A Cost Indirect Evaluation of Productivity Change in UK Universities

The study provides an empirical analysis of productivity change in publicly-funded UK universities, against a background of government policy specifically designed to enhance the productive efficiency of universities in the provision of teaching and research. The nonparametric analysis employs a cost indirect approach to measuring productivity change, taking explicit account of the quality of research output and decomposing productivity change into technical change and efficiency change. The latter is also decomposed into changes in pure technical efficiency, scale efficiency and output congestion. Changes in size efficiency are also computed. On average, productivity declined by 4% over 1989–92, mainly as a result of regressive technical change. Evidence of biased technological change was found, with the frontier shifting out in favour of the teaching outputs and in relative to the research output.     

Estimating total factor productivity using parametric,nonstochastic cost frontiers

The standard approach to measuring total factor productivity can produce biased results if the data are drawn from a market that is not in long-run competititve equilibrium. This article presents a methodology for adjusting data on output and variable inputs to the values they would have if the market were in long-run competitive equilibrium, given the fixed inputs and input prices. The method uses nonstochastic, parametric translog cost frontiers and calculates equilibrium values for output and varible inputs using an iterative linear programming procedure. Data from seven industries for 1970–1979 are used to illustrate the methodology.The editor for this paper was William H. Greene.     

A directional slacks-based measure of technical inefficiency

Radial measures of efficiency estimated using linear programming (LP) methods can be biased since slack in the constraints defining the technology suggests that at least one input can be reduced, or one output can be expanded, even though a firm is deemed to be “technically efficient.” In this paper, we propose a directional slacks-based measure of technical inefficiency to account for the potential of slack in technological constraints. When no such slacks exist, directional slacks-based inefficiency collapses to the directional technology distance function. Our proposed measure helps to generalize some of the existing slacks-based measures of inefficiency. We examine the financial services provided by Japanese cooperative Shinkin banks, and estimate their inefficiency during the period 2002–2005. This inefficiency declined slightly during the period. We thus propose that slack is an important source of inefficiency which is often not captured by the directional technology distance function.     

Scale Efficiency in Canadian Trust Companies

A new method for estimating a relative scale function is derived which does not require the specification or estimation of the firm's cost function. The method is applied to a panel of Canadian trust companies for the years 1985–1988. Results show that the industry scale function is convex with respect to firm size, as measured by the firm's assets. The method avoids a number of shortcomings associated with traditional studies of scale economies in financial institutions.     

A multiproduct Symmetric Generalized McFadden cost function

This paper introduces a flexible multiproduct cost function that permits zero values of one or more of the outputs and can impose restrictions quite easily, if not automatically satisfied, to ensure global concavity property. It satisfies linear homogeneity (in prices) property and is flexible in the output space. Thus the function is ideal for estimating, for example, economies of scope, cost complementarity, product-specific returns to scale, etc., without worrying about zero values of output(s) and extrapolations to points far from the point of approximation. As an empirical application, we use panel data (1978–1985) on 12 Finnish foundry plants to estimate technical progress, overall returns to scale, product-specific returns to scale and economies of scope.     

The Structure of Production in the Norwegian Fish-Processing Industry: An Empirical Multi-Output Cost Analysis Using a Hybrid Translog Functional Form

An empirical analysis of production structure in the Norwegian fish-processing industry is undertaken, based on data for the period 1985–90. This industry processes raw materials into fresh, frozen, salted and dried fish products. Two technologies coexist in the industry. Producer behaviour is represented by a multi-output variable, or restricted cost function for each technology. The hybrid translog functional form is adopted for estimation, as this form can be evaluated even if some of the output values are zero. Results from the empirical analysis provide important information for the restructuring currently taking place in the industry.     

Productivity gaps and capacity utilization in the manufacturing sectors of five OECD-countries, 1963–1982

The purpose of this paper is to apply some novel features in the theory of productivity indexes to the measurement of productivity gaps. It advances the proposition that one reason for the persistence of productivity gaps might be that the methodology of measuring gaps does not separate shifts of the production function due to intercountry efficiency from shifts due to intercountry differences in capacity utilization.In this paper we calculate productivity gaps for four OECD countries relative to the U.S., adjusted for cyclical variations in capacity utilization for the period 1963–1982. The theoretical foundation of our measurement is based on a variable cost function approach with short-run fixity of capital. Without adjusting for differences in capacity utilization within the countries, productivity gaps are a mixture of differences in productivity and in capacity utilization.The refereeing process of this paper was handled through C. Morrison.     

