Thinking about the relatively recent financial world crisis, it is crucial to investigate weather it was matter of banks inefficiencies or responsibilities, and in the latter case if the responsibilities are to be imputed to banks or governments.
With this aim, we propose a methodology capable to analyze the quality of the banks problem loans and their level of efficiency.
Our approach is based on the inclusion of the "Non performing loans'' variable (NPLs), as an undesirable output, in the distance-revenue function stochastic frontier, which lets us calculate the non-observable NPLs shadow price. Then, we consider the contribution to the degree of risk of the lending system deriving from governments and banks in order to evaluate their responsibilities, and draw some policy implications.
We conduct a panel study on all the US and European banks per each member state for the period pertaining the 2007-8 financial crisis by adopting -to our knowledge for first in the distance function context- the semi-nonparametric Fourier specification, which, among the functional flexible forms, ensures the convergence of both the estimated parameters and the related efficiency to their true values.
We intend to provide a methodology which allows
on one hand to alert in advance an incumbent state of crisis and on the other hand to
evaluate the responsibility to be imputed to the main actors in the credit sector policy,
i.e. banks and governments. As a natural outcome, it follows an economic prescription,
in terms of regulation, based on the NPLs price. In Maggi and Guida (2011)
there is also the possibility of evaluating a similar NPLs price indicator. However, from
the cost function there considered, the marginal cost calculated cannot be assumed as
a true price-quality indicator in that this would be possible with perfect competition,
which is not the case for the credit market.
From an econometric point of view, in the framework of the distance function, we
adopt -to our knowledge for first- the semi-nonparametric Fourier specification (FFF) which,
among the functional-flexible-form alternatives, is capable of guaranteeing the convergence
of both the estimated parameters and the related X-efficiency to their true values
(Gallant, 1981, Berger et al., 1997).
The distance function we consider defines the weak disposability of outputs and therefore the inefficiency,
which can explain, in our context, the presence of NPLs (undesirable outputs) that
banks generate in their production processes, and that cannot be freely eliminated either
because it would require a greater use of inputs, and/or because resources would
have to be diverted from marketable production.
By considering the NPLs as an output of a production process, besides giving the
advantage of deriving the correspondent price, eliminates the empirical complications
that would have occurred using a cost function approach. In fact, in this case a simultaneity
problem would have arisen between inefficiency, and therefore costs, and NPLs
considered as an explicative variable.
Our approach is based on the coincidence between the definition of inefficiency
and distance function. Hence, we may model inefficiency as a function of inputs and
outputs, including NPLs, on which the empirical analysis is focused. More specifically,
we exploit the duality of maximum revenue problem and derive the shadow price of NPLs, which, being
an undesirable output, is negative. It represents the quality of bad loans, which will be
as much worse as greater is its absolute value.
The novelty of our theoretical part is that the distance function now considers, with respect to the previous literature the NPLs as a negative output. This idea derives from the literature developed in the field of regulation for pollution.
Our database is particularly innovative in that considers all the banks present in all the member states of EU and US. Hence, we manage a double panel assessing both banks and countries. In particular, data are taken from Bankscope and are referred to 517 Commercial Banks in Europe and 2404 in the U.S., the sample period is 2000-2008. Europe includes the Euro system (within the sample period also UK is included) plus Sweden, Norway and Turkey.
As for the function used, the specification we adopt is the Fourier Flexible Functional form (FFF), which can globally approximate the unknown true function. The
FFF, developed by Gallant (1981), combines the standard TL with the non-parametric Fourier form. Following the rule of thumb expounded in Eastwood and Gallant (1981),
the number of trigonometric terms in the FFF has been chosen in order to get a total
number of parameters equal to the number of the observations raised to the power of
two-thirds. The FFF function avoid the bias of the standard TL, which, being a local approximation, fails the inference on the underlying true function. For this reason the empirical analysis is particularly innovative. Furthermore, to our knowledge, we use for first such a method in the framework of the distance function described.
Hence, we intend: 1) estimating the non performing loans price as an instrument
for the regulation of the default risk in the credit market and for alerting the crisis
period; 2) providing a rigorous method to calculate the efficiency in the presence of
undesired outputs; 3) finding the responsibilities of governments and banking system
in determining the pattern of NPLs and their price; 4) estimating a cost function and developing an impact analysis to improve and test the robustness of our results.
Gallant, A. R., February 1981. On the bias in flexible functional forms and an essentially
unbiased form : The fourier flexible form. Journal of Econometrics 15 (2),
211-245.