Efficiency in the provision of university teaching and research: An empirical analysis of UK universities

A flexible three-output, two-input cost function model is used to examine the cost efficiency of UK universities as producers of teaching and research ‘outputs’. Unlike previous studies, a comprehensive peer review of research quality is incorporated. Overall, product-specific and input-specific economies of scale, global and product-specific economies of scope, marginal costs and cost complementarities are estimated. Overall and product-specific scale results indicate considerable increasing returns, while the scope results generally suggest neither economies nor diseconomies. Sensitivity analysis is used to simulate the impact of current government policy, regarding the expansion of undergraduate teaching output, on these results.     

Productivity differences in multiple output industries: An empirical application to electricity distribution

Given that electricity distribution is undertaken via a network, it is expected that costs of production are affected both by the nature of the network and the volume of physical output distributed via the network. This two-dimensional concept of firm size, that is involving network size (number of customers) and the level of physical output (kWh), also corresponds to the distinction between productivity measures of returns to density and returns to scale.This approach has been used to specify a restricted multioutput cost function and to estimate this function for the Norwegian electricity distribution industry through the use of a flexible functional form (translog). The results indicate that no economies of scale are present in the industry even for small plants when measured correctly, but that economics of density are present.     

Scale economies in electricity distribution: a semiparametric analysis

We estimate the costs of distributing electricity using data on municipal electric utilities in Ontario, Canada for the period 1993–5. The data reveal substantial evidence of increasing returns to scale with minimum efficient scale being achieved by firms with about 20,000 customers. Larger firms exhibit constant or decreasing returns. Utilities which deliver additional services (such as water/sewage), have significantly lower costs, indicating the presence of economies of scope. Our basic specifications comprise semiparametric variants of the translog cost function where output enters non‐parametrically and remaining variables (including their interactions with output) are parametric. We rely upon non‐parametric differencing techniques and extend a previous differencing test of equality of non‐parametric regression functions to a panel data setting. Copyright © 2000 John Wiley & Sons, Ltd.     

Returns to scope: a metric for production synergies demonstrated for hospital production

Knowledge of the production function’s scope properties can provide insights for firms choosing their operating strategy, policy-makers considering industry structure, and analysts determining appropriate tools. We introduce a new property, returns to scope, which is distinct from scale properties and does not rely on price information. Based on desirable characteristics of an estimator of returns to scope, we propose two methods for assessment. We present examples using simulated data and hospital production data from the 2008 National Inpatient Sample of the Agency for Healthcare Research and Quality’s Healthcare Cost and Utilization Project. We find that hospitals experience negative returns to scope (productivity losses) from the joint production of minor and major diagnostic procedures. Based upon our results we conclude that the new returns to scope property allows sharper insights than classic economies of scope approaches.     

房地产企业多产品结构的经济效益分析

近年来，各地房地产企业发展迅速，实行多元化战略，呈现了多产品结构。本文运用Translog成本函数估算分析了多产品结构的经济效益，提出了“大公司、大企业有最大的范围经济，但其规模经济稳定不变，不能获得较大的成本效益；中等规模的公司可获得较大的规模经济和范围经济，能获得较好的成本效益”的观点。     

Analysis of Hospital Production: An Output Index Approach

In this study, we develop and implement an output index approach to the estimation of hospital cost functions that reflects the differentiated nature of hospital care. The approach combines the estimation of an output index within a flexible functional form. We find, in an application to California hospitals, evidence of scope economies across specialties within primary care, and diseconomies of scope within secondary and tertiary care. Minimum efficient scale is reached at larger levels of output than would be estimated by conventional techniques. These results indicate the importance of accounting for firm output heterogeneity when estimating cost functions. Copyright © 2014 John Wiley & Sons, Ltd.     

Economies of diversification in the US credit union sector

Significant scale economies have been recently cited to rationalize a dramatic growth in the US retail credit union sector over the past few decades. In this paper, we explore another plausible supply‐side explanation for the growth of the industry, namely economies of diversification. We focus on the fact that credit unions differ among themselves in the range of financial services they offer to their members. Since larger credit unions tend to offer a more diversified financial service menu than credit unions of a smaller size, the incentive to grow in size may be fueled not only by present scale economies but also by economies of diversification. This paper provides the first robust estimates of such economies of diversification for the credit union sector. We estimate a flexible semiparametric smooth coefficient quantile panel data model with correlated effects that is capable of accommodating a four‐way heterogeneity among credit unions. Our results indicate the presence of non‐negligible economies of diversification in the industry. We find that as many as 27–91% (depending on the type and the cost quantile) of diversified credit unions enjoy substantial economies of diversification; the cost of most remaining credit unions is invariant to the scope of services. We also find overwhelming evidence of increasing returns to scale in the industry.     

