Simulation Evidence on Theory‐based and Statistical Identification under Volatility Breaks
| Published date | 01 February 2016 |
| Author | Martin Plödt,Helmut Herwartz |
| Date | 01 February 2016 |
| DOI | http://doi.org/10.1111/obes.12098 |
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©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 78, 1 (2016) 0305–9049
doi: 10.1111/obes.12098
Simulation Evidence on Theory-based and Statistical
Identification under Volatility Breaks*
Helmut Herwartz† and Martin Pl ¨
odt‡
†Georg-August-University, G¨ottingen, Germany (e-mail: hherwartz@uni-goettingen.de)
‡Kiel Institute for the World Economy, Kiel, Germany (e-mail: martin.ploedt@ifw-kiel.de)
Abstract
Beside a priori theoretical assumptions on instantaneous or long-run effects of structural
shocks, sign restrictions have become a prominent means for structural vector autoregres-
sive (SVAR) analysis. Moreover, changes in second order moments of systems of time
series can be fruitfully exploited for identification purposes in SVARs. By means of Monte
Carlo studies, we examine to what degree theory-based and statistical identification ap-
proaches offer an accurate quantification of the true structural relations in a standard model
for monetary policy analysis. Subsequently, we discuss how identifying information from
theory-based and statistical approaches can be combined on the basis of a low-dimensional
empirical model of US monetary policy.
I. Introduction
Structural vector autoregressive (SVAR) modelling has become a widely used tool in
empirical macroeconomics. However, independently and identically distributed Gaussian
structural shocks, which represent innovations to the VAR system, cannot be recovered
from reduced form residuals without further assumptions. Against this background, im-
posing zero restrictions on some instantaneous effects (Sims, 1980) or on long-run effects
of the shocks (Blanchard and Quah, 1989) has been suggested for identification. More
recently, the imposition of theory-based sign restrictions upon impulse responses has be-
come one of the most popular approaches to either fully identify all structural relations
or, in a more ‘agnostic’ scenario, to leave some room for a rotation-based identification of
a few not directly restricted structural relations.1Zero restrictions on some instantaneous
effects have been criticized especially in the context of studies of the monetary trans-
mission mechanism, as the assumed time delays are usually at odds with recent dynamic
theoretical models (Carlstrom, Fuerst and Paustian, 2009). Albeit sometimes regarded as
less restrictive, identification by means of sign restrictions has also provoked a critical
*We wish to thank three anonymous referees for insightful comments and suggestions. Financial support by
Deutsche Forschungsgemeinschaft (He 2188/3-2) is also gratefully acknowledged.
JEL Classification numbers: C32, E47
1See Fry and Pagan (2011) for a summary of empirical studies employing sign restrictions.
Theory-based and statistical identification 95
discussion (Paustian, 2007; Fry and Pagan, 2011; J¨a¨askel¨a and Jennings, 2011), partic-
ularly with regard to the prevailing focus on median impulse responses for quantitative
conclusions. While using sign restrictions may offer useful information on the structural
interplay of variables within a dynamic system, it is fair to notice that a unique structural
decomposition of the covariance matrix of reduced form error terms does not exist. To
arrive at unique impulse responses by means of sign restrictions, an analyst willinglyrelies
on censored simulation outcomes. In the light of biases invoked by censoring, one may
critically recast the opting for sign restrictions, at least, if further data-based information
is available that could be used for identification purposes.
Rigobon (2003), Lanne and L¨utkepohl (2008) and others propose an identification
method that allows to refrain from a priori restrictions by exploiting changes in the (un-
conditional) (co)variance of residuals.2Numerous recent empirical evaluations of macro-
economic systems have uncovered a general tendency of decreasing macroeconomic risks
as a characteristic of a period beginning in the mid of the 1980s and lasting for about or
more than two decades, see for instance Perez-Quiros and McConnell (2000). The period
of the so-called ‘Great Moderation’is characterized by a general mitigation of second order
moment levels and dynamics. As shifts in the covariances of reduced form residuals have
become a stylized fact at least for mature economies, it appears worthwhile to shed more
light on the potential of volatility shifts in identifying structural macroeconomic relations.
In this study, we assess the relative merits of the more theory-based identification ap-
proaches and the statistical identification approach that rests on volatility shifts. The study
consists of two main parts. In the first part, we subject all identification approaches to a
simulation-based comparison using a common macroeconomic model as data-generating
process (DGP) that additionally features shifts in second order moments. Our simulation
set-up allows to investigatenumerous aspects of perfor mance and informational content of
these identification approaches. Firstly, bymeans of a new and intuitive evaluation criterion
we investigate the accuracy of impulse response patterns identified by employing changes
in the volatility structure of the residuals or by employing a set of sign restrictions. Sec-
ondly, we assess under which circumstances and how often the statistical approach might
be feasible. In this regard, we also consider the case of employing changes in the volatility
structure of the residuals only if such changes have been diagnosed by means of a suit-
able pretest, and otherwise proceeding with the theory-based approach. Such a ‘hybrid’
approach might mimic the proceeding of an analyst in practice. Thirdly, we compare the
outcome of imposing an agnostic and a fully restricted sign pattern. Fourthly, similar to
the study of Carlstrom et al. (2009), we additionally check howa standard Choleski identi-
fication performs, given our DGP and evaluation criterion. Fifthly, we investigate to what
extent omitted variable biases could change the relative performance of the identification
approaches for structural analysis.
To preview some of the results of the first part, we find that impulse response patterns
identified by means of (co)variance shifts offer the most precise measures of the true dy-
namics even though, as expected, the performance of this approach depends on the relative
2See Rigobon (2003) for a simple intuition of the method. Note that several approaches using statistical iden-
tification exist. For instance, Sentana and Fiorentini (2001) consider identification conditions of conditionally het-
eroskedastic models. Lanne and L¨utkepohl (2010) assume mixed normal distributed model innovations to identify
the shocks and impulse responses.
©2015 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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