Corrected Ordinary Least Squares Research Articles

Efektywność edukacyjna małopolskich liceów – analiza porównawcza

Objective: In the article the authors model and measure the educational efficiency of high schools in Małopolskie Voivodeship, which are treated as microeconomic production units.Research Design & Methods: Two alternative methods of assessment are presented for the proposed educational efficiency measure. In the first, based on the Cobb-Douglas production function, efficiency is modelled using a one-sided random term. The parameters of this model and the efficiency measure are estimated using the corrected ordinary least squares (COLS) method. In the second approach – Data Envelopment Analysis (DEA) – efficiency is determined using the optimal value of the objective function of an appropriate linear program. The variables used for the study and the set of data are described.Findings: The results for 34 high schools, obtained using both methods, are moderately similar, but diverge radically from the ranking based on the Educational Value Added (EVA) index used by the Central Examination Board (CEB).Implications / Recommendations: The high schools that lead the press rankings in Małopolskie Voivodeship are not the most efficient institutions in the microeconomic terms. Moreover, the most efficient high schools are located in smaller cities (not in Cracow).Contribution: A new measure of EVA, rooted in the microeconomic approach to schools as production units, is presented and empirically applied. This measure significantly differs from the EVA index used by CEB; in the authors’ opinion, it is clearer and easier to interpret; the efficiency measure based on it makes it possible to rank schools objectively.

Efficiency, productivity and returns to scale in ports: a comparison of data envelopment analysis and econometric estimation with application to Caribbean Small Island Developing States

This paper investigates the evolutionary technical efficiency and productivity of ports in Small Island Developing States (SIDS). The focus is primarily on Caribbean SIDS, benchmarked against two comparator groups: major top ports and ports in other SIDS in the Pacific and Indian Oceans. Both a non-parametric data envelopment analysis (DEA) and the econometric corrected ordinary least squares (COLS) Malmquist Productivity Index (MPI) model are used. The results reveal a significantly lower level of technical efficiency in the Caribbean when assessed against top ports, but higher when compared to other SIDS. Caribbean ports achieved a higher rate of productivity improvement compared to top ports, and thus partially closed the efficiency gap, but not as much as ports in other SIDS. This was primarily the result of higher returns to density due to the rising traffic levels of the latter group. Analysis of both SIDS groups against the top group revealed that there exist two “tiers” in terms of port development, with those in the first representing a level of efficiency that those in the second simply cannot match. In some respects, therefore, this “inefficiency” may be better described as port underutilization. This suggests that, for these ports, maximizing the efficient use of existing capacities, and only then considering port expansion, could be the most feasible option for improving technical efficiency in the medium to long run.

Long term productivity gains in the privatised British passenger rail industry – A case study of Malmquist productivity index measurements

This paper assesses long term productivity in the privatised British passenger rail industry using a Malmquist productivity index (MPI) generated using three different efficiency assessment methods, namely data envelopment analysis (DEA), corrected ordinary least squares (COLS) and the stochastic production frontier (SPF). The results indicate that over the period 1997 to 2015, the industry achieved annual average productivity gains of around 1% to 1 1/2%, with most of this improvement coming in the first half of the period, and the second half of the period displayed unitary productivity returns. Virtually all gains have come as a result of technical change, however the rate of increase was found to gradually decreasing throughout the whole time period, hence future productivity gains may be more difficult to achieve. The results from the three approaches are considered, and the COLS is found to be most consistent with the idea of total factor productivity and technical change ss long run concepts and efficiency change as a short run phenomenon.

The relationship between enterprise efficiency in resource use and energy efficiency practices adoption

The purpose of this paper is to investigate the relationship between enterprise efficiency in resource use and the adoption of energy efficiency practices recommended by the US Department of Energy (DOE) through the Industrial Assessment Center (IAC). Using non-parametric techniques such as Data Envelopment Analysis (DEA) and parametric techniques like Stochastic Frontier Analysis (SFA) and Corrected Ordinary Least Square (COLS) to measure the efficiency. The Regression Quantile (RQ) is carried out to test the hypothesis that the most efficient companies have adopted a higher level of practice. The main conclusion is that when the enterprise operates at increasing Returns-to-Scale (RTS) the impact of efficiency on adoption increases positively, inversely when the enterprise operates at decreasing (RTS) the impact of efficiency on adoption increases negatively.

