaries compared. The cost function and input distance function results both suggest that off-farm outputs and inputs can be modelled in a multi-activity framework and involve significant economies of scope.     

Slack-based directional distance function in the presence of bad outputs: theory and application to Vietnamese banking

In this paper we extend the slack-based directional distance function introduced by Färe and Grosskopf (Eur J Oper Res 200(1):320–322, 2010) to measure efficiency in the presence of bad outputs and illustrate it through an application on data of Vietnamese commercial banks. We also compare results from the slack-based directional distance function relative to the directional distance function, the enhanced hyperbolic efficiency measure (Färe et al. in Rev Econ Stat 71(1):90–98, 1989) and the Farrell-type technical efficiency and confirm that it has greater discriminative power.     

A ‘technically level playing-field’ profit efficiency analysis of enforced competition between publicly funded institutions

The study demonstrates how recent advances in the data envelopment analysis (DEA) of profit efficiency, and in combining DEA and stochastic frontier analysis (SFA) to measure producer performance, can be used to obtain a ‘technically level playing-field’ profit efficiency performance measure. A three-stage analysis is used to provide an empirical investigation of public-sector universities facing regulatory pressures to attain both profit efficiency and output quality. Stage one employs directional distance function analysis to decompose DEA profit efficiency measures into technical and allocative components. As these performance measures incorporate the impacts of managerial inefficiency, the operating environment and luck (statistical noise), stage two applies SFA to total (radial and non-radial) slacks to obtain a degree of disentanglement from the latter two impacts. The stage-two results are used to define a common environment and common luck scenario, thus permitting university producers’ inputs to be adjusted so as to reflect operation within this more level playing-field scenario. Stage three recomputes the first-stage DEA for this scenario, to yield an (input-focused) ‘technically level playing-field’ measure of profit efficiency that unifies the regulatory financial audit and output-quality indicators in a single, best-practice-benchmarked, performance measure.     

The Measurement of Dynamic Productive Efficiency

Measuring dynamic productive efficiency from observed input-output data raises several new issues which are absent in the static production frontier studies. The adjustment cost approach is developed here as an interface between the static and the dynamic frontier studies, and the non-parametric method of Farrell developed for static efficiency is extended for the specification of a dynamic production frontier.     

Non-convex Technologies and Cost Functions: Definitions,Duality and Nonparametric Tests of Convexity

This contribution is the first systematic attempt to develop a series of nonparametric, deterministic technologies and cost functions without maintaining convexity. Specifically, we introduce returns to scale assumptions into an existing non-convex technology and, dual to these technologies, define non-convex cost functions that are never lower than their convex counterparts. Both non-convex technologies and cost functions (total, ray-average and marginal) are characterized by closed form expressions. Furthermore, a local duality result is established between a local cost function and the input distance function. Finally, nonparametric goodness-of-fit tests for convexity are developed as a first step towards making it a statistically testable hypothesis. An erratum to this article is available at .     

Efficiency and Productivity Change of Non‐Life Insurance Companies in Japan

In a book published in 1994, Production Frontiers , Färe and colleagues developed an output‐based DEA (data envelopment analysis) technique to compute productivity change. The technique constructs the Malmquist index using Farrell measures of efficiency. The Farrell efficiency measures are derived from linear programming problems which allow slack in output constraints. The possible existence of output slack is less than desirable in the computation of efficiency. Therefore, the present paper constructs also the Russell and Zieschang measures of efficiency, which disallow output slack and compares them with the Farrell measures. The analysis uses data on Japanese non‐life insurance firms during the period 1983–94.     

Estimating technology in the postal sector: a Bayesian approach

The aim of this article is to study the technology of the sector represented by the Spanish national post-office and telegraph service, Sociedad Estatal Correos y Telégrafos, S.A. trading as Correos, and denominated as such hereafter. Concretely, we analyse economic efficiency (technical and allocative) and scale economies of the production units (cost centres) of Correos. To do this, we employ a methodology based on an input distance function which is the dual of the cost function. Moreover, and applying duality theory, we develop an economic model to assess the effect of postal infrastructures on the operators’ costs. In order to carry out the empirical model, Bayesian econometrics is applied to estimate the parameters in the input distance function and the technical and allocative efficiency terms.     

