Synchronisation of national business cycles in Europe?
Date: 2003-12-20
Institutions: Eurostat
Subjects: econometrics, economic cycle, economic integration, world economy

N
O

I
T
I

D
E

3
0
0
2

Synchronisation of
national business cycles
in Europe?

E U R O P E A N
C O M M I S S I O N

 
Europe Direct is a service to help you find answers to your questions about the European Union

New freephone number:
00 800 6 7 8 9 10 11

A great deal of additional information on the European Union is available on the Internet.
It can be accessed through the Europa server (http://europa.eu.int).

Luxembourg: Office for Official Publications of the European Communities, 2003

ISBN 92-894-6865-3
ISSN 1725-4825

© European Communities, 2003

4TH EUROSTAT AND DG ECFIN  
COLLOQUIUM ON MODERN TOOLS FOR BUSINESS CYCLE ANALYSIS 

"GROWTH AND CYCLE IN THE EURO-ZONE" 

20 TO 22 OCTOBER 2003 

Luxembourg, European Parliament 
Hémicycle, Schuman building 

Synchronisation of national business cycles in Europe? 

Gebhard Flaig,  ifo Institute for Economic Research, Munich, Germany 
Jan-Egbert Sturm, ifo Institute for Economic Research, University of Munich, Germany 
Ulrich Woitek, University of Munich, Germany 

 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Synchronization of National Business Cycles in Europe? 

Gebhard Flaig†, Jan-Egbert Sturm†,‡ and Ulrich Woitek‡ 

September 2003 

Paper prepared for the 4th Eurostat colloquium on  

Modern Tools for Business Cycle Analysis  

Luxembourg, October 20-22, 2003 

Abstract 

This  paper  explores  the  extent  to  which  co-movement  in  business  cycles  in  European 

countries has changed over the last fifty years. Several complementary methods are applied to 

check the robustness of the findings. The most important result is that the correlation between 

the national business cycles was already quite high during the fifties and early sixties of the 

last century, declined in the late sixties to in some cases even negative values and reached a 

peak  after  the  first  oil  price  shock.  Since  the  eighties  we  observe  a  stable  or  even  steadily 

increasing co-movement of the national business cycles. 

JEL Classification Numbers: C20, E32, F02 

Keywords: business cycles, economic integration 

† ifo Institute for Economic Research, Munich, Germany. 

‡ University of Munich, Germany. 

1 

 
 
 
 
 
                                                 
1. Introduction 

In an open economy, business cycle developments not only depend upon internal supply and 

demand factors, but also from shocks originating in other countries. The European integration 

of goods, capital and factor markets suggests that economic dynamism in a European country 

is  more  responsive  to  external  influences  as  used  to  be  the  case.  This  suggests  increasing 

business cycle affiliations at least within Europe. On the other hand, however, economic and 

financial 

integration  allows  countries 

to  exploit  comparative  advantage 

through 

specialization,  which  leads  to  increased  macroeconomic asymmetry  (Krugman,  1991). This 

paper explores the extent to which co-movement in business cycles in European countries has 

changed over  the  last  fifty  years.  Several  complementary  methods  will  be  applied  to  check 

the robustness of our findings. 

The degree of synchronization depends upon the  correlation of the external  shocks between 

countries  and  the  intensity  to  which  single  markets  are  internationally  integrated.  For 

instance, changes in oil prices affect countries simultaneously, but to a different extent. It is 

also  possible  that  shocks  that  originate  in  one  particular  country  expand  across  border  and 

affect  other  countries  as  well.  Following  the  European  Commission  (2001,  p.  7),  the 

transmission  channels  can  be  grouped  into  four:  international  trade,  the  corporate  channel, 

confidence effects and financial linkages. Ideally, one needs a structural model to be able to 

differentiate  between  these  channels  and  to  test whether  at  least  one  of  these  channels  has 

changed over time. There is a general feeling that all four channels have indeed become more 

important  in  recent  history.  Removal  of  trade  barriers  has  boosted  international  trade, 

especially between European countries. Recent years have witnessed exponentially increasing 

flows of foreign direct investment. Confidence  indicators throughout the world have moved 

in  tandem  in  recent  years.  As  confidence  influences  business  cycles,  the  increased 

international  co-movement  of  confidence  indicators  could  suggest  a  larger  transmission  of 

shocks. Finally,  linkages through financial markets  have become stronger as  investors have 

increased the international diversification of their portfolio. 

The  often  mentioned  intensification  of  international  business  cycle  co-movement  has  clear 

implication for economic policy. For instance, many economists argue that divergence among 

the EMU member countries still is so high and the flexibility of labor markets so low, that the 

euro-zone  common  currency  area  is  not  optimal  from  an  economic  point  of  view  (De 

Grauwe, 2000; Eijffinger and De Haan, 2000). Various studies have, in that respect, pointed 

out that business cycles in the euro-zone countries diverged considerably in the past (see, e.g. 

2 

 
Christodoulakis, Dimelis and Kollintzas, 1995). However, in assessing the economic case for 
EMU the crucial question is how likely it is that business cycles will diverge in the future.1  

This paper explores to which extent co-movement of business cycles in Europe actually has 

increased  over  time  and  should  therefore be  seen  as  an  –  in  our  view  –  first  and  necessary 

step  in  a  larger  project  on  European  business  cycle  synchronization.  The  next  section  will 

discuss  the  data  and  present  some  descriptive  statistics.  Section  3  uses  rolling  correlation 

coefficients  for  the  cyclical  component  generated  by  an  Unobserved  Components  Model, 

whereas  Section  4  applies  spectral  analysis  to  the  problem  at  hand.  We  end  with  some 

conclusions. 

2. Data 

In  order to  analyze  business  cycles  across  countries and  over  time, we  need  to observe  the 

evolution  of  a  measure  of production both  comparable  across  countries  and  over time.  The 

latter  implies  focusing  on  a measure  like  real  GDP.  Cross-country  comparison  forces  us  to 

convert real GDP into one unit of measure. As we do not want the data to be influenced by 

the  relatively  volatile  movements  of  exchange  rates,  we  turn  to  Purchasing  Power  Parities 

(PPPs). We use GDP measures based on constant PPPs. This approach to generate time series 

of PPPs is to fix a ‘base’ year and to extrapolate PPPs for other years. Extrapolation is done 

by  applying  the  relative  rates  of  inflation  observed  in  different  countries  to  the  base  year 

PPPs. GDP series in national currency and at current prices can now be converted with these 

PPPs to yield volume measures that are comparable across countries. The resulting measures 
of GDP comparisons are volume indices at constant prices and PPPs.2  

These  time  series  have  a  very  convenient  property:  they  replicate  exactly  the  relative 

movements  of  volume  GDP  growth  of  each  country,  which  facilitates  the  use  and 

interpretation of PPPs over time. Another advantage is that the resulting series is unaffected 
by methodological changes relating to the calculation of PPPs.3 For these reasons, the OECD 

1 Arthis and Zhang (1999) found evidence that business cycles are becoming more synchronous across Europe. 

This view is challenged by Inklaar and De Haan (2001). 