Measuring Technical Efficiency of Agricultural Inputs

The increasing use of modern technological inputs like fertilizers, pesticides and manure under the condition of unstable irrigation affects the agricultural productivity. The objective of the study is to determine the technical efficiency of agricultural inputs and input–output ratio. The study is conducted in Jhansi, Lalitpur and Jalaun districts of Jhansi division in Uttar Pradesh. The sampled farms were differentiated on the basis of soil type. In order to find the technical efficiency, the Cobb-Douglas production function method was applied in which Ordinary Least Square (OLS) estimators were converted into the Corrected Ordinary Least Square (COLS) estimators. To examine the technological equality between two districts, Chow Test has been used. The selected farm size categories are marginal (up to 2.5 acre land), small (> 2.5 acre land to 5 acre land) and large (> 5 acre land).

Statistical evaluation of Data Envelopment Analysis versus COLS Cobb–Douglas benchmarking models for the 2011 Brazilian tariff revision

In 2011, the Brazilian Electricity Regulator (ANEEL) implemented a benchmarking model to evaluate the operational efficiency of power distribution utilities. The model is based on two benchmarking methods: Data Envelopment Analysis (DEA) and Corrected Ordinary Least Squares (COLS) with a Cobb Douglas production function. Although the estimated scores are highly correlated, differences between the scores are as high as 41%. For some companies differences between the efficiency scores result in substantial reduction in regulatory operational costs. We provide a detailed statistical comparison which indicates that the COLS Cobb Douglas model has major deficiencies in terms of estimating efficiency scores.

Impact of Bank Operational Efficiency Using a Three-Stage DEA Model

In this study the authors use a three-stage sequential technique to develop a Data Envelopment Analysis (DEA) model for examining a bank's technical efficiency index. Internal risk and environmental risk are incorporated into this model to accommodate the well-known BASEL III Accord (required capital adequacy ratio in the financial industry) and to ensure the amount of derivatives turnover ratio is at the level defined by industry best-practices. Information is obtained from 34 Taiwanese commercial banks for the period from 2008 to 2011 following the global financial crisis. The Malmquist total factor productivity index (TFP) is also employed to measure the impact of changes in productivity on the panel data. Empirical results derived from the DEA approach show a gain in technical efficiency and scale efficiency in the industry after adjusting the slack variables when using the corrected ordinary least squares (COLS) regression model. The results indicate that commercial banks need to diversify to increase their market share when dealing with derivatives which are associated with higher risk. The Balk's Malmquisit TFP index shows a decrease in bank productivity and improvement in pure technical efficiency. In this study the authors found that after risk-adjustment there was a distinct inefficient unit decrease and but a marginal unit increase in efficiency.

Sensitivity of technical efficiency estimates to estimation methods: an empirical comparison of parametric and non-parametric approaches

This paper highlights the sensitivity of technical efficiency estimates to estimation approaches using empirical data. Firm specific technical efficiency and mean technical efficiency are estimated using the non parametric Data Envelope Analysis (DEA) and the parametric Corrected Ordinary Least Squares (COLS) and Stochastic Frontier Analysis (SFA) approaches. Mean technical efficiency is found to be sensitive to the choice of estimation technique. Analysis of variance and Tukey’s test suggests significant differences in means between efficiency scores from different methods. In general the DEA and SFA frontiers resulted in higher mean technical efficiency estimates than the COLS production frontier. The efficiency estimates of the DEA have the smallest variability when compared with the SFA and COLS. There exists a strong positive correlation between the efficiency estimates based on the three methods.

