Abberger, Klaus; Nierhaus, Wolfgang
Working Paper
The Ifo business cycle clock: Circular correlation with
the real GDP
CESifo Working Paper, No. 3179
Provided in Cooperation with:
Ifo Institute – Leibniz Institute for Economic Research at the University of Munich
Suggested Citation: Abberger, Klaus; Nierhaus, Wolfgang (2010) : The Ifo business cycle clock:
Circular correlation with the real GDP, CESifo Working Paper, No. 3179, Center for Economic Studies
and ifo Institute (CESifo), Munich
This Version is available at:
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The Ifo Business Cycle Clock:
Circular Correlation with the Real GDP
Klaus Abberger
Wolfgang Nierhaus
CESIFO WORKING PAPER NO. 3179
CATEGORY 12: EMPIRICAL AND THEORETICAL METHODS
S
EPTEMBER 2010
An electronic version of the paper may be downloaded
from the SSRN website: www.SSRN.com
from the RePEc website: www.RePEc.org
from the CESifo website: Twww.CESifo-group.org/wpT
CESifo Working Paper No. 3179
The Ifo Business Cycle Clock:
Circular Correlation with the Real GDP
Abstract
The Ifo Business Climate is the most important indicator for the business cycle in Germany.
In 1993 the connection between the two components of the business climate – business
situation and business expectations – was graphically portrayed by Ifo in a 4-quadrant
scheme: the Ifo Business Cycle Clock. Today similar monitoring systems are firmly
established and are presented by Eurostat, the OECD and others. The German Federal
Statistical Office presents the real GDP in a 4-quadrant scheme. In the following, important
qualities of the Ifo Business Cycle Clock are shown. The importance of orthogonal functions
for the circular correlation is examined.
JEL-Code: E32, C32, C39, C22.
Keywords: Ifo business climate, growth cycle, circular correlation, linear-circular correlation,
temporal disaggregation.
Klaus Abberger
Ifo Institute for Economic Research at the
University of Munich
Poschingerstrasse 5
81679 Munich
Germany
Wolfgang Nierhaus
Ifo Institute for Economic Research at the
University of Munich
Poschingerstrasse 5
81679 Munich
Germany
2
Introduction
Business cycle indicators are meant to describe cyclical economy activity in market-economy sys-
tems in a timely and accurate fashion. The characteristic of a good indicator is that it signals turn-
ing points in economic activity in a timely and clear fashion (i.e. without false alarms). In addi-
tion the lead of the indicator should be stable so that a relatively reliable estimate can be made
as to how early the signal of the indicator occurs. Finally, the results should be available in a
timely manner and not subject to any major revisions after publication (see Abberger and Wohl-
rabe, 2006, p.19).
An especially reliable indicator for the development of economic activity in Germany is the Ifo
Business Climate that was developed by the Ifo Institute in the mid-1960s on the basis of the
monthly company survey, the Ifo Business Survey (see Abberger and Nierhaus 2007).
The busi-
ness climate is determined according to the formula [(BS+200)(BE+200)]1
/2
– 200, whereby BS
designates the percentage balance of the positive and negative responses regarding the current
business situation and BE the percentage balance of the positive and negative responses for the
business outlook in the next six months. With the geometrical average the fluctuations of the Ifo
Business Climate in cases of extreme values are dampened slightly in comparison with an
arithmetic average. The two climate components reflect the current situation (the business situa-
tion is good/ satisfactory/ poor) and the outlook (the business situation is likely to be more fa-
vourable/ about the same/ somewhat more unfavourable) of the surveyed businesses. The ques-
tions have been combined by the Ifo Institute in order to show the cyclical situation from which
a specific anticipation is reported. Hence, a firm’s anticipation “will remain about the same” in a
boom phase has a different meaning than in a recession, i.e. a continuation of the boom or a
continuation of the recession.
The Ifo Business Climate was published for the first time in 1971, but initially only for manu-
facturing. On year later the business climate data for the survey sectors manufacturing, con-
struction, wholesaling and retailing were combined to form the indicator in its present form (Ifo
Business Climate for German Industry and Trade). The four quadrant scheme for the cyclical
relationship of business situation and business expectations from the Ifo Business Survey was
published for the first time in spring 1993. Initially the variables in the economic cycle moved
counter clockwise due to the arrangement of the axes (see Leibfritz and Nierhaus 1993). The
present quadratic depiction of the Ifo Business Cycle Clock, in which the direction of the busi-
ness situation and expectations move in the conventional clockwise direction, was introduced in
1999 (see Abberger and Nierhaus 2008b).
This article will examine the connections between the Ifo Business Cycle Clock for German
Industry and Trade and the quarterly Business Cycle Monitor for the Real GDP developed by
3
the German Federal Statistical Office. The GDP Business Cycle Monitor is an additional, mod-
ern monitoring system that is able to depict the developments of total economic activity in a
four quadrant scheme (see Oltmanns 2009). In this article the two monitoring concepts will be
described. Then the inputted series of the two systems will be examined for linear correlation.
This is followed by a discussion of the importance of orthogonal functions for the subsequent
circular analysis. This is done, first of all, by a visual examination of the two four-quadrant
schemes. By using the statistical procedure of circular correlation we then examine whether the
cyclical movements of the Ifo Business Cycle Clock and the GDP Business Cycle Monitor dis-
play statistically significant similarities. Then the selectivity of the Ifo Business Cycle Clock is
examined with regard to the classification of basic economic phases – upturns/downturnsby
means of an error display. Finally the linear circular correlation between the Ifo Business Cycle
Clock and the cyclical components of real GDP is discussed. This analysis is carried out using
monthly values; the monthly GDP values needed for the analysis were derived from the official
quarterly results by means of the temporal disaggregation methods developed by Chow & Lin.
The Ifo Business Cycle Clock
Business cycles can be defined on the basis of fluctuations in cyclically relevant variables over the
course of time. A two-phase division of cycles consists of an expansion and a contraction phase,
with the two phases being connected with each other by lower and upper turning points. Figure 1
shows how an artificially constructed business climate and its two components – business situation
and business expectations – ideally move. As the coincidental parameter for the economic situation
in the overall economy, the business situation indicator is used, whose cyclicality is described by a
two-year sine-wave oscillation. The expectation indicator anticipates the situation indicator by pre-
cisely six months; the business climate as the average of the situation and the expectations thus has
constant lead of three months over the business situation.