2 The same result would have been achieved by applying volume growth rates of GDP to the comparative GDP 

levels of the base year. 

3  A  drawback  of  this  approach  is  that  it  is  assumed  that  price  structures  do  not  change  over  time.  Economic 

reality has it, however, that relative  prices  do change over time  and it is  well known that ignoring these shifts 

3 

 
                                                 
recommends  indices  based  on  constant  PPPs  for  the  analysis  of  relative  business  cycle 
performance between countries and over time.4  

The  GDP  data  comes  from  the  GGDC  Total  Economy  Database  at  the  University  of 
Groningen  and  The  Conference  Board.5  This  database  is  strongly  rooted  in  the  work  of 

Angus Maddison. For most countries trends in GDP before 1990 are derived from Maddison 

(2001)  as  well  as  some  of  Maddison’s  other  publications.  GDP  series  since  1990  are 

constructed  by  researchers  of  the  Groningen  Growth  and  Development  Centre  and  The 

Conference Board. In some cases the long-run series were revised when new estimates came 

available.  We  use  the  tables  for  OECD  countries  expressed  in  1999  US  dollars,  for  which 

‘EKS’ purchasing power parities (as published by the OECD, 2002) have been used. For all 
European countries, data covers the period 1950 until 2002.6 Figure 1 shows the GDP growth 

rates for (the sum of) these countries. 

[Insert Figure 1 about here] 

To  analyze  the  issue  of  business  cycle  synchronization,  it  is  necessary  to  determine  the 

cyclical  component  of  output.  The  problem  we  face  here  is  that  the  widely  used  filtering 

methods cause artificial cyclical structure when applied to a series based on a data generating 
process  different  from  the  assumptions  underlying  the  chosen  filter.7  Following  Canova 

(1998),  we  chose  the  pragmatic  way  of  comparing  the  results  for  different  filters,  e.g.,  the 

difference  filter,  the  Hodrick-Prescott  filter  (HP,  Hodrick  and  Prescott,  1997),  the  Baxter-

over  longer  periods  can  generate  a  biased  picture  of  economic  developments.  Another  consequence  of  fixing 

price structures at a base year is the dependence of results on the choice of the base year. 

4  For  the  latest  ‘snapshot’  comparisons  of  GDPs  and  therefore  business  cycles  across  countries,  the  OECD 

recommends the use of indices based on current (benchmark) PPPs. 

5 http://www.eco.rug.nl/ggdc 

6 Our set of European countries include Austria, Belgium, Denmark, Finland, France, (West-) Germany, Greece, 

Ireland, Italy, the Netherlands, Norway, Portugal, Spain, Sweden, Switzerland and the United Kingdom. 

7 See the discussion in Cogley and Nason (1995), King and Rebelo (1993) and Harvey and Jaeger (1993). 

4 

 
                                                                                                                                                      
King filter (Baxter and King, 1999) and the filter generated by an  Unobserved Components 
Model.8 

2.1 Correlation Coefficients 

Arguably  the  most  commonly  used  measure  of  co-movement  is  correlation  analysis.9 

Correlation analysis is used to summarize the extent to which the cyclical components exhibit 

co-movements across countries. A high coefficient of correlation indicates that countries tend 

to  be  in  similar  states  of  cyclical  movement.  The  degree  of  synchronization  itself  is 

determined  on  the  basis  of  contemporaneous  cross-correlation,  while  the  overall  linkage 

between cyclical movements is measured by the maximum coefficient, which emerges from 

cross-correlation at different lags and leads. This allows for a fairly comprehensive analysis. 

Developments 
contemporaneous cross-correlation coefficients for rolling 10-year periods.10 

in  synchronization  over 

time  are  examined  on 

the  basis  of 

the 

While evidence of increasing or decreasing synchronization may emerge, there is uncertainty 

as  to  whether  this  is  due  to  generally  higher or  lower  linkages  in cyclical  developments  or 

simply to a phase shift of the cycles, effectively reducing the number of lag and lead periods 

during  which  the maximum  correlation  occurs.  Evidence  of  increased  synchronization  may 

thus  be  considered  most  convincing  if  the  contemporaneous  correlation  is  increasing  over 

time and tends to be equal to the maximum correlation at a zero lag or lead (ECB, 1999). 

There are drawbacks when using ‘moving windows’. For instance, the results might be quite 

dependent on the size of the window. For example, if the moving window covers a common 

shock (such  as  the  oil  price  shock  in  the  1970s),  correlation  is  very  high,  and  immediately 

drops once this common shock is no longer covered. 

8 Note that, Arthis and Zhang (1997, 1999) and De Haan et al. (2002) report that their results are not dependent 

on the choice of the detrending method. 

9  Recently,  Harding  and  Pagan  (2002)  proposed  a  new  ‘concordance’  measure  as  new  indicator  for  economic 

convergence. We will not focus on this new measure. 

10 For our purpose, to determine the evolution of co-movement over time subsamples need to be examined. This 

makes the measure sensible to the length of the samples. 

5 

 
                                                 
In  this  section  we  restrict  our  attention  to  a  correlation  analysis  for  the  period  1950  until 

2002.  In  a  first  step  we  explore  the  association  between  the  growth  rate  of  GDP  of  each 

country and the growth rate of GDP of the rest of the European countries.  

The  left-hand  side  of  Table  1  shows  the  highest  cross-correlation  coefficients  between  the 

growth rates of single countries versus the growth rate of the remaining European countries. 

As  the  first  column  indicates,  except  for  Greece,  Spain  and  the  United  Kingdom  the 

contemporaneous  correlation  coefficient  is  the  highest  among  all  lead/lag-relationships. 

