Properties of inefficiency indexes on ?input, output? space

We analyze efficiency measurement in the full á\langleinput, output?\rangle space. We posit four types of axioms: indication (of efficient production bundles), monotonicity, independence of units of measurement, and continuity (in technologies as well as input and output quantities). Impossibility results establish a tension between indication and continuity. We focus on seven well-known inefficiency indexes from the operations-research and economics literature, establishing the properties they satisfy—and do not satisfy—on a general class of technologies satisfying minimal regularity conditions and on the subset of these technologies satisfying convexity. We also discuss several other indexes that are dominated by or very similar to these seven indexes. The set of properties satisfied by these indexes elucidates the trade-offs faced in selecting among the indexes.     

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.      

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.     

Axiomatic foundations of efficiency measurement on data-generated technologies

We assess the ability of three well-known technical efficiency indexes, the Debreu-Farrell index, the Färe–Lovell index, and the Zieschang index, to satisfy the Färe–Lovell axioms and continuity axioms (for technologies as well as input quantities) on the class of technologies generated by standard mathematical-programming methods of measuring efficiency: data envelopment analysis (DEA) and free-disposal-hull (FDH) analysis. Our principal conclusions are that (a) restriction to these data-based technologies adds continuity in input quantities to the properties satisfied by the Färe–Lovell and the Zieschang indexes (thus eliminating a salient advantage of the Debreu–Farrell index), but (b) none of the indexes satisfies all Färe–Lovell axioms (nor all continuity axioms) on either DEA or FDH technologies, and hence (c) trade-offs among the indexes remain. These findings provide motivation for the search for an index that does satisfy these axioms on DEA and FDH technologies.     

Rents,resources, and multiple technologies; Ricardian mechanisms in input-output modelling

ABSTRACT

To allow for ‘multiple technologies’ to produce a homogeneous output in input–output models, Duchin and Levine [(2011) Sectors may use Multiple Technologies Simultaneously: The Rectangular Choice-of-technology Model with Binding Factor Constraints, Economic Systems Research, 23(3), 281–302] propose an optimization model constrained by primary resources. We show that the Duchin–Levine model contains two different mechanisms by which multiple technologies can arise. If a factor in short supply is shared by the original and the newly entering technology, the output of the original, lower-cost technology will be reduced to make room for the higher-cost technology which is less intensive in that factor. In contrast, if the factor in short supply is technology-specific, a higher-cost technology supplements the original lowest-cost one, which stays fully active. Either mechanism implies a mechanism-specific set of prices, quantities and rents. We relate these results to classical views on comparative advantage, fixed output levels and the origin of rents.     

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.     

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。     

Econometric estimation of distance functions and associated measures of productivity and efficiency change

Multi-input multi-output production technologies can be represented using distance functions. Econometric estimation of these functions typically involves factoring out one of the outputs or inputs and estimating the resulting equation using maximum likelihood methods. A problem with this approach is that the outputs or inputs that are not factored out may be correlated with the composite error term. Fernandez et al. (J Econ 98:47–79, 2000) show how to solve this so-called ‘endogeneity problem’ using Bayesian methods. In this paper I use the approach to estimate an output distance function and an associated index of total factor productivity (TFP) change. The TFP index is a new index that satisfies most, if not all, economically-relevant axioms from index number theory. It can also be exhaustively decomposed into a measure of technical change and various measures of efficiency change. I illustrate the methodology using state-level data on U.S. agricultural input and output quantities (no prices are needed). Results are summarized in terms of the characteristics (e.g., means) of estimated probability density functions for measures of TFP change, technical change and efficiency change.     

Homotheticity and Non-Radial Changes

Färe and Mitchell(1992) have shown that cost functions for a multi-output firmobey a particular output-scaling law if and only if the underlyingproduction technology is ray-homothetic. Multi-output firms,however, frequently change their output mix in addition to theirscale. Therefore, it is important to identify technologies thatpossess relatively tractable analytical characteristics whensubjected to non-radial changes in the output vector. This paperconsiders additive and other, more general, changes in the outputvector. One result shows that the cost function obeys an ``output-translationlaw' if and only if the input correspondence is input homothetic,thus suggesting that ``input homotheticity' is more than justan ``input-scaling' property.     

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.     

Incorporating ancillary measures of process and quality change into a superlative productivity index

One of the persistent problems plaguing the measurement of productivity and output is accounting for changes in product quality. A similar problem arises in attempting to explain shifts in a production function using information on changes in the characteristics of the production process itself. We consider these problems under a behavioral model in which the firm chooses a profit-maximizing bundle of input/output/process characteristics as well as the profit maximizing levels of input and output. This view of quality change is similar to the endogenous design index advocated by Triplett [1983] for industrial prices and the endogenous quality indexes analyzed by Pollak [1983] for consumer prices. We show how a price-characteristics locus can be used to adjust the Tornqvist output- and input-oriented multifactor productivity indexes of Caves, Christensen and Diewert [1982] for changes in input, output and process characteristics. To show the applicability of the methodology to services, we apply the results in the framework of the commercial banking measurement of Fixler [1988] to measure the impact of bank branching on multifactor productivity.The refereeing process of this paper was handled through R. Färe.     

Returns to scale in the United States intercity bus industry

This paper has taken into account the a priori restrictions available from neoclassical cost theory in evaluating the relationship between cost and the level of output and input prices for U.S. intercity bus service. A general translog cost function is used which allows tests of the degree of returns to scale, homotheticity and non-constant elasticities of substitution among input pairs. Major empirical findings are: (i) the intercity bus service can be modeled by a homothetic production function, (ii) operators can substitute labor for capital by using vehicles more extensively, (iii) there are potential economies of scale in the provision of intercity bus service, and (iv) the Cobb-Douglas functional form used in earlier studies of the industry is inappropriate.     