4
Fig. 1
Business Cycle
1)
: Assessment of Current Business Situation, Business
Expectations and Business Climate
0,0
90,0
12345678910111213141516171819202122232425262728293031323334353637383940414243444546474849
-1,5
-1,2
-0,9
-0,6
-0,3
0,0
0,3
0,6
0,9
1,2
1,5
Business situation
Business expectations
Business climate
%
Downswing
Recession Upswing
Boom
1) Two year sine-wave fluctuation. Lead of business expectations over business situation: 6 months.
Contraction period Expansion period
The economic expansion phase – measured by the course of the situation indicator – extends from a
lower turning point to an upper turning point. After having passed through the lower turning point,
the business situation improves, but is still initially poor on balance (i.e., negative). Only have hav-
ing passed the zero balance does the business situation become good, on balance (i.e., positive).
The two sub-phases can be labelled upswing and boom. The economic contraction phase extends
from an upper turning point to a lower turning point. Also here two sub-phases can be distinguished
and assigned labels: downturn and recession.
1
In the downturn the business situation worsens, but
on balance is still good (i.e., positive).
In recession with further worsening the business situation is
poor on balance, i.e., negative. Since the company responses regarding the business situation and
the business expectations are not subject to a trend, all four business cycle phases are identical in
this ideal-typical example, with the assumed two-year sine-wave oscillation, are equally long: pre-
cisely six months.
The basic idea of the Ifo Business Cycle Clock is to assign the business situation
(good/satisfactory/poor) at every point in time to the respective business expectations reported
by the companies (more favourable/about the same / more unfavourable). On the abscissa of the
business cycle clock the situation indicator is placed; on the ordinate the corresponding value of
the expectation indicator. The diagram is divided into four quadrants by means of the cross-
1
This term “recession” is employed here to designate a specific combination of situation and expecta-
tions. This does not correspond to the usual definition of a recession in the real economy. For a discus-
sion on the concept of recession, see Abberger and Nierhaus (2008a).
5
hairs of the two zero lines that mark, in terms of the course of the business situation, the four
sub-phases of the business cycle: upswing, boom, downturn, recession (see Fig. 2).
The assessments of the surveyed companies for the business situation and for the business ex-
pectations are poor, on balance, i.e., in minus, the business cycle is in “recession” (lower left
quadrant). When the expectation indicator moves into plus territory (with an improving but still
on balance poor business situation), the indicator moves into the upswing phase (upper left
quadrant). If both the business situation and business expectations are good on balance, that is in
plus, there is a “boom” (upper right quadrant). If the expectation indicator turns into minus terri-
tory (with a worsening but still on balance good business situation), a downturn sets in (lower
right quadrant). Since the expectation indicator leads the situation indicator systematically by
exactly sixth months in a business cycle totally two years, the business cycle in this diagram
moves in a clockwise direction. In doing so, the situation-expectation graph cuts the abscissa of
the business cycle clock when it reaches the maximum or minimum of the business situation
(upper and lower economic turning points). The ordinate of the clock is cut when the business
situation reaches the zero balance “from below” or “from above”.
The phase-division of the business cycle clock can also be anchored on another business survey
series. If one uses for example the business climate indicator as a central reference series, which
in the chosen example has a lead of three months over the situation indicator, the empirical bor-
derlines for the four cyclical phases of the business cycle clock would turn by 45° in a counter-
clockwise direction.
1
The upper or the lower turning points of the business cycle (defined here
as local maximum or minimum of the business climate) is now ideal-typically on the diagonal
that connects the corner-point of the lower left quadrant with the corner-point of the upper right
quadrant. On the second main diagonal of the clock that connects the two other corners of the
clock, are the zero balances of the business climate. The individual phases of the business cycle
are now within the four triangles that are formed by the two diagonals and their intersection
point in the centre of the clock (upswing in the left triangle, boom in the upper triangle, down-
turn in the right triangle, recession in the lower triangle). There would be yet another phase divi-
sion if the expectation indicator was used as a reference series.
1
For an empirical argumentation for this alternative quadrant division, see Abberger (2005).
6
Fig. 2
Ifo Business Cycle Clock
1)
-1.5
-1.2
-0.9
-0.6
-0.3
0.0
0.3
0.6
0.9
1.2
1.5
-1.5 -1.2 -0.9 -0.6 -0.3 0.0 0.3 0.6 0.9 1.2 1.5
Assessment
of Business
situation
Business
expectations
balance value of
the current
business
situation is zero
Lower
turning point
of business
situatation
1) Business cycle:
two year sine-wave
fluctuation. Lead of
business expectations
over business situation:
6 months.
BoomUpswing
DownwingRecession
Upper turning
point of
business
situation
balance value
of the current
business
situation is zero
Empirically the relationship tends to be somewhat less stringent than what we have in the ideal-
typical representation of the business cycle clock – modelling of the cycle via a constant 24-
month sine-wave oscillation, exact anticipation of the situation indicator by means of the expec-
tation indicator with a stable course of precisely six months. The exact circular course of the
business cycle clock results, in this example, because the two chosen indicator functions stand
orthogonally to each other. The length of the business cycle in Germany and in other industrial-
ised countries, however, is considerably longer that the two year period chosen here as a model.
In this case the empirically observed course of the expectation indicator vis-à-vis the situation
indicator is not large enough that the two curves are orthogonal to each other. This can distort
the rotation of the clock into an elliptical movement.
Moreover, short-term irritations in the firms’ assessment formations, erroneous appraisals,
asymmetric response behaviour, sampling errors, etc. can result in unsystematic movements of
the situation–expectation graphs within and between the individual quadrants of the business
cycle clock that cover up the actual cyclical movement and can even cause a temporary reverse
movement. This would correspond to the case of adaptive expectations. With rational expecta-
tions the usual course of the expectations sets in and the Ifo Business Cycle Clock runs clock-
wise.
7
A further basis for a systematic deviation from the circular process results from the different
types of the two indicators. While the survey question on the business situation is a matter of its
current level, the business expectations are surveyed in terms of changes over the previous sur-
vey. In purely mechanical terms this has two effects that counteract each other: the changes that
are expressed in the expectations can cumulate to those of the situation appraisal. If, for exam-
ple, in one month 100 survey participants expect a more unfavourable business situation, and in
the following month 100 again give this response, then it can be the case that a total of 200
companies have revised their situation assessments downwards. Conversely, not every reported
change must result in an adjustment of the business situation. Thus, a favourable business situa-
tion can develop more unfavourably but nevertheless remain good, having become merely less
favourable. Also a poor business situation can become even more unfavourable and continue to
be poor. These considerations show that the situation indicator and the expectations indicator
can have differently strong spikes.