The relationship between efficiency and profitability with respect to the size of firms: An empirical investigation for Austria

In this paper, an attempt is made to investigate the performance of Upper-Austrian firms by size class. Considering the six derived hypotheses, why small firms have a better performance measure, some of the hypothesis with respect to profitability and labour cost efficiency are confirmed. On average, the gross residual quota (profitability measure) of small firms is higher than the one of medium-sized and large firms. However, a similar result could not be found for the productivity development. Considering the influence of the firm size on the productivity measure, there is in three out of four cases no statistically significant influence at all and in one case the opposite result is obtained indicating the larger the firm, the higher is the productivity. In the case of labour cost efficiency, the hypothesis (the smaller the firm the lower the labour cost per employee) is clearly confirmed.     

A dual measure of economies of scope

A derivative-based measure of economies of scope is obtained by exploiting the duality between the shadow cost function and the input distance function. This is a useful measure when the econometric estimation of a cost function is not viable.     

Jensen’s Inequality in Finance

The purpose of this paper is to measure the size and the statistical significance of three inequalities in the field of financial economics. The three are variants of Jensen’s inequality. The first inequality is a comparison of the expected value of a ratio to the ratio of the expected value, a problem that arises in pricing foreign exchange rates. The second is a comparison of the log of the expected value to the expected value of the log, a problem that arises in testing forward market efficiency, money demand, production functions, and trade gravity models. The third is a comparison of the expected utility to the utility of the expected value, and helps in determining the importance of the expected utility paradigm, and the magnitude of the equity risk premium. The methodology used is by simulation of random normal variables, thereby introducing sampling error. Despite this sampling error the conclusion is general: all three inequalities are economically material, and stand statistically as inequalities. The major conclusion is that Jensen’s inequality is not a theoretical and superfluous exercise in finance as some have advocated.

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.     

Empirical tools to assess the sensitivity of directional distance functions to direction selection

Directional Distance Functions (DDFs) are becoming a popular way of measuring efficiency as they encompass the Shephard output and input distance functions as special cases. However, the most critical and still unsolved issue related to DDF remains the selection of the direction along which to measure the distance from the efficient frontier. In this article, we propose some empirical tools which allow to quantify the sensitivity of the efficiency measurement to the selection of the direction. The proposed tools are applied on a dataset on the Italian agricultural sector.     

Quality of service,efficiency and scale in network industries: an analysis of European electricity distribution

Quality of service (QoS) is of major economic significance in natural monopoly infrastructure industries. In this article, we present an efficiency analysis of electricity distribution networks from seven European countries. We apply the stochastic frontier analysis method to multi-output translog input distance function models to estimate cost efficiency and scale economies. We show that introducing the quality dimension into the analysis affects estimated efficiency significantly, especially that smaller utilities’ efficiency seems to decrease. Our results emphasize that QoS should be an integrated part of efficiency and economic analysis of regulated natural monopolies.     

An evaluation of ECB policy in the Euro's big four

The Taylor curve can be viewed as an efficiency frontier displaying the trade-off between the volatility of output and volatility of inflation. We build on the existing literature in this area and view Taylor curves as a lens through which to gauge the deviations of actual ECB policy from the optimum. We employ data over the period 1999-2013 period to measure the orthogonal distance of the observed volatilities from the Taylor curve in Germany, France, Italy, Spain, and the Euro area using a recursive VARs. We find that the distance has substantially increased in all four countries suggesting that monetary policy has become less efficacious for Germany, France, Italy, and Spain since the financial crisis in 2007-2008. We also estimate counterfactual Taylor rules and find that a simple Taylor rule would have only substantially improved monetary policy efficacy in Germany.     

Ecological Benchmarking to Explore Alternative Fishing Schemes to Protect Endangered Species by Substitution: The Danish Demersal Fishery in the North Sea

The cod stock in the North Sea is threatened by overexploitation. To recover this fishing stock, pressure needs to be reduced. This implies that catch compositions with small amounts of cod are preferred by public policy makers. The present analysis assesses the technological efficiency of fishing trips in terms of the substitution possibilities away from cod by considering landings of cod as an undesirable output. A conservative non-parametric frontier technology approach imposing minimal assumptions and based on directional distance functions is applied to explore alternative fishing activities for Danish gill netters operating in the North Sea with the goal of reducing cod catches. Since performance on different fishing trips may be influenced by the operating environment, a four-stage approach is applied to correct for exogenous factors (Fried et al., J Product Anal 12(3):249–267, 1999). The corrected directional distance function efficiency scores reveal the behavioural inefficiencies, i.e., prospects for decreasing the catch of cod while catch of other species are increased.      

