The Luenberger indicator and productivity growth: a note on the European savings banks sector

Abstract

We employ the Luenberger productivity indicator to estimate productivity growth and its decomposition into technical change and efficiency change components for savings banks sectors in 10 EU countries between 1996 and 2003. The Luenberger indicator requires less restrictive assumptions than standard nonparametric productivity indexes, and it allows the assumption of profit maximization to be made for sample firms. We estimate average productivity growth in the savings banks sector to be 2.78% per annum and driven almost entirely by technical change. Whilst the general results confirm earlier findings, this study is one of the earliest to identify cross-border differences in productivity growth in the savings banks sector.

Notes

¹ For further elaboration on productivity measurement by ratios (indexes) and differences (indicators), see Chambers (1996, 2002) and Diewert (2000, 2005).

² So far as we are aware, there is one other application of the Luenberger productivity indicator in banking (Park and Weber, 2006 for a study of productivity growth in Korean banks).

³ The role of savings banks varies across countries: in the EU savings banks account for roughly 25% of nonbank customer deposits, 50% in Spain and around 40% in Germany (as at January 2006).

⁴ We simplify the notations by posing z _t  = (x _t ,y _t ).

⁵ See Färe and Primont (2003) and Färe and Grosskopf (2004) for discussion of the aggregation of the Luenberger productivity indicator.

⁶ See also Guironnet and Peypoch (2007) for an empirical contribution using this measure.

⁷ All the computations are programmed in Mathematica language with the Mathematica 5.0 software.

⁸ There are several approaches to modelling the bank production process: the production approach, user-cost approach, value added approach and dual approach (Berger and Humphrey, 1992).

⁹ Our choice of bank output is consistent with the established literature. This is important because the definition and measurement of output could significantly affect the level of bank efficiency (Berger and Humphrey, 1997).