In terms of erratic disturbances in the movement of the clock, it is the case that the irregular
components of the initial series are weakly marked in comparison with the smooth trend busi-
ness-cycle components. The MCD measurement for the situation indicator amounts to two
months, but for the somewhat less volatile expectation indicator only one month. The MCD
measurement shows the point at which the change of the smooth component of a series out-
weighs the irregular movement, on average. It indicates the average delay before one can be
relatively sure that directional changes of indicators are not of erratic nature but are due to cy-
clical factors (see Abberger and Nierhaus 2009, 17).
The GDP–Business Cycle Monitor
In recent years various graphical monitoring systems that display the cyclical component of
selected indicators and their modification (vis-à-vis the previous period) in a 4 quadrant scheme
have been developed in Europe. These include the Economic Climate Tracer developed by
Gayer, the Business Cycle Tracer of the Central Statistical Office of the Netherlands, the Euro-
pean Business Cycle Clock of Eurostat, the OECD Business Cycle Clock as well as the Busi-
ness Cycle Monitor of the German Federal Statistical Office.
1
These monitoring systems focus
primarily on the cyclical component of sector-specific or macroeconomic indicators of the offi-
cial statistics. They also use business and consumer surveys. The trend adjustment necessary for
the extraction of the cyclical component is done with the help of statistical filter procedures. The
direction of the cyclical component depends on the filter used.
1
See Gayer (2010), Ruth, Schouten and Wekker (2005), Eurostat (2010), OECD (2010), Federal Statis-
tical Office (2010).
8
In the following, the business cycle monitor will not be presented on the sectoral level but in the
more comprehensive context of the system of national accounts (Abberger and Nierhaus 2010a).
Following a Study of the German Federal Statistical Office (Oltmanns 2009), a business cycle
monitor for real GDP in Germany will be presented and analysed. In modern business cycle
theory, business cycles are defined primarily as variations of the utilisation degree of the pro-
duction potential. If the trend of GDP is interpreted as a non-structural estimate of the produc-
tion potential, the phase in the business cycle can be equivalently identified by means of the
deviation of real GDP from its trend (cyclical component of GDP). Turning points are now
marked by the maximums and/or minimums of the trend deviation. GDP is regarded as the most
comprehensive aggregated measure of the economic output of an economy.
For a four-phase division of the cycle, the four ideal-typical business cycle phases can be identi-
fied here by means of the sign of the trend deviation of GDP or its changes. In a “downturn” the
trend deviation of real GDP is positive and the change of the trend deviation negative. In a “re-
cession” both the trend deviation and the change of the trend deviation are negative. In an “up-
swing” the trend deviation is negative; however, the change of the trend deviation is already
positive. In a “boom” the trend deviation of GDP is positive, and the same applies for change in
the trend deviation.
The Federal Statistical Office arranges the four possible value pairs (trend deviation – change of
the trend deviation) in a four-quadrant scheme, in which due to the axis arrangement, also a
clockwise movement results (see Oltmanns 2009, 968). The trend deviation of GDP is repre-
sented on the abscissa, the change of the trend deviation on the ordinate. The upper left quadrant
contains all paired values of the upswing phase, then there follow (clockwise) the quadrants for
boom, downturn and recession. All the points above the abscissa signal the basic economic
phase of expansion (with the partial phases: upswing and boom); all points below the abscissa
signal the basic phase of contraction (with the partial phases downturn and recession, see fig. 3).
For the construction of an empirical GDP business cycle monitor – in the following concretely
for the period 1971 to 2009 –the extraction of the cyclical component of GDP is necessary pre-
condition. First, however, the quarterly GDP time series must be cleared off all non-cyclical
components. For the elimination of the short-term seasonal fluctuations (including the elimina-
tion of calendar irregularities) the Census-X12-ARIMA procedure was selected. For the elimi-
nation of the long-term development path (trend) as well as the non-cyclical, short-term fluctua-
tions, the Baxter-King filter was employed.
9
Fig. 3
Business Cycle Monitor for Real GDP
1)
-1,5
-1,2
-0,9
-0,6
-0,3
0,0
0,3
0,6
0,9
1,2
1,5
-1,5 -1,2 -0,9 -0,6 -0,3 0,0 0,3 0,6 0,9 1,2 1,5
Deviation from
trend
Period-on-period
change of trend
deviation
Value of trend
deviation is
zero
Lower turning
point of trend
deviation
1) Business cycle is
given by a two year sine-
wave fluctuation around
a linear trend
BoomUpswing
Downswing
Recessio
Upper turning
point of trend
deviation
Value of trend
deviation is
zero
.
The Baxter-King-filter is a symmetrical filter which, in comparison to the Hodrick-Prescott
filter, removes not only the low-frequency trend component but also the high-frequency irregu-
larities contained in the time series. As a cycle the sum of all components of the time series with
oscillations between 6 and 32 quarters (= of 1.5 to 8 years) was applied; the filter length
amounts to 12 quarters (= 3 years). These settings correspond to the normal recommendations in
the literature on the extraction of business cycles (see Mills 2003, p.91).
1
To obtain a long time series, the lacking all-German GDP values for the period 1990 to 1971
were generated by linking the West German and all-German time series in 1991. Furthermore
additional series values were predicted at the end of the GDP series in order to be able to apply
a symmetrical filter here too. The "forecasts" were made with the help of autoregressive models
(AR); the lag length was chosen automatically by means of the Akaike information criterion
(AIC). Figure 4 shows the extracted cyclical component of real GDP and the turning points that
1
The Federal Statistical Office has chosen another approach for the extraction of the cyclical compo-
nent of real GDP: First, the trend business-cycle component of GDP is estimated with the help of the
Office’s own time series analysis procedures BV4.1 (Berlin procedure, version 4.1). Then the trend of
this series is determined with the help of the Hodrick-Prescott-filter with the parameter value typical
for quarterly data of λ = 1 600. The deviations of the trend business-cycle component of the HP trend
are then interpreted as business-cycle fluctuations. Via the parameter λ the smoothness of the HP trend
is controlled aprioristically. When λ = 0 the resulting trend is the original series; with λ up to “infinity”
a linear trend (see Oltmanns 2009).
10
were identified with the Bry-Boschan method (see Bry and Boschan 1971). This dating algo-
rithm determines the cyclical turning points according to a sequential decision rule.
