Nonparametric estimation of education productivity incorporating nondiscretionary inputs with an application to Dutch schools

In this paper we develop a Malmquist productivity index for public sector production characterized by the influence of environmental variables. We extend Johnson and Ruggiero (2011) to the more general case of variable returns to scale to further decompose the Malmquist productivity index into technical, efficiency, scale and environmental change. We apply our model to analyze productivity of Dutch schools using 2002–2007 data. The results indicate that the environment influences the productivity index as well as the technical, efficiency, scale and environmental change components. We see that schools with a moderate classification of environment have the highest productivity numbers. In line with expectations, schools with the worst environment also perform worse and would perform better with an improved environment.     

On the measurement of technical efficiency in the public sector

Existing measures of technical inefficiency obtained through linear programming models in the public sector do not properly control for environmental variables that affect production. It will be shown that the consequences of not controlling for these fixed factors are biased estimates of technical efficiency. This paper extends the mathematical programming approach to frontier estimation known as Data Envelopment Analysis to allow for environmental variables. This modified model will be then contrasted with the existing model that purportedly controls for exogeneous factors to measure public sector efficiency with simulated data. The results provide evidence that the existing Data Envelopment Analysis model will overestimate the level of technical inefficiency and that the modified model developed in this paper does a better job controlling for exogenous factors. The modified model is also applied to analyze the technical efficiency of school districts.     

Nonparametric analysis of educational costs

Traditional economic analyses of the public sector that assume cost minimization are not consistent with political models of bureaucracy. If costs are not minimized then estimated cost functions will be biased. The purpose of this paper is to provide a flexible nonparametric technique based on Farrell-type efficiency measures to estimate public sector costs. Standard indices need to be modified to fit the special nature of public sector service provision which is characterized by an influence of exogenous variables on cost. A useful by-product is an index of environmental harshness faced by local governments. For illustrative purposes, this technique is applied to a sample of New York State school districts. It is found that nearly 64% of districts are cost inefficient, spending on average $1200 per pupil above the cost minimizing level. In addition, it is estimated that the average school district faces environmental cost of over $1700 per pupil.     

A full-scale investigation of the directional returns to scale in data envelopment analysis

Returns to scale is considered as one of the important concepts in data envelopment analysis (DEA) which can be useful for deciding to increase or decrease the size of a particular decision making unit. Traditional returns to scale on the efficient surface of the production possibility set with variable returns to scale (VRS) technology is introduced as a ratio of proportional changes of output components to proportional changes of input components. However, a problem which may arise in the real world is the impossibility or undesirability of proportional change in the input or output components. One of the attempts which is made to solve the aforementioned problem is the work of Yang et al., 2014. They have introduced the “directional returns to scale” in the DEA framework and have proposed some procedures to estimate and measure it. In this paper, the introduced directional returns to scale is investigated from a new perspective based on the defining hyperplanes of the production possibility set with VRS technology. We propose some algebraic equations and linear programming models which in addition to measuring the directional returns to scale, they enable us to analyse it. Moreover, we introduce the concepts of the best input and output direction vectors for expansion of input components or compression of output components, respectively, and propose two linear programming models in order to obtain these directions. The presented equations and models are demonstrated using a case study and numerical examples.     

Linear programming solutions and distance functions under a constant returns to scale technology

In this paper, we investigate the various relationships among the linear programming solutions of data envelopment analysis (DEA) models under a constant returns to scale technology. We derive the analytical relationships among the efficiency measures and the activity variables for four separate models: the input-based, the output-based, the hyperbolic, and the proportional distance functions. We apply our results in order to derive a test of consistency that can be used in assessing the returns to scale among differing DEA models.     

Bicriteria efficiency/equity hierarchical location models for public service application

As is often the case in healthcare provision, public services may offer facilities at a hierarchy of levels in different locations, ranging from basic to specialised levels of care. In addition to efficiency objectives, with public services there is the concern of equity of provision when locating new facilities. We present, as a tool-kit for decision makers, a range of discrete hierarchical location models with bicriteria efficiency/equity objectives. These models are for use in location of facilities within hierarchical systems where a fair but efficient hierarchical service is sought. The hierarchical models have as efficiency criteria both p-median and maximal-covering types. These components are combined in a novel manner with appropriate equity objectives to give decision makers a range of choices of scenarios. We illustrate use of the models in a healthcare setting.     

