Notes on some inequalities in economics

Summary. Inequalities created by relating gauge (distance) functions and their dual support functions have been used in economics and operations research/management science to measure efficiency and productivity. The most familiar example is the Farrell (1957) measure of cost efficiency and its decomposition into technical and allocative components, which can be shown to be an application of the Mahler (1939) inequalities, although Farrell was probably unaware of the connection. In this short paper we add to this literature by providing explicit relationships between distance functions and support functions to form five different inequalities. These inequalities are derived from three support functions: the cost function, the revenue function and the profit function, and three gauge (distance) functions: the input distance function, the output distance function and the directional (technology) distance function.     

The contributions of technical and allocative efficiency to the economic performance of European railways

This paper provides an empirical analysis of the relative contributions of allocative and technical efficiency to the productivity performance of European railways over the period 1972 to 1999. A stochastic frontier approach is used to analyse the cost structure of the railway industry. We estimate a translog cost system in which allocative inefficiency is modelled through an exact relationship between the cost share equations and the cost function. To allow the estimation of such a model using the sample theory approach we assume that the share equation residuals represent deviations from first-order conditions and, therefore, that they represent exclusively allocative inefficiencies. The use of this simplifying assumption renders our analysis computationally tractable, but it could be inconsistent with the economic theory of duality and for that reason caution is required in interpretation of results. Acknowledging this caveat, we find that European railways have experienced significant cost increases due to inefficient behaviour, with a mean value of around 15%. In contrast to previous studies, however, our estimates indicate a larger role for allocative inefficiency, which accounts for around of a half of the total increase in cost inefficiency.

Economic inefficiency in a revenue setting: the Norwegian whitefish fishery

The main focus in the inefficiency literature is on suboptimal input use and how this causes increased costs, due to technical and allocative inefficiency. Production or cost functions are then typically used to describe the underlying technology of the firm. The possible revenue loss, due to lower than maximum production levels and suboptimal output mix, has received substantially less attention. By using a revenue function to measure inefficiency, the focus, model and estimation technique presented in this article differ from those of previous studies. A shadow revenue model is used to decompose revenue inefficiency into its technical and allocative components, in which the allocative inefficiency is due to a suboptimal output mix. The approach is illustrated using panel data of Norwegian whitefish trawlers. The results reveal large inefficiencies, with respect to output levels as well as output mix, indicating that this can be an important part of the picture when investigating economic inefficiency. To identify the determinants of revenue inefficiency, we conduct a second-step regression, in which technical and allocative inefficiency is regressed upon a set of explanatory variables. The inefficiencies are partly explained by the management system and fleet structure.     

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.     

Economic Reform and Total Factor Productivity Growth in Indian Manufacturing Industries

A stochastic frontier production function model is applied to Indian manufacturing industries, to decompose the sources of total factor productivity growth into technical progress, technical efficiency, scale efficiency, and allocative efficiency. Empirical results based on data from 2000 to 2006 suggest that increased investment needs time to deliver increased productivity and efficiency, because new technology combined with fresh investment requires higher numbers of skilled workers, better managerial practices and an advanced input mix, all of which generally take time to develop. Thus, the Indian economy must boost technical efficiency by providing skilled workers and high quality managers to further economic reform.     

Strategic planning of optimal resource allocation in response to global financial crisis – a study of international tourist hotels

This study is principally designed to examine the changes in the efficiency, effective resource allocation and future operation strategies of Taiwan's international tourist hotel in global economic downturn. At first, we set up critical input and output factors and construct an assessment model using Data Envelopment Analysis (DEA) for analysis of relative efficiency. Further, we apply an allocative efficiency model for additional considerations of each input cost and analyse proper and effective resource allocation. Finally, there are significant changes in overall efficiency of international tourist hotels under global financial crisis. We can also reach an effective allocation of the overall resources. In such cases, lowering cost has become a key issue for sustainable operation of international tourist hotel. Finally, the greatest contribution of this study is to further classify the competitiveness and optimal cost allocation of Taiwan's international tourist hotels into seven categories based on the study results and propose strategic planning of future operations for hotel administrators’ reference in making improvements in the future.     

Determinants of banks’ Nerlovian economic efficiency: a DEA-bootstrap approach

ABSTRACT

This study aims to evaluate the Nerlovian economic efficiency of Taiwanese commercial banks and its determinants by assuming the presence of an imperfectly competitive market using a two-stage estimation procedure: Nerlovian economic inefficiency and its components’ price, technical and allocative efficiencies computed and decomposed in the first stage, which are regressed on the explanatory variables with a bootstrapped truncated approach in the second stage. The estimation results show that in the first-stage analysis, the Nerlovian economic inefficiency of banks is primarily due to allocative inefficiency, and indicate the existence of price inefficiency in Taiwan. In the second-stage analysis, the results confirm that both the years in operation of the bank and the ratio of credit loans are the main determinants of banking profit efficiency. In addition, this study not only shows that publicly owned banks contribute to better price efficiency but also proves that loan loss reserve to total assets is negatively associated with technical efficiency. The equity ratio exerts an insignificant favourable impact on allocative efficiency. The findings of this research are essential for bank managers in Taiwan.     

