基于New-Cost-DEA模型的污水处理企业成本效率研究

近年来,中国污水处理企业的数量迅速增加,污水处理能力不断提高,但仍存在运行效率低下的问题。本文运用New-Cost-DEA模型,构建污水处理企业运行成本效率模型,测算13座污水处理企业的运行成本效率,并对运行成本进行分解,寻找造成运行成本损失的原因。结果显示:影响污水处理企业成本效率的因素不仅和投入要素数量有关,而且与投入要素价格有关;污水处理企业的成本效率低,是由于价格因素和配置效率引起的,需要通过降低投入要素的价格和对投入要素进行优化组合来降低运行成本,提高运行效率。     

Non-maximizing output behavior for firms with a cost-constrained technology

In many public service industries, firms are constrained by a cost (budget) and characterized by non-maximizing output behavior, due to bureaucratic behavior, for instance. This paper proposes a model based on the assumption that firms with a cost constraint do not maximize service levels due to resource preferences. It derives the exact relationships between services delivered, (shadow) input prices, cost constraints, and optimal input quantities. From these relationships, allocative efficiencies, technical efficiencies, output ray elasticities, and marginal cost can easily be derived.      

Prices and factor demand in an endogenized input–output model

This paper combines factor demand functions (for intermediate input and labour) and price equations (derived from a Generalized Leontief cost function) with the traditional input–output price model. The cost functions determine factor demands for materials and labour as well as output prices at given input prices. At the second level of aggregation, the intermediate demand as a single input is split proportional to the elements in the column of the technical coefficients matrix. The emphasis in this endogenization of technical coefficients is on two features. First, the repercussion of output on input prices, and, second, the link between the econometric model for the supply side and the input–output demand model.     

Weak Axiom of Cost Dominance: A Nonparametric Test of Cost Efficiency Without Input Quantity Data

Varian's Weak Axiom of Cost Minimization provides a nonparametric test of cost minimization, which can be applied only when both input price and quantity data are available for individual firms. In this paper we propose a Weak Axiom of Cost Dominance (WACD), which serves as the basis of an alternative test of cost-minimization applicable in situations where input quantity data are missing. Unlike a previous test developed by Diewert and Parkan, the proposed test does identify individual firms that violate the assumption of cost-minimizing behavior. It also provides an upper bound of the cost-efficiency of any observed firm. The test procedure is shown to be equivalent to applying dominance analysis using normalized input prices with reference to the Cost-indirect technology. The proposed method is applied to Nerlove's electrical utility data. The nonparametric results are also compared with parametric efficiency levels computed from a stochastic frontier cost function.     

Learning from input–output mixes in DEA: a proportional measure for slack‐based efficient projections

Several Data Envelopment Analysis (DEA) models use a radial distance measure that is based on the Debreu–Farrell notion of (in)efficiency. While this measure has an attractive interpretation, its use may be problematic if slacks or zeros are present in the data. The additive DEA model can perfectly deal with these problems, but the meaning of its associated scores is less intuitive than the one attached to the radial measures. We introduce an alternative efficiency measure, based on the results of the additive model, that can be decomposed in a Debreu–Farrell component and a factor that captures differences in input–output mixes with respect to those of the best practice reference observation. On an aggregate level, this second component can be considered as an indicator of the dispersion between radial efficiency measurement and results based on the Pareto–Koopmans efficiency notion. On the individual level, the measure allows us to regard relative inefficiency as resulting from (i) a divergence of implicit cost price vectors, and (ii) a cost level that is too high, even after adjustment for the implicit cost prices. Copyright © 1999 John Wiley & Sons, Ltd.     

