Modern Economy, 2012, 3, 713-717
http://dx.doi.org/10.4236/me.2012.36091 Published Online October 2012 (http://www.SciRP.org/journal/me)
Testing Business Cycles Asymmetry in Central
and Eastern European Countries
Viorica Chirila, Ciprian Chirila
Faculty of Economics and Business Administration, University Alexandru Ioan Cuza, Iaşi, Romania
Received July 11, 2012; revised August 25, 2012; accepted September 18, 2012
ABSTRACT
The idea of business cycles asymmetry is not new in economic theory. According to business cycles asymmetry, a
country’s economy behaves differently during economic growth periods as compared to economic recession periods.
The results achieved by business cycles asymmetry testing are far from unanimous: some are positive, others are nega-
tive. Business cycles asymmetry has major econometric implications: business cycles cannot be modeled using linear
models. This paper aims to test business cycles asymmetry in Central and Eastern European Countries, where few
business cycles analyses, and especially business cycles asymmetry researches, have been conducted. The industrial
production index was considered when testing business cycles asymmetry. We estimated business cycles using the
Hodrick-Prescott filter and Mills’ test of asymmetry. Mira’s test was also employed to test results reliability. According
to our results, business cycles in Central and Eastern European countries are not asymmetric.
Keywords: Business Cycles; Asymmetry; Hodrick-Prescott Filter
1. Introduction
Business cycles research enjoys a cyclical evolution itself.
Papers on this topic are published mostly at times of
economic recession. The explanation seems simple and it
relies on the researchers’ intent to forecast future eco-
nomic recessions likely to have a major negative impact
on economy, which in its turn influences the population’s
standard of living. The empirical characteristics of busi-
ness cycles are vital in business cycles modeling and
forecast. Therefore, special attention is paid to empirical
characteristics. The concept of asymmetry as a business
cycle characteristic is not new, yet converging results
have not been achieved so far. Authors such as Mitchell
[1], Keynes [2] Burns and Mitchell [3], and Hicks [4]
have mentioned business cycles asymmetry in their eco-
nomic theory papers.
Business cycles asymmetry roughly means that econ-
omy behaves differently during economic growth periods
than during economic recession periods. Boldwin [5]
argues that asymmetric business cycles only occur in the
case where recessions and expansions are not mirror im-
ages of each other. Business cycles asymmetry refers, on
the one hand, to the fact that decrease due to economic
recession is more abrupt than increase during economic
growth periods and, on the other hand, to the fact that the
minimum value reached at times of economic recession
is greater in absolute value than the peak reached during
economic growth. Siechel [6] defines the first type as
steepness asymmetry and the second as deepness asym-
metry and reckons that they may occur either simultane-
ously or separately. These types of asymmetry are also
called transversal and longitudinal asymmetry [7] or un-
conditional and conditional asymmetry [8].
Business cycles asymmetry has serious implications
on their econometric modeling: Business cycles cannot
be described by linear models. Deepness asymmetry en-
ables specialists to capture business cycles using a model
involving asymmetric price adjustments (as positive de-
mand shocks have greater relative negative impact on
output than positive shocks, which have less impact on
output). Steepness asymmetry allows capturing business
cycles by an asymmetric costs model, which relies on the
assumption that production may decrease very rapidly,
yet its increase is much slower.
The outcome of business cycles asymmetry testing is
different. Nefci [9], Falk [10] and Mills [11] did not get
positive results when testing business cycles asymmetry
in industrial production. On the other hand, there are
studies supporting the existence of asymmetry in a num-
ber of economic series by Ramsey and Rothman [7], An-
dreano and Savio [12] and Stanca [13].
Speight tests business cycles asymmetry [14] on a
sample of 16 OECD countries considering their volume
of industrial production, as he thinks that this variable
“displays as much cyclical variation as possible”, based
C
opyright © 2012 SciRes. ME

