Hypothesis tests using data envelopment analysis

A substantial body of recent work has opened the way to exploring the statistical properties of DEA estimators of production frontiers and related efficiency measures. The purpose of this paper is to survey several possibilities that have been pursued, and to present them in a unified framework. These include the development of statistics to test hypotheses about the characteristics of the production frontier, such as returns to scale, input substitutability, and model specification, and also about variation in efficiencies relative to the production frontier.     

基于DEA的北京市高技术产业R＆D效率比较分析

本文运用DEA模型全面测算了北京市高技术产业1996—2010年间R＆D的生产前沿面效率、综合技术效率、纯技术效率以及规模效率,对规模收益变化和投入产出的冗余与不足进行了具体分析,并针对北京市政府如何提高高技术产业的R＆D效率提出了建议。     

Technical efficiency in texas nursing facilities: A stochastic production frontier approach

A rapidly aging U. S. population is straining the resources available for long term care and increasing the urgency of efficient operations in nursing homes. The scope for productivity improvements can be examined by estimating a stochastic frontier production function. We apply the methods of maximum likelihood and quantile regression to a panel of Texas nursing facilities and infer that the average productivity shortfall due to avoidable technical inefficiency is at least 8 percent and perhaps as large as 20 percent. Non-profit facilities are notably less productive than comparable facilities operated for profit, and the industry has constant returns to scale.     

Estimation of stochastic frontier production functions with input-oriented technical efficiency

This paper deals with estimation of input-oriented (IO) technical inefficiency using a stochastic production frontier model. Econometrically the model is similar to a class of models that arise in specifying technical inefficiency in cost-minimizing and profit-maximizing frameworks. The standard maximum likelihood (ML) method that is used to estimate output-oriented (OO) technical efficiency cannot be applied to estimate these models. We use a simulated ML approach to estimate the IO production function and compare results from the IO and OO models, mainly to emphasize the point that estimated efficiency, returns to scale, technical change, etc., differ depending on whether one uses the model with IO or OO technical inefficiency.     

Productivity and efficiency at bank holding companies in the U.S.: a time-varying heterogeneity approach

This paper investigates the productivity and efficiency of large bank holding companies (BHCs) in the United States over the period 2004–2013, by estimating a translog stochastic distance frontier (SDF) model with time-varying heterogeneity. The main feature of this model is that a multi-factor structure is used to disentangle time-varying unobserved heterogeneity from inefficiency. Our empirical results strongly suggest that unobserved heterogeneity is not only present in the U.S. banking industry, but also varies over time. Our results from the translog SDF model with time-varying heterogeneity show that the majority of large BHCs in the U.S. exhibit increasing returns to scale, a small percentage exhibit constant returns to scale, and an even smaller percentage exhibit decreasing returns to scale. Our results also show that on average the BHCs have experienced small positive or even negative technical change and productivity growth.     

The Effect of Incentive Regulation in Telecommunications in the United States

Incentive regulation is now an important regulatory tool in the telecommunications industry in the United States. The issue explored here is whether incentive regulation has resulted in an increase in productive efficiency. After providing an overview of the nature of incentive regulation, one methodology for measuring the effects of incentive regulation on productive efficiency is reviewed. This methodology is data envelopment analysis (DEA) and allows for the measurement of both scale efficiency and technical efficiency of individual local exchange carriers. The results indicate that most local exchange carriers were technically efficient over the 1988–1998 period. Four LECs, however, consistently demonstrate scale inefficiency. In the aggregate, however, based on the DEA results there was no identifiable improvement in aggregate LECs' technical efficiency between 1988 and 1998. Subsequently, an alternative methodology, a stochastic frontier production function approach, is considered. The results from this methodology confirm that there was no change in technical efficiency over the period of study, something that incentive regulation was specifically designed to enhance.     

Market Concentration and Multifaceted Productive Efficiency

Developing the analytical framework of the decision making process of a possible entrant, a reduced form system equations model is estimated in order to examine the market concentration – productive efficiency relationship in an endogeneity context. Technical and scale efficiency estimates are obtained from an inter-industry stochastic production frontier using a panel dataset regarding the seven most energy intensive manufacturing industries in Greece over the period 1980–96. Several new versions of the concentration – efficiency relationship, may be derived from the alternatives of the entrant considering the possible conduct character of incumbents’ technical efficiency and excess capacity, which is depicted on their scale efficiency, on market concentration.     

