A fuzzy clustering approach used in evaluating technical efficiency measures in manufacturing

Comparing analytical approaches is crucial when important policy decisions of corporations or government agencies may be influenced by results that depend on the methodologies certain disciplines customarily use. Technical efficiency can be measured by a full-frontier production function model or by linear programming specifications. By using these modeling approaches observations pertaining to three linerboard manufacturing facilities are classified as efficient, inefficient, scale inefficient, and other. However, observations may or may not be consistently classified into these four groups when employing the two modeling approaches. In order to validate the efficiency designations of the two modeling approaches and to determine the uniqueness of observations, a fuzzy K-means clustering approach that uses a modified hat matrix H ^* as a similarity or information matrix is employed. This approach permits observations to be allocated to clusters in a fuzzy way by defining a membership function from 0 to 1. As the degree of fuzziness increases, a sensitivity analysis with respect to individual observations belonging to some cluster can be evaluated. At the same time, this fuzzy approach assists the analyst to assess the inconsistencies that can arise when using the mathematical programming and full-frontier modeling approaches of technical efficiency.The refereeing process of this paper was handled through Rolf Färe. The majority of this research work was completed when Bill Seaver was at the Department of Management Information Resources, College of Business Administration, Western Illinois University, Macomb, IL 61455.     

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.     

A new method for measuring congestion in data envelopment analysis

In data envelopment analysis (DEA), there are two principal methods for identifying and measuring congestion: Those of Färe et al. [Färe R, Grosskopf S. When can slacks be used to identify congestion. An answer to W. W. Cooper, L. Seiford, J. Zhu. Socio-Economic Planning Sciences 2001;35:1–10] and Cooper et al. [Cooper WW, Deng H, Huang ZM, Li SX. A one-model approach to congestion in data envelopment analysis. Socio-Economic Planning Sciences 2002;36:231–8]. In the present paper, we focus on the latter work in proposing a new method that requires considerably less computation. Then, by proving a selected theorem, we show that our proposed methodology is indeed equivalent to that of Cooper et al.     

Backward Integration by a Dominant Firm

This paper studies the welfare consequences of a vertical merger that raises rivals' costs when downstream competition is a la Cournot between firms with constant asymmetric marginal costs. The main result is that such a vertical merger can nevertheless improve welfare if it involves a downstream firm whose cost is low enough. This is because by raising the input price paid by the nonmerging firms the merger shifts production away from those relatively inefficient producers in favor of the more efficient firm. Yet, there is a trade-off between the gain in productive efficiency and the loss in consumers' surplus caused by the higher downstream price that follows a higher input price. It is also shown, through an example, that this result extends to price competition with differentiated products.     

Congestion in the Chinese automobile and textile industries revisited

This paper re-examines a problem of congested inputs in the Chinese automobile and textile industries, which was identified by Cooper et al. [Cooper WW, Deng H, Gu B, Li S, Thrall RM. Using DEA to improve the management of congestion in Chinese industries (1981-1997). Socio-Economic Planning Sciences 2001;35:227-242]. Since these authors employed a single approach in measuring congestion, it is worth exploring whether alternative procedures would yield very different outcomes. Indeed, the measurement of congestion is an area where there has been much theoretical debate but relatively little empirical work. After examining the theoretical properties of the two main approaches currently available, those of Färe et al. [Färe R, Grosskopf S, Lovell CAK. The measurement of efficiency of production. Boston: Kluwer-Nijhoff; 1985] and Cooper et al., we use the data set assembled by Cooper et al. for the period 1981-1997 to compare and contrast the measurements of congestion generated by these alternative approaches. We find that the results are strikingly different, especially in terms of the amount of congestion identified. Finally, we discuss the new approach to measuring congestion proposed by Tone and Sahoo [Tone K, Sahoo BK. Degree of scale economies and congestion: a unified DEA approach. European Journal of Operational Research 2004;158:755-772].     

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.     