中国钢铁主营上市公司规模效率分析及其启示

本文阐述了采用距离函数计算规模效率的方法.应用Tim Coelli的投入导向DEA模型多阶段求解方法,计算出了我国钢铁主营上市公司2005年、2006年的规模效率.结果表明,年产粗钢小于200万吨的上市公司几乎都是规模无效的;年产粗钢小于300万吨的上市公司处于规模报酬递增状态;年产粗钢大于300万吨的上市公司大都是规模有效的;年产粗钢大于300万吨的上市公司的规模效率均值显著大于年产粗钢小于300万吨的均值;而且规模最大的几个公司连续两年都是规模有效的,它们处于规模报酬不变状态,其规模尚未大到进入生产函数的规模报酬递减区域.上述结论,有效地支持上市钢企通过整体上市、并购重组,扩大规模,提高规模收益,同时,支持我国钢铁产业不断提高产业集中度。     

Stability of the classification of returns to scale in FDH models

This paper deals with the estimation of returns to scale (RTS) in free disposal hull (FDH) models and provides some stability intervals for preserving the RTS classification. It has been shown that the proposed stability intervals can be obtained via a polynomial-time algorithm based on the calculation of certain ratios of inputs and outputs, without solving any mathematical programming problem. The results of the study have been proved via some lemmas and theorems and have been illustrated by numerical examples and a real application.     

基于三阶段SBM模型的中国节能服务上市企业效率研究

节能服务企业效率对于推动节能服务产业发展和确保国家“双碳”目标实现具有重要意义。运用三阶段SBM模型,对2020年60家中国节能服务上市企业的综合效率进行实证研究,并分析效率的影响因素。研究结果表明,经济发展水平对综合效率具有双重影响,合适的产业结构和较高的投入资本回报率有利于综合效率提升,而政府补贴与企业存续时间制约了综合效率改进;剔除环境因素与随机误差影响后,多数企业综合效率下降,整体效率偏低;提高规模效率是提升综合效率的关键,且绝大部分企业处于规模收益递增状态。研究最后提出创新补贴方式、建立企业认证制度、开展综合能源服务和推动企业间兼并重组等可行建议,以提升节能服务企业的综合效率。     

Quality adjusted measures of services in public schools

This study considers specification and estimation of cost functions in public schools. A number of production characteristics are included in the specification to control for observable differences between municipalities in the provision of their school services. Both parametric and non-parametric approaches are used to take into account the quality differences in school services. These approaches are then compared to the alternative output measure without any adjustment for quality differences. The sensitivity of different elasticities and returns to scale (RTS) measures with respect to alternative model specifications and quality adjustments are also analyzed. In the empirical section we examine performances of 286 Swedish municipalities in the production of primary and secondary school education during the 1992/3–1994/5 school years.     

基于SFA和Malmquist方法的公共部门效率区域差异及其决定因素分析

利用测量Malmquist生产率指数的SFA方法和BC(1995)模型,分析了中国省级地方政府公共部门效率区域差异及其决定因素,结果显示,省级公共部门技术效率随时间变化存在持续改进趋势,同时也发现居民受教育水平、城镇居民家庭可支配收入、每一公职人员服务人数和政府支出规模对公共部门技术效率有显著正影响,而人口密度和人均行政管理费支出对公共部门技术效率有显著负影响.     

Stochastic models and variable returns to scales in data envelopment analysis

Stochastic Data Envelopment Analysis (DEA) models were developed by taking random disturbances into account for the possibility of variations in input-output data structure. The stochastic efficiency measure of a Decision Making Unit (DMU) is defined via joint probabilistic comparisons of inputs and outputs with other DMUs, and can be characterized by solving a chance constrained programming problem. Deterministic equivalents are derived for both situations of multivariate symmetric random disturbances and a single random factor in the production relationships. An analysis of stochastic variable returns to scale is developed.     

Exploring the use of DEA for formative evaluation in primary diabetes care: An application to compare English practices

Primary care is currently at the heart of the UK National Health Service policy. Primary care trusts have the crucial role of improving the efficiency and equity in primary care delivery. However, few studies have focused on performance assessment in primary care provision. In this paper, we examine the role of data envelopment analysis (DEA) in helping decision makers to understand and improve the performance of primary care practices. We discuss the results from a study of 14 practices in England in terms of their delivery of diabetes services. In order to take into account the multiple values that underlie public services provision, we have considered several different perspectives for evaluation. These were: technical, allocative and cost efficiency, clinical and patient-focused effectiveness, and equity. The approach adopted involved a deep engagement with the practices. The purpose was to understand the structures and processes supporting effective practice using DEA in a formative role rather than the more usual summative role with a large data set. This approach is in the tradition of the developmental engagement approach of operational research.     