Public support for performing arts. Efficiency and productivity gains in eleven European countries

This paper investigates the importance of public cultural expenditure for the efficiency and productivity of the performing arts (PA) firms. To this aim, we estimate a translog production function using the stochastic frontier approach (SFA), and we obtain the estimates of both technical efficiency and its determinants for the PA firms in EU-11 countries over the period 2009–2017. The large panel data set enables the application of robust true random-effects SFA techniques, which control for noise, unobserved firms' heterogeneity and endogeneity of the inputs. Moreover, by estimating a production function, the characteristics of the production technology in the PA sector is also derived. The empirical results demonstrate that PA firms are technically inefficient, implying that the investigated firms could increase their artistic output between 32 and 42% and that decreasing returns to scale are prevalent, due to the presence of too many micro and large-scale firms in the European PA sector. In contrast to the seminal Baumol and Bowen's [5] paper, we also demonstrate that the total factor productivity (TFP) increased in the EU PA firms over the examined period. Technical efficiency, although relatively low, was the main driver of this productivity growth, as opposed to scale efficiency change or technological change, which display very small or no increases. We also find that, contrary to the common wisdom on its negative effects on firm efficiency, public spending on culture increases the efficiency of PA firms. Within this context some policy implications are discussed.     

Calculation of scale elasticities in DEA models: direct and indirect approaches

The qualitative characterisation of returns to scale in DEA has been a research issue the last decade. However, quantitative information provides the ultimate information. This paper presents two ways of obtaining numerical values of scale elasticity by an indirect approach using efficiency scores and dual variables for radial projections of inefficient points to the frontier, and a direct approach that is more general and powerful and directly evaluates numerically scale elasticity at any point on the DEA surface along intersections with planes. The direct and indirect approaches are compared using real data and a very high correspondence is found.     

On the calculation of the scale elasticity in DEA models

An issue in the multiple-output case within the literature on piecewise linear frontier production functions has been how to determine the nature of the scale properties. It is shown that knowledge of scale efficiency does not permit calculation of scale elasticity or vice versa. For inefficient units there is a relationship between input-saving and output-increasing efficiency measures through the average value of the scale elasticity between the two different reference points on the frontier. A direct approach to determine the scale properties is to calculate the scale elasticity from the dual problem to the calculation of Farrell efficiency measures.     

Efficient Facet Based Efficiency Index: A Variable Returns to Scale Specification

The appearance of strictly positive slack variables in DEA solutions causes well known computational and analytical problems studied by Olesen and Petersen (1996) and Green et al. (1996) under constant returns to scale. This paper discusses variable returns to scale and suggests the use of efficient facets (EFs) in the reference technology. It is found to give a lower bound of the efficiency scores. Most importantly, efficiency measured with respect to EFs—the EF based efficiency index—may decrease if additional variables are introduced but are disposed in production. Thus, units are penalized for disposal of incoming variables, and the EF based efficiency index captures the net efficiency of a unit. EF is found to be a useful tool also to search a suitable set of variables for efficiency measurement. Its use is demonstrated with Finnish university data and it is found to change the measured performance of the university sector quite significantly.     

Are all Scales Optimal in DEA? Theory and Empirical Evidence

Policy recommendations concerning optimal scale of production units may have serious implications for the restructuring of a sector. The piecewise linear frontier production function framework (DEA) is becoming the most popular one for assessing not only technical efficiency of operations, but also for scale efficiency and calculation of optimal scale sizes. The main purpose of the present study is to investigate if neoclassical production theory gives any guidance as to the nature of scale properties in the DEA model, and empirically explore such properties. Theoretical results indicate that the DEA model may have more irregular properties than usually assumed in neoclassical production theory, concerning shape of optimal scale curves and the M-locus. The empirical results indicate that optimal scale may be found over almost the entire size variations in outputs and inputs, thus making policy recommendations about efficient scale difficult. It seems necessary to establish the nature of optimal scale before any practical conclusions can be drawn. Proposals for indexes characterizing the nature of optimal scale are provided.     

Efficiency Gains and Cost Reductions from Individual Transferable Quotas: A Stochastic Cost Frontier for the Australian South East Fishery

In this paper efficiency gains and associated cost reductions from increases in traded quota are estimated with a stochastic cost frontier for the Australian South East Trawl Fishery (SETF). Estimation of this frontier also provides key information on the relative importance of input costs in the SETF, returns to scale, variations in costs as a result of trade in quota and the economic performance of each fishing vessel, year to year. Final estimations indicate that increases in the volume of quota traded have resulted in considerable efficiency gains and cost reductions in the SETF, ranging from 1.8 to 3.5 cents per kilogram for surveyed vessels for every 1% increase in the volume of quota traded, or 1–2.4% of total variable costs, with considerable gains also accruing to crew and skipper in the form of larger share payments. Mean vessel efficiency is relatively high in the SETF, estimated at over 90%, and increases further to 92% over the sample period with increased trades in quota.Jel Classification: Q22, Q28     

A Cost Indirect Evaluation of Productivity Change in UK Universities

The study provides an empirical analysis of productivity change in publicly-funded UK universities, against a background of government policy specifically designed to enhance the productive efficiency of universities in the provision of teaching and research. The nonparametric analysis employs a cost indirect approach to measuring productivity change, taking explicit account of the quality of research output and decomposing productivity change into technical change and efficiency change. The latter is also decomposed into changes in pure technical efficiency, scale efficiency and output congestion. Changes in size efficiency are also computed. On average, productivity declined by 4% over 1989–92, mainly as a result of regressive technical change. Evidence of biased technological change was found, with the frontier shifting out in favour of the teaching outputs and in relative to the research output.     

