Costi e dimensioni delle banche popolari italiane: un'applicazione della Fourier flessibile

In Italy the M&A process that has involved the banking system in the '90s has revived the question about the real gain of these operations in terms of operative costs reduction for the institutions involved. The studies on scale and scope economies, however, do not provide univocal answers about such question. In this article we define an ad hoc model to study Italian cooperative banks' costs when output level and its composition are modified. This kind of bank deserves attention because of the variety of M&A processes in which they have been involved and the recent debate about the evolution of their model of governance. The basic elements of the model are: i) a new definition of bank output (which explicitly considers the fact that it is a bundle of services); ii) the specification and the inclusion of the distributive channels; iii) a functional form to represent the cost function which needs to be more flexible than the Cobb Douglas or translog functions usually adopted in literature; iv) indexes suitable to the study and consistent with the assumptions. In particular, the cost functional form adopted here is "Fourier flexible" (FF), an analytical form rarely used in the literature on the Italian banking system. The FF presents some problems about the cutting off of the series, that we solve with an a priori assumption on the interaction between the variables considered and the introduction of a number of parameters which make the estimate normally and asymptotically consistent. The results show that only small and medium size cooperative banks (regionally distributed) are characterised by positive scale economies. The small and the big ones (locally and nationally distributed) show instead diseconomies of scale. Nevertheless some of them have a good profitability. Finally, the analysis of economy of scale and subadditivity expansion path indexes does not reveal significant gains in terms of costs for banks that modify their bundle of products.