Whereas  the  United  Kingdom  leads  the  European  business  cycle  by  one  year,  Spain  and 

Greece have a lag of respectively one and two years. Strikingly low correlations we observe 

for  Ireland  and  Norway.  Also  the  United  Kingdom,  Greece  and  Denmark  have  correlation 

coefficients  below  0.5.  Except  for  maybe  Denmark,  this  list  is  not  really  surprising.  The 

United Kingdom and Ireland have traditionally rather strong economic relationships with the 

U.S. and other Common Wealth nations. Norway – as an oil-producing non-EU country – has 

probably been affected by oil price developments – which underlie most major international 

business  cycle  shocks  –  in  a  rather  different  way  than  most  European  countries.  Greece’s 

peripheral  location  within  the  EU  together  with  its  relatively  low  degree  of  economic 

development  might  be  able  to  explain  its  low  business  cycle  correlation  with  the  rest  of 

Europe.  

[Insert Table 1 about here] 

Using  the  cyclical  component  extracted  by  using  the  Hodrick-Prescott-filter  the  picture 

changes  slightly. The right-hand side of Table 1 shows that  in this case Norway, Denmark, 

Finland  and  the  UK  lead  the  other  European  countries  by  respectively  four,  three  and  one 

year; Germany on the other hand lags the other European countries by one  year. Except for 

Ireland  and  the  United  Kingdom,  the  differences  in  correlation  coefficients  are  not  large. 

Whereas  Belgium,  France,  the  Netherlands,  Portugal  and  Spain  all  report  correlation 

coefficients  of  around  0.8,  for  Germany,  Ireland  and  Norway  its  magnitude  is  below  0.5. 

With the clear exception of Germany, the initiators of European integration (by founding the 

European  Coal  and  Steel  Community  (ECSC),  the  European  Atomic  Energy  Community 

(EURATOM)  and  the  European  Economic  Community  (EEC)  in  respectively  1951  and 

1957) all belong to the group of countries with the highest correlations.  

6 

 
 
3. Synchronization of Business Cycles in the Time Domain 

3.1 The Unobserved Components Model 

In this section we employ an Unobserved Components Model in order to extract the cyclical 

component  from  the  yearly  GDP  series  for  single  countries  and  the  rest  of  the  European 

countries, respectively. In a second step, we use rolling correlation coefficients to analyze the 

changing pattern of synchronization between the national and international business cycles. 

The basic  assumption underlying  Unobserved Components Models is that an observed time 

series 

ty  can be decomposed into several interpretable components (for a general discussion 

see  Harvey,  1989;  Maravall,  1995).  In  the  following,  we  decompose  the  logarithm  of  the 

yearly GDP series into the unobserved components trend T , cycle  C , and the irregular  I : 

(1) 

y

t

=

+
CT

t

t

+

I

t

. 

The  trend  component  represents  the  long-run  development  of  GDP  and  is  specified  as  a 

random walk with a possibly time-varying drift rate 

µ : 

t

(2) 

T
t

=

T
t

−
1

ε+µ+
−
1
t

t

. 

The level impulse 

ε  is a white noise variable with mean zero and variance 

t

2

εσ . The drift rate 

µ  is allowed to vary over time and is also defined as a random walk: 

t

(3) 

ξ+µ=µ
t

−1

t

. 

t

The drift impulse 

ξ  is a white noise variable with variance 

t

2

ξσ . 

The  model  specified  in  equations  (2)  and  (3)  implies  that  the  trend  component  follows  an 

IMA(2,1)-process.  Special  cases  emerge  when we  set the  variance  of  the  shocks  to  zero.  If 

both are zero, we get a deterministic linear trend. If 

2

ξσ  is zero and 

2

εσ  is strictly positive, the 

model  collapses  to  a  random  walk  with  a  constant  drift  rate.  The  opposite  case  –  with  a 

strictly positive 

2

ξσ  and 

2

εσ  equal to zero – gives an  integrated random walk with  a usually 

smooth trend component. 

The  cycle 

tC   captures  the  business  cycle  fluctuations  around  the  trend  component  and  is 

modeled as the sum of  M  subcycles with different frequencies: 

7 

 
(4) 

=

C

t

∑

M

=
1

i

C

it
,

. 

The  specification  of  the  total  cycle  as  the  superposition  of  subcycles  with  different 

frequencies  is  able  to  represent  some  ideas  of  classical  business  cycle  theory  (e.g.,  the 

existence  of  Kitchin  or  Juglar  cycles)  and  to  capture  several  forms  of  business  cycle 

asymmetries (for some alternative specifications see Harvey, 2002, and Harvey and Trimbur, 

2001). 

Each subcycle is specified as a vector AR(1) process: 


+




ρ=


sin





















(5) 

i

i

i

cos
−

sin

λ
C
i
λ
C
i

λ
C
i
λ
C
i

cos

C
−
,1
t
∗
C
−
,1
t

i

C
,
t
∗
C
,
t

i





. 





κ

κ

,
it
∗
,
it

∗C  appears only by the construction of the recursion and has no intrinsic interpretation. 

The period of subcycle  i  is 

λπ /2

C
i

 with  C
i

λ  the frequency in radians. The damping factor 

ρ  

i

with 

0

≤ρ<
i

1

  ensures  that 

itC ,   is  a  stationary  ARMA(2,1) process  with  complex  roots  in 

the  AR-part  (see  Harvey,  1989).  This  guarantees  a  quasi-cyclical  behavior  of 

itC , .  The 

shocks 

κ   and 

it,

∗κ

it ,   are  assumed  to  be  uncorrelated  white  noise  variables  with  common 

variance 

2

κσ .  They  induce  a  stochastically  varying  phase  and  amplitude  of  the  wave-like 

i

process. The total cycle 

tC  is an ARMA(2M,2M-1) process with restricted MA-parameters. 

The irregular component is specified as a pure white noise process: 

(6) 

I = . 
u

t

t

It is assumed that all disturbances are normally distributed and are independent of each other. 

This is the usual assumption to assure the identification of the parameters (see, e.g., Watson, 

1986). 

Estimation  of  the  model  parameters  is  carried  out  by  maximum  likelihood  in  the  time 

domain. The initial values for the stationary cycle components are given by the unconditional 

distribution  and  for  the  nonstationary  trend  and  drift  components  by  a  diffuse  prior.  The 

filtered  and  smoothed  values  of  the  unobserved  components  are  generated  by  the  Kalman 

filter (for details see Harvey, 1989). 

8 

 
3.2 Empirical results 

After  an  intensive  specification  search  we  choose  a  model  with  two  subcycles.  This  model 

passes  all  specification  tests  and  delivers  plausible  estimates  for  the  trend  and  cycle 

components. The short subcycle varies between 3.5 and 5 years, the long subcycle between 9 

and 12 years.  

