stylized facts of business cycles in the oecd countries · stylized facts of business cycles in the...
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European Regional Science Association36th European CongressETH Zurich, Switzerland
26-30 August 1996
Jordi Pons, Ernest Pons and Jordi SuriñachDepartment of Econometrics, Statistics and
Spanish EconomyUniversity of Barcelona
Stylized Facts of Business Cyclesin the OECD Countries
ABSTRACT : This paper investigates the basic stylized facts of business cyles in the OECDcountries using quarterly data from 1970 to 1994. In the last years the study of businesscycles, on both theoretical and empirical levels, has been again in the forefront of research ineconomics. The purpose of this paper is to determine if the OECD business cycles are indeedin the terminology of Lucas (1977). Lucas concluded that because the coherence and phasecharacteristics of many economic time series appeared to be the same across countries,business cycles are all alike. The methodology used is based on spectral analysis. Thisapproach attempts to identify cycles in the frequency domain. Spectral analysis provides directand relevant information about leads and lags between economic time series and determinesif a substantial degree of coherence at a particular frequency or over a band of frequenciesdoes indeed exist.
Key words. business-cycle, spectral-analysis, frequency-domain.
I. Introduction
The stylized facts of business cycles were in the forefront of research in macroeconomics in
the first half of the twentieth century. Leading article of this literature is the work of Burns
and Mitchell (1946)1. The seminal contribution of Burns and Mitchell was influential because
it provided a comprehensive catalogue of the empirical features of the business cycles of
developed countries, notable, the United States. In recent years, most industrial countries
experienced pronounced cyclical behaviour in an important number of economic indicators.
Since the late sixties and early seventies the study of cycles has experienced a regeneration
of research effort, on both theoretical and empirical levels.
All economies experience recurrent fluctuations in economic activity that persist for periods
of several quarters to several years. Further, there is a definite tendency for the business
cycles of developed countries to move together. The challenge to theory is to develop
consistent explanation for these phenomena. On the theoretical level, renewed interest in
business cycle theory stems from an important article by Lucas (1977). Lucas concluded that
business cycles are all alike, because the coherence and phase characteristics of many
economic time series appeared to be the same across countries. In an attempt to explain this
apparent stylized fact, there has been a proliferation of theoretical business cycle models.
Lucas drew attention to a key business-cycle fact: outputs of broadly-defined sectors move
together. Some important articles in this area are by Kydland and Prescott (1982, 1990 and
1991) and Long and Plosser (1983).
The empirical studies of business cycles have been underpinned by two alternatives
methodologies. The first approach develops the original methodology of Burns and Mitchell
(1946). This method consists of identifying indicators and classifying these indicators as
leading, coincident and lagging by examining the timing and consistency of the turning points
of important economic time series. The second approach attempts to identify cycles in the
frequency domain. This approach consist of characterising business cycles identifying the
presence of peaks in the spectrum and determinying if a substantial degree of coherence at
1Surveys of more recent work on this field are Zarnowitz (1992) and Niemira and Klein (1994).
1
either a particular frequency or over a band of frequencies does indeed exist (see Layton,
1986 and Martin,1987 and 1990).
Perhaps the major limitation of these approaches is that they focus on either time or frequency
domain characteristics, but not on both2. In particular, the purpose of this paper is to
investigate the basic stylized facts of business cycles in the OECD countries using GDP
quarterly data from 1970 to 1994, applying the analysis in time and frequency domain. The
present paper contribute to this literature by applying a methodology based on spectral
analysis. This approach attempts to identify cycles in the frequency domain. Spectral analysis
provides direct and relevant information about leads and lags between countries and
determines if a substantial degree of coherence at a particular frequency or over a band of
frequencies does indeed exist. The series used are the GDP of OECD, Europe, European
Union, Australia, Canada, France, Germany, Italy, Japan, Norway, Spain, Switzerland, United
Kingdom and United States3.
The empirical focus of the paper is on isolating cyclic fluctuations in economic time series,
defined as cycles in the data between specified frequency bands. The scheme of the paper is
as follows. Section II summarises the methodology of the spectral analysis. Section III
presents and discusses the selected stylized facts. Section IV presents the leads and lags
between OECD contries. The main conclusions of the paper are presented in Section V.