1
Fig. 4
Cyclical Component of Real GDP
-4
-3
-2
-1
0
1
2
3
4
1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010
Cyclical component of real GDP (1)
Turning points of real GDP (Bry-Boschan routine)
1) Baxter-King filtered values; standardized.
Source: Federal Statistical Office, Ifo Business Survey.
Linear correlation with GDP
In the Ifo Business Cycle Clock, the business situation of the surveyed companies are allocated
to the business expectations at every point in time; the GDP-business cycle monitor shows the
cyclical components of real GDP and its change over the previous quarter. In an initial step we
discuss the linear correlation (Bravais-Pearson) between the series business situation and cycli-
cal component of GDP as well as between the series business expectations and change in the
cyclical GDO component. Since unlike the information on real GDP the data of the Ifo Business
Survey is not in a quarterly frequency, the monthly survey results were combined into quarterly
values for the business situation and the business expectations. Prior to this, all business survey
time series were seasonally adjusted using the standard Ifo ASA II method in order to ensure the
full compatibility with the regularly published business survey results.
1
The Baxter-King filtering and the turning point dating according to Bry-Boschan were carried out with
the software tool BUSY (see Fiorentini and Planas 2003).
11
Fig. 5
Ifo Assessment of Business Situation
and Cyclical Component of Real GDP
-4
-3
-2
-1
0
1
2
3
4
1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010
Cyclical component of real GDP (1)
Ifo assessment of business situation in industry and trade (1)
1) Standardized values; real GDP: Baxter-King filtered values.
Source: Federal Statistical Office, Ifo Business Survey.
Figure 5 shows that the course of business situation and cyclical component of real GDP in the
period 1971 to 2009 is quite similar; a narrow connection is manifest. Furthermore it is apparent
that the business situation has a slight lead on the cyclical GDP component. The narrowest cor-
relation between the business situation and the cyclical component of real GDP – measured in
terms of the maximum of the correlation coefficient in the cross-correlogram – is seen when the
business situation has a lead of one quarter; the correlation here amounts to 0.68. The lead of the
business situation can be explained by the fact that the profit situation, which plays an important
role when firms assess their business situation, leads the cycle in general (see Abberger, Birn-
brich and Seiler 2009, p.41). This is because the cost side of the firms is influenced by the la-
bour market situation and by capacity utilization. Thus, in the late phase of an upswing, labour
costs increase much faster than selling prices, which leads to a decline in profit margins. Con-
versely, in the late phase of a downturn, firms stabilize their profit situation via cost-cutting
rationalisation measures. Moreover, in the beginning of an upswing the increase in labour costs
is weak – if at all – due to the poor labour market and the mobilization of production reserves
(see Zarnowitz 1992, 42). To explicitly measure the profit situation of firms by using leading
indicators is very difficult, however. Zarnowitz (1991, 321) writes: “Important studies of busi-
ness cycles ascribe a major role to profits; also, there is evidence of a strong tendency for total
corporate profits to lead. But few concepts are more difficult to measure than profits in a true
economic sense.”
12
Figure 6 shows the corresponding connection between the business expectations and the modifi-
cation of the cyclical component of real GDP. Calculated along all the data points, the cross-
correlogram shows a coincidence between the two lines; the maximum correlation coefficient is
achieved accordingly at a parallel course and amounts to 0.76.
Fig. 6
Ifo Business Expectations
and Period-on-Period Change of the Cyclical Component of Real GDP
-4
-3
-2
-1
0
1
2
3
4
1971 1974 1977 1980 1983 1986 1989 1992 1995 1998 2001 2004 2007 2010
Cyclical component of real GDP (1), period-on-period change
.
Ifo business expectations for industry and trade (1)
1) Standardized values; real GDP: Baxter-King filtered values.
Source: Federal Statistical Office, Ifo Business Survey.
Circular correlation with GDP: Orthognalization of Ifo input time series
With the Ifo Business Cycle Clock, economic activity as a situation/expectations graph moves
through the 4 quadrant scheme ideal-typically clockwise and in a circle. In contrast, the business
cycle monitor shows whether and to what extent the cyclical component of real GDP is positive
or negative and whether and to what extent the cyclical component increases or falls. Also in
this system, ideal-typically a circular and clockwise movement of the business cycle results.
For the Ifo Business Cycle Clock, the assumption that economic activity move along a circular
path through the four quadrant scheme is often not the case in practice, however. Even with
ideal-typical sinusoidal curvatures of business situation and expectations, a completely round
course of the clock results only if the two initial series stand orthogonally to each other. This
characteristic is determined by the periodic time of the two functions and the phase shifts be-
tween them. If the initial series do not stand orthogonally to each other, an elliptic course of the
13
clock results already in the model.
1
This would be the case, for example, in the previously men-
tioned case of a two-yearn sinusoidal cycle if the (correctly anticipated) expectation indicator
has only a lead of three months over the business situation. The ideal-typical circular rotation of
the clock is thereby bent to a movement along the main diagonals that connect the boom quad-
rant with the recession quadrant. In these cases, the business situation can already improve (or
worsen), although the business expectations are still negative (or positive).
Empirical observations in the boom or recession quadrants are thus more frequent than observa-
tions in the upswing or downturn quadrants. The distortion of the Ifo Business Cycle Clock by
the violation of the orthogonality condition can however be eliminated by a purely data con-
trolled transformation of business situation and business expectations. The mathematical in-
strument for this is the principal component analysis. This is based in turn on the so-called spec-
tral decomposition or Jordan decomposition. Accordingly a symmetrical A matrix (p×p) can be
written as
A = Γ Λ Г
T
with Λ being a diagonal matrix of the eigenvalues of A, and Г an orthogonal matrix whose col-
umns are formed by the standardized eigenvectors. Since the business cycle clock is two-
dimensional, p=2 applies here, and there are two eigenvectors and two corresponding eigenval-
ues. λ
1
and λ
2.
are the eigenvalues of A. If the clock followed an exact circle, λ
1
=λ
2.
would re-
sult. If we have an ellipse, different eigenvalues result. If λ
1
>λ
2.
and if γ
1
and γ
2
are the corre-
sponding eigenvectors, then vector γ
1
indicates the direction of the greatest extension of the
ellipse (see Mardia, Kent and Bibby 2000, 484). Thus, the direction sought for in step 1 of the
procedure has been found. The direction for the second straight line is now also present and is
determined by γ
2
. Matrix Γ thus brings about the rotation described in step 2. In practical terms,
this means the following: let X be a (2×T) matrix that contains T observations for the two vari-
ables business situation and business expectations. It has the expectations value vector μ and the
variance-covariance matrix Σ. Step 1 of the procedure consists in the spectral decomposition of
the variance-covariance matrix Σ. Step 2 is thus the transformation
X Y = Г
T
(X
-
μ)
With Γ the rotation in step 4 is of course also determined, which reverses the turning in step 2.
