Input Distance Function Research Articles

Disentangling Costs of Persistent and Transient Technical Inefficiency and Input Misallocation: The Case of Norwegian Electricity Distribution Firms

Numerous studies have focused on estimating technical inefficiency in electricity distribution firms. However, most of these studies did not distinguish between persistent and transient technical inefficiency. Furthermore, almost none of the studies estimated the cost of input misallocation arising from non-optimal use of inputs. One reason is that the cost function (input distance function) typically used in the literature does not allow for the separation of technical inefficiency and allocative inefficiency. In this study, we estimate both the persistent and transient components of technical inefficiency and input misallocation of Norwegian electricity distribution firms, using panel data from 2000 to 2016. Our modeling and estimation strategy is to use a system approach, consisting of the production function and the first-order conditions of cost minimization. Input misallocation for each pair of inputs is modeled via the first-order conditions of cost minimization. We also estimate the costs of each component of technical inefficiency and input misallocation by deriving the cost function for a multi-output separable production technology. Our modeling and estimation strategy handles endogeneity of inputs. Finally, we allow for inclusion of determinants of persistent and transient technical inefficiency. Our results show that the costs of input misallocation of Norwegian electricity distribution firms are non-negligible.

Technological and operational characteristics of the Chilean water and sewerage industry: A comparison of public, concessionary and private companies

Evaluating the technological and operational characteristics of the water and sewerage industry is interesting for researchers and policy makers. In this study an input distance function was applied to evaluate the technical efficiency, synergies between water and sewerage services, economies of scale and input substitutability for a sample of fully private, concessionary and public Chilean water companies over the years 2007–2015. The results indicate that, on average, the water industry reported high levels of technical efficiency over time. Lower costs can be achieved by forming larger companies through mergers and keeping water and sewerage companies integrated. Companies can further improve their efficiency by substituting labour with capital and operating expenses and adopting innovative strategies that allow them to manage their assets more efficiently and improve their environmental performance. The findings of this study are useful for water regulators to support decision making and introduce policies, incentives, and penalties to improve the performance of water companies over time.

Diversification economies in dairy farming – empirical evidence from Germany

Abstract This article explores how farm size is related to economic benefits from diversification. Using a data set pertaining to Bavarian dairy farms (2000–2014), we estimate an input distance function (IDF) to derive cost complementarities between distinct outputs. A Bayesian estimation technique is used to improve the theoretical consistency of the IDF. The results show that small dairy farms are more likely to benefit from diversification between milk and livestock production, while larger farms tend to benefit from diversification between milk and crop production. Both managerial and policy implications are discussed.

A superlative indicator for the Luenberger-Hicks-Moorsteen productivity indicator: Theory and application

Consisting of the difference between an output indicator and an input indicator, the Luenberger-Hicks-Moorsteen (LHM) productivity indicator allows straightforward interpretation. However, its computation requires estimating distance functions that are inherently unknown. This paper shows that a computationally simple Bennet indicator is a superlative indicator for the LHM indicator when one can assume profit-maximizing behavior and the input and output directional distance functions can be represented up to the second order by a quadratic functional form. We also show that the Luenberger- and LHM-approximating Bennet indicators coincide for an appropriate choice of directional vectors. Focusing on a large sample of Italian food and beverages companies for the years 1995−2007, we empirically investigate the extent to which this theoretical equivalence translates into similar estimates. We find that the Bennet indicator is a close empirical alternative to the LHM indicator for the sample.

Measurement of technical inefficiency and total factor productivity growth: A semiparametric stochastic input distance frontier approach and the case of Lithuanian dairy farms

This paper presents a four-component stochastic frontier model in which the frontier function is represented by an unknown smooth input distance function, and inefficiency is decomposed into persistent and transient inefficiencies. Furthermore, the pre-truncation mean and variance of the transient inefficiency are functions of the environmental variables. By differentiating the four-component input distance frontier with respect to the time trend, total factor productivity (TFP) growth is estimated under the semiparametric smooth coefficient framework, and is decomposed into six components, i.e., technical change, scale component, allocative component, external component, efficiency change, and residual component. The empirical example focuses on the Lithuanian dairy sector with multiple outputs. Our results show that there are some persistent and transient inefficiencies in Lithuanian dairy farms. However, these farms maintained TFP growth of 2% per annum on average during 2004–2016, and much of it is attributed to the technical change and scale components.