Hölder Distance Function and Measurement of Technical Efficiency

In this paper we intend to establish relations between the way efficiency is measured in the literature on efficiency analysis, and the notion of distance in topology. In particular we study the Holder norms and their relationship to the shortage function (Luenberger (1995) and the directional distance function (Chambers, Chung and Färe (1995–96)). Along this line, we provide mathematical programs to compute the Holder distance function. However, this has a perverse property that undermines its attractiveness: it fails the commensurability condition suggested by Russell (1988). Thus, we introduce a commensurable Holder distance function invariant with respect to a change in the units of measurement. Among other things we obtain some continuity result and we prove that the well known Debreu-Farrell measure is a special case of the Holder distance function.     

The influence of industry concentration on merger motives—empirical evidence from machinery industry mergers

By linking industrial organization theory and capital market research, we provide empirical evidence that merger motives of firms are influenced by underlying industry concentration. Analyzing wealth effects on target, acquirer and rival firms in the machinery industry, we observe significant different capital market reactions among merger announcements in dependence of underlying industry concentration. suggesting that different takeover motives prevail in fragmented and concentrated industries. In contrast to previous studies, we find besides efficiency motives evidence for monopolistic collusion motives in fragmented industries. Mergers in concentrated industries are primarily motivated to achieve productive efficiency gains. The absence of collusion motives may be an indication for a successful enforcement of antitrust legislation. Our results suggest that the magnitude of the influence of industry concentration in empirical merger motive research may have been previously under-estimated leading to a potential distortion of results.     

A primal-dual approach to nonparametric productivity analysis: The case of U.S. agriculture

Nonparametric methods for measuring productivity indexes based on bounds for the underlying production technology are presented. Following Banker and Maindiratta, the lower bound is obtained from a primal approach while the upper bound corresponds to a dual approach to nonparametric production analysis. These nonparametric bounds are then used to estimate input-based and output-based distance functions. These radial measures provide the basis for measuring productivity indexes. Application to times series data on U.S. agriculture indicates a large gap between the primal lower bound and the dual upper bound. This generates striking differences between the primal and dual nonparametric productivity indexes.Respectively, professor and associate professor of Agricultural Economics, University of Wisconsin-Madison. Seniority of authorship is equally shared. We would like to thank Rolf Färe and an anonymous reviewer for useful comments on an earlier draft of the paper. This research was supported in part by a Hatch grant from the College of Agriculture and Life Sciences, University of Wisconsin-Madison.     

Upstream Mergers,Downstream Competition,and R&D Investments

In this paper, we provide an explanation for why upstream firms merge, highlighting the role of R&D investments and their nature, as well as the role of downstream competition. We show that an upstream merger generates two distinct efficiency gains when downstream competition is not too strong and R&D investments are sufficiently generic: The merger increases R&D investments and decreases wholesale prices. We also show that upstream firms merge unless R&D investments are too specific and downstream competition is neither too weak nor too strong. When the merger materializes, the merger‐generated efficiencies pass on to consumers, and thus, consumers can be better off.     

On the Functional Form of an Efficiency Index

An input efficiency index gives a numeric assessment of the degree to which a given input combination falls short of being efficient in producing a fixed amount of output. This paper presents a system of axioms which characterise a certain family of efficiency indices containing the well-known Farrell and Färe-Lovell indices. The family of indices satisfying the axioms can be obtained by minimizing a suitable function, called a performance evaluation, and different choices of performance evaluation will result in different indices.     

管理者激励机制、内部竞争与兼并效应分析

参与兼并企业作为子企业存在于兼并所形成的新企业时,新企业的所有者可能对子企业管理者设置与内部所有子企业利润都相关的激励机制,文章即对这种情形建立了两阶段博弈模型考察横向兼并效应问题。结果表明,当少于市场企业数目50％的企业进行兼并时,新企业所有者将确定导致内部竞争的管理者激励机制,社会福利将会增加;此时,兼并活动对参与兼并企业是有利的,对未参与兼并企业是不利的,从而部分地消除了“兼并悖论”。     

Public support for performing arts. Efficiency and productivity gains in eleven European countries