Revisiting the decomposition of cost efficiency for non-homothetic technologies: a directional distance function approach

In the early 1980’s Kopp and Diewert proposed a popular method to decompose cost efficiency into allocative and technical efficiency for parametric functional forms based on the radial approach initiated by Farrell. We show that, relying on recently proposed homogeneity and duality results, their approach is unnecessary for self-dual homothetic production functions, while it is inconsistent in the non-homothetic case. By stressing that for homothetic technologies the radial distance function can be correctly interpreted as a technical efficiency measure, since allocative efficiency is independent of the output level and radial input reductions leave it unchanged, we contend that for non-homothetic technologies this is not the case because optimal input demands depend on the output targeted by the firm, as does the inequality between marginal rates of substitution and market prices—allocative inefficiency. We demonstrate that a correct definition of technical efficiency corresponds to the directional distance function because its flexibility ensures that allocative efficiency is kept unchanged through movements in the input production possibility set when solving technical inefficiency, and therefore the associated cost reductions can be solely—and rightly—ascribed to technical-engineering-improvements. The new methodology allowing for a consistent decomposition of cost inefficiency is illustrated resorting to simple examples of non-homothetic production functions.     

Consistent estimation of technical and allocative efficiencies for a semiparametric stochastic cost frontier with shadow input prices

Conventional parametric stochastic cost frontier models are likely to suffer from biased inferences due to misspecification and the ignorance of allocative efficiency (AE). To fill up the gap in the literature, this article proposes a semiparametric stochastic cost frontier with shadow input prices that combines a parametric portion with a nonparametric portion and that allows for the presence of both technical efficiency (TE) and AE. The introduction of AE and the nonparametric function into the cost function complicates substantially the estimation procedure. We develop a new estimation procedure that leads to consistent estimators and valid TE and AE measures, which are proved by conducting Monte Carlo simulations.     

Decomposition of cost efficiency and its application to Japanese-US electric utility comparisons

This paper presents a new formula for decomposing cost efficiency into technical, price, and allocative efficiencies in an environment marked by the fact that unit input prices differ among certain enterprises. We employed this formula in comparing cost efficiency between Japanese and US electric power companies, and found a significant difference in the price-based efficiency. However, negligible differences were found in the technical and allocative efficiencies.     

Maximizing public value for subsidized non-profit firms: a mathematical economic model

In many public service industries, firms are assumed to maximize certain public goals and are not allowed to make any profits. These public service firms are financed by fixed and variable subsidies and fees-for-services paid by users. Standard economic models, such as the profit maximization and cost minimization model, are not suitable for describing the production structure and the economic behavior of these firms. Productivity and efficiency measures derived from these models therefore are not accurate. This paper derives a model that fits this type of firm and its economic context. It derives the exact mathematical relationships between public value, services delivered, (money) revenues, costs, service prices, resource prices and subsidies. In an empirical setting the model can be used as a reference to calculate productivity and efficiency scores. The usability of the model is demonstrated by an application to Social Labor Services in the Netherlands.     

Efficiency aggregation with enhanced Russell measures in data envelopment analysis

In aggregation for data envelopment analysis (DEA), a jointly determined aggregate measure of output and input efficiency is desired that is consistent with the individual decision making unit measures. An impasse has been reached in the current state of the literature, however, where only separate measures of input and output efficiency have resulted from attempts to aggregate technical efficiency with the radial measure models commonly employed in DEA. The latter measures are “incomplete” in that they omit the non-zero input and output slacks, and thus fail to account for all inefficiencies that the model can identify. The Russell measure eliminates the latter deficiency but is difficult to solve in standard formulations. A new approach has become available, however, which utilizes a ratio measure in place of the standard formulations. Referred to as an enhanced Russell graph measure (ERM), the resulting model is in the form of a fractional program. Hence, it can be transformed into an ordinary linear programming structure that can generate an optimal solution for the corresponding ERM model. As shown in this paper, an aggregate ERM can then be formed with all the properties considered to be desirable in an aggregate measure—including jointly determined input and output efficiency measures that represent separate estimates of input and output efficiency. Much of this paper is concerned with technical efficiency in both individual and system-wide efficiency measures. Weighting systems are introduced that extend to efficiency-based measures of cost, revenue, and profit, as well as derivatives such as rates of return over cost. The penultimate section shows how the solution to one model also generates optimal solutions to models with other objectives that include rates of return over cost and total profit. This is accomplished in the form of efficiency-adjusted versions of these commonly used measures of performance.     