Costs, Institutional Mobility Barriers, and Market Structure: Advertising Agencies as Multiproduct Firms

What accounts for the diversity and limited concentration that has long characterized the organization of the advertising agency industry? This question is addressed by treating an advertising agency as a multiproduct firm. The firm's product line or service mix is defined in terms of the set of different media categories where an agency places the advertising messages that it creates on behalf of its clients. Evidence is presented indicating that the structure of demand and costs in the advertising agency industry conforms to the conditions that MacDonald and Slivinski showed were required for an industry to sustain an equilibrium with diversified firms. Building on this framework, we formulate a set of three hypotheses relating to the realization of product-specific scale and scope economies. The first two hypotheses posit that given low fixed costs and minimal entry barriers, both media-specific scale and scope economies are available and can be exploited by relatively small-size agencies. The third hypothesis suggests that large agencies may experience diseconomies of scope as a consequence of excessive diversification induced by two pervasive industry institutional phenomena: (1) “bundling” of agency services to match client demand for a mix of media advertising, and (2) “conflict policy,” which prohibits an agency from serving competing accounts and operates as a mobility constraint. Utilizing a multiproduct cost function, we estimate media-specific scale and scope economies for a cross section of 401 U.S. agencies in 1987. The results obtained support the set of three hypotheses outlined above. The paper concludes with a discussion of the implications of these findings for the restructuring currently underway in this industry.     

Economic efficiency of multi-product structure: the evidence from Korean housebuilding firms

The Korean housebuilding industry has been subject to structural changes since the 1980s. One of the key features is that housebuilding firms have become diversified into a range of businesses and as a result display multi-product structure. This paper examines the efficiency of the multi-product structure of Korean housebuilding firms. For the analysis, translog cost functions were estimated using data for 201 building firms for the 3 years 1993–1995. The empirical results indicate that medium-size building firms enjoy increasing returns to scale, whereas large firms experience constant returns to scale. Korean building firms exhibit significant economies of scope in their diversification activities. Large firms have the greatest economies of scope. These results are consistent with cost efficiency for the multi-product structure of Korean housebuilding firms. The estimated optimum scale suggests that many large firms should expand only through diversification.     

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.     

Scale and scope economies of Japanese private universities revisited with an input distance function approach

This paper examines the scale and scope economies of higher education institutions in Japan assuming the presence of productive inefficiency. The standard approach to testing the scope economies is to apply the cost function. However, the cost function approach often entails the difficulty of obtaining reliable data on input prices, especially the input prices of capital for higher education institutions. This paper proposes a duality approach based on the input distance function. The scope economies are tested under a necessary and sufficient condition by retrieving the costs of joint and separate production from the input distance function. We apply the testing procedure to data pertaining to 218 Japanese private universities in 1999 and 2004. The results indicate the scale economies and the scope diseconomies.     

The Structure of Municipal Water Supply Costs: Application to a Panel of French Local Communities

Network losses and returns are importantissues for water resource management, that are addressed in thispaper by modeling the structure of production for municipal waterutilities with two outputs: water sold to final customers andwater network losses. We propose a measure of economies of scopeto assess the benefit associated with joint production of waterfor final customers and water losses, and several measures ofreturns to evaluate potential gains in exploiting technologicalflexibility of water networks. We estimate the cost structureof water utilities using a GMM procedure with a Translog costfunction and panel data. Estimation results reveal a positivedegree of economies of scope, and short-run returns to productiondensity and returns to customer density that are not significantlydifferent from 1. Significant economies of scale indicate thatlocal communities may benefit from merging into water districts.     

The Productivity Effects of Internal and External R&D: Evidence from a Dynamic Panel Data Model*

We examine the impact of internal and external R&D on labour productivity in a 6‐year panel of Dutch manufacturing firms. We apply a dynamic panel data model that allows for decreasing or increasing returns to scale in internal and external R&D and for economies of scope. We find complementarity between internal and external R&D, with a positive impact of external R&D only evident in case of sufficient internal R&D. These findings confirm the role of internal R&D in enhancing absorptive capacity. The scope economies are accompanied by decreasing returns to scale at high levels of internal and external R&D. The analysis indicates that productivity grows by increasing the share of external R&D in total R&D.     