This paper investigates the importance of public cultural expenditure for the efficiency and productivity of the performing arts (PA) firms. To this aim, we estimate a translog production function using the stochastic frontier approach (SFA), and we obtain the estimates of both technical efficiency and its determinants for the PA firms in EU-11 countries over the period 2009–2017. The large panel data set enables the application of robust true random-effects SFA techniques, which control for noise, unobserved firms' heterogeneity and endogeneity of the inputs. Moreover, by estimating a production function, the characteristics of the production technology in the PA sector is also derived. The empirical results demonstrate that PA firms are technically inefficient, implying that the investigated firms could increase their artistic output between 32 and 42% and that decreasing returns to scale are prevalent, due to the presence of too many micro and large-scale firms in the European PA sector. In contrast to the seminal Baumol and Bowen's [5] paper, we also demonstrate that the total factor productivity (TFP) increased in the EU PA firms over the examined period. Technical efficiency, although relatively low, was the main driver of this productivity growth, as opposed to scale efficiency change or technological change, which display very small or no increases. We also find that, contrary to the common wisdom on its negative effects on firm efficiency, public spending on culture increases the efficiency of PA firms. Within this context some policy implications are discussed.     

Hyperbolic Efficiency and Parametric Distance Functions: With Application to Spanish Savings Banks

Distance functions are gaining relevance as alternative representations of production technologies, with growing numbers of empirical applications being made in the productivity and efficiency field. Distance functions were initially defined on the input or output production possibility sets by Shephard (1953, 1970) and extended to a graph representation of the technology by Färe, Grosskopf and Lovell (1985) through their graph hyperbolic distance function. Since then, different techniques such as non parametric-DEA and parametric-SFA have been used to calculate these distance functions. However, in the latter case we know of no study in which the restriction to input or output orientation has been relaxed. What we propose is to overcome such restrictiveness on dimensionality by defining and estimating a parametric hyperbolic distance function which simultaneously allows for the maximum equiproportionate expansion of outputs and reduction of inputs. In particular, we introduce a translog hyperbolic specification that complies with the conventional properties that the hyperbolic distance function satisfies. Finally, to illustrate its applicability in efficiency analysis we implement it using a data set of Spanish savings banks.     

Price Discrimination under Customer Recognition and Mergers

This paper studies the interaction between horizontal mergers and price discrimination by endogenizing the merger formation process in the context of a repeated purchase model with two periods and three firms wherein firms may engage in behavior‐based price discrimination (BBPD). From a merger policy perspective, this paper's main contribution is twofold. First, it shows that when firms are allowed to price discriminate, the (unique) equilibrium merger gives rise to significant increases in profits for the merging firms (the ones with information to price discriminate), but has no ex‐post effect on the outsider firm's profitability, thereby eliminating the so‐called (static) “free‐riding problem.” Second, this equilibrium merger is shown to increase industry profits at the expense of consumers' surplus, leaving total welfare unaffected. This then suggests that competition authorities should scrutinize with greater zeal mergers in industries where firms are expected to engage in BBPD.     

Estimation of market power in the presence of firm level inefficiencies

“The quiet life hypothesis” (QLH) by Hicks (1935) argues that, due to management’s subjective cost of reaching optimal profits, firms use their market power to allow inefficient allocation of resources. Increasing competitive pressure is therefore likely to force management to work harder to reach optimal profits. Another hypothesis, which also relates market power to efficiency is “the efficient structure hypothesis” (ESH) by Demsetz (1973). ESH argues that firms with superior efficiencies or technologies have lower costs and therefore higher profits. These firms are assumed to gain larger market shares which lead to higher concentration. Ignoring the efficiency levels of the firms in a market power model might cause both estimation and interpretation problems. Unfortunately, the literature on market power measurement largely ignores this relationship. In the context of a dynamic setting, we estimate the market power of US airlines in two city-pairs by both allowing inefficiencies of the firms and not allowing inefficiencies of the firms. Using industry level cost data, we estimate the cost function parameters and time-varying efficiencies. An instrumental variables version of the square root Kalman filter is used to estimate time-varying conduct parameters.     