Using the cyclical components of both the Unobserved Components Model and the Hodrick-

Prescott  filter  (as  used  in  Section  2),  we  then  calculate  the  rolling  contemporaneous 

correlation  coefficients  between  each  country  and  the  rest  of  Europe.  Each  value  of  the 

correlation coefficient is computed over a window of the past 10 years. Due to lack of space, 
we do not comment in detail the results for each individual country.11 However, by graphical 

inspection  we  are  able  to  distinguish  five  groups  within  our  set  of  16  European  countries. 

Within  each  group  the  time  pattern  of  the  correlation  coefficients  is  rather  similar. 
Furthermore, the results are quite robust across the different filtering techniques we apply.12 

[Insert Figures 2 to 6 about here] 

Figure 2 depicts the contemporaneous cross-correlation coefficients for Belgium, France and 

the Netherlands. In general, these three countries show correlation coefficients well above 0.5 

throughout. Furthermore, these three countries show a relatively stable pattern over time. 

The  second  group  consists  of  the  two  oil-producing  countries  in  our  sample,  i.e.  United 

Kingdom  and  Norway.  In  the  fifties  and  early  sixties,  these  two  countries  move  in  clear 

concordance  with  the  rest  of  Europe.  This  abruptly  changed  at  the  end  of  the  sixties. 

Especially for Norway, its correlation with the rest of Europe remained low – and often even 

negative – until the end of the nineties. Only in recent years, both countries have witnessed a 

sharp increase in concordance with other European countries. 

11 In Appendix A we show the estimated cyclical component results using the Unobserved Components Model 

for each individual country and the rest of the European countries together with their rolling contemporaneous 

correlation coefficients. In order to capture some phase shifts between the cycles  of different countries we also 

report a centered three year moving average of each cycle component. 

12 Besides an Unobserved Components Model and the Hodrick-Prescott filter, we have also used annual growth 

rates and the Baxter-King filter. The results are much alike to ones presented and are available upon request. 

9 

 
                                                 
Austria, Denmark and Germany, i.e. the third group we distinguish, depict a steady increase 

in correlation until the seventies, after which it starts deteriorating again – reaching their low 

at  the  end  of  the  eighties  /  early  nineties.  Since,  there  we  observe  that  these  countries  start 

moving  in  line  with  the  rest  of  Europe  again.  For  Germany  we  can  identify  the  sluggish 

behavior of the German economy between 1982 and 1987, when other countries experienced 

a more or less  strong recovery  from the 1981/82 recession and the  idiosyncratic unification 

boom in Germany in the years 1990/91. 

The  countries  in  the fourth  group,  i.e.  Belgium,  Finland,  Ireland,  Sweden  and  Switzerland, 

start  of  from  a  level  above  0.6  in  the  fifties.  However,  these  cross-correlation  coefficients 

then  slowly  decline  and  –  except  for  Sweden  –  reach  their  lows  during  the  late  seventies, 

early eighties. When using the Unobserved Components Model, Sweden’s turning point was 

already  in  the  early  seventies.  During  the  nineties,  all  correlation  coefficients  are on  a  high 

and relatively stable level again. 

The last group, containing the southern European countries Greece, Italy, Portugal and Spain, 

show lows in the late sixties and early eighties. Except for Portugal – which already started 

from a very high level – we see a clear rise in concordance of these countries with the rest of 

Europe. For Portugal and Spain this pattern is interrupted during the late seventies and early 

eighties. In recent years, we see some slight regress for all countries within this group. 

[Insert Figure 7 about here] 

Figure 7 summarizes the business cycle synchronization in Europe by showing both (GDP-) 

weighted and unweighted average contemporaneous cross-correlations across our group of 16 

European countries using the Unobserved Components Model and the Hodrick-Prescott filter. 

It  reveals  that  the  correlation  between  the  national  business  cycles  was  already  quite  high 

during  the  fifties  and  early  sixties.  For  countries  from  group  2  and  5  we  observe  a  sharp 

decline in the business cycle synchronization during the late sixties, sometimes even leading 

to negative correlations. The first oil price shock induced a high synchronization between the 

national  business  cycles.  Consequently,  the  correlation  coefficients  show  a  sharp  increase 

from  the  mid-seventies  to  the  early  eighties  and  remain  then  fairly  stable  on  a  high  level. 

There is some evidence – especially when focusing on the Unobserved Components Model – 

that the strength of the co-movement of national business cycles has further increased during 

the nineties of the last century.  

10 

 
The last few years exhibit a tendency to a stronger co-movement of especially the British and 

German  business  cycles  with  those  of  remaining  European  countries.  So  –  except  for  the 

southern European countries (group 5) in which European integration has probably indeed led 

to a higher business cycle concordance with the rest of Europe – we have a convergence to a 

situation which is ‘normal’ for most other countries – in particular those from the first (and 

third)  group  –  over  the  last  two  or  three  decades.  ‘Normal’  means  that  we  observe  a 

correlation  coefficient  in  the  range  of  0.5  to  0.8  between  the  national  and  the  European 

business  cycle,  respectively.  There  is  a  significant  association  among  the  cycle  in  different 

countries, but the co-movement is far from a perfect synchronization. 

4. Synchronization of Business Cycles in Frequency Domain 

To go a step further and check the results in time domain for robustness, we employ spectral 

analysis  techniques.  This  method  has  the  advantage  that  it  allows  to  derive  a  measure  for 

synchronization frequency by frequency, which enables us to focus on the relevant business 
cycle  frequency  intervals.13  The  measures  are  based  on  those  developed  in  A’Hearn  and 

Woitek (2001). We focus on three cycle ranges: the 7-10 years range (Juglar cycle), the 5-7 

years range, and the 3-5 years range (Kitchin cycle). The dominant cycle band is identified by 

calculating the share of total variance attributable to cycles in these intervals. To address the 

issue  of  synchronization,  we  decompose  the  variance  for  each  frequency  band  into  an 

explained  and  an  unexplained  part.  In  addition,  we  adopt  the  dynamic  correlation  measure 

suggested by Croux, Forni and Reichlin (2001) to distinguish between  in-phase and out-of-

phase movements. 

To derive  these measures,  consider  two  stationary  time  series, 

tX   and 

tY . The  spectrum  is 

defined as the Fourier transform of the covariance function 

)(τΓ

xy

±±=τ

K,2,1,0

:14 

, 

13  An  example  for  potential  weaknesses  of  the  correlation  coefficient  in  time  domain  as  a  measure  of 

synchronization is the result in Backus and Kehoe (1992), who report a very low correlation coefficient (0.01) 

between the US and the UK cycle before World War I. Based on this result, one would have to conclude that the 

‘Atlantic  Economy’  did  not  exist.  Both  the  state  space  approach  (Solomou,  1998)  and  spectral  analysis 

(A’Hearn and Woitek, 2001), however, reveal that there is a strong relationship between cycles with periods in 

the range 7-10 years. 

