Welfare and Stochastic Dominance for the Measurement of Banks' Domestic Systemic Importance: Analytical Framework and Application

• Date: 01 April 2016
• Author: Gaston Andrés Giordana
• Published date: 01 April 2016
• DOI: http://doi.org/10.1002/ijfe.1542

INTERNATIONAL JOURNAL OF FINANCE AND ECONOMICS

Int. J. Fin. Econ.21: 192–208 (2016)

Published online 24 November 2015 in Wiley Online Library

(wileyonlinelibrary.com). DOI: 10.1002/ijfe.1542

WELFARE AND STOCHASTIC DOMINANCE FOR THE MEASUREMENT

OF BANKS’ DOMESTIC SYSTEMIC IMPORTANCE: ANALYTICAL

FRAMEWORK AND APPLICATION

GASTON ANDRÉS GIORDANA

Banque centrale du Luxembourg, Luxembourg,Grand Duchy of Luxembourg

ABSTRACT

This paper proposes an analytical framework to rank alternative measures of banks’ systemic importance in terms of their wel-

fare impact. The advantage of our approach is that it does not require knowing the exact mathematical form of the underlying

welfare function in the absence of a widely accepted model of systemic risk. The framework consists of two pillars. First,

economic welfare is linked to the measured degree of systemic importance of banks. Second, the association between the con-

cepts of stochastic and welfare dominance of distributions of the measured degree of systemic importance is defined. Then, the

alternative measures can be welfare-ranked by just establishing stochastic dominance relationships. An illustration is presented

using Luxembourg data. Copyright © 2015 John Wiley & Sons, Ltd

Received 22 February 2015; Revised 20 October 2015; Accepted 21 October 2015

JEL CODE: G21; G28

KEY WORDS: systemically important banks; banking regulation; stochastic dominance; welfare; Basel III; Luxembourg

1. INTRODUCTION

The financial crisis that hit in 2007 and 2008 triggered a strong commitment by world leaders to strengthen the

regulatory framework with the purpose of increasing the resilience of the international financial system. One of

the features of the regulatory reform consists in addressing the risks posed by systemically important financial

institutions (SIFIs).1A SIFI can be a bank, an insurance company, a central counterpart, and so on whose failure

compromises the functioning of the whole financial system. However, the identification of SIFIs poses challenges

to policymakers as the degree of systemic importance of an institution is unknown. Even if several measures exist,

not many are directly related to a notion of economic welfare. This is particularly the case of indicator-based

methodologies, which complicate comparisons. This paper proposes an analytical framework to rank alternative

measures in terms of the welfare impact of the resulting distributions of banks’ degree of systemic importance. Our

focus is on domestic systemically important banks (D-SIBs), although the proposed framework can be adapted to

the measurement of the systemic relevance of other financial institutions.

A special policy set-up for coping with D-SIBs is justified by the market failures associated with these insti-

tutions. Indeed, distress or failures of D-SIBs is likely to have a sizeable impact on the local financial sector and

the economy. Moreover, they can generate cross-border externalities, even if the effects are not global in nature.

Finally, moral hazard-related externalities, which tend to induce a mispricing of risk, can also be considerable

domestically. Indeed, banks that are too big to fail and/or too complex to fail would contribute to the build-up of

the latter type of externalities and reduce economic welfare.

Recent research and policy papers have proposed measures addressing the different aspects of the notion of sys-

temic importance. On the one hand, one finds measures based on theoretical models, which have the advantage of

Correspondence to: Gaston Andrés Giordana, Banque centrale du Luxembourg, Luxembourg, Grand Duchy of Luxembourg.

E-mail: gaston_andres.giordana@bcl.lu

Copyright © 2015 John Wiley & Sons, Ltd

WELFARE DOMINANCEOF BANKS’ SYSTEMIC IMPORTANCE MEASURES 193

capturing the extent of negative externalities related with SIBs. Some model-based measures quantify the contri-

bution of individual firms to systemic risk (e.g. Tarashev et al., 2009; Tarashev et al., 2010; Acharya et al., 2012;

Adrian and Brunnermeier, 2011). Other measures focus on interconnectedness externalities and consider as sys-

temically important those institutions whose failure is likely to trigger simultaneous failures of other institutions

in the system (e.g. Segoviano and Goodhart, 2009; Zhou, 2010; Xisong and Nadal De Simone, 2013). However,

model-based approaches for measuring systemic risk are still in their infancy, limiting policyapplications based on

their outputs (Freixas et al., 2015).

