Revenue efficiency in higher education institutions under imperfect competition

Published date01 October 2017
DOI10.1177/0952076716652935
Date01 October 2017
Subject MatterSymposium: Big data analytics and its use in the measurement of public organizations' performance and efficiencySymposium articles
untitled Symposium article
Public Policy and Administration
2017, Vol. 32(4) 282–295
! The Author(s) 2016
Revenue efficiency
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in higher education
DOI: 10.1177/0952076716652935
journals.sagepub.com/home/ppa
institutions under
imperfect competition
Geraint Johnes
Lancaster University Management School, UK
John Ruggiero
University of Dayton, USA
Abstract
A number of studies have considered the evaluation of efficiency in higher education
institutions. In this paper, we focus on the issue of revenue efficiency, in particular ascer-
taining the extent to which, given output prices, producers choose the revenue maximising
vector of outputs. We then relax the price taking assumption to consider the case in which
the market for some outputs is characterised by monopolistic competition. We evaluate
efficiencies for English institutions of higher education for the academic year 2012–13 and
find considerable variation across institutions in revenue efficiency. The relaxation of the
price-taking assumption leads to relatively small changes, in either direction, to the esti-
mated revenue efficiency scores. A number of issues surrounding the modelling process
are raised and discussed, including the determination of the demand function for each type
of output and the selection of inputs and outputs to be used in the model.
Keywords
Efficiency, higher education, monopolistic competition, revenue efficiency, UK university
sector
Introduction
The evaluation of ef‌f‌iciency comes in many dif‌ferent f‌lavours. The seminal work of
Farrell (1957) evolved in contributions by Boles (1971) and Førsund and
Hjalmarsson (1974) to produce the workhorse model of data envelopment analysis
(DEA) popularised by Charnes et al. (1978). An early ref‌inement of this model
Corresponding author:
Geraint Johnes, Lancaster University Management School, Lancaster University, Lancaster, LA1 4YX, UK.
Email: G.Johnes@lancs.ac.uk

Johnes and Ruggiero
283
introduced consideration of variable returns to scale (Banker et al., 1984) – the so-
called BCC model. Meanwhile, building on the early contribution of Leibenstein
(1966), Fa¨re et al. (1994) developed a host of linear programming methods that
allowed investigation of further aspects of ef‌f‌iciency, in particular introducing
prices and the notion of allocative ef‌f‌iciency into the model.
These techniques have come into widespread use, particularly in contexts where
production is complex, involving a multiplicity of inputs and outputs, and where –
as is common in public service settings – producers are heterogeneous in terms of
their objectives. One such area is that of higher education, where dif‌ferent providers
vary in the weights they attach to dif‌ferent outcomes that are of relevance to society
– teaching and research in a variety of subject areas. The analysis of ef‌f‌iciency in
this sector is facilitated by the existence of good data sources. It is not surprising,
therefore, that we have witnessed a proliferation of studies concerning the ef‌f‌iciency
of universities (Agasisti, 2011; Agasisti and Johnes, 2009; Athanassopoulos and
Shale, 1997).
These studies have, however, typically focused on technical and scale ef‌f‌iciency
and have not been extended to examine allocative ef‌f‌iciency. This has been largely
due to data limitations. To examine the extent to which institutions are responding
appropriately to market signals in choosing their output vectors we need data on
prices, in particular on tuition fees. Of‌f‌icial data sets have not routinely reported this
information. Our aim in the present paper is to exploit a new source of such data for
universities in England, namely the Reddin Tuition Fee Survey.1 This allows us to
consider allocative ef‌f‌iciency using the model of Fa¨re et al. (1994: 113). We go fur-
ther, however, by considering the possibility that universities might, in at least some
of the markets in which they operate, be price makers rather than price takers. The
Fa¨re et al. (1994) model implicitly assumes perfect competition; more recent work, by
Johnson and Ruggiero (2011) allows the possibility that there is monopolistic com-
petition so that producers face downward sloping demand curves for their output.
This means that, in adjusting their output vectors, they must, when seeking to maxi-
mise their revenue, take into account the impact that this has on the prices that they
can charge. We know from the literature (see, for example, Gallet, 2007) that the
demand for the output of a typical higher education institution has some measure of
price sensitivity, and so it is appropriate to accommodate this feature into our
models, and into our evaluation of institutions’ ef‌f‌iciency.
The paper proceeds as follows. In the next section, we describe the linear pro-
gramming models that will be used to evaluate the various ef‌f‌iciency measures of
interest. In ‘Data’ section, we introduce the sources of data used. This is followed
by an analytical section in which results are presented and discussed. The paper
ends with a conclusion and suggestions for further research.
Modelling strategy
DEA models involve evaluating the relative ef‌f‌iciency of producers or ‘decision-
making units’ that employ multiple inputs to produce multiple outputs.

284
Public Policy and Administration 32(4)
The method is non-parametric in that the objective for each producer is optimised
by selection of a producer-specif‌ic vector of weights on inputs and outputs.
The primal of an output-oriented DEA involves solving a set of linear pro-
grammes that choose, separately for each decision-making unit, values of input
and output weights to minimise the weighted sum of inputs required to produce
given output, subject to the constraint that the weights chosen should not for any
unit imply that the ratio of weighted output to weighted input exceeds one.
The BCC variant of the model adds a further constraint to allow identif‌ication
of inef‌f‌iciencies due to operation at scale that is below or above the optimum. In its
dual form, the linear programming problem is given by
Ei ¼ max
,
X
N
s:t:
lylj yij
j ¼ 1, . . . , S
l¼1
X
N

ð1Þ
lxlk xik
k ¼ 1, . . . , M
l¼1
X
N
l ¼ 1
l¼1
l 0 8l ¼ 1; . . . ; N
where i ¼ 1,. . .,N are the producers, each of which M inputs, x1,. . .,xM, to produce
S outputs, y1,. . .,yS.
Note that this problem does not involve any consideration of prices. If produ-
cers face prices for their inputs and outputs that dif‌fer from the (producer-specif‌ic)
weights that are the solution to the linear programming problem, then an appar-
ently ef‌f‌icient producer will likely produce quantities of output that do not serve to
maximise its revenue. The problem of revenue maximisation has been addressed by
Fa¨re et al. (1994: 113) for the case in which the ith producer faces prices for its
outputs given by pi ¼ (pi1,. . .,piS). Given its production technology, this producer
will maximise its revenue by solving the problem
X
S
R ¼ max
p
i
ijyj
yj, j¼1
X
N
s:t:
lylj yj
j ¼ 1, . . . , S
ð2Þ
l¼1
X
N
lxlk xik
k ¼ 1, . . . , M
l¼1

Johnes and Ruggiero
285
X
N
l ¼ 1
l¼1
l 0 8 l ¼ 1, . . . , N
P
The ratio R=
S
p
i
j¼1
ijyij 1 is a measure of the output revenue ef‌f‌iciency. A score
of 1...

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