II. Methodology
The spectral analysis describes the cycle in terms of a frequency and amplitude. The
frequency is defined as the inverse of the cycle lenght, whereas amplitude is the range
between peak and trough values. Granger and Hatanaka (1964) and Priestley (1981) argue that
the series must be stationary; the mean and variance of the series must remain constant over
2See Bowden and Martin (1992 and 1994).
3Each series is tested for a stochastic trend by using the augmented Dickey-Fuller and Phillips-Perron unit roottests. The results show that the null hypothesis of non-stationarity cannot be rejected.
2
time. If the series are not stationary, as most economic time series tend not to be, a first or
higher difference of the series would be necessary until the differenced series meet the
criterion of a stationary mean and variance. To determine the lead or lag between pairs of
economic indicators, two spectral statistics are used: coherence and phase. Coherence
measures the proportion of variance explained by one of the series at a given frequency of
the second series. This measure can take a value between 0 and 1; the concept is similar to
the square of the correlation coefficient from a regression. Phase measures the time difference
between two series in the frequency domain4.
Using a Fourier transform, one can express a stationary time series as a cyclical components
of different frequencies. The spectrum of the time series which decomposes the series’s total
variance into variance attributed to different frequencies. One can interpret the spectrum as
a density function. The area under the spectrum for an interval between two frequencies
equals the proportion of total variance attributed to components with frequencies within the
interval. We will also consider the coherence and phase between the GDP series of a country
and each of the other country.
It is not meaningful to consider spectra, coherence and phase for series that are not stationary.
We will refer to the statistical procedure used for rendering a time series stationary as
detrending. Given that we do not have a particular theoretical model in mind, and given the
weak power of most tests for stochastic versus deterministic trends, we prefer to take an
agnostic view towards detrending. Therefore, it’s possible to transform the raw economic
series into stationary series in two different ways.
One way to remove a trend from the data is simply to take the rates of growth. Another way
is to use the filter previously used by Hodrick and Prescott (1980) and many others
(application of two-sided moving averages, first-differencing and removal of linear or
quadratic time trends), known as the Whittaker-Henderson type filter. Finally, we apply the
4In the frequency domain, Sargent (1987, p. 282) offers the following update of Burns and Mitchell’s definition:"(...) the business cycle is the phenomenon of a number of important economic aggregates (such as GNP,unemployment, and layoffs) being characterized by high pairwise coherences at the low business cyclefrequencies".
3
rates of growth5. Many recent studies using a battery of such methods to measure business
cycles.
III. Stylized facts
An appropriate starting point in an investigation of business cycles, is to determine if a
substantial degree of coherence at either particular frequency or over a band or frequencies
does indeed exist. We adopt a traditionala priori definition of business cycles,namely
cyclical commovements between important macroeconomic variables with periods of around
five years(Lucas, 1977). Defining the business cycle by frequency of fluctuations, it becomes
natural to exploit spectral analysis.
The spectra for the each series (rates of growth) are shown in figure 1. We have previously
talked about the business cycle as fluctuations withperiods around five years. We make this
more precise by focusing on cycles with periods between six and thirty two quarters6. The
interval between six and thirty two quarters is marked by vertical lines in the spectra (the line
corresponding to thirty two quarters is the left one, since the period (frequency) is decreasing
(increasing) to the right). We specified that business cycles were cyclical components of no
less than six quarters (eighteen months) in duration and fewer that thirty two quarters (eight
years).
Table 1 and figure 1 show that most of the spectral mass for all series is between six and
thirty two quarters. We conclude that there is indeed some empirical support for business
cycles periods between six and thirty two quarters: most of the series have considerable
spectral mass in the corresponding frequency band.
5Because different filters have different transfer functions (that is, they pass through cyclical components atdifferents frequencies to different degrees) choosing a filter is equivalent to choosing which commovements toemphasize. The application of the rates of growth has two effects. A first effect is to reduce the fluctuations inall series and a second effect is to induce a more regular cyclical pattern with larger number of distinguishablecycles.