Hicks-Moorsteen versus Malmquist: a connection by means of a radial productivity index

A primal index of productivity change is introduced which decomposes exactly into three components: technical change, technical efficiency change and average scale economies (radial scale change). The productivity index is defined using variations of the distance function along pre-assigned input–output rays and, for this reason, it is deemed a radial productivity index (RPI). It is proven that: first, the RPI index collapses to the Malmquist productivity index when the technology is constant returns to scale (CRS); second the RPI index equals the Hicks-Moorsteen productivity index under homotheticity of technology (and non-CRS). The key to these results is a new definition and measure of the contribution of scale economies to productivity change.     

Unbiased determination of production technologies

To determine whether an industry exhibits constant returns to scale, whether the production function is homothetic, or whether inputs are separable, a common approach is to specify a cost function, estimate its parameters using data such as prices and quantities of inputs, and then test the parametric restrictions corresponding to constant returns, a homothetic technology, or separability. Statistically, such inferences are valid if the true cost function is a member of the parametric class considered, otherwise the inference is biased. That is, the true rejection probability is not necessarily adequately approximated by the nominal size of the statistical test. The use of fixed parameter flexible functional forms such as the Translog, the generalized Leontief, or the Box-Cox will not alleviate this problem.The Fourier flexible form differs fundamentally from other flexible forms in that it has a variable number of parameters and a known bound, depending on the number of parameters, on the error, as measured by the Sobolev norm, of approximation to an arbitrary cost function. Thus it is possible to construct statistical tests for constant returns, a homothetic technology, or separability which are asymptotically size α by letting the number of parameters of the Fourier flexible form depend on sample size. That is, the true rejection probability converges to the nominal size of the test as sample size tends to infinity. The rate of convergence depends on the smoothness of the true cost function; the more times is differentiable the true cost function, the faster the convergence.The method is illustrated using the data on aggregate U.S. manufacturing of Berndt and Wood (1975, 1979) and Berndt and Khaled (1979).     

Big and beautiful? On non-parametrically measuring scale economies in non-convex technologies

Knowledge on the scale economies drives the incentives of regulators, governments and individual utilities to scale-up or scale-down the scale of operations. This paper considers the returns to scale (RTS) in non-convex frontier models. In particular, we evaluate RTS assumptions in a Free Disposal Hull model, which accounts for uncertainty and heterogeneity in the sample. Additionally, we provide a three-step framework to empirically analyze the existence and extent of RTS in real world applications. In a first step, the presence of scale (and scope) economies is verified. Secondly, RTS for individual observations are examined while in a third step we derive the optimal scale for a sector as a whole. The framework is applied to the Portuguese drinking water sector where we find the optimal scale to be situated around 7–10 million m³.     

The Henry George Theorem in a second-best world

The Henry George Theorem (HGT) states that, in first-best economies, the fiscal surplus of a city government that finances the Pigouvian subsidies for agglomeration externalities and the costs of local public goods by a 100% tax on land is zero at optimal city sizes. We extend the HGT to distorted economies where product differentiation and increasing returns are the sources of agglomeration economies and city governments levy property taxes. Without relying on specific functional forms, we derive a second-best HGT that relates the fiscal surplus to the excess burden expressed as an extended Harberger formula.     

A quality and risk-adjusted cost function for banks: Evidence on the “too-big-to-fail” doctrine

We estimate a multiproduct cost function model incorporating measures of bank output quality and the probability of failure. We model a bank's uninsured deposit price as an endogenous variable depending on the bank's output level, output quality, financial capital level, and risk measures. Accounting for these aspects in the cost model significantly affects measures of scale and scope economies. We find evidence that the too-big-to-fail doctrine significantly affects the price a bank pays for its uninsured deposits. For large banks, an increase in size, holding default risk and asset quality constant, significantly lowers the uninsured deposit price.     

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.     

Non-jointness and scope economies in the multiproduct symmetric generalized McFadden cost function

The multiproduct symmetric generalized McFadden cost function is increasingly prominent in empirical production analysis. Researchers should be aware that the scope for imposing and testing non-jointness in this model is limited. In the general version of the model non-jointness requires the non-testable maintained hypothesis of similar (in a sense we define) single-output production technologies, a maintained hypothesis for which there is not normally any basis. The apparent imposition and testing of non-jointness must be qualified accordingly. The attempt to impose non-jointness and global separability simultaneously necessarily imposes constant returns to scale and the implication that outputs are identical up to a scalar multiple. In this special case the model therefore effectively describes merely the production of a single output, and in this sense is only trivially multiproduct.