for a sample of European co-operate banks between 1996 and 2003. So far as we are aware,
the only other application of the Luenberger indicator to banking is the Park and Weber
(2006) application to Korean banks.
In this application, the indicator is constructed for a sample of European co-operative
banks. According to the European Association of Co-operative Banks (2004) there are over
3,800 such banks which deal with around 100 million customers through 50,000 or so
branches. Co-operative banks play an important role in retail and SME banking and have
significant deposit market shares in Austria, France, Germany, Italy and the Netherlands
although they play a lesser role in other countries.4 Analysing the productivity characteristics
of co-operative banks is of interest because if productivity has improved then it should be
reflected in better performance, lower customer prices and improved service quality. It may
also reflect more prudent operations if productivity gains are fed through into capital that
helps absorb greater risk. Analysing productivity differences of co-operative banks across
countries can benchmark the performance of similar banks and possibly indicate the different
strategies undertaken by banking firms across markets (Molyneux and Williams, 2005).
The remainder of the paper is organized as follows: section 2 presents the methodology
framework adopted. Section 3 presents the data and the results. Finally, section 5 concludes.
2. Methodological Framework
In proposing new, more flexible, measures involving production theory, Chambers et
al (1996, 1998) introduced the “directional distance function”5, which is the transposition in
production theory of Luenberger’s (1992) “benefit function” in a consumer context. The
directional distance function determines a shortcut in one direction which permits an observed
production unit to reach the production frontier. In economic terms, this function makes it
possible to evaluate the scale of the economies which can be achieved and the possible
improvements in production. It also provides a “benchmark” by defining a reference point to
be reached. The principal advantage of this function lies in its ability to take account
simultaneously, and in a broader context, of both inputs and outputs. This function therefore
4 According to the European Association of Co-operative Banks (2004) co-operative banks deposits market share
in 2003 was: 32% in Austria, 47% in France, 21% in Germany, 29% in Italy and 38% in the Netherlands.
5 See also Fare and Grosskopf (2000) for an overview of the directional distance function.