6This definition of the business cycle was suggested by the procedures and findings of NBER researchers likeBurns and Mitchell (1946). See Baxter and King (1995) for illuminating surveys.
4
Looking at the coherences in table 2 and figure 2, we note that there is relatively high
coherence between OECD and most countries for periods longer that six quarters.
Finally, table 3 shows the commovements of the different countries, as measured by their
correlation with OECD7. This table displays the correlation coefficient between OECD and
each other country lagged from one to five quarters, contemporaneous, and led from one to
five quarters. Most of the correlation coefficients are positive, indicating commovements
between the countries. For most countries, the contemporaneous correlation are the highest.
Of these, the correlation coefficients for Europe and European Union are highest, followed
by those for United States and Canada. The correlation coefficients for Norway are lower.
IV. Leads and lags between OECD countries
The present epigraph benefits from the tools providing with the spectral analysis of time
series in order to obtain an estimation of the lag the economical evolution of some countries
go through in comparison with some others. The estimation of the time lag by using the phase
function presents an important problem since this function is not easy to be interpreted in
practice. It is already known that a null and constant phase function corresponds to a
contemporary relation, whereas a linear phase function with slope being equal to thed lag
corresponds to lag relations of the Xt=aYt-d type. Although, in general, the interpretation of
the estimated phase function seems to be very difficult mainly because of various aspects:
a) When the relation between two variables is more complex, the phase function can
obtain a great deal of different forms depending moreover on the relation parameters.
b) There is a certain indetermination in the phase function. When concerning an angle,
it is not possible to distinguish a value from another being in time different from the
former one in a certain number of entire rounds of a circumference.
The series used for this paper also present those difficulties. Figure 3 shows the phase
function estimated between the OECD variable (the total OECD GNP rates of growth of a
7 The rates of growth of that series are stationary.
5
quarter with respect to the same quarter of the former year) and the EUR variable (referred
to the whole OECD European countries)8.
Figure 3. Phase between OECD and Europe. Figure 4. Phase between Germany and Spain.
The fact that this phase function is so close to the value 0 refers to the almost equality of
both series being then their relation contemporary. A statistical test based on the phase
function as it follows below can confirm that the relation between two variables is
contemporary. By using a spectral window of convenient properties, an estimation of the
individual and cross spectral densities of both variables can be obtained. Noting each variable
for X and Y and the estimated spectral densities for fX,fY and fXY, consistent estimators of the
coherence and the phase function being:
and
(1)κ̂XY(ω)fXY(ω)
fX(ω)fY(ω) 1/2
(2)φ̂XY(ω) tan 1
Im fXY(ω)
Re fXY(ω)
considering that the phase angle must be taken in the [-π,π] interval. Whenever the coherence
is strictly positive, the phase function will asymptotically spread itself as a normal one:
8 The phase function is expressed in sexagesimal degrees to highlight that we are dealing with angles.
6
where am2 depends on the Wk ponderations and the m width of the spectral window used:
(3)φ̂XY(ω) ∼ AN
φXY(ω),a 2
n α̂2XY(ω)
2
1
κ̂XY(ω) 21
andαXY(w) being the width of the cross spectral density between both variables. If the value
a 2m
k <m
W2k
of the coherence is replaced by expression (1), andαXY(w) by a consistent estimator:
the null hypothesis can be contrasted considering that the phase function is null when
(5)α̂XY(ω) fXY(ω)
comparing the following statistical value:
with the table value of a normal distribution. Figure 4 shows when the null hypothesis of a
(6)ZXY(ω) φ̂XY(ω)2 κ̂XY(ω) 2
a 2mα̂2
XY(ω) κ̂XY(ω) 2 1
contemporary relation can be refused by using this test.