English

In Ethiopia, agricultural production and productivity are very low, and hence increase in production and productivity are vital to meet increasing food demand. This study identifies and quantifies the main sources of productivity growth in Ethiopian agriculture using the translog (TL) stochastic input distance function and the Ethiopian Rural Household Survey (ERHS) panel dataset. The true fixed effects (TFE) panel data estimator is used to separate inefficiency effects from observed and unobserved heterogeneity. The parametric Malmquist productivity index (MPI) is used to decompose total agricultural growth into three major sources. The average technical efficiency score was 0.875; this finding indi¬cates that on average a farmer produces 87.5% of the value of the output that is produced by the most efficient farmer using the same technology and inputs. This implies that they can reduce the inputs required to produce the average output by 12.5% if their farming operation becomes technically efficient. MPI shows that the average annual productivity growth was 17.9% between 1994 and 2009. Further decomposition of the index shows that scale efficiency change is the most important source of this growth, and accounts for about 14.5%. Technological improvement accounts for approximately 4.8% while the contribution of technical efficiency change is negative, leading to an annual productivity decline of 1.3%. This finding suggests that increasing productivity is possible via improving these components by improving training to the farmers, extension services, research and development, and agronomic practices. Keywords: Productivity growth, translog stochastic input distance function, Malmquist productivity index, Ethiopia.

Analysis of Environmental Total Factor Productivity Evolution in European Agricultural Sector

ABSTRACTProductivity analysis has been an important avenue for economic research. Therefore, medleys of quantitative techniques have been proposed to operationalize productivity analysis. In this article, an extended by‐production model is discussed and applied to ensure a link between the production and the pollution‐generating subtechnologies. The corresponding dual formulations are provided to interpret the economic role of pollution‐generating inputs in the subtechnologies. Finally, we integrate the proposed model with the environmental Luenberger–Hicks–Moorsteen productivity indicator based upon input and output directional distance functions. The proposed model is applied to measure the green economic growth of agricultural sectors of the selected European countries.

Evaluating complementary synergies in integrated crop-livestock systems in Ghana

PurposeThe purpose of this paper is to investigate the characteristics of crop-livestock diversification among smallholders in the forest-savannah agroecological zone of Ghana.Design/methodology/approachThe study uses a stochastic input distance function to investigate the evidence of economies of diversification and its effect on determining diversification decisions of smallholders in Ghana. Furthermore, this study also explores evidence of scale economies in integrated crop-livestock systems among smallholder farmers.FindingsThe empirical results show that economies of diversification are significant in determining diversification decisions of smallholders. The economies of scale are evident in integrated crop-livestock systems in Ghana, suggesting that opportunities exist to expand crop-livestock outputs without employing additional inputs or improved production technologies. Crop-livestock diversification is a desirable strategy for improving overall farm productivity among smallholders in Ghana. Economies of diversification were found to be significant among the output combinations, maize with other crops and other crops with livestock, in integrated crop-livestock production systems.Research limitations/implicationsThis study is based on a cross-sectional data set. Hence, the findings may be subject to some limitations; however, the authors have sought to minimise such limitations.Practical implicationsThe results imply that crop-livestock diversification is a desirable strategy for improving overall farm productivity. Therefore, the findings are useful for policymakers to design appropriate strategies for enhancing the production of specific output combinations in crop-livestock diversification systems among smallholders in Ghana. Specifically, such policies should promote the production and integration of crops such as legumes with other crops, and livestock with other crops in diversified farming systems to enhance overall farm productivity. This will reduce food insecurity and poverty among rural farm households and the entire rural population.Originality/valueThese results indicate that to improve crop-livestock productivity through diversification, and reduce the effect of climate variability, it is imperative to provide the enabling environment that will facilitate and encourage production of these output combinations among smallholders in Ghana. The empirical results enhance the literature by providing empirical evidence of the complementary synergies and economies of diversification in integrated farming systems and, hence, make recommendations for improving these farming systems.Peer reviewThe peer review history for this paper is available at: https://publons.com/publon/10.1108/IJSE-04-2019-0274.

