A New Input‐Oriented Plant Capacity Notion: Definition and Empirical Comparison

• Published date: 01 October 2017
• Author: Giovanni Cesaroni,Kristiaan Kerstens,Ignace Van de Woestyne
• Date: 01 October 2017
• DOI: http://doi.org/10.1111/1468-0106.12201

A NEW INPUT-ORIENTED PLANT CAPACITY NOTION:

DEFINITION AND EMPIRICAL COMPARISON

GIOVANNI CESARONI Italian Prime Minister's Office, Department for Economic

Policy

KRISTIAAN KERSTENS*CNRS-LEM (UMR 9221), IESEG School of

Management

IGNACE VAN DE WOESTYNE KU Leuven, Research unit MEES

Abstract. Starting from the existing output-oriented plant capacity measure, this paper proposes a

new input-oriented plant capacity measure. Furthermore, we empirically illustrate both input-

oriented and output-oriented decompositions of technical efficiency integrating these technical

concepts of capacity utilization. In particular, we pay attention to the impact of convexity of the tech-

nology on both input-oriented and output-oriented plant capacity measures.

1. INTRODUCTION

Empirical studies on efficiency and productivity grounded in frontier specifica-

tions are abundantly available and these frontier methodologies have become

standard empirical tools that serve a variety of academic, regulatory and mana-

gerial purposes. Apart from its prolific application in the academic literature

analysing private and public sector performance-related issues (see e.g. Liu

et al. (2013) for a survey of empirical frontier applications), the implementation

of incentive regulatory mechanisms using frontier-based performance bench-

marks is rather widespread in liberalized network industries (e.g. for the electric-

ity sector see the Jamasb and Pollitt (2001) survey). To cite but one example of a

managerial application, the Sherman and Ladino (1995) study documents how a

US bank employed a basic frontier model to find sufficient savings in its branch

network to fund its strategy of expansion.

Many empirical applications take a long-run perspective in that it is assumed

that all inputs and/or outputs are under managerial control. While a focus on a

sub-vector of, for example, inputs is straightforward, the large majority of the

frontier-based literature, in fact, ignores the notion of capacity utilization.

Consequently, a part of the measured amount of inefficiency may well be due

to the short-run fixity of some of the inputs. Caves (2007) argues that a variety

of efficiency concepts and capacity notions have yielded a rich body of empirical

knowledge on firm behaviour that is part of the so-called old industrial organi-

zation literature. There are, indeed, many examples of empirical research on

organizations focusing on capacity utilization. For example, Ghemawat and

Nalebuff (1985) show how the probability of firm survival depends on the ability

to adjust capacity in order to keep production costs under control when facing

*Address for Correspondence: CNRS-LEM (UMR 9221), IESEG School of Management 3 rue de la

Digue, FR-59000 Lille, France. E-mail: k.kerstens@ieseg.fr. We thank a referee of this journal for

constructive comments.

Pacific Economic Review, 22: 4 (2017) pp. 720–739

doi: 10.1111/1468-0106.12201

© 2017 John Wiley & Sons Australia, Ltd

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changes in demand. Managing capacity utilization smoothly is an organiza-

tional factor of strategic value.

This paper concentrates on the development of plant capacity measures using

nonparametric frontier technologies. More specifically, this paper makes two

contributions to the literature. First, it proposes a new input-oriented plant

capacity measure that complements the existing output-oriented counterpart,

as applied by, for instance, Valdmanis et al. (2004). Second, we empirically

explore the differences between both these plant capacity notions using tradi-

tional convex as well as nonconvex technology specifications.

The paper is structured as follows. Section 2 offers a brief literature review on

the different capacity notions around in the literature and their use in a nonpara-

metric frontier context. It devotes some particular attention to the small litera-

ture having utilized the plant capacity concept. The next section introduces

technologies and distance functions allowing us to define the traditional

output-oriented plant capacity measure as well as its new input-oriented coun-

terpart. Then, the new input-oriented plant capacity measure is illustrated using

a numerical example. An empirical section illustrates these new plant capacity

measures for both convex and nonconvex nonparametric frontier technologies

using a sample of Canadian farms specialising in milk production. Conclusions

are drawn in a final section.

2. LITERATURE REVIEW

2.1. Economic and technical capacity utilization: A taxonomy

The economic literature contains a variety of capacity notions. A useful taxon-

omy is to distinguish between technical (engineering) and economic (mainly

cost-based) capacity concepts (see e.g. Johansen, 1968; Nelson, 1989). We first

pay attention to the technical or engineering notion, and then to the economic

concepts using a cost function approach.1

Johansen (1968) followed a technical approach by introducing the notion of

plant capacity.2Plant capacity is defined as the maximum output vector that

can be produced with existing equipment with unrestricted variable inputs per

unit of time. This capacity notion clearly takes an engineering perspective. Färe

et al. (1989a,b) transpose this notion into a multi-output frontier framework

using some combination of output efficiency measures (see also Färe et al., 1994).

At least three ways of defining a cost-based notion of capacity have been pro-

posed in the literature (see Nelson, 1989). Each of these notions aims to isolate

the short-run excessive or inadequate utilization of existing fixed inputs (e.g. cap-

ital stock). A first notion is defined in terms of the output produced at short-run

1Briec et al. (2010) show that it is possible to develop dual capacity measures using nonparametric

technologies for the case of other objective functions: e.g. profit maximization (following Squires,

1987). The case of revenue maximization (see Segerson and Squires, 1995) remains to be developed.

2Johansen (1968) also proposes a synthetic capacity concept as the maximal output with existing

plant and equipment while accounting for the restricted availability of variable inputs. This seems

to correspond to technical efficiency.

NEW INPUT-ORIENTED PLANT CAPACITY NOTION 721

© 2017 John Wiley & Sons Australia, Ltd