Inference in stochastic frontier analysis with dependent error terms

Stochastic frontier analysis (SFA) is often used to estimate technical efficiency of entities such as firms, countries or municipalities. A potential dependence between the two components of the error term can be taken into account by a copula function. While estimation of the model is straightforward using the Corrected Ordinary Least Squares (COLS) and Maximum Likelihood (ML) methods, an open issue concerns the inference of the technical efficiencies. We propose a parametric bootstrap algorithm which is suitable for the dependence case. This allows us to estimate the efficiency percentile confidence intervals. We apply the model to the estimation of technical efficiencies of moroccan municipalities.

ANALYSIS OF POVERTY AND EFFICIENCY: AN EARNINGS FRONTIER APPROACH

The paper introduces the concept of an earnings frontier in explaining monthly consumption expenditure (a proxy for income) in terms of human capital and endowments of a household. Individuals who translate their potential earning into actual earnings enjoy a fully efficient position. In contrast, individuals who earn less than their potential earnings suffer from some kind of earnings inefficiency. The paper estimates an earnings frontier using the Corrected Ordinary Least Square (COLS) method and classifies households in terms of efficiency scores. Splitting the sample into an efficient and an inefficient part based on the estimated frontier and a bench mark efficiency score, the status of poverty in the two parts (groups) is studied. The poverty gap between the groups is then decomposed into a characteristics effect and a coefficients effect using the familiar Oaxaca decomposition methodology. The paper also tries to establish a link between the notion of efficiency and the coefficients effect in the Oaxaca decomposition methodology. The results obtained are interpreted in light of the poor but efficient hypothesis.

Technical Efficiency of Agricultural Farms and Capital-Output Ratio: A Study on Jhansi Division of Uttar Pradesh

The increasing use of modern technological inputs like fertilizers, pesticides and manure under the condition of unstable irrigation could be the responsible factors for increasing the agricultural productivity. The mechanical inputs like tractor power, threshers, diesel pumps, electric motors are useful to save time, money and water. These inputs increase the farmer’s income and efficiency. Present study contains the objective to find out the technical efficiency of capital use resources and capital output ratio. In order to find the technical efficiency, the Cobb-Douglas production function method was applied in which Ordinary Least Square (OLS) estimators were converted into the Corrected Ordinary Least Square (COLS) estimators. To examine the technological equality between two districts, Chow Test has been used. The study is on Jhansi, Lalitpur and Jalaun districts of Jhansi division in Uttar Pradesh. Soil type was the main criteria for differentiating the areas for sampling. The selected farm size categories are marginal (up to 2.5 acre land), small (> 2.5 acre land to 5 acre land), and large (> 5 acre land). The study finds that, in selected regions, the maximum percentage of farmers lies in 51% to 60%, 51% to 70%, 71% to 80% and 81% to 90% categories of technical efficiency. But the 61% to 70% and 71% to 80% technical efficiency categories are followed by majority of farm size categories in the selected regions. In Jhansi and Lalitpur districts, marginal and small farmers are used the different amount of inputs but large farmers are used same amount of inputs in two regions. In the case of Jhansi and Jalaun districts and Lalitpur and Jalaun districts, there is no significant difference among the marginal-marginal, small-small and large-large farm size categories in the used amount of different inputs. In selected regions, the individual shares of each input for different categories of farmers are likely to be same to raise the output.

A consistent approach for performance measurement of electricity distribution companies

PurposeThe purpose of this paper is to present an integrated algorithm composed of data envelopment analysis (DEA), corrected ordinary least squares (COLS) and principal component analysis (PCA) to estimate efficiency scores of electricity distribution units.Design/methodology/approachSeveral DEA and COLS models are prescribed and their results are verified and validated by the algorithm. To calculate efficiency scores, three standard internal consistency conditions between DEA and COLS results are checked by the algorithm. If these conditions are satisfied, DEA is chosen as the superior model because it could be used for optimization as well. Otherwise, the geometric mean of DEA and COLS model is used as the final efficiency scores.FindingsThe algorithm of this paper may be easily applied to decision‐making units because of its robustness (combined DEA‐COLS input and output) and validity gained through PCA.Originality/valueThe integrated approach has several unique features which are: verification and validation mechanism by PCA, consideration of internal consistency conditions between DEA and COLS and consolidation of DEA and COLS for improved ranking given consistency conditions are violated.