A metastochastic frontier analysis for technical efficiency comparison of water companies in England and Wales.

Evaluating the performance of water companies is of great importance for both water utilities and water regulators. This paper explores comparative levels of technical efficiencies and technology gap ratios with the metafrontier concept by estimating an input distance function using stochastic frontier techniques. The metafrontier framework is employed in the water services of water and sewerage companies (WaSCs) and water-only companies (WoCs) in England and Wales. The results show that the English and Welsh water industry is an efficient industry, with WaSCs more efficient than WoCs. On average, a water company can increase its technical efficiency by operating in more densely populated areas and by investing in technology to reduce bursts in water mains. We also link the efficiency results with the regulatory cycle to assess the impact of regulation on the efficiency levels of water companies.

Are water tariffs sufficient incentives to reduce water leakages? An empirical approach for Chile

Given a changing and uncertain future climate with increasedwater scarcity, one of the main challenges of water companies is to reduce leakage in the water distribution system. To deal withthis challenge, water regulators should introduce efficient economic incentives. In this study, shadow prices of water leakage for 23 Chilean water companies over the period 2007–2015 were computed by estimating a translog input distance function using stochastic frontier techniques. The results indicate that the average shadow price of water leakage is 0.441€/m3, which means that on average the cost of losing one cubic metre from the water distribution system is 0.441€. Moreover, a comparison of the volumetric water tariffs and the shadow prices of water leakage evidenced that most water companies have economic incentives to reduce water losses, but they do not. Hence, the water regulator should introduce direct penalties to achieve water leakage targets. The findings of our study are of great importance for policy makers to define incentives to water companies to achieve environmental targets and more efficiently manage water resources.

An Application of Linear Programming in the Estimation of Technical Efficiency of DMU

The main objective of this research article is to propose linear programming problems for estimating the technical efficiency of DMU. This research article deals with the Shepard’s [1] input distance function and its properties are also evaluated. In addition to these extreme efficiency, efficiency but not extreme, weak efficiency and inefficient of a DMU are specifically examined here. In DEA the nature of returns to scale can be inferred. But we cannot quantify the returns to scale. The computations for the classification of RTS of a DMU are also derived in this discourse. In 2009, Barbara A. Mark et.al [2] in their paper, depicted an innovative method which is non-parametric to estimate technical efficiency. In 2011 S. Nuti et.al [3] inquired into the interrelations among technical efficiency scores, weighted per capita cost and overall performance. Gahe Zing Samuel Yannik et.al [4] used DEA to calculate technical assessment in banking sectors. In 2015 Smita Verma and others chosen a random sample of ten textile mills in India over the time period 2011-2013 and measures its technical efficiency using Data Envelopment Analysis

Efficiency of New Zealand’s District Health Boards at Providing Hospital Services: A stochastic frontier analysis

The majority of secondary and tertiary healthcare services in New Zealand are provided through public hospitals managed by 20 local District Health Boards. Due to data issues and ill-judged generic public perceptions, efficiency studies are insufficient in spite of the extensive empirical literatures available. This inevitably leads to criticisms about the perverse incentives which might be created by the National Health Targets designed to improve the performance of public health services. Utilizing a multifaceted administrative hospital dataset, this is the first case study to measure both the technical and cost efficiency of New Zealand public hospitals during the period of 2011–2017. More specifically, it deals with the question of how hospital efficiency varies with respect to activities accounted for by the National Health Targets. The empirical results show no evidence that these targets are achieved at the expenses of lowering the overall efficiency of hospital operations. The national technical efficiency is averaged at 86 percent over the period and cost efficiency is 85 percent. The results are derived by stochastic input distance function and cost frontier in order to accommodate multiple outputs and limited number of census observations. Efficiency ranking is sensitive to specifications of the inefficiency error term, but reasonably robust to the choice of functional form and different proxies for capital input.

