Using the dynamic conditional correlation (DCC) model due to Engle (2002), we estimate time varying correlations of quarterly real GDP growth among the G7 countries. In general, we find that rathe heterogeneous patterns of international synchronization exist during U.S. recessions. During the 2007 - 2009 recession, however, international co-movement increased substantially.Dynamic conditional correlation, Business cycle synchronization, Recession

Johann Scharler

Nikolaos Antonakakis

English

Research Papers in Economics

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
The Synchronization of GDP Growth in the G7  
During U.S. Recessions. Is this Time Different? 
 
 
by 
Nikolaos ANTONAKAKIS, Johann SCHARLER
*) 
Working Paper No. 1005 
April 2010 
D DE EP PA AR RT TM ME EN NT T   O OF F   E EC CO ON NO OM MI IC CS S
J JO OH HA AN NN NE ES S   K KE EP PL LE ER R   U UN NI IV VE ER RS SI IT TY Y   O OF F
L LI IN NZ Z
Johannes Kepler University of Linz 
Department of Economics 
Altenberger Strasse 69 
A-4040 Linz - Auhof, Austria 
www.econ.jku.at 
johann.scharler@jku.at 
phone +43 (0)732 2468 -8360, -9679 (fax) 
 The Synchronization of GDP Growth in the G7
During U.S. Recessions. Is this Time Dierent?
Nikolaos Antonakakis Johann Scharlery
April 2010
Abstract
Using the dynamic conditional correlation (DCC) model due to Engle (2002),
we estimate time varying correlations of quarterly real GDP growth among the G7
countries. In general, we nd that rather heterogeneous patterns of international
synchronization exist during U.S. recessions. During the 2007 - 2009 recession,
however, international co-movement increased substantially.
Key words: Dynamic conditional correlation, Business cycle synchronization,
Recession
JEL codes: E3, E32, F4, F41
Department of Economics, Institute for International Economics and Development, Vienna University
of Economics and Business, Augasse 2-6, A-1090, Vienna, Austria, e-mail:
nikolaos.antonakakis@wu.ac.at.
yDepartment of Economics, University of Linz, Altenbergerstrasse 69, A-4040 Linz, Austria, e-mail:
johann.scharler@jku.at.
11 Introduction
Conventional wisdom holds that during the slow down in economic activity such as that
during 2007 to 2009 was highly synchronized across industrialized countries. However,
so far only anecdotal evidence in favor of such statements is available. In this paper we
present formal evidence indicating a strong increase in output growth correlations among
the G7 countries during this period. According to our results, this increase was rather
unusual in the sense that we nd only little evidence suggesting that output growth rates
became more synchronized during previous recessions.
We estimate time-varying correlations using the dynamic conditioning correlation
(DCC) model introduced by Engle (2002). To our knowledge, this is the rst application
of the DCC model to macroeconomic data.
Our analysis is closely related to the empirical literature on business cycle synchro-
nization (see e.g. Imbs, 2004; Kose et al., 2003; Otto et al., 2001) and especially to Crucini
et al. (2008), Ayhan Kose et al. (2008), Doyle and Faust (2005) and Stock and Watson
(2005) who also study the correlation of business cycles in the G7 countries. In contrast to
the existing literature, we focus explicitly on the synchronization of GDP growth during
recessions. The only paper we are aware of that analyzes the synchronization of recessions
is Claessens et al. (2009). They show that recession periods typically occur simultaneously
across countries, whereas we investigate the cross-country correlation of output growth
dynamics during recessions.
2 Data and methodology
Let yt = (y1;t;:::;y7;t)0 denote the vector of quarterly growth rates of per capita real GDP
in the G7 countries (Canada, France, Germany, Italy, Japan, UK and US). We calculate
yi;t as the fourth dierence of the log of quarterly real GDP per capita. The sample ranges
from the rst quarter of 1960 to the third quarter of 2009. Data are obtained from the
OECD Main Economic Indicators.
The estimation of the DCC model involves two steps: In the rst step, we specify each
conditional variance as a univariate Generalized Autoregressive Conditional Heteroskedas-
2ticity (GARCH) process and in the second step, we use the standardized residuals from
the rst step to construct the conditional correlation matrix. Specically, the DCC model
is dened as:
yt = t + t; where tj
t 1  N(0;Ht); (1)
t = H
1=2
t ut; where ut  N(0;I); (2)
Ht = DtRtDt; (3)
where t = (1;t;:::;7;t)0 is the conditional mean vector of yt, which we specify to follow an
autoregressive process of oder four. t is the vector of residuals based on the information
set available at time t 1, 
t 1. The residuals are normally distributed with zero mean and
conditional covariance matrix Ht = (hi;j;t). Dt = diag(h
1=2
1;1;t;:::;h
1=2
7;7;t)0 is a diagonal matrix
of square root conditional variances, where hi;i;t follow univariate GARCH processes, and
Rt is the matrix containing the time-varying conditional correlations dened as:
Rt = diag(q
 1=2
1;1;t ;:::;q
 1=2
7;7;t )Qtdiag(q
 1=2
1;1;t ;:::;q
 1=2
7;7;t ); (4)