What remains is the standardization in step 3. Here we can make use of the fact that the deter-
mined eigenvalues are equal to the variances of Y. It is the case that Var(y
1
)= λ
1
and Var(y
2
)= λ
2
1
Two functions f(x), g(x) are orthogonal in the interval [a,b], when the product f(x)g(x) is a function
with the integral nought in the range [a,b].
14
(see Mardia, Kent and Bibby 2000, 215). With Φ=diag(λ
1
1/2
, λ
2
1/2
) it follows that the entire trans-
formation that is described above in steps 1 to 4 can be represented by
X Z = (Г
T
)
-1
Ф
-1
Г
T
(X -
μ)
Since Γ is an orthogonal matrix, the transformation can be simplified to
X Z = Г Ф
-1
Г
T
(X -
μ)
whereby Ф
-1
=diag(1/λ
1
1/2
, 1/λ
2
1/2)
. This demonstrated transformation can be understood as an
expanded standardization. In addition to the usual standardization of averages and variance, the
covariance is additionally set to nought. For the following calculations for the circular correla-
tion, the Ifo Business Cycle Clock has been orthogonalized in this form. For the GDP business
cycle monitor, this transformation has not been carried out because the cyclical component of
GDP cannot rise (fall) as long as the negative (positive) trend deviation has not reached its local
minimum (maximum), so that here a round, although not exactly circular course, is mathemati-
cally predetermined.
Circular correlation with the GDP: Visual test
By means of the cyclical component of real GDP, a total eight complete business cycles can be
identified in period under investigation – 1971 to 2009 (see Fig. 4); the average cycle duration –
measured by the space of time between two turning points that follow on each other – is ap-
proximately 4½ years. For the following visual test of the two monitoring systems with regard
to agreement as to the basic cyclical movements, the period under investigation was divided into
seven 5-year sections (beginning with 1971 to 1975) as well as a 4-year section that contains the
remaining years 2005 to 2009. In total, 156 quarters are thus considered.
In Figure 7, the interplay of Ifo Business Cycle Clock for industry and trade with the business
cycle monitor for real GDP is present in a four-part graph for 1971 to 1990. This period con-
tains, first of all, the serious recession in the wake of the first oil crisis 1973/74, from which the
western German economy first began to free itself again in 1975 (upper left graph, Fig. 7). The
upper right graph in Fig 7 shows both upswing years 1978/79, after that economic activity –
measured by the worsening expectations and the declining cyclical GDP components –
15
Fig. 7
1/1986 - 4/1990
-3,5
-2,8
-2,1
-1,4
-0,7
0,0
0,7
1,4
2,1
2,8
3,5
-3,5 -2,8 -2,1 -1,4 -0,7 0,0 0,7 1,4 2,1 2,8 3,5
1/1986
4/1990
Ifo Business Cycle Clock for Industry and Trade and Business Cycle Monitor for Real GDP
a)
1/1976 - 4/1980
-3,5
-2,8
-2,1
-1,4
-0,7
0,0
0,7
1,4
2,1
2,8
3,5
-3,5 -2,8 -2,1 -1,4 -0,7 0,0 0,7 1,4 2,1 2,8 3,5
Y Axis
1)
1/1976
4/1980
1/1971 - 4/1975
-3,5
-2,8
-2,1
-1,4
-0,7
0,0
0,7
1,4
2,1
2,8
3,5
-3,5 -2,8 -2,1 -1,4 -0,7 0,0 0,7 1,4 2,1 2,8 3,5
Y Axis
1)
1/1971
4/1975
1/1981 - 4/1985
-3,5
-2,8
-2,1
-1,4
-0,7
0,0
0,7
1,4
2,1
2,8
3,5
-3,5 -2,8 -2,1 -1,4 -0,7 0,0 0,7 1,4 2,1 2,8 3,5
1/1981
4/1985
a)
Ifo business cycle clock
: saisonally adjusted results using ASAII; orthogonalized values;
business cycle
monitor for real GDP (dashed line): saisonally and calender adjusted results using Census X12-ARIMA;
Baxter-King filtered. All values are scale-standardized using the transformation Z / S, where Z is the original
value and S is the standard deviation.of the sample.
1) Y Axis: Ifo business cycle clock: business expectations for the next six months (balances); business cycle
monitor for real GDP: period-on-period change of cyclical component.
2) X Axis: Ifo business cycle clock: business situation (balances); business cycle monitor for real GDP:
cyclical component.
Source: Federal Statistical Office, Ifo Business Survey.
X Axis
2)
X Axis
2)
X Axis
2)
X Axis
2)
Y Axis
1)
Y Axis
1)
deteriorated rapidly in connection with the second oil crisis. The lower left graph contains con-
ditional stagflation year 1981 caused by the oil crisis (growth rate of real GDP: 0.5 %; inflation
rate: 6.3%). Not until the conservative/liberal coalition assumed power in autumn 1982 was
there an improvement in economic activity; the introduction of an investment grant started up
the investment engine. In spring 1984, however, a 7-week strike in the metal industry over the
introduction of the 35-hour week led to high losses in production that caused firms business
16
expectations to collapse and which also can be seen in the cyclical component of GDP. The
lower-right graph ends with the western German unification boom of 1989/90, whereby busi-
ness activity had already been positively stimulated before by gradual tax reductions and lower
oil prices. The graphs of the Ifo Business Cycle Clock and the GDP business cycle monitor both
remain at the end of 1990 in the northeast boom quadrant.
Figure 8 shows the interplay between the Ifo Business Cycle Clock for industry and trade with
the business cycle monitor for real GDP in reunited Germany since 1991. The upper left graph
in Figure 8 shows firstly the end of the unification boom: beginning with the first quarter of
1991 the business situation and cyclical GDP component fall as order stock decrease strongly.
