Identification in Structural Vector Autoregressive Models with Structural Changes, with an Application to US Monetary Policy
| Author | Luca Fanelli,Emanuele Bacchiocchi |
| DOI | http://doi.org/10.1111/obes.12092 |
| Published date | 01 December 2015 |
| Date | 01 December 2015 |
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©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 77, 6 (2015) 0305–9049
doi: 10.1111/obes.12092
Identification in Structural Vector Autoregressive
Models with Structural Changes, with anApplication
to US Monetary Policy*
Emanuele Bacchiocchi† and Luca Fanelli‡
†Department of Economics, Management and Quantitative Methods, University of Milan,
Milan, Italy (email: emanuele.bacchiocchi@unimi.it)
‡Department of Statistical Sciences and School of Economics, Management and Statistics,
University of Bologna, Bologna, Italy (email: luca.fanelli@unibo.it)
Abstract
A growing line of research makes use of structural changes and different volatility regimes
found in the data in a constructive manner to improve the identification of structural
parameters in structural vector autoregressions (SVARs). A standard assumption made
in the literature is that the reduced form unconditional error covariance matrix varies while
the structural parameters remain constant. Under this hypothesis, it is possible to iden-
tify the SVAR without needing to resort to additional restrictions. With macroeconomic
data, the assumption that the transmission mechanism of the shocks does not vary across
volatility regimes is debatable. We derive novel necessary and sufficient rank conditions
for local identification of SVARs, where both the error covariance matrix and the structural
parameters are allowed to change across volatility regimes. Our approach generalizes the
existing literature on ‘identification through changes in volatility’ to a broader framework
and opens up interesting possibilities for practitioners. An empirical illustration focuses
on a small monetary policy SVAR of the US economy and suggests that monetary policy
has become more effective at stabilizing the economy since the 1980s.
I. Introduction
Structural vector autoregressions (SVARs) are widely used for policy analysis and to pro-
vide stylized facts about business cycle.As is known, it is necessary to identify the structural
*The authors wish to thank two anonymous referees, Anindya Banerjee, and the following people for useful
comments on previous versions of this article: Efrem Castelnuovo, Marcu Lanne, Riccardo ‘Jack Lucchetti, Helmut
L¨utkepohl, Alessandro Missale,Aleksei Netsunajev, Paolo Paruolo and Tao Zha. We also thank seminar participants
at the University of Trieste,the ‘DIW Seminar on Macroeconomics and Econometrics’ in Berlin (December 2014),
the workshop on ‘Identification in Macroeconomics’in Warsaw, (December 2014) and conference participants at the
‘Sixth Italian Congress of Econometrics and Empirical Economics’,Salerno (January 2015). We are solelyresponsible
for any remaining errors. A previous versionof this paper circulated with the title: ‘Identification in str uctural vector
autoregressive models with structural changes’. Both authors gratefully acknowledge partial financial support from
the Italian MIUR Grant PRIN-2010/2011, prot. 2010RHAHPL 003. The second author also acknowledges RFO
grants from the University of Bologna.
JEL Classification numbers: C32, C50.
762 Bulletin
shocks to run policy simulations. Magnusson and Mavroeidis (2014) have recently shown
how structural changes, which are pervasive in the macroeconomy, can be used construc-
tively to identify structural relations which are time invariant. In this paper, we focus on the
identification of SVARs characterized by changes in the error covariance matrix, allowing
for changes also in the structural parameters.
The identification of structural dynamic macro models through heteroscedasticity was
originally proposed by Rigobon (2003), who formalized the intuition that the information
that there exist different volatility regimes in the data represents an ‘additional’identifica-
tion source that can be exploited to identify the shocks without the need to resort to other
type of restrictions.1Lanne and L¨utkepohl (2008) have extended this idea to the case of
SVARs, see also Lanne and L ¨utkepohl(2010), Lanne, L ¨utkepohl and Maciejowska(2010)
and Ehrmann, Fratzscher and Rigobon (2011).2However, this literature is exclusively based
on the idea that the structural parameters remain constant across volatility regimes. This
assumption appears reasonable in certain applications, but is in general questionable with
macroeconomic data, where there is widespread evidence of parameter instability. It is well
recognized that structural breaks may have markedconsequences on both the transmission
and propagation mechanisms of the shocks.
This paper shows that the identification approach suggested by Rigobon (2003) and
Lanne and L¨utkepohl (2008) can be generalized to a broader framework, opening up
interesting possibilities for SVAR’s practitioners. By applying the seminal identification
rules of Rothenberg (1971), we derive novel necessary and sufficient rank conditions for
local identification which apply when discrete permanent (not recurring) breaks occur
simultaneously in the reduced form VAR error covariance matrix and in the (structural)
parameters which define the relationships between theVAR disturbances and the structural
shocks. The results in Rigobon (2003) and Lanne and L¨utkepohl (2008) obtain as special
cases of our analysis. Unlike Rigobon (2003) and Lanne and L¨utkepohl (2008), in our
setup the patterns of SVAR impulse response functions may vary across volatility regimes.
As is known, structural changes offer identifying power only if some parameters do
not change. The difficult open question is what these parameters are. In our approach,
different structural models are imposed on different volatility regimes through a balanced
combination of the statistical information provided by the data, and ‘conventional’linear
restrictions. It is economic reasoning that providesindications about which are the structural
parameters likely to change across the volatility regimes, and which are the structural
parameters which are likely to remain unchanged.
Our approach opens up interesting possibilities for practitioners. We discuss new iden-
tification schemes that stem from our analysis, using examples taken from the empirical
monetary policy literature. SVARs which would typically be unidentified in the case of
constant structural parameters, can be identified or overidentified and hence tested against
the data, when also the structural parameters are allowed to vary across volatility regimes.
1In the recent literature, Sentana (1992) and Sentana and Fiorentini (2001) have introduced similar ideas in the
context of factor models, Klein and Vella (2010) and Lewbel (2012) in the context of simultaneous systems of
equations. See also Keating (2004) for the case of SVARs.
2Other examples include Caporale, Cipollini and Demetriades (2005a), King, Sentana and Wadhwani (1994),
Caporale, Cipollini and Spagnolo (2005b), Rigobon and Sack (2003, 2004) and Normandin and Phaneuf (2004).
©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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