Evaluating the productive performance of UK universities as cost-constrained revenue maximizers: an empirical analysis

The study presents an empirical analysis of the relative revenue efficiency of UK universities in providing teaching and research. With government policies pressurizing the largely public-funded universities to secure efficiency in both input usage and output revenue, university producers are modelled as cost-constrained revenue maximizers. Taking explicit account of the quality of research output, the methodology uses linear programming techniques to construct nonparametric cost indirect production frontiers and to compute revenue efficiency relative to these frontiers. Revenue efficiency is then decomposed into its (output) allocative and technical components. Further analysis investigates the sources of allocative and technical inefficiencies.     

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.     

中国地区工业生产绩效:结构差异、制度冲击及动态表现

This paper is dedicated to probing into the dynamic performances of industrial productivity across regions of transitional China, using the panel data of provincial level. Based on the approach by Kumbhakar (2000), TFP (total factor productivity) growth is decomposed into four components. The main results are as follows. First, since 1988, the industrial TFP growth has been commonly accelerated across regions, with a rising technical change rate as the principal impetus. Second, meanwhile, technical efficiency and factors’ allocative efficiency are deteriorated with scale efficiency switching from being retrogressive to being progressive. Third, although the SOE (state-owned enterprise) reform in the late 1990s has constituted a common shock to the industrial productivity, the eastern area with relatively few SOEs suffers the least from this policy enforcement. Fourth, by exploring the sources of productivity differences, we further confirm that the institutional shock launched by SOE reform in the late 1990s is crucial for the enhancement of scale effects as well as the temporarily rapid decline of factors’ allocative efficiency; in addition, the educational level of the labor-force and the share of non-SOEs in the industrial output contribute positively to the acceleration of technical change and the improvement of allocative efficiency. The economic transition, accompanied by gradual institutional reforms, is reshaping the map of regional industrialization through various channels. Translated from Jingji Yanjiu 经济研究 (Economic Research Journal), 2006, (11): 48–59     

Allocative efficiency measurement revisited—Do we really need input prices?

The traditional approach to measuring allocative efficiency exploits input prices, which are rarely known at the firm level. This paper proves allocative efficiency can be measured as a profit-oriented distance to the frontier in a profit-technical efficiency space. This new approach does not require information on input prices. To validate the new approach, we perform a Monte-Carlo experiment providing evidence that the estimates of allocative efficiency employing the new and the traditional approach are highly correlated. Finally, as an illustration, we apply the new approach to a sample of about 900 enterprises from the chemical manufacturing industry in Germany.     

Measurement of technical and allocative efficiencies using a CES cost frontier: a benchmarking study of Japanese transmission-distribution electricity

This paper estimates the technical and allocative inefficiencies of the transmission-distribution sector of Japanese electric utilities using a panel data during the 1981–1998 period. A stochastic production frontier of the CES form is jointly estimated with input demand equations. Taking advantage of the self-duality, we retrieve the cost frontier by which the impacts of technical and allocative inefficiencies on costs and input demands are measured. The estimated elasticity of substitution is significantly different from unity in favor of the CES specification over the Cobb–Douglas. The results show that observed costs are 9 to 48% higher than the efficient level; technical inefficiency raises costs by 1 to 28%, while allocative inefficiency does so by 8 to 30%. Although their impacts on costs are similar, technical inefficiency more fluctuates so the differences in the performance of utilities are mainly due to technical inefficiency. We also find a substantial over-utilization of capital for all utilities.

基于DEA方法的农作物成本效率测度及区域特征分析——以大豆为例

农作物的成本效率是影响农业生产的重要因素。以大豆为例,利用DEA的成本效率模型对2004—2008年大豆的成本效率进行测度,并从纯技术效率、规模效率和配置效率三个方面对其进行分析。同时,结合变异系数比较了大豆主产区的不同成本效率特征,并分析了纯技术效率、规模效率和配置效率对成本效率造成的影响。结果表明,大豆的成本效率并不高,配置效率是主要影响因素,因此应调整资源配置以提高成本效率。另外,大豆主产区之间的成本效率相差较大,应调整大豆生产区域以发挥地区比较优势。     

Government Interventions, Market Imperfections, and Technical Inefficiency in a Mixed Economy: A Case Study of Indian Agriculture

This paper uses an output-maximizing framework in the presence of expenditure constraint to measure output loss and input misallocation resulting from market distortions and technical inefficiency. A generalized indirect production function accommodating allocative distortions and technical inefficiency is used. Allocative distortions are captured in terms of effective (shadow) prices in which distortion parameters are both farm- and input-specific. The stochastic frontier approach is used to model technical inefficiency. Using farm-level data on 105 jute growers from West Bengal, India, we find that average output losses due to allocative distortions and technical inefficiency are 6.3% and 14%, respectively.     