Imposing regional monotonicity on translog stochastic production frontiers with a simple three-step procedure

We show that the monotonicity condition is conceptually important in Stochastic Frontier Analysis (SFA). Despite its importance, most empirical studies do not impose monotonicity—probably because existing approaches are rather complex and laborious. Therefore, we propose a three-step procedure that is much simpler than existing approaches. We demonstrate how monotonicity of a translog function can be imposed regionally at a connected set (region) of input quantities. Our method can be applied not only to impose monotonicity on translog production frontiers but also to impose other restrictions on cost, distance, or profit frontiers.     

Efficiency of insurance firms with endogenous risk management and financial intermediation activities

Risk management is now present in many economic sectors. However, none of existing studies consider risk management as a potential determinant of firm performance. In this paper, we investigate the role of risk management and financial intermediation in creating value for financial institutions by analyzing U.S. property-liability insurers. Our main goal is to test how risk management and financial intermediation activities create value for insurers by enhancing economic efficiency through cost reductions. We consider these two activities as intermediate outputs and estimate their shadow prices. Insurer cost efficiency is measured using an econometric cost function. The econometric results show that both activities significantly increase the efficiency of the property-liability insurance industry.     

Duality and continuity

This paper fills the one remaining lacuna in (multiple-output) duality theory by provingjoint continuity (in input and output vectors) of cost, benefit, and (input and output) distance functions. Continuity is an important property where measurement error exists, for it provides assurance that small errors of measurement (of quantities or prices) result only in small errors in concepts like minimal cost. We consider continuity not only in prices and quantities, but also in technologies. Continuity in technologies might be more important than continjity in prices or quantities, because production technologies are almost certainly measured (or estimated) with error.     

Commodity house prices

This paper studies how commodity price movements have affected the local house prices in commodity-dependent economies, Australia and New Zealand. We build a geographically hierarchical empirical model and find that the commodity prices influence local house prices directly and also indirectly through macroeconomic variables. The impacts of commodity price changes are analogous to “income shocks” rather than “cost shocks”. Regional heterogeneity is also observed in terms of differential dynamic responses of local house prices to energy versus non-energy commodity price movements. The results are robust to alternative approaches. Directions for future research are also discussed.     

Decompositions of profitability change using cost functions

The paper presents a decomposition of a production unit’s cost ratio over two periods into explanatory factors. The explanatory factors are growth in the unit’s cost efficiency, output growth, changes in input prices and technical progress. In order to implement the decomposition, an estimate of the industry’s best practice cost function for the two periods under consideration is required. Profitability at a period of time is defined as the value of outputs produced by a production unit divided by the corresponding cost. Using the earlier work by Balk and O’Donnell, the paper provides a decomposition of profitability growth over two periods into various explanatory factors that are similar to the cost ratio decomposition except that change in outputs explanatory factor is replaced by two separate factors: an index of output price growth and a measure of returns to scale.     

COEFFICIENT CHANGE,PRICE EFFECTS,AND IMPLICIT ELASTICITIES: ESTIMATING MICROECONOMIC DETERMINANTS OVER TWO TIME PERIODS

This paper presents and estimates an input–output model in which input coefficient changes are functions of changing prices. The model produces results that mirror the characteristics of input demand functions based on the model of cost minimization subject to producing a desired level of output. It does not rely on the specification of a functional form for input coefficients, and it does not require the use of assumptions regarding the elasticity of substitution. Instead, it allows the actual price and coefficient changes that occur between periods to identify the implicit elasticities and own- and cross-price derivatives. Using this model, it is shown how accurate measures of price effects, including the full array of own and cross-elasticities of demand, can be estimated for models comprising up to 15 sectors given data for only two time periods.     