14 See e.g. Harvey (1993, 175-179), Granger and Newbold (1986, 48-53), Brockwell and Davis (1991, 434-443), 

Priestley (1981) and Koopmans (1974, 119-164). 

11 

 
                                                 
(7) 

F
xy

=ω
)

(

1
π
2

∑∞

−∞=τ

ωτ−τΓ
)(

e

i

xy

]ππ−∈ω
[

,

. 

, 

The  diagonal  elements  of  the  spectral  density  matrix 
]ππ− ,
Integrating  the  autospectra  over  the  frequency  band  [

xyF

)(ω

  are  called  autospectra. 

,  we  obtain  the  variance  of  the 

respective  series.  After  dividing  the  autospectrum  by  the  variance,  we  can  calculate  the 
contribution of cyclical components in a frequency band  [

. The off-diagonal elements 

]

1, ωω

2

or cross-spectra are complex numbers and given by  

(8) 

=ω
)

(

c

f

xy

xy

−ω
)

(

iq

xy

ω
)

(

, 

]ππ−∈ω
[

,

, 

where 

xyc

(ω
)

  is  the  cospectrum  and 

xyq

(ω
)

  is  the  quadrature  spectrum.  The  cospectrum 

measures  the  covariance  between  the  ‘in-phase’  components  of 

tX   and 

tY ,  whereas  the 

quadrature  spectrum  measures  the  covariance  between  the  ‘out-of-phase’  components. 

Together with the autospectra, the cross spectrum can be used to calculate a measure similar 
to R2 in linear regression analysis. This measure is the squared coherency 

(ωsc
)

: 

(9) 

sc

(

=ω
)

f

(

(

xy
ω
)

f

x

2

ω
)

ω
)

(

f

y

, 

0

≤ sc

≤ω
1)(

. 

This  measure  assesses  the  degree  of  linear  relationship  between  two  series,  frequency  by 

frequency. If we are interested in the extent to which the variance of cyclical components of 
]

  can  be  attributed  to  corresponding  cyclical 

tX   in  the  frequency  band  [

the  series 

1, ωω

2

components in series 

tY , we can use 

)(ωsc

 to decompose the fraction of overall variance in 

this interval into an explained and an unexplained part: 

∫

ω

s

(10) 

ω
1

=ωω
d
)(

f

x

∫

ω

s

sc

ω
+ωω
f
d
)(
)(
x
44 21
44 3
ω
1
"
explained"
 variance

∫

ω

s

u

f

ωω
d
)(
43421
ω
1
"
unexplaine
d"

 variance

. 

We will use this decomposition to compare the degree of linear relationship between cycles 

in  the  aggregate  of  the  European  countries  and  each  of  the  member  countries  in  the  three 

business cycle frequency intervals mentioned above. 

As pointed out by Croux, Forni and Reichlin (2001), a measure like the  squared coherency 

presented above is not suited for analyzing the co-movement of time series, because it does 

not contain information about possible phase shift between cycles in the series 

tX  and 

tY . In 

12 

 
this  sense,  the  correlation  coefficient  in  time  domain  used  in  the  previous  sections  is  more 

informative,  since  it  is  calculated  lag  by  lag,  providing  both  information  on  the  lead-lag 

structure  and  the  degree  of  linear  relationship  between  the  two  series.  Croux,  Forni  and 

Reichlin  (2001)  propose  an  alternative  measure,  the  so-called  dynamic  correlation 

)(ωρ

, 

which  measures  the  correlation  between  the  ‘in-phase’  components  of  the  two  series  at  a 
frequency  ω : 

ω
)

(

c
xy
ω
)

(

ω
)

(

f

y

≤ωρ≤−
(

1)

1

. 

, 

(11) 

=ωρ
)

(

f

x

Using 

(12) 

sc

(

=ω
)

f

(

(

xy
ω
)

f

x

2

ω
)

ω
)

(

f

y

=

c

xy

(

+ω
2
)
ω
)

(

x

f

f

q

y

2

ω
)

(
xy
ω
)
(

, 

we can use this idea to further decompose explained variance: 

∫

ω

s

ω
1

(13) 

=ωω
d

)

(

f

x

=

=

∫

ω

s

ω
1

∫

ω

s

sc

ω
+ωω
f
d
)
(
)
(
x
44 21
44 3
ω
1
explained"
"
 variance
∫

ω

+ω
2
)

(

ω
)

(

2

s

c

xy

u

f

ωω
d
(
)
43421
ω
1
unexplaine
"
d"
∫

ω
s

 variance

+ω

d

ωω
d
)

(

f

u

q
xy
ω
)

f

(

s

ω

2

(

c

∫

y
ω
)
ω
)
(
4434421
ω
1
 variance
-
phase)

xy
f

(in 

y

+ω
d

"
explained"

"
explained

ω
1
ω

∫

s

2

(

q

xy
f

ω
)
ω
ω
)
(
4434421
ω
1
-of-

 variance"

(out

d

y

∫

ω

s

+

phase)

u

f

ωω
d
)
(
43421
ω
1
unexplaine
"
d"

 variance

.

Thus, it is possible to decompose explained variance  into the ‘in-phase’ component and the 

‘out-of-phase’ component, adding some information on the importance of the phase shift in a 
frequency interval to the R2 interpretation of the decomposition in equation (10) above. 

To estimate the spectra, we fit VAR models in time domain, and calculate the spectra of the 
estimated models.15 With a VAR model of order p, the spectral density matrix is given by 

15 This method is based on the seminal work by Burg (1967), who shows that the resulting spectrum is formally 

identical  to  a  spectrum  derived  on  the  Maximum  Entropy  Principle.  This  is  seen  to  be  a  more  reasonable 

approach then the normally used periodogram estimator. The periodogram employs the assumption that all the 

covariances  outside  the  sample  period  are  zero.  Given  that  economic  time  series  are  notoriously  short,  this 

seems to be a problematic assumption (see the discussion in Priestley, 1981, 432 and 604-607). 

13 

 
 
 
                                                 
(14) 

F

=ω
)

(

1
π
2

A
(

−
ωΣω
1
)

A
(

)

−
*

]ππ−∈ω
[

,

. 

