Measuring Business Cycles Intra‐Synchronization in US: A Regime‐switching Interdependence Framework
| Published date | 01 August 2017 |
| Author | Danilo Leiva‐Leon |
| Date | 01 August 2017 |
| DOI | http://doi.org/10.1111/obes.12157 |
513
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd.
Measuring Business Cycles Intra-Synchronization
in US:A Regime-switching Interdependence
Framework*
Danilo Leiva-Leon
DG Economics and Research, Banco de Espa˜na, Alcal´a 48, 28014 Madrid, Spain (e-mail:
danilo.leiva@bde.es)
Abstract
This paper proposes a Markov-switching framework to endogenously identify periods
where economies are more likely to (i) synchronously enter recessionary and expansion-
ary phases, and (ii) follow independent business cycles. The reliability of the framework
is validated with simulated data in Monte Carlo experiments. The framework is applied to
assess the time-varying intra-country synchronization in the US. The main results report
substantial changes over time in the cyclical affiliation patterns of US states, and show
that the more similar the economic structures of states, the higher the correlation between
their business cycles. A synchronization-based network analysis discloses a change in the
propagation pattern of aggregate contractionary shocks across states, suggesting that the
US has become more internally synchronized since the early 1990s.
I. Introduction
Since Hamilton (1989), Markov-switching (MS) models have become a useful tool for
policy makers and investors to construct inferences about the state of the economy(expan-
sionary or recessionary regimes), financial markets (high or low volatileregimes), monetary
policy (active or passive policy regimes), etc. Also, multivariate extensions of MS models
have been used to provide helpful insights about issues such as business cycles synchro-
nization (Camacho and Perez-Quiros, 2006), business cycles and stock market volatility
interdependence (Hamilton and Lin, 1996), real activity and inflation cycles synchroniza-
tion (Leiva-Leon, 2014), monetary and fiscal policy interaction (Davig and Leeper, 2006),
among other types of relationships. In these studies, a key component of the analysis is the
dependency relationship between the underlying Markovian latent variables governing the
model’s dynamics.
JEL Classification numbers: E32, C32, C45.
*I thank Maximo Camacho, Marcelle Chauvet, James D. Hamilton and Gabriel Perez-Quiros,the editor and two
anonymous referees for their helpful comments and suggestions. I also benefited from conversations with James
Morley and Michael T. Owyang. Thanks to the seminar participants at the Bank of Canada, Bank of Mexico, Central
Bank of Chile and the University of California Riversidefor helpful comments. Supplementar y material of this paper
can be found at the author’s webpage: https://sites.google.com/site/daniloleivaleon/media. The views expressed in
this paper are those of the author and do not represent the views of the Banco de Espa˜na or the Eurosystem.
OXFORD BULLETIN OF ECONOMICSAND STATISTICS, 79, 4 (2017) 0305–9049
doi: 10.1111/obes.12157
514 Bulletin
The modelling approaches of multivariate MS specifications can be sorted into two
categories. The first category includes studies where the relationship between the latent
variables is a priori defined. Hence, it is based on the researcher’s judgment, relyingon four
different settings (Hamilton and Lin, 1996; Anas et al., 2007). The first refers to the case
where all series in the model are subject to a single latent variable (Krolzing, 1997; Sims
and Zha, 2006). The second uses different latent variables which are modelled as totally
independent Markov chains (Smith and Summers, 2005; Chauvet and Senyuz, 2012). In
the third, the dynamics of one latent variable precedes those of other latent variables
(Hamilton and Perez-Quiros, 1996; Cakmakli, Paap and Van Dijk, 2011), allowing for a
possibly different number of lags.1Fourth, there is also the case of a general Markovian
specification that involves the full transition probability matrix (Kim, Piger and Startz,
2007). However, it raises computational difficulties and is less straightforward to interpret
as the number of series, states or lags, increase.Accordingly, the obtained regime inferences
and final interpretations of the model’s output may vary substantially depending on the
approach chosen.
The second category focuses on making a posteriori assessments of the synchronization
between MS processes, providing ‘average’ dependency relationship estimates. Works in
this line are Guha and Banerji (1998) andAr tis, Marcellino and Proietti (2004), whichfocus
on business cycles synchronization.The authors first estimate different MS univariate mod-
els and then compute cross-correlations between the probabilities of being in recession as
measures of synchronization.2Phillips (1991) points out the two extreme cases presented
in the literature: the case of complete independence (two independent Markov processes
are hidden in the bivariate specification) and the case of perfect synchronization (only one
Markov process for both variables). Camacho and Perez-Quiros (2006) and Bengoechea,
Camacho and Perez-Quiros (2006) focus on assessing whether the latent variablesin multi-
variate models are either unsynchronized or perfectly synchronized by modelling the
data-generating process as a linear combination between the two cases. Leiva-Leon (2014)
extends this approach to state-space representations, where the state vector is driven by
latent variables following dynamics that are modelled as a linear combination between the
two polar cases. However, Leiva-Leon (2014) and previous related studies, assume that
the weights assigned to each polar case, which are used to measure the synchronization
between the latent variables, are assumed to be constant over time.