Persistent and transient cost efficiency—an application to the Swiss hydropower sector

Electricity prices on the European market have decreased significantly over the past few years, resulting in a deterioration of Swiss hydropower firms’ competitiveness and profitability. One option to improve the sector’s competitiveness is to increase cost efficiency. The goal of this study is to quantify the level of persistent and transient cost efficiency of individual firms by applying the generalized true random effects (GTRE) model introduced by Colombi et al. (Journal of Productivity Analysis 42(2): 123–136, 2014) and Filippini and Greene (Journal of Productivity Analysis 45(2): 187–196, 2016). Applying this newly developed GTRE model to a total cost function, the level of cost efficiency of 65 Swiss hydropower firms is analyzed for the period between 2000 and 2013. A true random effects specification is estimated as a benchmark for the transient level of cost efficiency. The results show the presence of both transient as well as persistent cost inefficiencies. The GTREM predicts the aggregate level of cost inefficiency to amount to 21.8% (8.0% transient, 13.8% persistent) on average between 2000 and 2013. These two components differ in interpretation and implication. From an individual firm’s perspective, the two types of cost inefficiencies might require a firm’s management to respond with different improvement strategies. The existing level of persistent inefficiency could prevent the hydropower firms from adjusting their production processes to new market environments. From a regulatory point of view, the results of this study could be used in the scope and determination of the amount of financial support given to struggling firms.     

Comparisons of Economic Inefficiency Between Output and Input Measures of Technical Inefficiency Using the Fourier Flexible Cost Function

The current paper constructs a Fourier flexible cost function, which is commonly known to be a more general function form than the typical translog form, and can globally approximate a true (but unknown) cost function. Both allocative and technical inefficiencies are considered using the Fourier function in the context of the parametric approach. The former is modeled using shadow input prices and the latter is formulated either by adding an extra term of scale parameter (when the Farrell's (1957) input technical inefficiency is assumed), or by correcting all the terms involving output quantities by a scale parameter (when the Farrell's output technical inefficiency is assumed). It is found that sample banks could save up to 23% of total costs, within the range of 3 and 69% uncovered by the previous works, in which allocative inefficiency plays a more important role than technical inefficiency. Furthermore, the cost of misallocated labor input alone constitutes more than 80% of total allocative inefficiency. Financial deregulation starting from 1991 in Taiwan appears to have improved economic efficiency of the banking industry.     

An econometric approach to estimating support prices and measures of productivity change in public hospitals

In industry sectors where market prices for goods and services are unavailable, it is common to use estimated output and input distance functions to estimate rates of productivity change. It is also possible, but less common, to use estimated distance functions to estimate the normalised support (or efficient) prices of individual inputs and outputs. A problem that arises in the econometric estimation of these functions is that more than one variable in the estimating equation may be endogenous. In such cases, maximum likelihood estimation can lead to biased and inconsistent parameter estimates. To solve the problem, we use linear programming to construct a quantity index. The distance function is then written in the form of a conventional stochastic frontier model where the explanatory variables are unambiguously exogenous. We use this approach to estimate productivity indexes, measures of environmental change, levels of efficiency, and support prices for a sample of Australian public hospitals.     

Price Discrimination in Input–Output

Modern economies are characterized by a great variety of pricing rules. Therefore, the commodities' prices and the primay factors' prices are discriminated in reality. However, in practical input–output tables, as well as in theoy, the prices are uniform and relative. In this work, an input–output model is described with absolute and different prices for final uses commodities and production's primay factors (wages, profits, etc.). In this case, the economic relationships are based on the commodities' demand curves for all the categories of final uses, and the factors' supply curves for all production's branches. In this way, we can establish the linkage and the feedback between factors' prices and quantities, and final uses commodities' prices and quantities. This is obtained by a novel interpretation of input–output, which approximates reality better.