When using this contrast in the case of the OECD and Europe, the null hypothesis saying that
the relation is contemporary cannot be rejected. But when comparing other variables, the
interpretation might be less clear9. Figure 4 presents the phase estimated between the quarter
evolution of Germany and Spain. Apparently, in this figure the relation between both
variables can no longer be accepted as contemporary. Precisely, when implementing the
former test both evolutions are refused to be simultaneous. Through the sign of the phase
function, it can also be deduced that the German evolution leads the Spanish one. And then
another problem must be faced. How to know wether this lag consists of one, two or even
more quarters
9 Table 4 shows countries in which the null hypothesis of a contemporary relation can be rejected.
7
Figure 5. Phase between OECD(+1) and Europe.Figure 6. Phase between OECD(-1) and Europe.
When a phase function is linear, the interpretation is then clear. But focusing on our case,
neither the estimated phase functions are linear (both for the case of those countries and for
other variables), nor has it sense to think that the relations between the variables seem so
simple to present such a clear lag. Anyhow, it is worthwhile asking oneself which the
dominant lag is. In most cases, the phase function can give an answer to this question. As far
as the OECD and Europe comparison is concerned, only ask ourselves what effect would
leading or lagging one of both variables a quarter have in the estimated phase function before
considering it. If the relation is mostly contemporary, then the new phase functions should
respectively indicate a lag of 1 and -1. Figures 5 and 6 enclose these new phase functions.
Both estimations cooroborate the already mentioned hypothesis in the sense that the relation
between both variables has neither a lag nor a lead of a quarter. In order to complete the
analysis, it would be also interesting to estimate the phase when a lag or a lead of two
quarters of the OECD variables is previously imposed. Figures 7 and 8 show the new phase
functions.
Figure 7. Phase between OECD(+2) and Europe.Figure 8. Phase between OECD(-2) and Europe.
8
In the case of the OECD and Europe those movements allow the rejection of a likelihood
two-quarter lag. In addition, it is clear that when moving one of both series more than two
quarters, the phase functions will adopt behaviours every time further from a constant value;
consequently the hipothesis is corroborated in the sense that the relation between both
variables is contemporary. On the other hand, in the case of Germany and Spain those
movements provide with some information. As it can be seen in Figure 9 where the variable
enclosing the German evolution leads one quarter, then the phase function reaches the value
0 so that now a contrast of the phase function nullity does not allow the rejection of such
hypothesis. If the DEU variable leads instead of lags a quarter (Figure 10), the phase function
will then confirm that the lag between both evolutions has increased, becoming a realtion with
a lag of two quarters.
Figure 9. Phase between Germany(-1) and Spain.Figure 10. Phase between Germany(+1) and Spain.
Even if all is basically about a graphical analysis, these previous movements of one of both
compared variables can be combined with contrasts over the phase function to determine
roughly the time lag a certain relation among variables dominates. This kind of analysis
implemented in all possible paired variables10 allows the construction of a time lag table as
it is shown in Table 5. The results obtained from the frequency domain are not fully coherent.
For example, it is deduced from the results that no lag exists neither between the OECD and
Spain nor between the OECD and the USA. On the contrary when comparing the USA and
Spain a lag of two quarters is obtained. This fact is influenced by various reasons:
a) Having independently obtained each lag from the others.
10 From the fourteenvariables used in the present research.
9
b) That the null values, more than being something evident of the contemporary relation,
they enclose the impossibility of rejecting that null hypothesis.
c) That the relations among variables are necessarily more complex and the
determination of a whole number as lag supposes a large simplification. Consequently,
the Table 4 results should be understood as simple explanations of a more complex
reality.
If all these factors are gathered as estimation errors it is then senseful trying to obtain a
slightly different table also allowing the whole results to seem reasonable. Through the
average of the results of the initial table of lags the present approach can be then obtained.
This research follows this procedure:
a) The series referred to the OECD total is used as a reference point.
b) All variables related to the OECD are placed in each single row and then a lag related
to OECD is obtained.
c) As in general a different lag can be obtained according to the information of each row,
all these lags are then averaged for each variable. Consequently, a final estimation of
each variable lag related to the OECD is obtained.
Figure 11. Estimated lag at frequency domain. Figure 12. Estimated lag at time domain.