The effect of environmental policy on Chinese firm's green productivity and shadow price: A metafrontier input distance function approach

In this paper, a new parametric meta-frontier estimation method, which we call the metafrontier input distance function (MIDF), is proposed to construct a new green productivity index and the shadow price for Chinese coal-fired power plants. Taking the policy heterogeneity into account, 93 Chinese coal-fired power plants are divided into two groups based on whether they are located in China's key “environmental protection cities”, a Chinese environmental protection policy. Using this method, the productivity and the shadow price of the two groups are compared. We find that the average annual growth rate of green productivity of coal-fired power plants in key environmental protection cities is 5.11% from 2005 to 2010, while in the non-key environmental protection cities it is 9.43%, suggesting that environmental regulation will damage productivity growth. Interestingly, although coal-fired power plants in key environmental protection cities face more stringent environmental regulation, their green productivity index still shows an overall upward trend, which partially supports the Porter hypothesis. For the shadow price of sulfur dioxide (SO2), the group-based shadow price of coal-fired power plants in key environmental protection cities is 5419 US dollar per ton on average, while in non-key environmental protection cities it is 1628 US dollar per ton, which also indicates that power plants facing more stringent regulation bear greater abatement costs.

Inefficiency in Childcare Production: Evidence from Italian Microdata

The purpose of the paper is to study inefficiency in the production technology of the childcare service and to carry out a comparative analysis of public and private day-care centres. An empirical analysis on cross-section micro-data from a region of northern Italy has been conducted by using an input-distance function with a translog specification. Estimates of the multi-output production technology and input-oriented technical inefficiency are obtained in a stochastic frontier model with a half-normally distributed one-sided error. Heteroscedasticity has been modelled to investigate the determinants of inefficiency and estimate their marginal effects. We find that production exhibits increasing returns with an estimated elasticity of scale of 1.21. Separability between inputs and outputs is rejected at a 5% level of significance. The average estimate of technical inefficiency is 10% and public centres are more inefficient than private centres by 4.1 percentage points. The proportion of part-time children and the presence of mixed-age classrooms are significant determinants of inefficiency which equally affect both public and private centres.

Inefficiency of manual weeding in rainfed rice systems affected by parasitic weeds

AbstractManual weeding is the predominant weed control practice and the most labor‐consuming activity in smallholder, rainfed rice systems in sub‐Saharan Africa. This study investigates the technical inefficiency of weeding labor, other labor, and overall inputs, and identifies sources of technical inefficiency of weeding labor in the context of parasitic weed infestation. The analysis applies a two‐stage approach. First, a directional input distance function DEA approach was used to compute input‐specific technical inefficiencies. Second, sources of technical inefficiency of weeding labor were identified using a truncated bootstrap regression. Data from 406 randomly selected smallholder farmers from Benin (n = 215) and Côte d'Ivoire (n = 191) were used. The technical inefficiency of weeding labor was high in both countries (58% in Côte d'Ivoire and 69% in Benin). This implies that a substantial fraction of weeding labor could be saved without reducing rice productivity or increasing the use of other inputs. A decrease in the technical inefficiency of weeding labor with an increase in production scale was observed. In addition, weeding regime and education level were each associated to significant changes in the technical inefficiency of weeding labor.

New Definitions of Economic Cross-Efficiency

Overall efficiency measures were introduced in the literature for evaluating the economic performance of firms when reference prices are available. These references are usually observed market prices. Recently, Aparicio and Zofio (2019) have shown that the result of applying cross-efficiency methods (Sexton et al., 1986), yielding an aggregate multilateral index that compares the technical performance of firms using the shadow prices of competitors, can be precisely reinterpreted as a measure of economic efficiency. They termed the new approach ‘economic cross-efficiency’. However, these authors restrict their analysis to the basic definitions corresponding to the Farrell (1957) and Nerlove (1965) approaches, i.e., based on the duality between the cost function and the input distance function and between the profit function and the directional distance function, respectively. Here we complete their proposal by introducing new economic cross-efficiency measures related to other popular approaches for measuring economic performance. Specifically those based on the duality between the profitability (maximum revenue to cost) and the generalized (hyperbolic) distance function, and between the profit function and either the weighted additive or the Holder distance function. Additionally, we introduce panel data extensions related to the so-called cost Malmquist index and the profit Luenberger indicator. Finally, we illustrate the models resorting to Data Envelopment Analysis techniques from which shadow prices are obtained, and considering a banking industry dataset previously used in the cross-efficiency literature.