The business expectations, however, remained unchanged to a large extent until 1992; many
companies presumably anticipated a quick improvement of US economic activity. The eco-
nomic downturn intensified in the second half of 1992, fed by the flaring up of the solidarity
pact discussion with regard to drastic increases in taxes and fiscal charges and by turbulence in
the European monetary system (EMS). In the second half of 1993 an economic recovery began
that intensified in 1994, boosted by strongly rising exports and much improved profit outlooks.
In 1995 the business expectations worsened considerably and also the cyclical GDP component
declined. The upper right graph in Figure 8 begins with the new upswing of 1996/97: key inter-
est rates had fallen to historical lows and moderate wage settlements had improved firms’ profit
situation. In the course of 1998 the economic crisis in eastern Asia, the difficulties in Russia and
the weakening in Latin America became apparent. The export economy and also the cyclical
component of real GDP reached their lows in the first quarter of 1999. After that the buoyancy
forces strengthened, culminating in the New Economy boom of 2000.
The lower left graph in Figure 8 reflects the overall weak and unstable development of eco-
nomic activity in the years 2001 to 2005; unlike all the other examined periods, both the Ifo
Business Cycle Clock and the GDP Monitor show no unambiguous cyclical pattern. In 2001,
contrary to expectations, economic activity experienced a “hard landing”, intensified by the
terror attacks of 11 September. In the following year the increasing tension in the Iraq conflict
led to insecurity; additional factors were the rise in crude oil prices as well as the strong declines
on the financial markets. In 2003 the Iraq conflict escalated into an open military confrontation.
The euro also increased in value strongly against the US dollar, which had an affect on exports.
In the domestic economy, consumer sentiment worsened in connection with the Agenda 2010
reforms. The downturn in the business cycle that occurred with a negative business situation
17
Fig. 8
1/2006 - 4/2009
-3,5
-2,8
-2,1
-1,4
-0,7
0,0
0,7
1,4
2,1
2,8
3,5
-3,5 -2,8 -2,1 -1,4 -0,7 0,0 0,7 1,4 2,1 2,8 3,5
1/2006
4/2009
Ifo Business Cycle Clock for Industry and Trade and Business Cycle Monitor for Real GDP
a)
1/1996 - 4/2000
-3,5
-2,8
-2,1
-1,4
-0,7
0,0
0,7
1,4
2,1
2,8
3,5
-3,5 -2,8 -2,1 -1,4 -0,7 0,0 0,7 1,4 2,1 2,8 3,5
Y Axis
1)
1/1996
4/2000
1/1991 - 4/1995
-3,5
-2,8
-2,1
-1,4
-0,7
0,0
0,7
1,4
2,1
2,8
3,5
-3,5 -2,8 -2,1 -1,4 -0,7 0,0 0,7 1,4 2,1 2,8 3,5
Y Axis
1)
1/1991
4/1995
1/2001 - 4/2005
-3,5
-2,8
-2,1
-1,4
-0,7
0,0
0,7
1,4
2,1
2,8
3,5
-3,5 -2,8 -2,1 -1,4 -0,7 0,0 0,7 1,4 2,1 2,8 3,5
1/2001
4/2005
a)
Ifo business cycle clock
: saisonally adjusted results using ASAII; orthogonalized values;
business cycle
monitor for real GDP (dashed line): saisonally and calender adjusted results using Census X12-ARIMA;
Baxter-King filtered. All values are scale-standardized using the transformation Z / S, where Z is the original
value and S is the standard deviation.of the sample.
1) Y Axis: Ifo business cycle clock: business expectations for the next six months (balances); business cycle
monitor for real GDP: period-on-period change of cyclical component.
2) X Axis: Ifo business cycle clock: business situation (balances); business cycle monitor for real GDP:
cyclical component.
Source: Federal Statistical Office, Ifo Business Survey.
X Axis
2)
X Axis
2)
X Axis
2)
X Axis
2)
Y Axis
1)
Y Axis
1)
and strong fluctuations in the business expectations of the surveyed firms did not end until the
second quarter of 2005 when business expectations brightened and also the cyclical component
of GDP began to rise. The growth engine was once again foreign demand that unfolded not least
because of dynamic growth in the world economy and the once again more favourable euro-
dollar exchange rate.
18
The lower right graph in Figure 8 shows the cyclical development up to the fourth quarter of
2009. In 2006 upswing continued, with exports being the most important support amidst the
continuingly favourable international environment. In 2007 the upswing went on although VAT
had been increased substantially to help consolidate the government budget. In the first quarter
of 2008, the upper cyclical turning point was reached, thereafter the economy cooled off in the
wake of the recessions in the US and Japan. Finally in autumn 2008 the German economy also
went into the recession. With the collapse of the US investment bank Lehmann Brothers, the
financial crisis reached a climax worldwide. The lower economic turning point – measured by
the cyclical component of real GDP – was reached in the second quarter of 2009; since then
economic activity stabilised at a low level. Both the Ifo Business Cycle Clock and the GDP
business cycle monitor point upwards again; since the third quarter of 2009 both graphs are in
the upswing quadrant. Summing up, the correlation of the two monitoring systems is quite sub-
stantial also in this period.
Circular correlation with GDP: Statistical results
The two input series employed for the Ifo Business Cycle Clock and the corresponding time
series of the GDP Monitor display a high degree of correlation. With the help of a circular cor-
relation analysis, the similarity in the movement pattern of the two systems can be quantified.
This analysis technique examines the connection between circular random variables, or between
a circular random variable and linear random variables. A random variable is deemed to be cir-
cular if its two-dimensional direction can be measured as angles in relation to a chosen “nought
direction”. In order to examine the movement patterns of the two 4-quadrant schemes, circular
variable are defined for both.
1
To do this, the data sections presented in Figure 7 and 8 are indi-
vidually standardised and for every data point of the movement line of the angle between the
abscissa and the vector from the beginning to the respective data point is calculated. Since both
the Clock and the Monitor are treated in this manner, two data sets result, each with circular
variables. By means of the described transformation in circular variables, in the correlation an-
alysis the focus is exclusively on the direction of the motion of the two systems. The concrete
location of the points does enter into the analysis.
1
The Business Cycle Clock and the Business Cycle Monitor cannot be examined with the usual correla-
tion analysis of Bravais-Person since it is not a matter of an observation on a time axis but a rotating
representation. For example, the number pair 0.05 and 11.55, interpreted as numbers, lie quite far from
each other. Interpreted as times on a clock, they are however very close together (nearer for example
than 11.55 and 11.15).
19
Concretely, we examine the linear connection between two circular random variables Θ and Φ.