V. CHIRILA, C. CHIRILA 714
on available data. The analyzed period is 1961:1-1994:4
for most countries, except for Spain, Greece and OECD
aggregates. It uses Sichel’s methodology (1993), as well
as Newey’s and West’s corrections [15] with two parzen
windows: T/4 and T/3. Although negative asymmetry is
present in very many countries, deepness asymmetry is
significant, considering an up to 10% risk, only for Ger-
many, Japan, Sweden and UK. He also achieves signifi-
cant steepness asymmetry for Japan, Sweden and UK,
taking an up to 10% risk.
Business cycles asymmetry has not been tested for
Central and Eastern European countries. Therefore, our
study is designed to fill this gap. The following countries
were included in our business cycles asymmetry analysis:
Bulgaria, Croatia, Czech Republic, Estonia, Latvia, Li-
thuania, Hungary, Poland, Romania, Slovenia and Slova-
kia. The analyzed period was 1998.1-2011.3. We used
the Hodrick-Prescott filter [16] to estimate business cy-
cles, and the Mills test [17] and Mira test [18] to test
asymmetry. The two estimation and testing variants al-
lowed us to check the reliability of the reported results.
The rest of the paper is structured as follows: the sec-
ond section includes a synthetic presentation of, on the
one hand, the methods employed to estimate business
cycles and, on the other hand, the methods devoted to
business cycles asymmetry testing; the third section de-
scribes the data used, whereas the fourth section reveals
the reported results. This paper ends with a set of conclu-
sions.
2. Methodology
When testing business cycles asymmetry, the cyclical
component should be estimated first and the asymmetry
tests should be conducted afterwards. Business cycles
estimation relies on the general assumption that an un-
seasonable variable may be decomposed in three com-
ponents, namely the trend, cycle and random components.
There are several methods applied to exclude the trend
component. Nevertheless, none of them has been de-
clared as the best variable trend exclusion method so far.
Canova [19] provides a well-structured detailed presenta-
tion of these methods. It is important to say that the pre-
vious studies proved that the trend determination method
may influence the results.
Some of these trend exclusion methods consider the
assumption according to which the variable only includes
the trend and cycle components:
ttt
yxc
where: t
x
is the non-stationary trend component and
t is the cyclical stationary component, which is trend-
dependent.
c
 
2
2
-1-1 -2
12
tt
ttttt
tt
cgggg 

In our paper, we decided to determine the cyclical
component using the Hodrick-Prescott filter.
Even if the Hodrick-Prescott filter was very much
criticized by Rand and Tarp [20], it is also the most used
in business cycles analysis. Therefore, we will also use it
in our study. By means of the Hodrick-Prescott filter, the
trend is determined by minimizing the expression:

  


 (1)
where:




*
ln ln
t
cytyt

*
ln 1
t
gyt


*
1ln t
g
yt
, , ,



*
2ln 1 t
gyt
*
and

y
—the long-term trend of the
variable y.
The most frequent value used for the parameter

in
the case of quarterly data is 1600.
To test the existence of the cyclical component for a
time series we use the Ljung-Box test. The tested hy-
potheses are the following: the null hypothesis H0 pre-
supposes that the variable is a white noise and the alter-
native hypothesis H1 presupposes that the variable is
autocorrelated. The test statistics is calculated according
to the relation:

2
1
ˆ
2
ki
ki
QTT Ti


 
 (2)
For asymmetry testing purposes, we will consider the
test proposed by Mills [17], which modifies the test pro-
posed by Sichel [6] by a Newey-West adjustment of
variance for lack of normality.
The test relies on the following asymmetry coefficient
3
3/2
2
S

(3) 

where
j

is the moment j of the cyclical component of
the series. If the sample is large and the component is
normal and independently distributed, the variance of the
estimated asymmetry coefficient would be equal to 6/T.
Yet, since these assumptions are not observed, we calcu-
late variance S as follows:

2
653
34
22
3 169 935
4
SS
KK
T



 


(4)
where:
4
2
2
K




is the kurtosis coefficient (Jaba, 2001),
T is the sample volume.
Mills [17] adjusts the variance as follows
22
1
2
1
l
SS jj
j
lf
T






 (5)

where:
is the autocorrelation coefficient j of the variable
j


V. CHIRILA, C. CHIRILA 715
3
3/2
2
t
c

, 11
jj
fl  calculates the weights and
2/9
4100
T




l.
The statistical test employed is asymptotically stan-
dard normal
ss
S
zl

 (6)
and it determines whether asymmetry is significantly ne-
gative. According to the null hypothesis, business cy-
cles have no deepness asymmetry, whereas according to
the alternative hypothesis, business cycles do have deep-
ness asymmetry.
In order to test results reliability, we applied Mira’s
alternative test [18], which is calculated as follows:
g
g
g
z (7)


where:
tmed
g
cc med t c
22
44DDE
, is the median c
g
 

2
1
1
T
t
t
cc
T




 
4/5
1/2 2TT
c
 

 
 



