On the Identification of Interdependence and Contagion of Financial Crises

Date01 December 2017
Published date01 December 2017
AuthorEmanuele Bacchiocchi
DOIhttp://doi.org/10.1111/obes.12188
1148
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
doi: 10.1111/obes.12188
On the Identification of Interdependence and
Contagion of Financial Crises*
Emanuele Bacchiocchi
Department of Economics, Management and Quantitative Methods, University of Milan,
Italy (email: emanuele.bacchiocchi@unimi.it)
Abstract
In this paper we propose a new framework for modelling heteroskedastic structural vector
autoregressions. The identification of the structural parameters is obtained by exploiting
the heteroskedasticity in the data naturally arising during crisis periods. More precisely,
we provide identification conditions when heteroskedasticity and traditional restrictions
on the parameters are jointly considered. Although the framework is general enough to
find potential applications in many empirical economic fields, it proves to be well suited
for distinguishing between interdependence and contagion in the literature related to the
transmission of financial crises. This methodology is used to investigate the relationships
between sovereign bond yields for some highly indebted EU countries.
I. Introduction
The recent global crisis and the subsequent European debt sovereign crisis, in their drama,
offer economists and econometricians a rich laboratory to study the transmission of finan-
cial shocks during periods of high turbulence. Since the seminal contribution by King and
Wadhwani (1990), many studies have been proposed to capture the rational and irrational
aspects of the spread of financial crises. Contagion is the term which mainly represents this
stream of research, although there is not a clear consensus as to what precisely contagion
is. Masson (1999), for example, separates the international transmission mechanism in
monsoonal effects, spillovers and pure contagion.While the first two are mainly related to
macroeconomic fundamentals and external economic linkages, the latter indicates all those
cases where the co-movements can be considered ‘excessive’. The definition of contagion
we have in mind for the aim of the present paper is to look at whether shocks propagate
JEL Classification numbers: C01, C13, C30, C51.
*I wish to thank two anonymous referees, the Editor Heino Bohn Nielsen, and the following people for useful
comments on previous versions of this article: Efrem Castelnuovo, Luca Fanelli,Piergiorgio Alessandri, Massimil-
iano Caporin, Francesco Ravazzolo, Giuseppe Cavaliere,Anders Rahbek, Peter Boswijk, Riccardo ‘Jack’ Lucchetti,
Alessandro Missale. I also thank seminar participants at the University of Lecce, Prometeia Association (Bologna),
the University of Bologna, and conference participants at the ‘Padua MacroTalks’, Padua (July 2016), and ‘Seventh
Italian Congress of Econometrics and Empirical Economics’,Messina (Januar y 2017). I am solelyresponsible for any
remaining errors. I gratefully acknowledge partial financial support from the Italian MIUR Grant PRIN-2010/2011,
prot. 2010RHAHPL 003 and RFO grants from the University of Milan.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 79, 6 (2017) 0305–9049
On the identification of interdependence and contagion 1149
differently during normal and turbulent periods. This notion, designated ‘shift contagion’
by Forbesand Rigobon (2002) and Caporin et al. (2013), is largely accepted in the literature
(see, among many others, Corsetti, Pericoli and Sbracia, 2005) and, importantly, does not
depend on the theoretical explanation for the propagation in excess of what is expected.
According to the definition of contagion as a break in the international transmission
mechanism of macroeconomic and financial shocks, following Forbesand Rigobon (2002),
we distinguish between interdependence, indicating the market co-movements occurring
even in periods of stability, and pure contagion (or, simply, contagion), occurring only if
cross-markets’ co-movements increase significantly after the shock. Several authors have
provided empirical methods to distinguish between interdependence and contagion; most
of them are based on testing for different cross-market correlations over tranquil and
turbulent periods. In particular, Forbes and Rigobon (2002) correct the traditional tests
for comparing cross-market correlations for the upward bias caused by heteroskedasticity,
naturally arising during crises. This approach, however, is not immune to the endogeneity
problem, that is, when there are bi-directional simultaneous linkages between the two
investigated countries (the originating and the affected countries).
Ciccarelli and Rebucci (2007) propose a time-varying coefficient model to measure
contagion and interdependence in a Bayesianframework that jointly deals with the presence
of heteroskedasticity and omitted variables. However, as recognizedby the authors, they do
not attempt to address the possible simultaneity problems that might arise when modelling
strictly linked countries or markets.
In order to address the issue of bi-directional linkages between countries or mar-
kets, we propose a new specification of structural vector autoregressive (SVAR) models
that accounts explicitly for possible heteroskedasticity of the endogenous variables. Such
heteroskedasticity is exploited to identify different volatility regimes and to understand
whether the transmission of shocks is different across these regimes. As an example, in
periods of high instability in the financial markets, a shock hitting one particular market
might propagate in a different waythan in relatively tranquil periods. The effect of the same
shock at a different period of time might be completely different. The turbulence of the
market could either amplify the effect of the shock in the same market in whichit originates,
or allow for a propagation to other financial markets, or create both effects. In this context,
the proposed model, although general enough to find potential applications in many macro-
economic and financial frameworks, proves to be well suited for distinguishing between
interdependence and contagion of financial markets as discussed above.
The particular structure of the model, in fact, helps in the distinction between these
two phenomena, while the endogeneity drawback highlighted by Forbes and Rigobon
(2002) is solved using the ‘identification through heteroskedasticity’ approach proposed
by Rigobon (2003) and extended by Lanne and L¨utkepohl (2008) for the identification of
SVAR models.1
1The intuition, originally introduced by Wright (1928), consists of using the second moments to increase the
number of relations mapping the parameters of the reduced and structural forms. Over recent years, other authors
have proposed approaches to obtain identification using heteroskedasticity in the data. See Klein and Vella (2010),
Prono (2013), Lewbel (2012), Lanne, L¨utkepohl and Maciejowska (2010), Bacchiocchi and Fanelli (2015) and
Sentana and Fiorentini (2001) for theoretical contributions. See also, among others, Bacchiocchi, Castelnuovo and
Fanelli (2017), King, Sentana and Wadhwani (1994) and Rigobon and Sack (2003, 2004).
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd

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