Efficiency Analysis of Electricity, Thermal Power Production and Supply Industries in China

In this paper, the input-oriented distance function is applied to the efficiency analysis of China’s electricity, thermal power production and supply industries. Due to the obvious gap between China’s east, central and west, we use the metafrontier method to divide the data into three parts according to east, central and west. On the basis of the previous research, this paper makes some innovations in the estimation method, that is, using the two-stage linear programming method to estimate the common boundary input distance function. The results show that the technical efficiency of the eastern, central and western regions is significantly different, which is mainly reflected in that the technical efficiency of the eastern region is higher than that of the central and western regions, and the efficiency gap between the three regions shows no signs of narrowing during the “eleventh five-year plan” and “twelfth five-year plan”. Therefore, the electricity, thermal power production and supply industries in central and western China still need to change the development mode and improve the development quality.

Total Factor Energy Productivity and Efficiency Changes of the Gher (Prawn-Carp-Rice) Farming System in Bangladesh: A Stochastic Input Distance Function Approach

This paper measures energy performance, Total Factor Energy Productivity (TFEP), technical change (TC) and energy efficiency change (EEC) of the gher (prawn-carp-rice) farming system using a unique panel data of 90 farmers covering a 14 year period (2002–2015) from southwest Bangladesh by employing a stochastic input distance function approach. Results reveal that all inputs contribute significantly to energy productivity of the gher farming system with male labor energy input being the major contributor followed by energy from machineries, seeds and chemicals. Energy performance of the High Yielding Variety (HYV) rice enterprise is highly efficient whereas the prawn enterprise is highly energy inefficient. Furthermore, energy performance of the HYV rice enterprise improved significantly over time. Significant competition exists between HYV rice and prawn enterprises as well as prawn and carp enterprises. Experience and education significantly improve energy efficiency whereas gher area and household size significantly reduces it. TFEP grew at the rate of 2.56% per annum (p.a.) solely powered by technical progress at the rate of 2.57% p.a. Gher system can be sustained in the long-run driven by technical progress and improvements in energy productivity of the HYV rice enterprise. Policy implications include investments in R&D and education targeted at the gher farmers.

Measuring technical efficiency and marginal costs in the performing arts: the case of the municipal theatres of Warsaw

The aim of this paper is to bring new contributions to the analysis of efficiency and productivity in the performing arts. Firstly, we consider how the behaviour of a performing arts company can be analysed using multi-output production technology, given that these companies offer different products in terms of quantity and quality. Secondly, and to the best of our knowledge for the first time in the literature, we propose a procedure to measure the marginal costs associated with the production of performing arts firms. Moreover, this procedure can be applied to any other cultural sector successfully. To achieve our goals, we estimate a stochastic input distance function for a panel data set of 19 public municipal theatres in Warsaw over the period 2000–2012. Additionally, we calculate the technical efficiency indices for these theatres and characterize some determinants of their efficiency, paying special attention to the effect of public grants. Our findings suggest that, at the sample mean, these municipal theatres in Warsaw could have used 7% less inputs to achieve the same level of outputs. At the same time, the presence of public grants improves efficiency and, so, contributes to extending innovation and diversity. The marginal cost of a new performance is around 7149 PLN, and introducing a new title costs up to 3.33 times more than one which stages one title already established in the repertoire. And, as already highlighted in other researches, we also confirm the presence of the cost disease and the positive effect of public subsidies on efficiency and quality in the performing arts.

Impact of High-Powered Incentive Regulations on Efficiency and Productivity Growth of Norwegian Electricity Utilities

This study examines the hypothesis that changes to high-powered incentive regulations have a positive efficiency and productivity growth effects in a regulated electricity distribution industry. We estimate an input distance function using the stochastic frontier analysis method to compute technical efficiency scores for 121 Norwegian utilities over the period 2004-2012. We explore sources of productivity growth by parametrically decomposing the Malmquist productivity index into efficiency change, technical change, and scale change. Unlike previous studies, we examine the difference in performance across two regulatory regimes: yardstick competition (2007-2012) and RPI-X incentive regulation (2004-2006). Results show significant efficiency and productivity growth improvements with embodied technical change as the main driver.