10
d) The value 0 is then assigned to the most leading variable with respect to the OECD
(this case being the USA) and the other lags have their importance diminished in
relation to this variable. Consequently, an ordering of the whole countries is obtained
according to the time lag they go through in relation to the most leading variable
(USA)
Figures 11 and 12 summarize this ordering and the lag in months of each variable. In one
case (Figure 11) the lags obtained in the frequency domain have been used as a reference,
whereas in another one (Figure 12) the lags obtained in the time domain. The following
conclusions are then deduced from this average:
a) Larger lags are obtained when using the time domain results instead of using the
frequency domain ones.
b) The order obtained by using both methodologies is very similar excepting in the case
of Japan. The time domain obtains that Japan finds itself in phase with the USA,
whereas the phase function obtains a significative lag between one and two months.
This paper intends only to be a first approach to the research tackling which lags produce the
different countries economical evolution. That is the reason why, a methodology has been
briefly presented allowing the benefit from the tools of the time series spectral analysis in
order to establish those lags, even if some aspects of this methodology can be criticized:
a) The final result aims to obtain an estimation of the phase function, although this
estimation does not have very clear aspects. Among them, for example, the choice of
the spectral window to be used and its width.
b) The phase function interpretation is not an immediate interpretation despite using the
leading and lagging variables. In some variable combinations, it has been impossible
to determine by using this analysis which is the prevailing lag between two countries.
c) The obtained differences by using the time and frequency domains should catch the
11
researcher’s eye so that in future researches these may allow to find the causes of
those differences.
V. Concluding remarks
In this paper, one examines stylized facts in the frequency domain via the spectral density
function, the Fourier transform of the autocovariance function. The spectral density matrix
decomposes variation and covariation among variables by frequency, permitting one to
concentrate on the periods of interest (business-cycle, for example, correspond to periods of
roughly 6-32 quarters). Transformations of both the real and imaginary parts of the spectral
density matrix have immediate interpretation in business-cycle analysis; the coherence
between any two economics series effectively charts the strenght of their correlation by
frequency, while the phase charts lead/lag relationships by frequency.
We conclude that is indeed some empirical support for business cycles periods between six
and thirty two quarters, because most of the series have considerable spectral mass in the
corresponding frequency band. The commovement of the different countries, as measured by
their correlation with OECD, indicating that the contemporaneous correlation coefficients are
the highest. Of these, the correlation coefficients for Europe and European Union are highest,
followed by those for United States and Canada. The correlation coefficients for Norway are
lower.
And finally, a methodology has been presented allowing to determine the existing lags in the
economical evolution of the analyzed areas. It has been confirmed that the USA is the country
having a more leading evolution with respect to the OECD’s and Switzerland having a larger
lag.
References
-Baxter, M. and King, R.G. (1995):Measuring business cycles: approximate band-pass filtersfor economic time series, National Bureau of Economic Research, Working Paper 5022
-Bowden, R.J. and Martin, V.L. (1992): No, business cycles are not all alike: The UnitedStates and Australia compared,Australian Economic Papers, 31, 385-398.
12
-Bowden, R.J. and Martin, V.L. (1994): International business cycles and financial integration,The Review of Economics and Statistics, 77, 305-320.
-Burns, A.F. and Mitchell, W.C. (1946):Measuring business cycles, National Bureau ofEconomic Research, New York.
-Diebold, F.X. and Rudebusch, G.D. (1996): Measuring business cycles: a modernperspective,The Review of Economics and Statistics, 78, 67-77.
-Granger, C.W.J. and Hatanaka, M. (1964):Spectral analysis of economic time series,Princeton University Press, Princeton, New York.
-Hodrick, R.J. and Prescott, E.C. (1980): Postwar U.S. business cycles: an empiricalinvestigation, Carnegie-Mellon University, Discussion Paper, 451.
-Kydland, F.E. and Prescott, E.C. (1982): Time to build and aggregate fluctuations,Econometrica, 50, 1345-1370.
-Kydland, F.E. and Prescott, E.C. (1990): Business cycles: real facts and a monetary myth,Federal Reserve Bank of Minneapolis Quarterly Review, 14, 1-18.
-Layton, A.P. (1986): A causality analysis of Australia’s growth cycle and the compositeindex of leading indicators,Australian Economic Papers, 25, 57-66.