TESTING FOR INVERSE HOMOTHETICITY: A NONPARAMETRIC APPROACH

The efficiency of a decision-making unit can be estimated relative to the direct output possibility set or the indirect (cost-constrained) output possibility set. For the direct and indirect output sets we show that the ratio of two Farrell (radial) efficiency measures equals the ratio of two Zieschang (non-radial) efficiency measures if and only if the production technology is inverse-homothetic. A consequence of inverse homotheticity is that the input and output expansion paths are linear.     

Constrained output maximization and US agriculture

This paper presents a framework for estimating an indirect production function and then applies it to aggregate US agriculture. Issues addressed include tests of standard hypotheses about the underlying technology (homotheticity, neutral technical change, etc.) as well as examination of consistency in aggregation and the effects of changes in the level of aggregate expenditure on farm output. Since there already exist several studies empirically describing agricultural production technologies with indirect objective functions, one might fairly ask whether this paper really breaks any new ground? We feel that it does. One reason is that existing studies (e.g. Binswanger, 1974; Lopez, 1980; Ball and Chambers, 1982; Ray, 1982; and Weaver, 1983) all rely on either profit or cost functions. To date there appears to be only one study using an indirect production (Appelbaum, 1979), and it is not in agriculture. This seems unfortunate because there are many instances in agriculture for which an indirect production function (or revenue function approach) seems more appropriate. The reason why relates directly to one's belief about the objective function and constraints farmers face. Ultimately, it seems plausible in a certainty framework that producers maximize profits. And since cost minimization and output maximization are just constrained versions of profit maximization, both cost and indirect production functions are more appropriately viewed as restricted profit functions. What differs is the constraint. Assuming cost minimization implies that farmers are constrained by a fixed output which they must produce; in most instances, this is implausible. More likely, the level of output is itself a choice variable. Output maximization, on the other hand, suggests that the main constraint is the amount of money that producers can muster to hire resources. In other words, farmers may face binding constraints in obtaining the profit maximizing level on expenditure on input utilization. One might think that expenditure may not be a binding constraint because there exists a relatively active US credit market. However, the US credit market is far from being perfectly competitive in a stylized sense, and thus, the possibility of a farmer being able to finance a given level of expenditure may be limited.

Readers familiar with the dual approach to production problems may already be asking why these ideas rule out cost functions since it is well known that the cost function is the distance function of the indirect production function (Blackorby et al., 1978)? In principle, therefore, one could always estimate a cost function and then invert it to obtain the indirect production function. There are two problems with this approach: the first is that if output maximization is truly the objective, output is not predetermined and cannot be treated as exogenous in cost function estimation. Second, estimation of direct and indirect functions using the same data set does not always yield comparable results. Estimation of a transcendental logarithmic (translog) indirect production function and a translog cost function, separately, does not generally yield identical estimates of the Allen elasticities of substitutions. Solving the first problem in simple, but the second suggests that estimation should proceed on the basis of the objective function the researcher deems most appropriate. Therefore, if output maximization is more plausible than cost minimization an indirect production function should be used.

The plan of the paper is as follows. We first outline the theoretical developments necessary to our approach (included are conditions necessary for consistent aggregation over firms). We then present estimates of an indirect production function and use these estimates to investigate the plausibility of various restrictions on the technology, consistency in aggregation, substitution possibilities in agricultural production, and the effect of expenditure on agricultural input utilization. The paper closes with a discussion of the results and suggestions for future research.     

The Antonelli Versus Hicks Elasticity of Complementarity and Inverse Input Demand Systems

A true measure of input substitution associated with exogenous changes in input quantities requires that the output level be held constant. To this effect, this study presents the Antonelli elasticity of complementarity characterised by the distance function. The more common Hicks elasticity of complementarity assumes that marginal cost is constant and hence does not capture pure substitution effects. The two elasticities of complementarity are related to inverse demand systems and are shown to be equivalent under constant returns to scale. A framework for estimating the Antonelli elasticity from the uncompensated demand system is presented. Estimation results reveal substantial bias of input substitutability with the use of Hicks' measure.