Estimating efficiencies from frontier models with panel data: A comparison of parametric,non-parametric and semi-parametric methods with bootstrapping

The aim of this article is first to review how the standard econometric methods for panel data may be adapted to the problem of estimating frontier models and (in)efficiencies. The aim is to clarify the difference between the fixed and random effect model and to stress the advantages of the latter. Then a semi-parametric method is proposed (using a non-parametric method as a first step), the message being that in order to estimate frontier models and (in)efficiences with panel data, it is an appealing method. Since analytic sampling distributions of efficiencies are not available, a bootstrap method is presented in this framework. This provides a tool allowing to assess the statistical significance of the obtained estimators. All the methods are illustrated in the problem of estimating the inefficiencies of 19 railway companies observed over a period of 14 years (1970–1983).Article presented at the ORSA/TIMS joint national meeting, Productivity and Global Competition, Philadelphia, October 29–31, 1990. An earlier version of the paper was presented at the European Workshop on Efficiency and Productivity Measurement in the Service Industries held at CORE, October 20–21, 1989. Helpful comments of Jacques Mairesse, Benoît Mulkay, Sergio Perelman, Michel Mouchart, Shawna Grosskopf and Rolf Färe, at various stages of the paper, are gratefully acknowledged.     

The effect of mergers on firms’ costs: evidence from the HMO industry

We examine the effect of mergers on firms’ costs, using a national data set that contains information on both pre- and post-merger costs for firms in the Health Maintenance Organization (HMO) industry. By utilizing data on all HMOs that operated in the United States from 1985 to 1997, we observe enough mergers to obtain estimates of both short-run and relatively permanent merger effects. On average, we do not find evidence that mergers allowed HMOs to realize greater economies of scale or that mergers improved efficiency by shifting the cost function. On the other hand, mergers between HMOs that produce Medicare and other products are likely to create dis-economies of scope that increase costs.     

The Impact of the Big 8 Mergers on Market Power: Evidence from the Hong Kong Market

This study examines the impact of the Big 8 mergers on market power in an audit market where the merging firms have little presence. Audit fee changes for each merger participating firm are identified and fee changes for several post‐merger years are examined. The pre‐merger differential market power between the merging and non‐merging long‐established Big 8 firms (Price Waterhouse and KPMG Peat Marwick) in Hong Kong provides a unique opportunity to examine whether the mergers could help the merging firms to increase their market power. The results are consistent with the hypotheses that the audit fees of the merging firms were significantly lower than that of the non‐merging, long‐established Big 8 firms before the mergers, but the audit fees of the merged firms increased significantly to a level comparable with that of the latter group after the mergers. In addition, the market share of the merged firms increased significantly after the mergers. However, no association is found between market concentration and market power. Overall, the results show that the Big 8 mergers have helped the merged firms increase their market power and market share in the Hong Kong audit market where they had little presence.     

Measuring productivity growth, technical progress, and efficiency changes of CPA firms prior to, and following the Sarbanes–Oxley Act

This paper investigates productivity growth, technical progress, and efficiency change for a group of the 56 largest CPA firms in the US from the period 1996–1999 through the period 2003–2006, where the former preceded, and the latter followed, enactment of the Sarbanes–Oxley Act (SOX). Data envelopment analysis (DEA) is used to calculate Malmquist indices of three measures of interest: productivity growth, technical progress, and efficiency change. Results indicate that CPA firms, on average, experienced a productivity growth of approx. 17% from the pre- to post-SOX period. Consistent with the finding of Banker et al. [Banker RD, Chang H, Natarajan R. Productivity change, technical progress and relative efficiency change in the public accounting industry. Management Science 2005;51:291–304], this productivity gain can be attributed primarily to technical progress rather than a change in relative efficiency. In addition, results indicate that the “Big 4” firms underperformed their non-Big 4 counterparts in both productivity growth and technical progress.