Alternative functional forms for production,cost and returns to scale functions

We consider generalized production functions, introduced in Zellner and Revankar (1969), for output y=g(f) where g is a monotonic function and f is a homogeneous production function. For various choices of the scale elasticity or returns to scale as a function of output, differential equations are solved to determine the associated forms of the monotonic transformation, g(f). Then by choice of the form of f, the elasticity of substitution, constant or variable, is determined. In this way, we have produced and generalized a number of homothetic production functions, some already in the literature. Also, we have derived and studied their associated cost functions to determine how their shapes are affected by various choices of the scale elasticity and substitution elasticity functions. In general, we require that the returns to scale function be a monotonically decreasing function of output and that associated average cost functions be U- or L-shaped with a unique minimum. We also represent production functions in polar coordinates and show how this representation simplifies study of production functions' properties. Using data for the US transportation equipment industry, maximum likelihood and Bayesian methods are employed to estimate many different generalized production functions and their associated average cost functions. In accord with results in the literature, it is found that the scale elasticities decline with output and that average cost curves are U- or L-shaped with unique minima. © 1998 John Wiley & Sons, Ltd.     

Theory and Application of Directional Distance Functions

In 1957 Farrell demonstrated how cost inefficiency could be decomposed into two mutually exclusive and exhaustive components: technical and allocative inefficiency. This result is consequence of the fact that—as shown by Shephard—the cost function and the input distance function (the reciprocal of Farrell's technical efficiency measure) are dual to each other. Similarly, the revenue function and the output distance function are dual providing the basis for the decomposition of revenue inefficiency into technical and allocative components (see for example, Färe, Grosskopf and Lovell (1994)). Here we extend those results to include the directional distance function and its dual, the profit function. This provides the basis for defining and decomposing profit efficiency. As we show, the output and input distance functions (reciprocals of Farrell efficiency measures) are special cases of the directional distance function. We also show how to use the directional distance function as a tool for measuring capacity utilization using DEA type techniques.     

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.     

Decomposing hospital productivity changes, 1985–1988: A nonparametric Malmquist approach

Annual data on U.S. hospitals from 1985–1988 are evaluated by ownership type—profit, nonprofit, state and local government, and U.S. Department of Veterans Affairs (VA)—for changes in hospital productivity over time. Distance functions are used to measure Malmquist indices of productivity change, which are then decomposed into indices of efficiency change and technology change. In contrast to previous studies using this approach, we allow for variable returns to scale and use both input and output orientations. We find that changes in technology dominate changes in inefficiency in determining changes in productivity.     

Autoregresive conditional volatility, skewness and kurtosis

This paper proposes a GARCH-type model allowing for time-varying volatility, skewness and kurtosis. The model is estimated assuming a Gram–Charlier (GC) series expansion of the normal density function for the error term, which is easier to estimate than the non-central t distribution proposed by [Harvey, C. R. & Siddique, A. (1999). Autorregresive Conditional Skewness. Journal of Financial and Quantitative Analysis 34, 465–487). Moreover, this approach accounts for time-varying skewness and kurtosis while the approach by Harvey and Siddique [Harvey, C. R. & Siddique, A. (1999). Autorregresive Conditional Skewness. Journal of Financial and Quantitative Analysis 34, 465–487] only accounts for non-normal skewness. We apply this method to daily returns of a variety of stock indices and exchange rates. Our results indicate a significant presence of conditional skewness and kurtosis. It is also found that specifications allowing for time-varying skewness and kurtosis outperform specifications with constant third and fourth moments.     