where Qt = (qi;j;t) is a symmetric, positive denite matrix:
Qt = (1      )  Q + ut 1u
0
t 1 + Qt 1; (5)
where ut = (u1;t;:::;u7;t)0 is the vector of standardized residuals,  Q is the unconditional
covariance matrix of ut, and  and  are nonnegative scalars such that  +  < 1.
Since normality of the residuals is rejected, we estimate the DCC model using the
Quasi-Maximum Likelihood estimator under the multivariate Student distribution.
3 Estimation Results
Table 1 shows the estimation results.1 We see from Table 1 that 12 out of the 21 dynamic
correlations are signicant at 5% level of signicance. Moreover, 16 correlations are sig-
nicant at the 10% level. In addition, the estimated correlations are large and signicant
for countries closely geographically related such as the European countries, and the U.S.
1For the sake of brevity, the GARCH estimation results for the rst step are not presented here.
Detailed results are available upon request.
3and Canada. For instance, we obtain the highest and most signicant correlations be-
tween Germany and France, Italy and France, and the U.S. and Canada. In contrast, the
correlations between the U.S. and Italy, Canada and Italy, and Japan and Germany are
quantitatively small and insignicant.
Note that the DCC model is well specied as the multivariate versions of the Port-
manteau statistic of Hosking (1980) and Li and McLeod (1981) do not reject the null
hypothesis of no serial correlation in the standardized and squared-standardized residu-
als, respectively, up to 10 lags.
Figure 1 shows the dynamic conditional correlations obtained from the DCC for each
pair of countries along with U.S. recessions as dened by the National Bureau for Economic
Research Business Cycle Dating Committee.2 Note that using U.S. recessions to dene
periods of economic downturns is not restrictive, since Claessens et al. (2009) show that
the occurrence of recessions is quite synchronized across countries. The question remains:
how synchronized output dynamics are during these periods of downturns? According to
the gure, the highest degree of business cycle synchronization occurs during the 2007 to
2009 downturn as correlations reached a peak.
Although Figure 1 suggests that correlations increased during the 2007 to 2009 re-
cession, we now formally test the hypothesis that recessions, and in particular the 2007
to 2009 recession, are indeed associated with a stronger international synchronization of
output growth. To do so we estimate panel regressions of the form
dci;j;t = i;j + rect + i;j;t; (6)
where dci;j;t = log((1 + i;j;t)=(1   i;j;t)) and i;j;t is the estimated dynamic correlation
between countries i and j. Note that we transform the dynamic correlations to ensure
that our dependent variable is not conned to the interval [ 1;1]. Our results are not
sensitive to this transformation. i;j are cross-section specic eects and rect denotes a
dummy variables which is dened as rect = 1 if the U.S. economy was in a recession in
quarter t and rect = 0 otherwise.
Table 2 shows the results. From Column (1) we see that U.S. recessions are associated
2For the 2007 to 2009 recession we set the end date to the third quarter of 2009 which coincides with
the end of our sample.
4with signicantly higher international correlations. However, Column (2) shows that the
correlations behave rather heterogeneously during individual recessions. Here, we estimate
(6) with the dummies rec1980 = 1 for the period 1980q1 to 1982q4 and zero otherwise.
rec1990, rec2001 and rec2007 are dened analogously to capture the 1990, the 2001 and
the 2007 to 2009 recessions.3 According to our estimates, the recession during the early
1980s was associated with signicant, albeit quantitatively small, increase in international
synchronization. During the recessions in 1990 and 2001 we nd no signicant eect and
in the former episode, the point estimate is even negative. However, during the 2007 -
2009 recession we obtain a highly signicant and quantitatively large eect. According to
the point estimate, the conditional correlations increased on average by slightly more than
0:2 points, which is not just statistically signicant, but also economically substantial.
In Column (3), we add the dummy rec<1980 which is equal to unity during recessions
that occurred before 1980 and equal zero otherwise. We see that, although we obtain
similar eects for the recessions that occurred after 1980, rec<1980 enters with a negative
sign and signicantly at the 10 percent level. Thus, it appears that before 1980, U.S.
recessions were associated with a de-synchronization of GDP growth rates. To illustrate
this point further we estimate a specication with rec<1980 and a dummy that captures
recessions after 1980: rec>1980. According to Column (4), a high degree of international
synchronization during U.S. recessions occurs only since the early 1980s. And together
with the results reported in Columns (2) and (3), this last result suggests that the overall
higher synchronization during recessions we see in Column (1) is to some extent due to
the early 1980s, but mostly to the 2007 to 2009 recession. This result illustrates further