Despite the usefulness of the approaches used in the literature stream to deal with multi-
variate MS models, they assume, or estimate, constant overtime dependency relationships
between the underlying latent variables governing the model’s dynamics. This assump-
tion makes unfeasible assessments of endogenous changes in the structural relationship
between the latent variables. For example, in the case of business cycles synchronization,
two economies maybecome more synchronized due to trade ag reements, economic unions,
etc. Therefore, the analysis of changes in the structural relationship between the business
1Another type of relationship, under a univariate framework,is presented in Bai and Wang (2011), where the state
variable governing the mean of the process is conditional to the one governingthe variance of that process.
2However, as shown in Camacho and Perez-Quiros (2006), these approaches may lead to misleading results,
since they are biased towards showing relatively low values of synchronization precisely for countries that exhibit
synchronized cycles. This suggests that a bivariate framework would provide a better characterization of pairwise
synchronization than two univariate models.
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
Business cycles intra-synchronizationin US 515
cycles of these economies (identified with the underlying latent variables) becomes crucial
for the evaluation of specific policies.
Moreover, the study of business cycle synchronization is useful to assess the degree
of exposure that a given economy has to its external environment. Previous works have
used multivariate MS models to study the synchronization of national economies (Smith
and Summers 2005; Camacho and Perez-Quiros, 2006), or regional economies (Owyang,
Piger and Wall, 2005; Hamilton and Owyang, 2012), providing synchronization patterns
that are constant over time. However, such degree of exposure may experience changes
over time, which can be caused bya variety of factors, such as global recessionar y shocks,
global financial crises, etc. Therefore, changes in synchronization over time, using MS
models can only be captured by splitting the sample into sub-periods. The problem with
this approach is that its output relies on specific date breaks, which sometimes may be
controversial and might increase the risk of pretesting bias (Diebold, 2015). To the best of
my knowledge, the time-varying relationship between the latent variables of a MS model
is an issue that still has not being studied from an endogenous perspective.
This paper proposes an approach to endogenously infer structural changes in the rela-
tionship between the latent variables governing multivariate MS models. For simplicity of
the presentation and without loss of generality,in the sequel, I focus on the case of business
cycles synchronization, however, the proposed framework can be applied to a wide range
of applications of multivariate MS models. The proposed framework endogenously iden-
tify regimes where two economies enter recessions and expansions synchronously, from
regimes where the economies are unsynchronized and experience independent business
cycle phases. In contrast to existing MS models in the literature, the filter of the proposed
framework not only provides the inferences associated to each latent variable, but it also
provides simultaneous inferences on the dependency relationship between the latent vari-
ables for each period of time. The model is estimated by Gibbs sampling and its reliability
is assessed with Monte Carlo experiments, suggesting it as a suitable approach to track
changes in the synchronization of cycles.
Dynamic Factor Models have been widely used is assessing business cycles synchro-
nization by looking at the variability of an economy’s output growth explained by a ‘global
component’, see Kose, Otrok and Prasad (2012), Kose, Otrok and Whiteman (2003) for a
constant parameter version, and Del Negro and Otrok (2008) for a time-varying parameter
version. However, theyprovide no information on bilateral synchronizations, i.e. economy-
specific business cycles pairwise interlinkages, which is fundamental to study the dynamic
propagation mechanism of business cycle shocks from a disaggregated perspective. The
proposed framework provides time-varying pairwise synchronizations obtained from
bivariate MS models that can be easilyconverted into measures of dissimilarity, or business
cycle distances. These distances can be used to assess changes in the interdependence and
clustering patterns experienced by a large set of economies by relying on network analy-
sis. In such a network, the economies take the interpretation of nodes, and the stochastic
links between pairs of nodes is given by the estimated synchronicity, fully characterizing
a business cycle network governed by Markovian dynamics.
The proposed framework is applied to investigate potential variations in the business
cycles interdependence of US states, and to assess the explanatory factor of the complex
interactions at the regional level, obtaining four main findings. First, the results report the
©2017 The Department of Economics, University of Oxford and JohnWiley & Sons Ltd
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