2


4/5
1/5
1/2 TT
DT c








ttmed
t
EccIc c
T
 

cc
1
2T
Just like Mills’ test [17], Mira’s test [18] tests whether
asymmetry is significantly negative. According to the
null hypothesis, business cycles have no deepness asym-
metry, whereas according to the alternative hypothesis,
business cycles do have deepness asymmetry. In order to
test steepness asymmetry existence, the first variable
difference t is considered instead of the variable t.
The first difference enables us to test whether the deep
series decreases are more considerable and less common
than series increases.
3. Empirical Results
We considered the actual industrial production index to
estimate business cycles in Central and Eastern European
countries. Industrial production is a poly-cyclical vari-
able and it is one of the most commonly used variables,
although there is no evidence supporting its asymmetric
character. Asymmetry testing is more recommended in
industrial production rather than in GDP, since the latter
is a more comprehensive variable, which may have
counter-cyclical components.
The quarterly data were taken from the Eurostat data-
base and the time period considered was dependent on
the availability of the data in this database. We found
data for the analyzed countries (Bulgaria, Croatia, Czech
Republic, Estonia, Latvia, Lithuania, Hungary, Poland,
Romania, Slovenia, Slovakia), whose common registra-
tion period was 1998.1-2011.3. We employed X 12
ARIMA for data deseasoning.
To estimate economic cycles, we used the Hodrick-
Prescott filter described in the paragraph above.
Tables 1 and 2 show the results of the statistical tests
for deepness and steepness asymmetry. The asymmetry
indicator is negative for Bulgaria, Czech Republic, Esto-
nia, Latvia, Lithuania, Hungary, Slovenia and Slovakia
and positive for Croatia, Poland and Romania. The busi-
ness cycles of these countries would be characterized by
deepness asymmetry if the resulting asymmetry indica-
tors were significantly negative. The results of Mills’ [17]
and Mira’s [18] asymmetry tests do not support this.
Therefore, the business cycles of Central and Eastern
European countries are not characterized by deepness
asymmetry.
In order to test steepness asymmetry, we first calcu-
lated the asymmetry indicator, yet, this time, for the first
business cycles values difference for each analyzed
country. In this case, almost all the countries in the sam-
ple have negative asymmetry indicator, with the excep-
tion of Croatia and Romania. Mills’ [17] and Mira’s [18]
tests show no evidence of any significant asymmetry,
hence they do not support the presence of steepness
asymmetry.
Table 1. Tests results for deepness asymmetry.
S(c)
s
z
g
z
Bulgaria –0.310 –1.373 –0.182
Czech Republic –0.063 –0.198 0.040
Croatia 0.294 1.579 0.089
Estonia –0.747 –3.611 –0.039
Latvia –0.356 –1.492 0.062
Lithuania –0.447 –1.517 –0.084
Hungary –0.271 –1.291 –0.034
Poland 0.014 0.069 –0.024
Romania 1.182 1.331 0.060
Slovenia –0.056 –0.183 0.035
Slovakia –0.068 –0.176 0.121
Remark: The business cycles were estimated using the Hodrick-Prescott
filter of the Eviews 7 software.