that the strong increase in international output co-movements is a rather unique feature
of the latest downturn.
Stock and Watson (2005) nd that business cycles have generally become less synchro-
nized since 1985. To allow for such a structural break, we re-estimate (6) and include a
dummy, Dt, which is equal to unity if t > 1984q4 and equal to zero otherwise. Column (5)
of Table 2 shows the dummy enters negatively and signicantly, whereas rec1980, rec1990
3Note that the recession during the early 80s was actually a sequence of two recessions. The rst one
occurring between 1980q1 to 1980q3 and the second one between 1981q3 to 1982q4. Since our results
remain unchanged, we pool these two intervals and treat them as a single recession period.
5and rec2001 become insignicant. However, the dummy for the 2007 to 2009 recession
remains highly signicant.
As a robustness analysis we repeated the estimation with the correlation between
contemporaneous GDP growth in the U.S. and lagged GDP growth in the remaining G7
countries. In addition, we augmented (6) with aggregate as well as cross-section specic
time trends. Our results remain unchanged.
4 Conclusion
In this paper we show that the 2007 to 2009 recession in the U.S. is associated with
unusually highly synchronized output growth dynamics in the G7 countries. We estimate
that, on average, the conditional correlations of GDP growth rates increased by roughly
0:2 points during this period. A key question that arises is why output dynamics during
this downturn were so synchronized across the G7 countries.
According to Mendoza and Quadrini (2009) nancial integration and contagion may
have been a source of the high synchronization. Buch et al. (2010) nd that banks transmit
shocks internationally. To the extent that banking sectors suered from severe adverse
shocks during the 2007 to 2009 downturn, this transmission channel may have contributed
substantially and more than usually to the high synchronization of output growth rates.
A detailed analysis of these issues remains an interesting direction for further research.
References
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7F
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8Table 1: Estimation Results of AR(4)-DCC models, Period: 1960q1 - 2009q3
 CAN FRA GER ITL JPN UK
FRA 0.1590
(1.966)
GER 0.1158 0.5370
(1.332) (8.743)**
ITL 0.0875 0.4049 0.2554
(1.079) (5.291)** (2.830)**
JPN 0.1439 0.2164 0.1072 0.1399
(1.807) (2.522)* (1.265) (1.703)
UK 0.1589 0.3020 0.2552 0.2086 0.1939
(1.884) (3.825)** (2.764)** (2.484)* (2.489)*
US 0.3992 0.2645 0.2485 0.0171 0.1356 0.1734
(5.532)** (3.158)** (2.944)** (0.200) (1.613) (2.171)*
 0.0534 (3.22)**
 0.6580 (9.10)**
df 9.5963 (4.24)**
Log-Lik 4460.44
AIC -44.9276
SBC -43.5848
HQC -44.3839
Shibata -45.1490
H(10) 358.399 [0.13]
H2(10) 374.152 [0.09]
Li   McL(10) 349.188 [0.15]
Li   McL2(10) 372.186 [0.10]
Notes: H(10), H2(10) and Li   McL(10), Li   McL2(10) are the multivariate Portmanteau statistics
of Hosking (1980) and Li and McLeod (1981), respectively, up to 10 lags. t-values in parenthesis and
p-values in square brackets. ** p < 0:05, * p < 0:01.
9Table 2: International Correlations and U.S. Recessions
(1) (2) (3) (4) (5)
rec 0.0408***
(0.00795)
rec1980 0.0211** 0.0197** 0.0148
(0.00963) (0.00964) (0.0101)
rec1990 -0.0332 -0.0345 -0.0270
(0.0215) (0.0216) (0.0216)
rec2001 0.00414 0.00282 0.0104
(0.0111) (0.0111) (0.0112)
rec07 0.212*** 0.211*** 0.219***
(0.0201) (0.0201) (0.0201)
rect<1980 -0.0203* -0.0203*
(0.0111) (0.0111)
rect>1980 0.0679***
(0.00905)
D1985 -0.0125***
(0.00473)
Obs 4095 4095 4095 4095 4095
R2 0.740 0.757 0.758 0.744 0.758
Notes: In each specication, the dependent variable is the transformed conditional correlation dci;j;t =
log((1+i;j;t)=(1 i;j;t)), where i;j;t is the estimated dynamic correlation between countries i and j. All
specications include cross-section specic eects. Robust standard errors in parentheses, *** p < 0:01,
** p < 0:05, * p < 0:1.
10

Breaks in the variability and comovement of G-7 economic growth.

Distribution of the Residual Autocorrelation in Multivariate ARMA Time Series Models.

Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models.

Financial globalization,  crises and contagion. NBER Working Papers 15432,

How does globalization aect the synchronization of business cycles?

Macroeconomic shocks and banks' foreign assets.

The Multivariate Portmanteau Statistic.

Trade,  specialization, and synchronization.

Understanding Changes in International Business Cycle Dynamics.

Understanding OECD output correlations. RBA Research Discussion Papers rdp2001-05, Reserve Bank of Australia.

Understanding the evolution of world business cycles.

What are the driving forces of international business cycles? NBER Working Papers 14380,

What happens during recessions, crunches and busts?

The Synchronization of GDP Growth in the G7 during U.S. Recessions. Is this Time Different?

http://www.econ.jku.at/papers/2010/wp1005.pdf

The Synchronization of GDP Growth in the G7 during U.S. Recessions. Is this Time Different?

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