Non-parametric, unconditional quantile estimation for efficiency analysis with an application to Federal Reserve check processing operations

This paper examines the technical efficiency of US Federal Reserve check processing offices over 1980–2003. We extend results from Park et al. [Park, B., Simar, L., Weiner, C., 2000. FDH efficiency scores from a stochastic point of view. Econometric Theory 16, 855–877] and Daouia and Simar [Daouia, A., Simar, L., 2007. Nonparametric efficiency analysis: a multivariate conditional quantile approach. Journal of Econometrics 140, 375–400] to develop an unconditional, hyperbolic, α-quantile estimator of efficiency. Our new estimator is fully non-parametric and robust with respect to outliers; when used to estimate distance to quantiles lying close to the full frontier, it is strongly consistent and converges at rate root-n, thus avoiding the curse of dimensionality that plagues data envelopment analysis (DEA) estimators. Our methods could be used by policymakers to compare inefficiency levels across offices or by managers of individual offices to identify peer offices.     

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.     

China's total factor productivity estimates by region, investment sources and ownership

This paper constructs China national and provincial physical capital and human capital for the period 1984–2006. The estimation of physical capital is extended to the use of sources of fund and ownership of fund. The growth accounting framework is used to calculate the output, input and total factor productivity growth rates. The relative variance method is used to compare the relative importance to output growth by input growth and productivity growth. The empirical findings show that although output growth in post-reform China has been contributed much by growth in total factor productivity, output volatility has relied more on input growth, and TFP growth has not been supported by complementary changes. There are regional differences when looking at the performance of individual growth rates.     

Cost-based decision rules for output,quality, and price

The present paper develops a theoretical model to address the relationship between a firm's pricing policy and its cost of increasing product quality. The model expresses both firm costs and firm revenues as functions of the quantity of a firm's output and overall product quality, where quality is expressed as quantity times quality per unit. The model starts with a generic good that measures output, and models quality as priced quality enhancement for each unit of the generic good. The model leads to decision rules by which the price of quality is a mark-up over the marginal cost of increasing product quality. The relationship between the price of quality and revenues from increasing output is also determined, and is conditioned by the sign and magnitude of the elasticity of demand for quality.     

Efficiency and ownership in Swedish electricity retail distribution

This article examines the efficiency of electricity retail distributors in Sweden in a multiple output multiple input framework. Productive efficiency measures are calculated by use of different versions of the non-parametric Data Envelopment Analysis (DEA) method. Comparisons are made between different types of ownership and between different types of service areas.The study indicates a rather low level of technical efficiency, a high level of scale efficiency in urban service areas, but a fairly low level of scale efficiency in rural areas. The results show no significant differences in efficiency between different types of ownership or economic organization.Paper presented at ORSA/TIMS joint national meeting, Productivity and Global Competition, Philadelphia, October 29–31, 1990.     

A Graph-Type Extension of Farrell Technical Efficiency Measure

We have two goals we wish to accomplish in this article. The first is the development of a framework for measuring efficiency in the full input–output space. This approach introduces a graph-type extension of the Farrell measure of technical efficiency. The second is the introduction of a weighting scheme for inputs and outputs, taking account of the particularity of the market summarized by input and output prices.     

Output scaling in a cost function setting

A significant result in production theory is that even under a very weak condition on the technology, the cost function is well defined and linearly homogeneous in factor prices. We could term this homogeneity a scaling law, for an equiproportionate scaling of all factor prices results in an identical scaling of the value of the cost function. The purpose of this paper is to determine sets of conditions under which an analogous result may hold for the output variable in the cost function. Our analysis initially focuses on the cost function of a multioutput technology so that the output variable in the cost function is vector-valued. The results we obtain are that some output-scaling laws exist if and only if the underlying technology is ray-homothetic. In the final section we consider the meaning of the results for the single-output case.The refereeing process of this paper was handled through R. Robert Russell. An earlier version of this paper was presented at the 1989 Conference on Current Issues in Productivity, December 6–8, 1989, Rutgers University, Newark, NJ.     

The Unemployment–Output Tradeoff in Transition Economies: Does Okun''s Law Apply?

This paper investigates whether an Okun-type relationship between output and unemployment is taking hold in formerly planned economies as they move towards the market. Using a first-differences variant of Okun's Law, we test for its presence in 25 transition countries divided into groups of ``reform leaders' and ``reform laggards.' For leaders, represented by the 10 European Union (EU) accession countries, Okun's Law is detected in both 1991–94 and 1995–2000 periods. For laggards, represented by the remaining group, it is present only for the later period and only when countries affected by wars are removed from the sample. A comparison of unemployment–output elasticities and unemployment levels in EU candidates and EU members themselves indicates that their labor markets might be converging.