A flexible and dynamic algorithm for assessment and optimization of utility sectors

This paper presents a flexible and dynamic algorithm for total assessment, ranking, and optimization of utility sectors. Data envelopment analysis (DEA), corrected ordinary least square (COLS), and stochastic frontier analysis (SFA) are employed for assessment and ranking purpose. The proposed algorithm is flexible due to utilizing both constant return to scale (CRS) and variable return to scale (VRS) DEA models. One-way analysis of variance (ANOVA) is applied to test the equality of the results obtained by DEA, COLS, and SFA models in terms of mean efficiency scores. In this regard, if all the three methods reveal equal performance, the DEA model (either CRS or VRS) with higher efficiency score is selected for optimization purpose. Otherwise, through Duncan’s multiple range test (DMRT), the method with the highest efficiency score is selected and then, using Spearman correlation test, the DEA model with higher correlation with the selected method is identified and applied for optimization of the utility sectors. The proposed algorithm is dynamic due to simultaneous application of deterministic (i.e. DEA and COLS) and stochastic (i.e. SFA) methods in order to improve the ranking and optimization of utility sectors. Two real case studies are considered in order to illustrate the applicability and usefulness of the proposed algorithm in assessment, ranking, and optimization of the utility sectors.

Data Envelopment Analysis as Nonparametric Least-Squares Regression

Data envelopment analysis (DEA) is known as a nonparametric mathematical programming approach to productive efficiency analysis. In this paper, we show that DEA can be alternatively interpreted as nonparametric least-squares regression subject to shape constraints on the frontier and sign constraints on residuals. This reinterpretation reveals the classic parametric programming model by Aigner and Chu [Aigner, D., S. Chu. 1968. On estimating the industry production function. Amer. Econom. Rev. 58 826–839] as a constrained special case of DEA. Applying these insights, we develop a nonparametric variant of the corrected ordinary least-squares (COLS) method. We show that this new method, referred to as corrected concave nonparametric least squares (C2NLS), is consistent and asymptotically unbiased. The linkages established in this paper contribute to further integration of the econometric and axiomatic approaches to efficiency analysis.

Energy efficiency assessment in automobile assembly plants by a hybrid COLS, DEA and PCA approach

Organisations that implement strategic energy management programs undertake a set of activities that, if carried out properly, have the potential to deliver sustained energy savings. One key management opportunity is determining an appropriate level of energy performance for a plant through comparison with similar plants in its industry. Performance-based indicators are one way to enable companies to set energy efficiency targets for manufacturing facilities. This article demonstrates a hybrid approach composed of corrected ordinary least square (COLS), data envelopment analysis (DEA) and principal component analysis (PCA) to analyse energy efficiency (plant-level) for assembly automobile plants that produce passenger cars, light-duty trucks, sport utility vehicles, and vans. Various assembly plants of Toyota, Volkswagen, DaimlerChrysler and Saypa in Japan, USA, Germany and Iran, are considered respectively, as the case of this study. This is the first study which introduces an integrated approach for multi objective energy efficiency problems in auto industries.

RANKING AND SCHOOL AUTONOMY: EFFICIENCY EFFECTS OF NEW INITIATIVES ON THE SINGAPORE EDUCATION SYSTEM

From 1979, the Singapore government started to transform the nature of secondary education in Singapore. In 1979, nine schools were chosen as Special Assistance Plan (SAP) schools. After the call towards reforming the school system in the 1980s, the development of Independent schools evolved. In 1994, a new category — the autonomous school — was established. Besides reforming the school structure, in 1992, the "ST Schools 100" (first published by The Straits Times on 19 August 1992) started to rank the top 50 schools in the Special/Express stream and the top 40 schools in the Normal stream, along with separate tables listing the top value-added schools in both streams. Until quite recently, this ranking scheme had been endorsed by the Ministry of Education since 1992 and published on their website annually since 1995. This paper looks at how these new initiatives have affected secondary school outcomes. Comprising a panel data set of 30 of the top 50 schools in Singapore over the 1991–2001 period, the study looks at the technical efficiency of schools as a response to the introduction of new initiatives using two methodologies. The first baseline approach is that of a Corrected Ordinary Least Squares (COLS) multiple-output distance function. The second methodology used is the technical efficiency frontier effects model as described by Battese and Coelli (1995) and Coelli and Perelman (1996) which is a maximum likelihood estimation technique.