, 

The error variance-covariance matrix is denoted by  Σ , and 

)(ωA

 is the Fourier transform of 

the  matrix  lag  polynomial 

)(
LA

−=

LALAI

−

2

1

K2
−

−

P

P LA

.16  But  before  we  can  actually 

estimate the spectrum, we have to solve the problem that the  series under consideration are 

not stationary. Since it is widely used in the literature, we present the results for the Hodrick-
Prescott (1997) filter.17 

‘Synchronization’  describes  a  process;  hence,  we  need  the  measure  in  equation  (13)  to  be 

time-varying.  Since  the  estimator  for  the  spectrum  is  parametric,  it  is  straightforward  to 

obtain a time dependent measure: we re-cast the VAR-model into state-space form, treating 

the parameters as unobservables. The starting point is a VAR of order p 

+=
c

x
t

∑

p

=
1

j

xA
t
j

−

j

+

u

t

(15) 

=

(
Ac
44 21
1

1









)
K
A


44 3
p




x
321
−
pt

x
t

−
1

A

+

u
t

=

AZ

−
1

t

+

u

t

,

Z

−
1

t

where 

tu  is iid(0,H). Vectorizing the above equation and treating the parameters of the VAR 

as state variables, results in 

(16) 

(

=

Z

⊗′
t

I

)

x

t

vec

+
uA

t

t

=

(
Z

)
+α⊗′
t

−1

I

t

u

t

, 

which  is  the  measurement  equation  in  the  state-space  version  of  equation  (15).18  The 

transition equation describes the time path of the VAR parameters and is given by 

(17) 

η+α=α

t T

−1

t

, 

t

16 L is the backshift operator, and the superscript ‘*’ denotes the complex conjugate transpose. 

17 As smoothing weight we use 6.25 as suggested by Ravn and Uhlig (2002). 

18 For the following, see Harvey (1989). 

14 

 
 
                                                 
where 

η  is iid(0,Q). We assume the matrix T to be a diagonal matrix with elements 

t

9.0=ρ

on the diagonal, forcing the time path of the parameters to be a damped AR(1) process. The 

elements  in  the  covariance  matrices  H  and  Q  are  treated  as  hyperparameters,  and  the 

likelihood function based on the cumulated prediction errors of the Kalman filter applied to 

equations (16) and (17) is maximized with respect to these parameters. The solution implies a 

time path for 

α , thus allowing the measures in equation (13) to be time dependent. 

t

[Insert Figure 8 about here] 

The time path for the in-phase proportion of explained variance for the European countries is 

displayed  in  Figure  8  (data  in  logs).  Explained  variance  is  calculated  as  the  proportion  of 

variance  of  a  European  member  explained  by  the  variance  of  the  rest  in  the  business  cycle 

intervals  (7-10  years,  5-7  years,  and  3-5  years).  The  results  are  summarized  for  the  five 
groups  identified  above19  by  taking  averages  over  the  group  members.  Note  that  the  time 

paths are smoothed to facilitate the identification of overall patterns.  

It  is  obvious  that  for  Belgium,  France  and  the  Netherlands,  in-phase  explained  variance  is 

highest,  i.e.  above  50  per  cent  in  all  three  business  cycle  intervals  for  almost  the  entire 

observation period, with the exception of the 7-10 years range, where it is below 50 per cent 

before 1955. Compared with the other 4 groups, the United Kingdom and Norway exhibit the 

lowest  link  to  the  European  cycle:  explained  variance  is  constantly  below  50  per  cent. 

Austria, Germany and Denmark have an average explained variance above 50 per cent, with 

the exception of short periods at the end of the 60s and the beginning of the 90s.  Group 4 

(Finland, Ireland, Sweden and Switzerland) starts with explained variance above 50 per cent. 

After  1965,  the  measure  declines,  and  increases  again  after  1985,  at  least  in  the  3-5  years 

range.  Finally,  Greece,  Italy,  Portugal  and  Spain  start  with  an  average  explained  variance 

below 50 per cent, which, in the 5-7 and 7-10 years range, decreases until about 1965. After 

1965, the measure increases again to reach values above 50 per cent around 1980 in the 7-10 

years range. For the other two business cycle ranges, it crosses the 50 per cent line not before 

the start of the 90s. A comparison with the outcome for the difference filter shows that with 

the exception of Group 4, these results are robust. 

19 Group 1: Belgium, France, the Netherlands; Group 2: United Kingdom, Norway; Group 3: Austria, Germany, 

Denmark; Group 4: Finland, Ireland, Sweden, Switzerland; Group 5: Greece, Italy, Portugal, Spain.  

15 

 
 
                                                 
Ahmed, Levin, and Wilson (2002) interpret synchronization in the high frequency ranges as 

due  to  converging  business  practices 

like 

improved  inventory  management,  while 

synchronization in the lower frequency range is caused by fiscal and monetary policies aimed 

at  smoothing  out  the  business  cycle.  Reducing  the  variance  of  innovations  would  affect  all 

frequencies.  Since  our  results  do  not  favor  a  particular  range,  and  are  also  not  entirely  the 

same  over  all  three  ranges,  there  seems  to  be  a  mixture  of  causes  responsible  for  the 

synchronization process of the European cycles.  

5. Concluding remarks 

This  paper  presents  an  exploratory  study  concerning  the  strength  of  business  cycle  co-

movement  of  the  European  countries  from  1950  to  2002.  Special  emphasis  is  given  to  the 

question  of  whether  the  correlation  between  the  national  business  cycles  has  changed  over 

time. We find that the association between the national and the European business cycle was 

already quite high during the fifties and early sixties. Since the mid-sixties we see a dramatic 

decrease in the strength of co-movement with even negative correlation coefficients for some 

countries.  The  first  oil  price  shock  induced  a  closer  co-movement  of  the  national  cycles. 

Since  then  we  observe  over  more  than  20  years  a  stable  or  even  steadily  increasing 

correlation. However, there  is  no clear evidence that the  co-movement  is  higher than  in the 

fifties or seventies. These findings are generally corroborated by an analysis in the frequency 

domain. Looking at co-movement in three different frequency bands (7-10  years, 5-7  years, 

3-5 years) reveals additional insight. It turns out especially Norway can be seen as an outlier 

with respect to synchronization with the aggregate European business cycle. For the most part 

of the observation period, the Norwegian cycle is not in phase with the European cycle.  

16 

 
References 

A’Hearn, B. and U. Woitek (2001), More International Evidence on the Historical Properties 

of Business Cycles, Journal of Monetary Economics, 47, 299-319. 