Banking deregulation and allocative efficiency in Pakistan

This article examines the impact of deregulation policies on allocative efficiency of banks in Pakistan. It investigates whether deregulation has impacted the pattern of allocative efficiency of banks and explores which bank ownership segment has been more responsive. It uses data from 1991 to 2005 and explicitly models allocative inefficiency by using the translog shadow cost-share system. Empirical results show that overregulation and imperfect market structure hampers the ability of banks to make competitive decisions. We find evidence of allocative inefficiency leading to over-utilization of labour and deposits vis-à-vis operating cost. Empirical results for time-varying allocative efficiency show declining levels of allocative inefficiency for state-owned and private banks in post-reform period. Deregulation policies induce state-owned banks to decrease over-utilization of labour relative to deposits and operating cost while private banks succeed in using operating cost closer to optimal levels. Hence, policymakers have latitude to introduce more reforms without jeopardizing allocative efficiency.     

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.     

A two-stage translog marginal cost pricing approach for Floridian hospital outputs

Since the passage of the Affordable Care Act (ACA) of 2010, issues still remain regarding the mandated purchase of insurance to ensure more universal coverage. One such issue is the pricing of these insurance packages and whether or not the reimbursements will cover necessary services. Therefore, policy concerns exist that increasing the number of insured individuals may not curtail costs. Conversely, providers may not wish to treat patients covered by excessively frugal plans such as Medicaid; hence the trade-offs between access and cost control. In this article, we present findings from a cost function and a productivity approach to determine the marginal cost of providing inpatient hospital care for hospitals operating in Florida during 2005. Using these methodological approaches, we are able to use the marginal rate of transformation to determine the relative marginal costs while controlling for hospital technical and allocative inefficiency. Our work differs from earlier articles as we avoid the Greene problem for cross-sectional models through a two-step approach. By including both reimbursement rates under conditions of hospital efficiency, we can ascertain payment schemes that should, at least in theory, cover necessary costs for patient care without leading to excessive input usage.     

Technical efficiency effects of input controls: evidence from Australia's banana prawn fishery

This paper provides the first ex post estimates of the effects of input controls on technical efficiency in a fishery. Using individual vessel data from the northern prawn fishery of Australia for the years 1990–1996 and 1994–2000, stochastic production frontiers are estimated to analyse the efficiency impacts of input controls on engine and vessel size. The results indicate that technical efficiency is increasing in a measure of vessel size and engine capacity that was controlled by the regulator from 1985 to 2001, and decreasing in an unregulated input, gear headrope length. The study shows that fishers have substituted from regulated to unregulated inputs over the period 1990–2000 and technical efficiency has declined coincident with increasing restrictions on vessel size and engine capacity. The decline in technical efficiency indicates that the goal of the regulator to increase economic efficiency has not been realized.     

中国地区工业生产绩效:结构差异、制度冲击及动态表现

本文利用省级面板数据研究转型过程中中国地区工业生产绩效的动态表现。基于Kumbhakar(2000)的方法,我们将TFP增长分解为四个因素的变化。结果发现:(1)自1988年以来各地区工业部门的TFP增长率都出现了增长的趋势,其首要推动力在于技术进步率的不断提高;(2)与此同时,技术效率和要素配置效率出现了恶化,而规模效率则从恶化走向了改善。(3)上世纪90年代末的国企改革对各地区的工业生产绩效的构成造成了普遍的冲击,而民营化程度较高的东部地区受到的冲击最小。(4)通过分析绩效差异的源泉,我们进一步确认90年代末国企改革的制度性冲击促成了工业规模效率的提高,却导致了要素配置效率的短期下降,而劳动力教育水平和非国有经济比重的提高,则有助于促进工业技术进步、改善配置效率。伴随着制度变革的经济整体转型正从多个向度重构着中国地区工业化的版图。     

Efficiency in the factoring industry

The efficiency and productivity in the Italian factoring industry between 1993 and 1997 is investigated using DEA. The factoring industry is an important part of many financial systems and it has established itself as a major source of finance and credit management for a growing number of companies. However, as far as the authors are aware no studies have applied frontier methodologies to examine the efficiency and productivity of this industry. This paper focuses on the Italian market, the second largest in the world after the UK. The results suggest that there are substantial cost savings to be had in the Italian factoring industry: the mean cost inefficiency in the Italian factoring industry over the period 1993–1997 ranged between 14% and 22%. These inefficiencies are mainly generated by allocative rather than technical inefficiencies. Scale and technical inefficiencies seem to be similar in magnitude and the supposed importance of the latter typically found in the banking efficiency literature, are not observed in Italian factoring. Firm size does not appear to be related to technical, allocative and economic efficiency and the hypothesis that ownership structure influences factoring firm efficiency could not be rejected. In order to analyse efficiency change over time the Malmquist index is used. Total factor productivity was decomposed into technical change and efficiency change and the latter was further divided into pure efficiency and scale efficiency change. Productivity changes were slight over the period 1993–1996, while a substantial increase in productivity occurred between 1996 and 1997: the latter appears to be the result of a large improvement in the technology and a positive scale efficiency change, however, this was slowed down by a negative pure efficiency change.