-Long, J.B. and Plosser, C.I. (1983): Real business cycles,Journal of Political Economy, 91,39-69.
-Lucas, R.E. (1977): Understanding business cycles. In Brunner, K. and Meltzer, A.H. (1977)(eds.): Stabilisation of the domestic and international economy, Carnegie-RochesterConference Series on Public Policy, 5, North Holland, Amsterdam.
-Martin, V.L. (1987): Leads and lags in the Australian business cycle: a canonical approachin the frequency domain,Australian Economic Papers, 26, 188-196.
-Martin, V.L. (1990): Derivation of a leading index for the United States using Kalman filters,The Review of Economics and Statistics, 72, 657-663.
-Niemira, M.P. and Klein, P.A. (1994):Forecasting financial and economic cycles, Wiley,New York.
-Priestley, M.B. (1981):Spectral analysis and time series, Academic Press, New York.
-Sargent, T.J. (1987):Macroeconomic theory, 2nd edition, Academic Press, Boston.
-Zarnowitz, V. (1992):Business cycles: Theory, history, indicators and forecasting, NationalBureau of Economic Research, Ballinger Publishing Company, Cambridge.
13
Table 1. Variance attributed to different frequencies
Country >32 quarters 6-32 quarters <6 quarters
OECD
Europe
European Union
Australia
Canada
France
Germany
Italy
Japan
Norway
Spain
Switzerland
United Kingdom
United States
29.06
29.07
29.06
20.69
29.70
28.50
26.04
19.29
31.43
16.16
38.91
29.53
28.44
27.05
63.91
66.39
66.60
64.26
64.20
66.08
60.88
76.68
62.14
42.36
60.34
67.34
60.77
67.18
7.03
4.54
4.34
15.05
6.10
5.43
13.09
4.04
6.42
41.48
0.75
3.13
10.79
5.77
Table 2. Coherence estimated with OECD at different frequencies
Country >32 quarters 6-32 quarters <6 quarters
Europe
European Union
Australia
Canada
France
Germany
Italy
Japan
Norway
Spain
Switzerland
United Kingdom
United States
0.87
0.86
0.67
0.78
0.72
0.64
0.86
0.80
0.50
0.56
0.79
0.71
0.89
0.79
0.78
0.55
0.66
0,64
0.67
0.73
0.60
0.49
0.49
0.67
0.52
0.82
0.72
0.71
0.29
0.36
0.57
0.37
0.30
0.37
0.41
0.45
0.32
0.56
0.73
14
Tab
le3.
Cro
ss-c
orre
latio
nw
ithO
EC
D
GD
P t-5
GD
P t-4
GD
P t-3
GD
P t-2
GD
P t-1
GD
P tG
DP t
+1
GD
P t+
2G
DP t
+3
GD
P t+
4G
DP t
+5
Eur
ope
-0.0
20.
090.
290.
460.
650.
780.
730.
650.
490.
290.
12
Eur
opea
nU
nion
-0.0
30.
080.
290.
450.
640.
770.
720.
640.
490.
290.
13
Aus
tral
ia0.
020.
110.
220.
320.
450.
540.
510.
430.
310.
09-0
.04
Can
ada
0.14
0.24
0.40
0.55
0.64
0.68
0.62
0.48
0.35
0.19
0.04
Fra
nce
0.03
0.05
0.14
0.29
0.44
0.60
0.60
0.56
0.48
0.34
0.25
Ger
man
y-0
.11
0.01
0.23
0.37
0.52
0.60
0.52
0.42
0.27
0.09
0.05
Italy
-0.2
6-0
.20
-0.0
40.
200.
460.
630.
710.
680.
580.
410.
23
Japa
n0.
080.
280.
450.
550.
620.
630.
550.
460.
380.
270.
19
Nor
way
0.09
0.14
0.29
0.32
0.33
0.29
0.10
0.04
-0.0
2-0
.05
-0.1
1
Spa
in0.
020.
090.
200.
310.
420.
490.
520.
500.
450.
380.
31
Sw
itzer
land
-0.2
3-0
.16
-0.0
30.
160.