Ahmed, S., A. Levin and B.A. Wilson (2002), Recent  U.S. Macroeconomic Stability: Good 

Policies, Good Practice, or Good Luck?, Board of Governors of the Federal Reserve System: 

International Finance Division Discussion Paper, no 730. 

Arthis,  M.J.  and  W.  Zhang  (1997),  International  business  cycles  and  the  ERM:  is  there  a 

European business cycle?, International Journal of Finance and Economics, 2:1, 1-16. 

Arthis, M.J. and W. Zhang (1999), Further evidence on the international business cycle and 

the ERM: is there a European business cycle?, Oxford Economic Papers, 51:1, 120-132. 

Backus, D K. and P. J. Kehoe (1992), International Evidence on the Historical Properties of 

Business Cycles, American Economic Review, 82, 864-888. 

Baxter,  M.  and  R.  G.  King  (1999),  Measuring  Business  Cycles.  Approximate  Band-Pass 

Filters for Economic Time Series, Review of Economics and Statistics, 81, 575-593. 

Brockwell, P.J. and R.A. Davis (1991), Time Series: Theory and Methods (Springer, Berlin, 

Heidelberg, New York, Tokyo), 2nd ed. 

Burg, J.P. (1967), Maximum Entropy Spectral Analysis, reprinted in Childers, D.G. (1978), 

Modern Spectrum Analysis (IEEE Press, New York). 

Canova,  F.  (1998),  Detrending  and  Business  Cycle  Stylized  Facts,  Journal  of  Monetary 

Economics,  41, 475-512. 

Christodoulakis, N., S. Dimelis and T. Kollintzas (1995), Comparisons of business cycles in 

Greece and the EC: idiosyncrasies and regularities, Economica, 62:245, 1-27. 

Cogley,  T.  and  J.  M.  Nason  (1995),  Effects  of  the  Hodrick-Prescott  Filter  on  Trend  and 

Difference  Stationary  Time  Series:  Implications  for  Business  Cycle  Research,  Journal  of 

Economic Dynamics and Control, 19, 253-278. 

Croux,  T.,  Forni,  M.  and  L.  Reichlin  (2001),  A  Measure  of  Comovement  for  Economic 

Variables: Theory and Empirics, Review of Economics and Statistics, 83, 232-241. 

De  Grauwe,  P.  (2000),  The economics  of  monetary  integration,  Oxford:  Oxford  University 

Press. 

17 

 
De  Haan,  J.,  R.  Inklaar  and  O.  Sleijpen  (2002),  Have  Business  Cycles  Become  More 

Synchronized?, Journal of Common Market Studies, 40:1, 23-42. 

Eijffinger,  S.C.W.  and  J.  De  Haan  (2000),  European  monetary  and  fiscal  policy,  Oxford: 

Oxford University Press. 

European  Central  Bank  (1999),  Longer-term  developments  and  cyclical  variation  in  key 

economic indicators across euro area countries, ECB Monthly Bulletin, July, 33-54. 

European  Commission,  Directorate-General  for  Economic  and  Financial  Affairs  (2001), 

Supplement A, Economic Trends, No 10/11 – October/November 2001. 

Granger,  C.W.J.  and  P.  Newbold  (1986),  Forecasting  Economic  Time  Series,  (Academic 

Press, London), 2nd ed. 

Harding, D. and A.R. Pagan (2002), Dissecting the Cycle: A Methodological  Investigation, 

Journal of Monetary Economics, 49, 365-381. 

Harvey,  A.C.  (1989),  Forecasting,  Structural  Time  Series  Models  and  the  Kalman  Filter 

(Cambridge University Press, Cambridge). 

Harvey,  A.C.  (1993),  Time  Series  Models  (Harvester  Wheatsheaf,  New  York,  London, 

Toronto, Sydney, Tokio, Singapore), 2nd ed. 

Harvey, A.C. (2002), Test for Cycles. Mimeo. 

Harvey,  A.C.  and  A.  Jaeger  (1993),  Detrending,  Stylized  Facts  and  the  Business  Cycle, 

Journal of Econometrics, 8, 231-247. 

Harvey, A.C. and Trimbur, T. (2001), General Model-based Filters for Extracting Cycles and 

Trends in Economic Time Series. Mimeo. 

Hodrick,  R.  and  E.  Prescott  (1997),  Postwar  U.S.  Business  Cycles:  An  Empirical 

Investigation, Journal of Money, Credit and Banking, 29, 1-16. 

Inklaar,  R.  and  J.  De  Haan  (2001),  Is  there  really  a  European  business  cycle:  a  comment, 

Oxford Economic Papers, 53:2, 215-220. 

King,  R.G.  and  S.T.  Rebelo  (1993),  Low  Frequency  Filtering  and  Real  Business  Cycles, 

Journal of Economic Dynamics and Control, 17, 207-231. 

Koopmans, L.H. (1974), The Spectral Analysis of Time Series (Academic Press, London). 

Krugman, P. (1991), Geography and trade, Cambridge: MIT Press. 

18 

 
Maddison, A. (2001), The World Economy. A Millennial Perspective, OECD Development 

Centre. 

Maravall, A. (1995), Unobserved Components in Economic Time Series. In: Pesaran, H. and 

Wickens,  T.R.  (eds.),  Handbook  of  Applied  Econometrics  -  Macroeconomics,  Oxford: 

Blackwell, 12-77. 

OECD  (2002),  Purchasing  Power  Parities  and  Real  Expenditures  1999  Benchmark  year, 

Edition 2002. 

Priestley, M. (1981), Spectral Analysis and Time Series (Academic Press, London). 

Ravn,  M.  O.  and  H.  Uhlig,  (2002),  On  Adjusting  the  Hodrick-Prescott  Filter  for  the 

Frequency of Observations, Review of Economics and Statistics, 84, 371-376. 

Sicsic,  P.  and  C.  Wiplosz  (1996),  France,  1945-92,  in:  Crafts,  N.  and  G.  Toniolo  (eds.), 

Economic Growth in Europe since 1945, chap. 8 (Cambridge University Press: Cambridge), 

210-239. 

Solomou,  S.N.  (1998),  Economic  Cycles.  Long  Cycles  and  Business  Cycles  since  1870, 

Manchester University Press: Manchester and New York. 

University of Groningen and The Conference Board, GGDC Total Economy Database, 2003, 

http://www.eco.rug.nl/ggdc. 

Watson,  M.  (1986),  Univariate  Detrending  Methods  with  Stochastic  Trends.  Journal  of 

Monetary Economics, 18, 49-75. 

