Hodges–Lehmann Detection of Structural Shocks – An Analysis of Macroeconomic Dynamics in the Euro Area
| Published date | 01 August 2018 |
| DOI | http://doi.org/10.1111/obes.12234 |
| Author | Helmut Herwartz |
| Date | 01 August 2018 |
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©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 80, 4 (2018) 0305–9049
doi: 10.1111/obes.12234
Hodges–Lehmann Detection of Structural Shocks –
An Analysis of Macroeconomic Dynamics in the Euro
Area*
Helmut Herwartz†
†Department of Economics, Goettingen University, Humboldtallee 3, D-37073 G ¨ottingen,
Germany (e-mail: hherwartz@uni-goettingen.de)
Abstract
Structural shocks in multivariate dynamic systems are hidden and often identified with
reference to a priori economic reasoning. Based on a non-Gaussian framework of indepen-
dent shocks, this work providesan approach to discriminate between alternative identifying
assumptions on the basis of dependence diagnostics. Relying on principles of Hodges–
Lehmann estimation, we suggest a decomposition of reduced form covariance matrices
that yields implied least dependent (structural) shocks. A Monte Carlo study underlines
the discriminatory strength of the proposed identification strategy.Applying the approach
to a stylized model of the Euro Area economy, independent shocks conform with features
of demand, supply and monetary policy shocks.
I. Introduction
The scientific treatment of monetary policy has gained markedly from the consideration
of microfounded low-dimensional models (Gertler, Gali and Clarida, 1999). The so-called
trinity model formalizes the contemporaneous and dynamic interplay among core macro-
economic aggregates such as real economic activity, prices and a monetary policy instru-
ment. The consensual view on such central dynamics might reflect the notion of stylized
independent structural shocks which are better justified in small dimensional systems in
comparison with larger models that more likely comprise closely related economic pro-
cesses. For identification of contemporaneous relations in structural vector autoregressive
(SVAR) models, the imposition of exclusion restrictions (Sims, 1980; Bernanke, 1986), or
restrictive long-run effects of structural shocks (Blanchard and Quah, 1989; King et al.,
JEL Classification numbers: C32, G15.
*Helpful comments from three anonymous reviewers and the Editor Anindya Banerjee are gratefully acknowl-
edged. I am also grateful to Martin Ademmer,J ¨org Breitung, Ralf Br¨uggemann, Kai Carstensen, Jonas Dovern, Oliver
Grothe, Christian Gouri´eroux, Carsten Jentsch, Roman Liesenfeld, Helmut L¨utkepohl, Oskar Martinez and Mathias
Trabandt, and visitors of research seminars at the Universities of Cologne, Goettingen and Nuernberg/Erlangen,
Universitat Rovira-i-Virgili, DIW Berlin, ifo Institute Munich, Deutsche Bundesbank and DAGStat 2016 for their
interest and discussions. I thank Alexander Lange, Simone Maxand andTilo Schnabel for computational assistance.
This work has been supported by the Deutsche Forschungsgemeinschaft (HE 2188/8-1).
Hodges Lehmann detection of structural shocks 737
1991) have been suggested. More recently, theoretically motivated sign restrictions have
become popular (Faust, 1998; Uhlig, 2005).
Introducing additional assumptions on the innovation generating distributions may of-
fer both implications for the underlying structural relations, and diagnostic tools that allow
evaluating if the data are in line with the presumed distributional framework. Along these
lines Rigobon and Sack (2003) and, similarly, Lanne and L¨utkepohl (2008) propose an
identification scheme distinguishing states of lower and higher (co)variance. Herwartz
and L¨utkepohl (2014) show how statistical identification can be fruitfully combined with
external information gathered from economic theory. Herwartz and Pl¨odt (2016a) com-
pare theory and data driven identification approaches in quantitative terms. They suggest
drawing upon the informational content of the data if possible, and complement it with
theory-based information.
Recently, Moneta et al. (2013) have adopted independent component analysis to deter-
mine optimal variable orderings in recursive systems of non-Gaussian structural shocks.
Their a priori focus on triangular schemes could be criticized, however. For the case of
causal VAR models, the approaches in Lanne, Meitz and Saikkonen (2017) (Maximum-
likelihood, ML) and Gouri´eroux, Monfor t and Renne (2017) (Pseudo ML, PML) allow
the identification of non-recursive structural relations under the assumption of indepen-
dent structural shocks with at most one marginal distribution being Gaussian (Comon,
1994). While ML estimation is the method of choice for structural modelling under cor-
rect specification of the log-likelihood, Gouri´eroux et al. (2017) show that under suitable
assumptions PML estimation retains consistency even under log-likelihood misspecifica-
tion. Adding a non-parametric approach to identification, Matteson and Tsay (2017) show
that the minimization of a statistical independence diagnostic – in their case the distance
covariance of Sz´ekely, Rizzo and Bakirov (2007) – also results in a consistent assessment
of the structural model.
Similar to Matteson and Tsay (2017), this work builds upon the idea of minimizing a
dependence score for structural modelling. Opposite to parametric (ML, PML) estimation
and the non-parametric approach of Matteson and Tsay (2017), the dependence score sug-
gested for minimization in this work – the Cram´er-von-Mises (CvM) distance of Genest,
Quessy and R´emillard (2007) – is completely distribution free. The minimization of the
CvM distance, or the maximization of its P-value under the null hypothesis of indepen-
dence, follows the principle of Hodges–Lehmann (HL) estimation (Hodges and Lehmann,
1963, see also Dufour, Khalaf and Kichian (2006)). Complementing computational merits,
Genest et al. (2007) compare the powerproper ties of their global approach to independence
testing with more specialized diagnostics designed against local alternatives. According
to their conclusions, the suggested CvM statistic amounts to an ‘ideal’ choice for de-
pendence diagnosis unless the analyst is sufficiently confident to opt for a particular local
dependence alternative. Specifically, the identification of least dependent structural shocks
(LDS) might benefit from the robustness of the CvM statistic. Analyzing the global crude
oil market, Herwartz and Pl¨odt (2016b) illustrate that such independence criteria give rise
to well distinguished supply, general demand, and oil specific demand shocks. In addition,
this work proposes a bootstrap scheme that supports the analyst beyond the assessment of
parameter significance or the determination of impulse response areas. Resampling tech-
niques are employed to evaluate the informational content of the data for the extraction
©2018 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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