V. CHIRILA, C. CHIRILA 716
Table 2. Tests results for steepness asymmetry.
S() c
s
z
g
z
Bulgaria –0.115 –0.429 –0.111
Czech Republic –0.514 –1.236 0.011
Croatia 0.450 1.443 0.046
Estonia –0.724 –1.116 –0.035
Latvia –0.726 –1.735 –0.114
Lithuania –0.413 –2.143 –0.106
Hungary –0.251 –0.658 –0.115
Poland –0.592 –2.414 –0.019
Romania 0.385 0.264 –0.097
Slovenia –0.611 –1.633 –0.074
Slovakia –0.806 –2.434 –0.034
Remark: The business cycles were estimated using the Hodrick-Prescott
filter of the Eviews 7 software.
4. Conclusion
The concept of business cycles asymmetry is not new in
economic theory. The results of business cycles asym-
metry testing are both positive and negative. The asym-
metric nature of business cycles has been tested espe-
cially in developed countries, where large series of data
on macroeconomic indicators are available. The Central
and Eastern European countries started to embrace mar-
ket economy in 1989. Consequently, the macroeconomic
indicators series recorded in accordance with the re-
quirements of the European Union are much smaller.
This accounts for the relatively small number of papers
devoted to business cycles in Central and Eastern Euro-
pean countries. We preferred the industrial production
index to test steepness asymmetry and deepness asym-
metry. According to the results of Mills’ test [17], ap-
plied to determine the two types of asymmetry, they are
absent in the Central and Eastern European countries.
This lack of asymmetry is also supported by the results
of Mira’s test [18]. Business cycles asymmetry in the
Central and Eastern European countries should be reana-
lyzed in the future, when a larger data sample and further
macroeconomic indicators are available.
5. Acknowledgements
This work was cofinanced from the European Social
Fund through the Sectorial Operational Programme Hu-
man Resources Development 2007-2013, project number
POSDRU/1.5/S/59184 “Performance and excellence in
postdoctoral research in Romanian economic science do-
main”.
REFERENCES
[1] W. C. Mitchell, “Business Cycles: The Problem and Its
Setting,” NBER, New York, 1927.
[2] J. M. Keynes, “The General Theory of Employment, In-
terest and Money,” Macmillan, London, 1973.
[3] A. F. Burns and W. C. Mitchell, “Measuring Business
Cycles,” National Bureau of Economic Research, New
York, 1946.
[4] J. Hicks, “A Contribution to the Theory of the Trade Cy-
cle,” Clarendon, Oxford, 1950.
[5] M. D. Boldin, “Should Policy Makers Worry about Asym-
metries in the Business Cycle?” Studies in Nonlinear Dy-
namics and Econometrics, Vol. 3, No. 4, 1999, pp. 203-
220. doi:10.2202/1558-3708.1049
[6] D. E. Sichel, “Business Cycle Asymmetry: A Deeper
Look,” Economic Inquiry, Vol. 31, No. 2, 1993, pp. 224-
236. doi:10.1111/j.1465-7295.1993.tb00879.x
[7] J. B. Ramsey and P. Rothman, “Time Irreversibility and
Business Cycle Asymmetry,” 1993.
http://econ.as.nyu.edu/docs/IO/9389/RR93-39.pdf
[8] A. Peiró, “Are Business Cycles Asymmetric? Some Euro-
pean Evidence,” Applied Economics, Vol. 36, No. 4, 2004,
pp. 335-342. doi:10.1080/00036840410001674268
[9] S. N. Nefci, “Are Economic Time Series Asymmetric over
the Business Cycle?” The Journal of Political Economy,
Vol. 92, No. 2, 1984, pp. 307-328. doi:10.1086/261226
[10] B. Falk, “Further Evidence on the Asymmetric Behavior
of Economic Time Series over the Business Cycle,” Jour-
nal of Political Economy, Vol. 94, No. 5, 1986, pp. 1096-
1109. doi:10.1086/261423
[11] T. C. Mills, “Business Cycle Asymmetries and Non-Li-
nearities in UK Macroeconomic Time Series,” Ricerche
Economiche, Vol. 49, No. 2, 1995, pp. 97-124.
doi:10.1016/0035-5054(95)90018-7
[12] M. S. Andreano and G. Savio, “Further Evidence on Busi-
ness Cycle Asymmetries in G7 Countries,” Applied Eco-
nomics, Vol. 34, No. 7, 2002, pp. 895-904.
doi:10.1080/00036840110060984
[13] L. Stanca, “Asymmetries and Non-Linearities in Italian
Macroeconomic Fluctuations,” Applied Economics, Vol.
31, No. 4, 1999, pp. 483-491.
doi:10.1080/000368499324192
[14] A. E. H. Speight, “Testing for Business Cycle Asymme-
try: Some International Evidence,” Applied Economics
Letters, Vol. 4, No. 10, 1997, pp. 603-606.
doi:10.1080/758533282
[15] W. Newey and K. West, “A Simple Positive Semi-Defi-
nite Heteroskedasticity and Autocorrelation Consistent
Covariance Matrix,” Econometrica, Vol. 55, No. 3, 1987,
pp. 703-708. doi:10.2307/1913610
[16] R. Hodrick and E. C. Prescott, “Postwar Business Cycles:
An Empirical Investigation,” Journal of Money, Credit
and Banking, Vol. 29, No. 1, 1997, pp. 1-16.
doi:10.2307/2953682
[17] T. C. Mills, “Business Cycle Asymmetry and Duration
Dependence: An International Perspective,” Journal of

V. CHIRILA, C. CHIRILA 717
Applied Statistics, Vol. 28, No. 6, 2001, pp. 713-724.
doi:10.1080/02664760120059246
[18] A. Mira, “Distribution-Free Test for Symmetry Based on
Bonferroni’s Measure,” Journal of Applied Statistics, Vol.
26, No. 8, 1999, pp. 959-972.
doi:10.1080/02664769921963
[19] F. Canova, “Detrending and Business Cycle Facts,” Jour-
nal of Monetary Economics,” Elsevier, Vol. 41, No. 3,
1998, pp. 475-512.
[20] J. Rand and F. Tarp, “Business Cycles in Developing
Countries: Are They Different?” World Development, Vol.
30, No. 12, 2002, pp. 2071-2088.
doi:10.1016/S0305-750X(02)00124-9