360.
500.
580.
610.
560.
450.
29
Uni
ted
Kin
gdom
0.25
0.34
0.45
0.45
0.52
0.52
0.39
0.30
0.14
-0.0
1-0
.11
Uni
ted
Sta
tes
0.17
0.29
0.48
0.65
0.75
0.77
0.59
0.36
0.15
-0.0
8-0
.27
Tab
le4.
Cou
ntrie
sin
whi
cha
cont
empo
rary
rela
tion
can
bere
ject
ed.
OE
CD
Eur
ope
E.
Uni
onA
ustr
alia
Can
ada
Fra
nce
Ger
man
yIta
lyJa
pan
Nor
way
Spa
inS
witz
erla
ndU
.K
ingd
omU
.S
tate
s
OE
CD
**
Eur
ope
**
*
Eur
opea
nU
nion
**
Aus
tral
ia
Can
ada
**
**
**
Fra
nce
**
**
Ger
man
y*
**
**
Italy
**
**
**
*
Japa
n*
**
**
Nor
way
**
**
Spa
in*
**
*
Sw
itzer
land
**
**
*
Uni
ted
Kin
gdom
**
**
**
**
Uni
ted
Sta
tes
**
**
**
**
*
Tab
le5.
Est
imat
edla
gsan
dle
ads
from
GD
Pph
ase
OE
CD
Eur
ope
E.
Uni
onA
ustr
alia
Can
ada
Fra
nce
Ger
man
yIta
lyJa
pan
Nor
way
Spa
inS
witz
erla
ndU
.K
ingd
omU
.S
tate
s
OE
CD
00
00
00
01
0-1
00
00
Eur
ope
00
00
-10
00
00
00
-1-1
Eur
opea
nU
nion
00
00
-10
00
00
00
0-1
Aus
tral
ia0
00
00
22
2-
--
--1
0
Can
ada
01
10
01
11
--
-2
00
Fra
nce
00
0-2
-10
00
-1-1
00
-1-1
Ger
man
y0
00
-2-1
00
10
-11
10
-1
Italy
-10
0-2
-10
-10
-2-1
00
-1-1
Japa
n0
00
--
10
20
-0
2-1
-1
Nor
way
10
0-
-1
11
-0
-2
--
Spa
in0
00
--
0-1
00
-0
2-2
-2
Sw
itzer
land
00
0-
-20
-10
-2-2
-20
-2-2
Uni
ted
Kin
gdom
01
01
01
01
1-
22
0-1
Uni
ted
Sta
tes
01
10
01
11
1-
22
10
Figure 1. Estimated spectrum of quarterly GDP series
Figure 1.1 Spectrum of OECD. Figure 1.2 Espectrum of Europe.
Figure 1.3 Spectrum of European Union. Figure 1.4 Spectrum of Germany.
Figure 1.5 Spectrum of France. Figure 1.6 Spectrum of Italy.
18
Figure 1 (continued)
Figure 1.7 Spectrum of United Kingdom. Figure 1.8 Spectrum of Spain.
Figure 1.9 Spectrum of United States. Figure 1.10 Spectrum of Canda.
Figure 1.11 Spectrum of Japan. Figure 1.12 Spectrum of Australia.
Figure 1.13 Spectrum of Norway. Figure 1.14 Spectrum of Switzerland.
19
Figure 2. Estimated coherences with OECD
Figure 2.1 Coherence of OECD and Europe. Figure 2.2 Coherence of OECD and E. Union.
Figure 2.3 Coherence of OECD and Germany. Figure 2.4 Coherence of OECD and France.
Figure 2.5 Coherence of OECD and Italy. Figure 2.6 Coher. of OECD and Un. Kingdom.
20
Figure 2 (continued)
Figure 2.7 Coherence of OECD and Spain. Figure 2.8 Coherence of OECD and USA.
Figure 2.9 Coherence of OECD and Canada. Figure 2.10 Coherence of OECD and Japan.
Figure 2.11 Coherence of OECD and Australia. Figure 2.12 Coherence of OECD and Norway.
Figure 2.13 Coh. of OECD and Switzerland.
21