DEA model with shared resources and efficiency decomposition

Data envelopment analysis (DEA) has proved to be an excellent approach for measuring performance of decision making units (DMUs) that use multiple inputs to generate multiple outputs. In many real world scenarios, DMUs have a two-stage network process with shared input resources used in both stages of operations. For example, in hospital operations, some of the input resources such as equipment, personnel, and information technology are used in the first stage to generate medical record to track treatments, tests, drug dosages, and costs. The same set of resources used by first stage activities are used to generate the second-stage patient services. Patient services also use the services generated by the first stage operations of housekeeping, medical records, and laundry. These DMUs have not only inputs and outputs, but also intermediate measures that exist in-between the two-stage operations. The distinguishing characteristic is that some of the inputs to the first stage are shared by both the first and second stage, but some of the shared inputs cannot be conveniently split up and allocated to the operations of the two stages. Recognizing this distinction is critical for these types of DEA applications because measuring the efficiency of the production for first-stage outputs can be misleading and can understate the efficiency if DEA fails to consider that some of the inputs generate other second-stage outputs. The current paper develops a set of DEA models for measuring the performance of two-stage network processes with non splittable shared inputs. An additive efficiency decomposition for the two-stage network process is presented. The models are developed under the assumption of variable returns to scale (VRS), but can be readily applied under the assumption of constant returns to scale (CRS). An application is provided.     

Measuring the efficiency of decision making units

A nonlinear (nonconvex) programming model provides a new definition of efficiency for use in evaluating activities of not-for-profit entities participating in public programs. A scalar measure of the efficiency of each participating unit is thereby provided, along with methods for objectively determining weights by reference to the observational data for the multiple outputs and multiple inputs that characterize such programs. Equivalences are established to ordinary linear programming models for effecting computations. The duals to these linear programming models provide a new way for estimating extremal relations from observational data. Connections between engineering and economic approaches to efficiency are delineated along with new interpretations and ways of using them in evaluating and controlling managerial behavior in public programs.     

Developing geographical indicators of mileage-related costs: a case study exploring travelling public services in English local areas

The context of this study is the public sector provision of services involving travelling in local authority areas in England. Such travelling services are costly and the relative levels of these costs across different local areas have raised a number of policy issues, particularly how performance assessments of local authorities and capitation-based funding by central government take into account (or fail to take into account) the differential travel costs faced in geographical areas that differ in population dispersion (sparsity) characteristics. The research presented here is concerned with identifying and evaluating practical indicators of mileage-related costs faced in local areas and a range of indicators have been explored for three services: domiciliary care, refuse collection and home-to-school transport. The findings suggest that currently used population dispersion indicators could be improved and that the current sparsity allowances in England underestimate the relative cost effects by a considerable amount.     

Estimating technical and allocative efficiency in the public sector: A nonparametric analysis of Dutch schools

Public sector output provision is influenced not only by discretionary inputs but also by exogenous environmental factors. In this paper, we extended the literature by developing a conditional DEA estimator of allocative efficiency that allows a decomposition of overall cost efficiency into allocative and technical components while simultaneously controlling for the environment. We apply the model to analyze technical and allocative efficiency of Dutch secondary schools. The results reveal that allocative efficiency represents a significant 37 percent of overall cost efficiency on average, although technical inefficiency is still the dominant part. Furthermore, the results show that the impact of environment largely differs between schools and that having a more unfavorable environment is very expensive to schools. These results highlight the importance of including environmental variables in both technical and allocative efficiency analysis.     

Measurement of returns to scale using non-radial DEA models

There are some specific features of the non-radial data envelopment analysis (DEA) models which cause some problems for the returns to scale measurement. In the scientific literature on DEA, some methods were suggested to deal with the returns to scale measurement in the non-radial DEA models. These methods are based on using Strong Complementary Slackness Conditions from optimization theory. However, our investigation and computational experiments show that such methods increase computational complexity significantly and may generate as optimal, solutions contradicting optimization theory. In this paper, we propose and substantiate a direct method for the returns to scale measurement in the non-radial DEA models. Our computational experiments documented that the proposed method works reliably and efficiently on the real-life data sets.     

Sense and sensibility: using a model to examine the relationship between public pre-school places and fertility

This paper presents a stochastic dynamic mathematical model, in which a Family Policy Index (XFPI) is included to measure and compare two different models of provision of resources to support families with children from 0 to 3 years old. The main variables in this model are the XFPI, fertility, mortality, emigration and immigration rates. This mathematical model was validated in two different countries, Spain and Norway, during the 2007–2015 period. A sensitivity analysis was applied to simulate the future trend (2016–2030), examining the influence of providing public pre-school services (0 to 3 years) on (XISF). The results obtained show that these services may indeed have an influence on fertility rates, as long as they are developed extensively.     

DEA方法进行规模收益分析的几点注记

自从 Banker等人 ( 1 984)用 DEA方法进行规模收益分析 ,已有越来越多的学者也在进行相关的研究 .研究主要从两个方面进行 :基于 DEA输入模型的方法和基于 DEA输出模型的方法 .这两类方法所应用的模型、条件、结论都有所不同 ,但在应用中有些文章将它们混淆在一起 .本文针对应用中容易出现的错误 ,给出反例和正确的判别规模收益状况的充分必要条件 .并由规模收益的定义 ,建议使用 DEA—输出模型进行规模收益分析 .