Let p
1
=(θ
1
,φ
1
),...,p
n
=(θ
n
,φ
n
) be a coincidence random sample of the circular random variables
P=(Θ,Φ). Then a T-linear relationship exists between the variables if
Φ= Θ+θ
0
(Modulo 360
o
)
or
Φ= -Θ+θ
0
(Modulo 360
o
),
with θ
0
as a constant angle. The strength of such a linear connection can be measured by
ˆ
ρ
T
=
sin(
θ
i
θ
j
)sin(
φ
i
φ
j
)
1i < j n
sin
2
(
θ
i
θ
j
)
1i < j n
sin
2
(
φ
i
φ
j
)
1i< j n
1
2
Jammalamadaka and SenGupta (2001) in addition present a test for this type of correlation. The
null hypothesis on the presence of no T-linear relationship is accordingly rejected when
ˆ
ρ
T
de-
viates too far from zero. The p-values for this test are also indicated in the following.
Table 1 shows the amounts and the p-values for the circular correlation. The impressions from
the visual comparison the 4-quadrant depictions are clearly confirmed. The null hypotheses on
the presence of no T-linear relationship are rejected for the significance level 0.05 for all time
windows except for one. The hypothesis is (barely) not rejected for the period 1/2001 to 4/2005,
which was already identified as crucial. Nevertheless, here too the correlation with a value of
0.44 is considerable. On the whole, the calculations for the circular correlation confirm that the
movement patterns of the Ifo Business Cycle Clock and the Business Cycle Monitor show great
similarity.
In a further step we analyse how clear the signals are of the survey-based Ifo Business Cycle
Clock in the two basic phases expansion/contraction – measured in terms of the results of the
GDP Monitor. The Business Cycle Monitor shows the basic phase expansion (contraction),
when the data points in the two quadrants are above (below) the abscissa. This is always the
case when the change of the cyclical component of real GDP is positive (or negative). On the
other hand, the Ifo Business Cycle Clock signals the basic phase expansion (contraction), when
the transformed expectations of the firms are on balance positive (or negative). Also in this
monitoring system, the data points lie in the two quadrants (below) the abscissa.
20
Tab. 1
Correlation coefficient p-value
1/1971-4/1975 0.68 0.0070
1/1976-4/1980 0.86 0.0019
1/1981-4/1985 0.71 0.0045
1/1985-4/1990 0.57 0.0108
1/1991-4/1995 0.89 0.0007
1/1996-4/2000 0.43 0.0310
1/2001-4/2005 0.44 0.0653
1/2006-4/2009 0.85 0.0084
1)
Standardized series.
Period
Ifo Business Cycle Clock for Industry and Trade and Business
Cycle Monitor for Real GDP
1)
In the period under investigation, there are a total of 156 observations; of these 81 observations
fall in the categories upswing or boom according to the classification of the GDP Monitor; the
Ifo Business Cycle Clock is able to identify 64 cases (see Tab. 2). Conversely, 75 observations
fall in the categories downturn or recession. The Ifo Business Cycle Clock accurately identifies
55 cases. However in 37 cases there is a false classification. Thus, in 20 cases the Ifo Business
Clock signals a downturn or recession, which according to the GDP Monitor would have to be
classified as upswing or boom. The error rate is thus 24%. This shows that the Ifo Business
Cycle Clock is less suitable for an exact separation of the two basic phases expan-
sion/contraction. Even though the movement patterns of the clock are reasonable, for an exact
dating analysis, however, instruments especially optimised for this purpose should be used.
1
Tab. 2
Total
is positive
1)
is negative
2)
Balance value
is positive
3)
64 20 84
of the current
business situation
5)
is negative
4)
17 55 72
Total 81 75 156
1)
Business Cycle Monitor for real GDP is in upswing quadrant or in boom quadrant.
2)
Business Cycle Monitor for real GDP is in downswing quadrant or in recession quadrant.
1)
Ifo Business Cycle Clock is in upswing quadrant or in boom quadrant.
2)
Ifo Business Cycle Clock is in downswing quadrant or in recession quadrant.
5)
Industry and trade, orthogonalized values.
Cross Table
Change of the
cyclical component of real GDP
1
The Ifo Business Cycle Traffic Light, based on a Markov regime-change approach, is particularly well
suited for dating the basic phases of expansion or contraction (see Abberger and Nierhaus 2010b).
21
Linear-circular correlation with the monthly gross domestic product: Disaggregation after
Chow & Lin
In order to have to manipulate as little as possible the quarterly input series from the official
statistics, the comparison of the Ifo Business Cycle Clock with the GDP Business Cycle Moni-
tor presupposes the use of quarteralised business cycle survey data. If, however, we focus only
on the cyclical connection between real GDP and the Ifo Business Cycle Clock (linear-circular
correlation), a limitation to quarterly data is not longer absolutely necessary. The use of original,
i.e. monthly business cycle data, presupposes, however, that the quarterly results supplied by the
Federal Statistical Office are converted into consistent monthly values for real GDP (temporal
disaggregation). The well established Chow & Lin method is used here for the generation of
monthly GDP values (see Chow and Lin 1971).
In concrete terms, with the help of quarterly data, the estimated regression relationship between
real GDP and a higher frequency business cycle indicator is converted to months. This approach
is based on the hypothesis that the higher frequency (in this case monthly) indicator series pro-
vides a correct depiction of real GDP. In order to exclude a possible distortion of the temporal
disaggregation by seasonal effects, here too the seasonally and calendar adjusted quarterly re-
sults of GDP were employed. As a monthly indicator series for the temporal dissection of quar-
terly GDP, firstly the production index for the producing trade was used, which in addition to
manufacturing also includes construction and the energy and water supply. Secondly, the index
of real retail sales was employed.
1
These economic sectors, which correspond in their sum ap-
proximately to the sector industry and trade in delimitation of the Ifo Institute, account for
about a third of domestic GDP. These two indices were compacted for the period 1994 to 2009
with the help of the value-added shares to form a comprehensive monthly indicator “industry
and trade” (see Fig. 9).
In order to serve as a reference for a temporal disaggregation of real GDP, this indicator must
satisfy two criteria. On the one hand, it should be co-integrated with the real GDP, on a quar-
terly basis. On the other hand, the cyclical component of the index should agree as much as
possible with the cyclical component of real GDP.