Incorporating Price-Induced Innovation in a Symmetric Generalised McFadden Cost Function with Several Outputs

This paper proposes a multiple-output Symmetric Generalised McFadden (SGM) cost function, incorporating both exogenous and endogenous technological change. Whilst exogenous technological change is captured by the usual time trend, endogenous or price-induced technological change is cast within a partial-adjustment framework involving lagged input prices. The study points to various dimensions or components of technological change, and allows to disentangle pure factor substitution, given the state of the technology, from factor substitution due to price-induced changes in technology. Under the conditions of non-jointness in input quantities, the model further allows to identify technological change biases for each output separately. An empirical application is presented in which the proposed model is applied to time-series data on the feed manufacturing industry in Belgium. To improve on the econometrics, the SGM cost function also incorporates linear splines.     

IMPLICIT ELASTICITIES AND PRICE EFFECTS: AN UPDATED PROCEDURE

Based on the general procedure described by Casler [(2011) Coefficient Change, Price Effects, and Implicit Elasticities: Estimating Microeconomic Determinants over Two Time Periods. Economic Systems Research, 23, 153–174], this paper presents an updated approach to the estimation of input coefficient changes as functions of changing prices. The procedure makes direct use of relationships that emerge from the model of cost minimization subject to producing a desired level of output. Based on an initial specification of constant cross-price derivatives, the imposition of adding up and symmetry conditions allows the actual price and coefficient changes that occur between periods to identify implicit own and cross-price derivatives and corresponding elasticities, using data for only two time periods. With this updated approach, the calculation of derivatives is far simpler and leads to far more accurate measures of price-induced input–output coefficient changes than the original version.     

The measurement of the gains or losses to an enterprise through relative price changes: The terms-of-trade effect and real income

This paper provides a framework for measuring the terms-of-trade effect for an enterprise. This effect is the impact on the organization of changes in input to output prices as well as in the prices of goods and service upon which the income is utilized. The measurement of the effect is outlined with illustrative data and applied to the German Telecom sector, which has suffered particularly badly through adverse relative price changes. The case study of the German Telecom sector is also used to introduce the concept of real income. The framework advocated is argued to be particularly useful, since it allows not only the effects ex post of relative price movements to be evaluated, but also the effects ex ante of particular spending scenarios to be simulated (for example, investment). As such, it should be a useful addition to the ‘toolbag’ of managerial economists.     

Corporate hedging and input price risk

Input price variability is an important source of risk for corporations that process raw commodities. Models of optimal input hedging are developed in this paper based on the maximization of managerial expected utility. The relationship between hedging strategies and output decisions is examined to assess the impact of the ability to set output prices on futures market participation. As a firm's ability to set output prices diminishes in the short run, input futures positions increase although the optimal hedge ratio may either increase or decrease. For a perfectly competitive firm, however, shifts in output price caused by input price changes provide a natural cash market hedge of input price risk and reduce the firm's optimal input futures position.     

PRICE AND QUANTITY RESPONSES TO COST AND DEMAND SHOCKS*

ABSTRACT When prices are inflexible, real variables like production and inventories must bear the brunt of responding to cost and demand shocks. In these circumstances, one expects to observe rather more variation in quantities than in prices, and that is, in fact, what we observe in the data. To explain this observation, one must explain why prices are inflexible. Our goal in this paper is to ascertain whether it is selectivity in response to demand shocks or just a more extensive smoothing of prices than quantities which accounts for the relatively higher variation in quantities which we observe. We conclude that selectivity in response is clearly evident in the data: demand shocks have only very weak effects on prices, but they have substantial (if rather transitory) effects on quantities.     

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.     

Price-induced technical progress in 80 years of US agriculture

This paper presents a theory of technical progress that interprets the price-induced conjecture of Hicks. It provides also an exhaustive set of comparative statics conditions that constitute the scaffolding for an empirical test of the theory. A crucial assumption is that entrepreneurs make decisions about techniques on the basis of expected information about prices and quantities. Another assumption is that these decisions are made in order to fulfill a profitability objective. The novelty of our approach is that expected relative prices enter the production function as shifter of the technology frontier. The consequence of this assumption is an expansion of the traditional Shephard lemma that is useful for identifying the portion of input quantities that has been determined by the conjecture of price-induced technical progress (PITP). The theory is applied to a sample of 80 years of US agriculture. Three versions of the general model are presented. The first version deals only with expected relative prices. The empirical results do not reject the PITP hypothesis. The second and third versions introduce lagged expected relative prices, lagged R&D expenditures and lagged extension expenditures as explanatory variables of the portion of the input quantities that may be attributable to technical progress. I acknowledge invaluable discussions on this subject held over several years with Michael R. Caputo. I also acknowledge the use of the theory and its justifications that were presented in previous papers by Paris and Caputo (2001) and by Caputo and Paris (2005). All the errors are mine. I dedicate this paper to my wife, Carlene, who died of a rare cancer on May 5, 2001.     

Measuring productivity in the public sector: some conceptual problems

In many sectors of the economy, governments either provide various services at no cost or at highly subsidized prices. Examples are the health, education and general government sectors. The paper analyzes three possible general methods to measure the price and quantity of nonmarket government outputs. If quantity information on nonmarket outputs is available, then the first two methods of price valuation rely on either purchaser based valuations or on cost based valuations. If little or no information on the quantity of nonmarket outputs produced is available, then the method recommended in the System of National Accounts 1993 must be used, where aggregate output growth is set equal to aggregate input growth. The paper also discusses various methods of adjusting for quality change.