19 

 
Table 1: Maximum cross-correlations for single countries versus European countries 

Austria 
Belgium 
Denmark 
Finland 
France 
Germany 
Greece 
Ireland 
Italy 
Netherlands 
Norway 
Portugal 
Spain 
Sweden 
Switzerland 
United Kingdom 

Growth rates: 
lead/lag  corr. 
0 
0 
0 
0 
0 
0 
-2 
0 
0 
0 
0 
0 
-1 
0 
0 
1 

0.75 
0.77 
0.49 
0.57 
0.85 
0.64 
0.47 
-0.08 
0.70 
0.71 
0.26 
0.67 
0.65 
0.62 
0.76 
0.41 

corr. 

HP filtered series: 
lead/lag 
0 
0 
3 
1 
0 
-1 
0 
0 
0 
0 
4 
0 
0 
0 
0 
1 

0.67 
0.87 
0.53 
0.54 
0.87 
0.48 
0.60 
0.48 
0.69 
0.77 
0.44 
0.82 
0.77 
0.59 
0.65 
0.69 

Figure 1: Growth rates for European GDP 

7%

6%

5%

4%

3%

2%

1%

0%

-1%

1950 1953 1956 1959 1962 1965 1968 1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001

20 

 
 
 
 
Figure 2: Rolling Correlation Coefficients for Group 1 

Unobserved Components Model 

Hodrick-Prescott filter 

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

bel

net

fra

bel

net

fra

Figure 3: Rolling Correlation Coefficients for Group 2 

Unobserved Components Model 

Hodrick-Prescott filter 

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

nor

ukd

nor

ukd

Figure 4: Rolling Correlation Coefficients for Group 3 

Unobserved Components Model 

Hodrick-Prescott filter 

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

aut

den

ger

aut

den

ger

21 

 
 
 
 
 
 
 
 
 
 
Figure 5: Rolling Correlation Coefficients for Group 4 

Unobserved Components Model 

Hodrick-Prescott filter 

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

fin

swe

swi

ire

fin

swe

swi

ire

Figure 6: Rolling Correlation Coefficients for Group 5 

Unobserved Components Model 

Hodrick-Prescott filter 

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

1.0

0.8

0.6

0.4

0.2

0.0

-0.2

-0.4

-0.6

-0.8

-1.0

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

gre

ita

por

spa

gre

ita

por

spa

Figure 7: Average Correlation Coefficients across European Countries 

Unobserved Components Model 

Hodrick-Prescott filter 

0.8

0.7

0.6

0.5

0.4

0.3

0.2

0.8

0.7

0.6

0.5

0.4

0.3

0.2

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

9
5
-
0
5

2
6
-
3
5

5
6
-
6
5

8
6
-
9
5

1
7
-
2
6

4
7
-
5
6

7
7
-
8
6

0
8
-
1
7

3
8
-
4
7

6
8
-
7
7

9
8
-
0
8

2
9
-
3
8

5
9
-
6
8

8
9
-
9
8

1
0
-
2
9

weighted mean

mean

weighted mean

mean

22 

 
 
 
 
 
 
 
 
 
 
Figure 8: Synchronization of European Business Cycles 

Notes:  

Averages of in-phase proportions of explained variance. Smoothing weight for the Hodrick-

Prescott filter is 6.25 (Ravn and Uhlig, 2002).  

Group 1:  Belgium,  France,  the Netherlands;  Group 2:  United  Kingdom,  Norway;  Group 3: 

Austria,  Germany,  Denmark;  Group  4:  Finland,  Ireland,  Sweden,  Switzerland;  Group  5: 

Greece, Italy, Portugal, Spain. 

23 

 
 
 
 
Appendix A 

Figure A.1: Austria 

0.025

OG-Austria 

OG-Eu-Austria 

0.000

-0.025

0.8

0.6

0.4

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Figure A.2: Belgium 

0.02

0.01

0.00

-0.01

-0.02

0.8

0.6

0.4

OG-Belgium 

OG-Eu-Belgium 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

 
 
 
 
Figure A.3: Denmark 

OG-Denmark 

OG-Eu-Denmark 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

0.02

0.01

0.00

-0.01

-0.02

0.5

0.0

-0.5

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Figure A.4: Finland 

0.10

0.05

0.00

-0.05

1.0

0.5

0.0

OG-Finland 

OG-Eu-Finland 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

 
 
 
 
Figure A.5: France 

OG-France 

OG-Eu-France 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

0.02

0.01

0.00

-0.01

-0.02

1.0

0.8

0.6

0.4

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Figure A.6: Germany 

0.02

0.00

-0.02

0.75

0.50

0.25

OG-Ger 

OG-Eu-Ger 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

 
 
 
 
Figure A.7: Greece 

OG-Greece 

OG-Eu-Greece 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

0.02

0.01

0.00

-0.01

-0.02

1.0

0.5

0.0

-0.5

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Figure A.8: Ireland 

0.050

0.025

0.000

-0.025

1.0

0.8

0.6

OG-Ireland 

OG-Eu-Ireland 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

 
 
 
 
Figure A.9: Italy 

OG-Italy 

OG-Eu-Italy 

0.02

0.00

-0.02

1.0

0.5

0.0

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Figure A.10: Netherlands 

OG-Netherlands 

OG-Eu-Netherlands 

0.02

0.00

-0.02

0.9

0.8

0.7

0.6

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

 
 
 
 
 
 
Figure A.11: Norway 

OG-Norway 

OG-Eu-Norway 

0.025

0.000

-0.025

1.0

0.5

0.0

-0.5

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Figure A.12: Portugal 

0.075

0.050

0.025

0.000

-0.025

-0.050

1.00

0.75

0.50

0.25

OG-P ortugal 

OG-Eu-Portugal 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

 
 
 
 
Figure A.13: Spain 

OG-Spain 

OG-Eu-Spain 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

0.02

0.00

-0.02

0.75

0.50

0.25

0.00

-0.25

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Figure A.14: Sweden 

0.02

0.01

0.00

-0.01

-0.02

0.50

0.25

0.00

OG-Sweden 

OG-Eu-Sweden 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

 
 
 
 
Figure A.15: Switzerland 

OG-Switzerland 

OG-Eu-Switzerland 

0.025

0.000

-0.025

0.9

0.8

0.7

0.6

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Figure A.16: United Kingdom 

0.050

0.025

0.000

-0.025

1.00

0.75

0.50

0.25

0.00

OG-UK 

OG-Eu-UK 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000

Corr 

Corrm 

1950

1955

1960

196 5

1970

1975

1980

1985

1990

1995

2000