The approach chosen here is based on a regression between the quarterly time series “produc-
tion index in industry and trade” and GDP. These time series, however, are not stationary so that
a regression of the level variables is only reasonable from statistical viewpoint if the variables in
the model are co-integrated. For the regression used here, test procedures developed by Johan-
sen for the examination of co-integration were used (Johansen’s trade test). The model underly-
1
On the other hand the real sales in the wholesale are not considered, because for these no official sea-
sonally and calendar adjusted data according to Census-X12-ARIMA is available.
22
ing the test was specified so that it contains an unrestricted “drift term”. This test rejects the null
hypothesis for the significance level 0.01, that no co-integration relationship exists between the
two variables. In purely visual terms, in Figure 9 one sees a similar trend behaviour of the two
variables, whereby also intermittently prominent differences consist in the development path of
the variables. On the whole, however, the regression between the two level variables appears to
be justified.
Fig. 9
Quarterly Real GDP
and Output in Industry and Trade, Seasonally and Calender Adjusted
1)
80,0
85,0
90,0
95,0
100,0
105,0
110,0
115,0
120,0
1994 1996 1998 2000 2002 2004 2006 2008 2010
Quarterly real GDP, index 2000=100
Quarterly output in industry and trade,
index 2000=100
1) Output in manufacturing, mining, energy, construction and real turnover in retail trade.
Source: Federal Statistical Office.
2000=100
A further criterion for the suitability of the employed monthly reference indicator industry and
trade is whether its cyclical component agrees well with the cyclical component of the tempo-
rally disaggregated GDP.
1
For extracting the cyclical components, the Baxter-King filter was
used once again. Figure 10 shows the great visual agreement between the two series; the maxi-
mum value of the cross correlation function is reached in the case of coincidence and amounts
to 0.92.
1
The disaggregation is done with the help of the software tool ECOTRIM (see Barcellan and Buono
2002).
23
Fig. 10
Cyclical Component of Monthly Real GDP
and Monthly Output in Industry and Trade
1)
-4
-3
-2
-1
0
1
2
3
4
1994m1 1996m1 1998m1 2000m1 2002m1 2004m1 2006m1 2008m1 2010m1
Cyclical component of monthly real GDP (2)
Monthly output in industry and trade, cyclical
component (2)
Source: Federal Statistical Office.
1) Output in manufacturing, mining, energy, construction and real turnover in retail trade. 2) Standardized
values, Baxter-King filtered.
Linear-circular correlation with monthly GDP: statistical results
The cyclical component of monthly GDP is a “common” linear variable, whereas the Ifo Busi-
ness Cycle Clock is a circular variable. For the following analysis a measurement is thus needed
for a linear-circular correlation, that is a correlation between a linear and a circular variable. A
suitable measurement of the correlation between a linear variable and a circular variable is the
multiple correlation between the linear variable X and the components (cosine α, sin α) of the
circular variables α (see Mardia 1976 as well as Johnson and Wehrly 1977). Such a measure-
ment is
2
22
2
1
2
cs
csxsxcxsxc
r
rrrrr
r
+
= , with
r
xc
= correlation(x,cos
α
)
r
xs
= correlation(x,sin
α
)
r
cs
= correlation(cos
α
,sin
α
)
.
For the Ifo Business Cycle Clock variable α is computed as
α
t
= arctan
net balances BE
t
net balances BS
t
,
24
whereby the two time series of the net balances are both adjusted for mean values. The com-
puted correlation between the Clock and the cyclical component of GDP amounts to 0.69 and is
thus clearly positive. The correlation between the Clock and production in industry and trade is
even greater, displaying a value of 0.71. Thus, also for these results based on monthly input
series, it is clear that the Ifo Business Cycle Clock displays and reflects the movement of the
German economy very well.
Conclusion
For many years, the Ifo Business Climate has been the most important leading indicator for the
economic developments in Germany. Since the 1990s the cyclical connection between the two
components of the business climate is displayed by the Ifo Institute as a 4-quadrant business
cycle scheme (Ifo Business Cycle Clock). In the meantime, similar monitoring systems have
been established, such as the Monitor for Real GDP by the German Federal Statistical Office.
These monitoring systems focus on the cyclical component of an indicator or on their changes.
For the input series of the Ifo Business Cycle Clock and the GDP Monitor constructed for Ger-
many with the help of the Baxter-King filter, a close correlation exists already in the time com-
ponent. A visual examination of both 4-quadrant schemes shows a largely consistent match of
over the past 40 years. The impressions from the optical comparison are clearly confirmed by a
statistical test. On the whole, the calculations show that the movement patterns of the Ifo of
Business Cycle Clock and the GDP Monitor display great similarity. With the measure of the
linear-circular correlation, the interplay of the direction of motion of The Business Cycle Clock
with the cyclical components of real GDP is analyses on a monthly basis. With the help of the
Chow & Lin procedure, the official quarterly GDP results were converted into monthly values
for the examination.
In comparison to the GDP Monitor, the Ifo Business Cycle Clock shows the cyclical develop-
ment without the need for a previous trend adjustment of the input series. This can be a consid-
erable advantage, since in practice the extraction of the cyclical component with the aid of sta-
tistical filter procedures is not unproblematic. The course of economic activity and the cyclical
turning points are based on the filter that is used – a connection that Canova pointed out at in a
widely read study of 1998. A further problem is that the filtered developments at the current
edge of the time series, which is very important for forecasts, are very unstable and substantial
revisions may occur, when new data are available. Thus, the evaluation of the filtered time se-
ries is very unsure at the edge of the observation area. New data can change the picture drawn
through the filter clearly (see emperor and Maravall
2001). In the case of the survey-based Ifo
Business Cycle Clock, this problem does not occur, since here there are no data revisions, no
filtering and the additional orthogonalisation is carried out for all data points, so that new values
do not have an appreciable influence on the result.
25
All in all, the Ifo Business Cycle Clock is capable of representing the development of economic
activity in the overall economy and the associated economic dynamics only on the basis of
company assessments and appraisals. For business cycle analysis it has the advantage that it is
available at an early point in time, is not subject to revisions and gives clear signals without
many disturbances. In this way it possess the features that are important for business cycle an-
alysis (see Moore and Shiskin 1967). However, the Ifo Business Cycle Clock is less suitable for
a sharp distinction of the individual business cycle phases from each other. For an exact cycle
classification, one should use instruments that have been optimised for this purpose. On the
other hand, the strength of the Ifo Business Cycle Clock is its very good visualization of the
economic dynamics.
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26
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CESifo Working Paper Series
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