Modern efficiency measurement beings with Farrell (1957) who drew upon the
work of Debreu (1951) to define a simple measure of firm efficiency which
could account for multiple inputs. Worthington (2001) identifies three main
measures of efficiency; technical, allocative and economic. Technical efficiency
refers to use of productive resources in the most technologically efficient
manner - the maximum possible output from a given set of inputs. Within the
context of education, technical efficiency may then refer to the physical
relationship between the resources used (say, capital, labor and equipment)
and some education outcome. These educational outcomes may either be
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final education outcome (such as graduate employment rates, starting salaries
or acceptance rates into higher education) (p.245). Allocative efficiency is
concerned with choosing between different technically efficient combinations of
inputs used to produce the maximum possible outputs. Finally and when taken
together, allocative efficiency and technical efficiency determine the degree of
productive efficiency (also known as total economic efficiency) (p.245). Based
on the above description and when applied to the education sector it can be
said that, first, efficiency is about allocating efficiently between different kinds of
resources – e.g., between teachers and blackboards, or between more teachers per student and better-qualified teachers – that is, about choosing the most efficient input mix (allocative efficiency). Second, efficiency is also about
using each resource efficiently, that is, making the best use of each given input
(technical efficiency).
A number of analytical techniques have been developed to estimate the form
of cost and production frontier and associated inefficiency of individual
organizations. Green (1993) while giving an overview of techniques for
econometric analysis of technical (production) and economics (cost) efficiency
describes two broad paradigms for measuring economic efficiency. One based
on an essentially nonparametric, programming approach to analysis of
observed outcomes, and the other one based on an econometric approach to
estimation of theory-based models of production, cost, or profit. He further
elaborates that the empirical estimation of production and cost functions is a standard exercise in Econometrics. He says, ―the frontier production function or production frontier is an extension of the familiar regression model, based on
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or the convex conjugate of the two, the profit function, represents an ideal, the
maximum output attainable given a set of inputs, the minimum cost of
producing that output given the prices of the inputs, or the maximum profit
attainable given the outputs, and prices of the inputs‖ (p.92-93).
Thus, resultantly there are two basic approaches to the measurement of
efficiency: the statistical (or econometric) approach and the non-statistical (or
programming approach). The distinction between the two approaches derives
from the underlying assumptions. In summary, a method for measuring
efficiency can be statistical or no statistical, parametric or non-parametric,
deterministic or stochastic. Of the eight possible permutations of these
characteristics, the most common methods fall into one of three of these
categories: statistical parametric methods (deterministic or stochastic) and
deterministic non-statistical non-parametric methods (Johnes, 2004, p.625).
According to Zamorano (2004) the choice of estimation method has been an
issue of debate, with some researchers preferring the parametric and others
the non parametric approach. In his opinion, no approach is strictly preferable
to any other measurement of efficiency in education is definitely a complicated
issue. Several methodological approaches have been used to overcome
problems in educational efficiency measurement. They all have their
advantages and shortcomings. The early studies of educational production
function mostly used least-squares regression techniques. From the 1980s the
use of non-stochastic Data Envelopment Analysis (DAE) has become quite
common. DEA is a programming technique that envelopes the observed data
to determine the best practice frontier. This technique has become popular in
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multiple outputs, is nonparametric, and does not require input prices. An
alternative econometric approach (parametric and statistical techniques) has
progressed from ordinary least squares (OLS) regression to Stochastic Frontier
Analysis, where the simple ratio of one output to one input have been replaced
by composite ratios of efficiency derived from linear programming (LP)
methods.
4.5.1. Parametric techniques
Parametric techniques use econometric methods to estimate the parameters of
a specific functional form of cost or production function. There are a number of
methods that fall directly under this heading, including ordinary least squares
regression analysis and stochastic frontier analysis. Ordinary least squares
(OLS) are one of a variety of techniques that fall under the heading of
regression analysis. It involves the identification of a statistical relationship
between variables. OLS regression analysis fits a line of best fit to these points,
such that the line minimizes the sum of the squared vertical distances of the observed country‘s coasts. The line of best fit can be written as follows:
Ci= α + ßLi + ui
Where i represent the observations for different institutions, α is the fixed cost involved, β is the cost of educating another student, and µi is the regression residual (the difference between actual costs and those predicted by the line of
best fit).
A stochastic production frontier model were first introduced by Aigner et al.
(1977) and Meeusen and Van den Broeck (1977) and has been a significant
contribution to the econometric modeling of production and the estimation of
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components, one associated with the presence of technical efficiency and the
other being the traditional random error (Battese and Coelli, 1992, p.149). In
contrast OLS regression models implicitly assume that the whole of the residual
for a particular observation (in this context a country) is the result of genuine inefficiency. This decomposition of residuals between ‗error‘ and ‗genuine efficiency‘ provides a more accurate reflection of the true level of inefficiency. A number of studies have used these approaches to estimate the efficiency of
educational institutions. These include Sengupta (1987), Barrow (1991), Deller
and Rudnicki (1933), Cubbin and Zamani (1996) , Bates (1997), Moomaw
and Adkins (2005) and Kirjavainen (2007), details of last two are presented
in the later part of this chapter.
4.5.2. Non-parametric techniques
Non-Parametric techniques place no conditions on the functional form and use
observed data to infer the shape of the frontier. Most non-parametric methods
take the form of data envelopment analysis (DEA) and its many variants. DEA
essentially calculates the economic efficiency of a given organization relative to
the performance of other organizations producing the same good or service,
rather than against an idealized standard of performance. It is a nonstochastic
method in that it assumes all deviations from the frontier are the result of
inefficiency. It can be used as an alternative to regression-based techniques. It
does not involve statistical estimation, but instead makes use of linear
programming or some other form of mathematical programming methods to
characterize the set of efficient producers and then derive estimates of
efficiency for inefficient observations based on how far they deviate from the
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(1988), Ganely and Cubbin (1992), Beasley (1995) and Haksever and
Muragishi (1998) and others (for details see appendix 4-C) have applied these
approaches to educational institutions (Worthington, 2001, p.250).