An integrated DEA–COLS–SFA algorithm for optimization and policy making of electricity distribution units

This paper presents an integrated data envelopment analysis (DEA)–corrected ordinary least squares (COLS)–stochastic frontier analysis (SFA)–principal component analysis (PCA)–numerical taxonomy (NT) algorithm for performance assessment, optimization and policy making of electricity distribution units. Previous studies have generally used input–output DEA models for benchmarking and evaluation of electricity distribution units. However, this study proposes an integrated flexible approach to measure the rank and choose the best version of the DEA method for optimization and policy making purposes. It covers both static and dynamic aspects of information environment due to involvement of SFA which is finally compared with the best DEA model through the Spearman correlation technique. The integrated approach would yield in improved ranking and optimization of electricity distribution systems. To illustrate the usability and reliability of the proposed algorithm, 38 electricity distribution units in Iran have been considered, ranked and optimized by the proposed algorithm of this study.

Modeling Efficiency at the Process Level: An Examination of the Care Planning Process in Nursing Homes

To examine the efficiency of the care planning process in nursing homes. We collected detailed primary data about the care planning process for a stratified random sample of 107 nursing homes from Kansas and Missouri. We used these data to calculate the average direct cost per care plan and used data on selected deficiencies from the Online Survey Certification and Reporting System to measure the quality of care planning. We then analyzed the efficiency of the assessment process using corrected ordinary least squares (COLS) and data envelopment analysis (DEA). Both approaches suggested that there was considerable inefficiency in the care planning process. The average COLS score was 0.43; the average DEA score was 0.48. The correlation between the two sets of scores was quite high, and there was no indication that lower costs resulted in lower quality. For-profit facilities were significantly more efficient than not-for-profit facilities. Multiple studies of nursing homes have found evidence of inefficiency, but virtually all have had measurement problems that raise questions about the results. This analysis, which focuses on a process with much simpler measurement issues, finds evidence of inefficiency that is largely consistent with earlier studies. Making nursing homes more efficient merits closer attention as a strategy for improving care. Increasing efficiency by adopting well-designed, reliable processes can simultaneously reduce costs and improve quality.

Data Envelopment Analysis as Nonparametric Least Squares Regression

Data Envelopment Analysis (DEA), a nonparametric mathematical programming approach to productive efficiency analysis, envelops all observed data. In this paper we show that DEA can be interpreted as nonparametric least squares regression subject to shape constraints on frontier and sign constraints on residuals, and that classic parametric programming model is a constrained special case of DEA. Applying these insights, we present a nonparametric variant of the corrected ordinary least squares (COLS) method. We show that this new method, which we term corrected concave nonparametric least squares (C2NLS) is consistent and asymptotically unbiased. The linkages established in this paper contribute to further integration of the econometric and linear programming approaches.

International Benchmarking in Electricity Distribution: A Comparison of French and German Utilities

In this paper we present an international cross-country benchmarking analysis for utility regulation of France and Germany, the two largest electricity distribution countries in Europe. We examine the relative performance of 99 French and 77 German distribution companies operating within two different market structures. This paper applies several parametric benchmarking approaches to assess the relative technical efficiency of the utilities, such as deterministic Corrected Ordinary Least Squares (COLS) and Stochastic Frontier Analysis (SFA). Our base model uses the number of employees as a proxy for labor and network length as a proxy for capital as inputs. Units sold and the numbers of customers are considered as outputs. Our model variations and extensions analyze the effect of different characteristics of distribution areas (e.g. population density and the choice of investment in underground cable network). We find that utilities operating in urban areas feature higher efficiency scores and that investment in underground cables increase the technical efficiency of the distribution utilities.