Abstract: A cross-country comparison of business cycle asymmetry is conducted. The present analysis extends the existing literature in two ways. First, the 152 economies examined allows a larger cross-country comparison than presented in previous studies. Second, a new non-parametric test is employed which, unlike the typically applied test of asymmetry, is robust to outliers. The results obtained show asymmetric behaviour over the course of the business cycle to exist for a large number of economies. The implications of these findings for the implementation of economic policy and the specification of econometric models are noted.
INTRODUCTION
Interest in the possibility of the business cycle displaying asymmetric behaviour has a long history in economics. Following the early studies of Mitchell[1], Keynes[2] and Burns and Mitchell[3], it has typically been suggested that asymmetry exists in the form of recessionary periods being shorter and more volatile than expansionary periods. More recently, formal tests have been employed to evaluate this proposition. A feature of this recent literature is the examination of cyclical asymmetry via application of Sichel's[4] moment-based tests. Following this approach, a detrending filter is applied to data to derive the underlying cyclical component of a time series, before Sichel's tests are employed[5-7]. In the present paper, this approach to examining business cycle asymmetry is extended in two ways. First, a much larger range of economies is examined than has previously been considered. In the present paper, national output is examined for 152 economies to provide a more complete analysis of asymmetry at an international level. Second, a non-parametric test recently introduced to the economics literature by Verbrugge[8] is employed to overcome noted problems with the moment-based tests of Sichel[4]. In particular, Mills[7] has noted that the results obtained from application of Sichel’s[4] tests can be biased by the presence of outliers in data. Consequently, when considering to national output for 22 OECD economies, Mills[7] applies the tests to a trimmed sample with detected outliers removed. In contrast, the non-parametric Triples test of Randles et al.[9] applied here has been found to be both robust to outliers and possess high power[10]. Therefore the present application of an alternative test to a large sample of economies complements the recent analysis of Mills[7] in which an absence of cyclical asymmetry at an international level was noted using a longer run of data for a more limited number of economies. Should asymmetry be uncovered, it will have a number of obvious implications for economic analysis. If the sizes of expansionary peaks and recessionary troughs, or the speeds at which they are approached, differ this will clearly have consequences for the implementation and impact of economic policy. At another level, detection of asymmetry will have implications for the specification of econometric models (which are typically linear and symmetric in nature), the understanding of economic behaviour and may also aid in the comparison and evaluation of alternative economic theories.
MATERIALS AND METHODS
The data examined in this paper are annual observations on real, per capita GDP over the period 1970 to 2001. The data are obtained from the International Monetary Fund’s World Economic Outlook and cover 28 ‘advanced’ and 124 ‘developing and transition’ economies.
Testing for cyclical asymmetry
Detrending: To examine whether cyclical asymmetry is present, the
cyclical component of GDP has to be derived for each of the economies considered.
Following the standard approach in the literature, the cyclical component of
the natural logarithm of per capita GDP is derived via application of a filter.
Therefore, denoting the natural logarithm of real, per capita GDP for economy
yi,t, the cyclical component of the series can be expressed
as:
| (1) |
where τi,t is the trend underlying yi,t. Again, following the standard approach in the literature, the Hodrick-Prescott (HP)[11] filter is employed to derive τi,t. Essentially, subtraction of the HP trend allows the data examined to be filtered to isolate movements corresponding to business cycle fluctuations. Although numerous detrending procedures exist[12,13] the HP filter has a number of attractive features and advantages over its rivals in the present context. In particular, because of its linear structure, the HP filter will not induce spurious asymmetry in the derived cyclical components. Using the above notation, the HP filter derives a smooth trend τi,t as the solution to the following convex minimisation problem:
| (2) |
where L is the lag operator and λ is the smoothing parameter. It can be seen from the structure of HP filter that the extreme values of λ = {0,∞} result in the derived trend equaling the original series yi,t and a linear trend, respectively. Previously, the choice of the appropriate value of λ to employ in practice for annual data has not been well defined. However, the recent research of Ravn and Uhlig[14] presents convincing arguments for the adoption of 6.25 as the optimal value of the smoothing parameter λ. It is this value that is adopted here.
The triples test: Despite their frequent application in the economics literature, the moment-based tests of Sichel[4] are problematic as they are sensitive to outliers. It is therefore possible to draw misleading inferences from the application of these tests as a result of a single or a small number of unusual observations. In contrast, the alternative non-parametric Triples test of Randles et al.[9] has been shown to be robust to outliers and also possess high power[9,10]. It is for these reasons that its recent introduction to economics literature by Verbrugge[8] is to be welcomed. The mechanics of the Triples test can be explained as follows.
Consider a sample containing N observations of the variable X. The sample contains
| (3) |
where:
| (4) |
the triple (Xi, Xj, Xk) is a right triple if f * (Xi, Xj, Xk) = 1/3, while a left triple is given by f * (Xi, Xj, Xk) = –1/3. Obviously f * (Xi, Xj, Xk) = 0 corresponds to a triple which is not skewed. The test proposed by Randles et al.[9] is based upon the estimated value:
| (5) |
The Triples test of the null of symmetry (H0: η ≠ 0) against the alternative of asymmetry (H1: η ≠ 0) is then given by:
| (6) |
The numerator of this expression is provided in equation (5). The denominator is derived as below:
| (7) |
where:
| (8) |
| (9) |
| (10) |
| (11) |
Randles et al.[9] showed that the test statistic T is asymptotically distributed as standard normal variate, with conventional critical values used to test the null hypothesis.
In the present study, the Triple test was employed to examine two possible
forms of asymmetry. Application of the Triples test to the derived cyclical
components (ci,t ) of GDP for each economy allows possible asymmetry
to be uncovered in the form of a difference in the size of cyclical peaks and
troughs. Therefore, if
RESULTS AND DISCUSSION
Considering the results for the advanced economies, evidence of deepness is
found for China (Hong Kong), Germany, Japan and Norway, although in the case
of Germany significance is marginal. For these economies, the calculated measure
of asymmetry (
| Table 1: | Deepness and steepness tests for advanced economies |
Considering the developing and transition economies, significant deepness is
found for the following economies: Bolivia, The Dominican Republic, Egypt, Fiji,
Guatemala, Jordan Madagascar, Nepal, Romania, Rwanda, St. Vincent and Grenadines
and Turkey. However, it should be noted that the evidence for The Dominican
Republic and Fiji is marginal. From inspection of sign of
| Table 2: | Deepness tests for developing and transition economies |
| Table 3: | Steepness tests for developing and transition economies |
In this study business cycle asymmetry has been examined using a range of economies. In contrast to previous studies, a recently proposed non-parametric test has been employed which is robust to outliers. In a further development of the literature, a larger range of economies has been examined than has previously been considered. The results of the analysis have show asymmetry to exist in a number of different forms. The analysis has also shown developing and transitional economies to possess asymmetry with the relative sizes of peaks and troughs and the speeds at which they are approached found to differ. As the presence of asymmetry has implications for economic policy, the understanding of economic behaviour and the specification of econometric models, the present results illustrating the existence of asymmetry for a number of economies have clear implications.