两种等效益面生产函数与全要素生产率变化率的分解

本文根据规模报酬可变还是规模报酬不变，分别定义了一般等效益面生产函数和典型等效益面生产函数。由一般等效益面生产函数的离散型分解式可以测算一个生产单元的纯技术进步，以及纯技术效率变化对经济增长的贡献；而由典型等效益面生产函数可以将全要素生产率的变化率分解为典型技术进步率、纯技术效率和规模效率的变化率之和。进而由具有明确几何意义的离散型分解式分别测算典型技术进步和规模效率对经济增长的贡献。等效益面生产函数与分解式的几何意义还说明，全要素生产率的改变最终是由技术创新、制度创新和管理创新共同推动的。     

Efficiency and Global Scale Characteristics on the “No Free Lunch” Assumption Only

In a production technology, the type of returns to scale (RTS) associated with an efficient decision making unit (DMU) is indicative of the direction of marginal rescaling that the DMU should undertake in order to improve its productivity. In this paper a concept of global returns to scale (GRS) is developed as an indicator of the direction in which the most productive scale size (MPSS) of an efficient DMU is achieved. The GRS classes are useful in assisting strategic decisions like those involving mergers of units or splitting into smaller firms. The two characterisations, RTS and GRS, are the same in a convex technology but generally different in a non-convex one. It is shown that, in a non-convex technology, the well-known method of testing RTS proposed by Färe et al. is in fact testing for GRS and not RTS. Further, while there are three types of RTS: constant, decreasing and increasing (CRS, DRS and IRS, respectively), the classification according to GRS includes the fourth type of sub-constant GRS, which describes a DMU able to achieve its MPSS by both reducing and increasing the scale of operations. The notion of GRS is applicable to a wide range of technologies, including the free disposal hull (FDH) and all polyhedral technologies used in data envelopment analysis (DEA).     

Variation in productive efficiency in French workers' cooperatives

In this study, we explore the distribution of productive efficiency among workers' cooperatives operating in each of four sectors of French manufacturing. We use stochastic frontier panel data techniques to estimate production relationships in each sector, and to decompose output variation into input variation, variation in the effects of two indicators of the degree of worker participation in management, variation in productive efficiency, and an unexplained residual. In all four sectors we find that conventionally measured capital and labor inputs make a significant contribution to productivity. In only one sector do participation indicators contribute significantly. Variation in productive efficiency contributes significantly in all four sectors.Earlier versions of this article were presented at the ORSA/TIMS Joint National Meeting in Philadelphia, PA, October 1990, and at the Allied Social Science Associations meetings in Washington, DC, December 1990. Helpful comments from discusants at both meetings, and from two good referees, are gratefuly acknowledged, as is financial support of AUPELF and the UNC University Research Council.     

Measuring Scale Efficiency from a Translog Production Function

In parametric analysis based on a frontier production function, usually the scale elasticity rather than scale efficiency level is reported. In this paper we show how one can use an estimated translog production function to obtain output- and input-oriented measures of scale efficiency at an observed input bundle. We also show how the estimated model can be used to determine the optimal quantity of labor input for an exogenously fixed quantity of capital.     

Stochastic non-smooth envelopment of data: semi-parametric frontier estimation subject to shape constraints

The field of productive efficiency analysis is currently divided between two main paradigms: the deterministic, nonparametric Data Envelopment Analysis (DEA) and the parametric Stochastic Frontier Analysis (SFA). This paper examines an encompassing semiparametric frontier model that combines the DEA-type nonparametric frontier, which satisfies monotonicity and concavity, with the SFA-style stochastic homoskedastic composite error term. To estimate this model, a new two-stage method is proposed, referred to as Stochastic Non-smooth Envelopment of Data (StoNED). The first stage of the StoNED method applies convex nonparametric least squares (CNLS) to estimate the shape of the frontier without any assumptions about its functional form or smoothness. In the second stage, the conditional expectations of inefficiency are estimated based on the CNLS residuals, using the method of moments or pseudolikelihood techniques. Although in a cross-sectional setting distinguishing inefficiency from noise in general requires distributional assumptions, we also show how these can be relaxed in our approach if panel data are available. Performance of the StoNED method is examined using Monte Carlo simulations.     

ICT Adoption and Heterogeneity in Production Technologies: Evidence for Chilean Retailers*

The adoption of information and communication technology (ICT) can have far‐reaching effects on the nature of production technologies. Because ICT adoption is incomplete, especially in developing countries, different groups of firms will have different production technologies. We estimate a latent class stochastic frontier model, which allows us to test for the existence of multiple production technologies across firms and consider the associated implications for efficiency measures. We use a unique data set of Chilean retailers, which includes detailed information on ICT adoption. We find three distinct production technologies. The probability of membership in a more productive group is positively related to ICT use.