On the other hand, indicator-based methods construct composite indices by aggregating bank-level variables

related with the systemic relevance of banks. These methodologies might be more easily and widely implementable

than the model-based ones and therefore are supported by regulatory bodies (BCBS, 2011, 2012) Moreover, some

studies have found clear links between model-based measures and simple indicators (e.g. Drehmann and Tarashev,

2011; Moore and Zhou, 2013). However, constructing composite indices of systemic importance also poses some

challenges. In addition to selecting the set of indicators, an index of systemic importance requires a transformation

function and aggregation parameters (i.e. relative weights and the elasticity of substitution between indicators). The

wide range of possibilities for each of these components produces an infinite number of potential calibrations. So,

a general criterion is needed to choose among these different calibrations.

In line with the tradition initiated by Shorrocks (1983) and Atkinson (1987) (and further developed by Foster

and Shorrocks (1988a, 1988b) and Jenkins and Lambert (1997)), we propose an analytical framework for ranking

alternative methodologies/calibrations in terms of their welfare impact. The advantage of this approach is that

welfare orderings can be established without knowing the exact mathematical form of the underlying welfare

function. The framework relies on two pillars.

The first pillar characterizes the link between economic welfare and the measured degree of systemic impor-

tance. While there is no need for a structural model in our framework, a minimum understanding of the

characteristics of the welfare function is nevertheless required. Therefore, we argue for a positiverelation. Our point

is that a bank with higher measured degree of systemic importance would be subject to more constraints, limiting

negative externalities and thereby improving welfare. However, these constraints would also affect the capacity of

the bank to fund welfare-enhancing investment projects, so the marginal improvement in welfarecould be decreas-

ing (i.e. a convex welfare loss function). Moreover, the possibility that indicator-based assessment methodology

over(under)-estimates the true degree of systemic importance tends to reinforce the concavity of the welfare func-

tion. Unlike the social welfare literature cited in the previous paragraphs, in our framework, the welfare function

does not represent the policymaker’s preferences. Rather, in the absence of a widely accepted structural model of

systemic risk measurement, it should be seen as a reduced form of the economic impact resulting from the market

failures induced by D-SIBs

The second pillar relates the concepts of stochastic and welfare dominance of distributions of the measured

degree of systemic importance. Indeed, under certain conditions, stochastic dominance implies welfare dominance.

The distributions of the measured degree of systemic relevancefrom different methods or calibrations are compared

on the basis of stochastic dominance relationships. The comparisons are performed at several orders of stochastic

dominance. For example, if the distribution of the degree of systemic importance from method Astochastically

dominates the one from B, then method Aresults in higher economic welfare than B. The order of stochastic

dominance at which strict relationships have been established determines the shape of the welfare function (e.g.

linear and strictly concave) required to derive a welfare dominance relation.

The paper is organized as follows. Section 2 sets up the analytical framework to rank alternative assessments

of individual banks’ domestic systemic importance. The two pillars of the framework are explained in detail. In

particular, the welfare function is defined, and the link between stochastic and welfare dominance is formalized.

Section 3 provides a practical illustration of how the framework would work to calibrate an indicator-based

measurement methodology for the identification of D-SIBs. It starts by defining a general index and discussing

alternative settings for the components of the index. In particular, several transformation functions, methods for

calculating the relative weights of the individual indicators and alternative criteria for determining the parame-

ter of substitutability are proposed. Finally, an empirical application for the case of Luxembourg is presented.

Section 4 concludes.

Copyright © 2015 John Wiley & Sons, Ltd Int. J. Fin. Econ.21: 192–208 (2016)

DOI: 10.1002/ijfe