(^) ∑

=
n
j ij
ij
i
i
PEX
PSP
PEX
PSP
1

. (4)

The input measures for opportunity indicators are:

(1) Public consumption as proxy for input to produce administrative outcomes (explained later in section
4.2.1);

(2) Health expenditure (for health performance/outcome indicators);

(3) Education expenditure (for education performance).

Our earlier study also included a measure of the outcome of public investment, but due to a lack of
comparable data, this measure is not used in this study.

Inputs for the standard or “Musgravian indicators” are:

(1) Transfers and subsidies as proxies for input to affect the income distribution;

(2) Total spending as proxy for the input to affect economic stabilization (given that larger public sectors
are claimed to make economies more stable);^6 and

(3) Total spending also as a proxy input for economic efficiency and the distortive effects of taxation
needed to finance total expenditure.

However, there are some caveats: it is not easy to accurately identify the effects of public sector spending
on outcomes and separate the impact of public spending from other influences. Moreover, comparing
expenditure ratios across countries implicitly assumes that production costs for public services are
proportionate to GDP per capita.^7

3.2. Non-parametric analysis of performance and efficiency

Some recent papers have used non-parametric approaches for measuring relative expenditure efficiency
across countries. One such approach is the Free Disposal Hull (FDH) analysis.^8 This analysis is broadly
based on the concept of X-efficiency advanced by Leibenstein (1966). In the words of Gupta and
Verhoeven (2001), the “...central premise of the FDH Analysis is...that a producer is relatively inefficient
if another producer uses less or an equal amount of input to generate more or as much output.”

An alternative non-parametric technique that has recently started to be applied to expenditure analysis is
Data Envelopment Analysis (DEA). This technique, which is applied also later in this study, was
originally developed and applied to firms that convert inputs into outputs (Coelli, Rao and Battese (1998)
and Sengupta (2000) for a number of applications). The term “firm”, sometimes replaced by the more
encompassing term “Decision Making Unit” (henceforth DMUs) may include non-profit or public
organisations, such as hospitals, universities, local authorities, or countries.

(^6) For a differing view on the limits of the stabilising effect of growing government, see Cuaresma, Reitschuler and
Sillgoner (2005) and Buti and van den Noord (2003).
(^7) See Afonso, Schuknecht, and Tanzi (2005) for a discussion of the several caveats of such approach.
(^8) These approaches also often suffer from the logical fallacy of “post hoc non est propter hoc”. They attribute the
outcomes or the benefits to the expenditure when other factors may have contributed to these outcomes or benefits. For
example, effects from changing diets may be attributed to expenditure on health. In addition, many of these approaches
suffer from the difficulty of distinguishing output from outcomes. For an overview of the FDH analysis see for instance
Tulkens (1993).