Testing European Business cycles asymmetry

Kovacic, Zlatko J.; Vilotic, Milos Working Paper Testing European Business cycles asymmetry Institute of Economic Research Working Papers, No. 48/2017 Provided in Cooperation with: Institute of Economic Research (IER), Toruń (Poland) Suggested Citation: Kovacic, Zlatko J.; Vilotic, Milos (2017) : Testing European Business cycles asymmetry, Institute of Economic Research Working Papers, No. 48/2017, Institute of Economic Research (IER), Toruń This Version is available at: https://hdl.handle.net/10419/219871 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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Kovačić, Miloš Vilotić Article prepared and submitted for: 9th International Conference on Applied Economics Contemporary Issues in Economy, Institute of Economic Research, Polish Economic Society Branch in Toruń, Faculty of Economic Sciences and Management, Nicolaus Copernicus University, Toruń, Poland, 22-23 June 2017 Toruń, Poland 2017 © Copyright: Creative Commons Attribution 3.0 License Zlatko J. Kovačić [email protected] School of Health & Social Sciences The Open Polytechnic of New Zealand Miloš Vilotić [email protected] My Statistical Consultant Ltd. Testing European business cycles asymmetry JEL Classification: C12, C14, E32 Keywords: business cycle; asymmetry; Mills test; Mira test; Sichel test Abstract Research background: One of business cycles stylised facts is that contractions are shorter than expansions, but less persistent, more volatile and therefore asymmetric. Investigating existence and type of business cycles asymmetry is important for analysis of economic policy and statistical modeling. Economic implication of business cycles asymmetry is that economic policy should be different in period of contractions than expansion. Statistical implication is that linear models of business cycles cannot capture this stylised fact. Purpose of the article: The article has two objectives: extend the literature on the business cycles asymmetry by testing data from 36 European countries including countries never been analysed before and test robustness of the results to extraction methods and asymmetry tests used. Methodology/methods: Quarterly GDP series from Eurostat database covering period 2000q1-2016q3 were used. Series were prepared by removing seasonal component using X13-ARIMA procedure. To assess robustness of asymmetry tests results to alternative methods of detrending business cycles were extracted using two filters: Corbae-Ouliaris ideal band filter and double Hodrick-Prescott filter. For testing the deepness and steepness asymmetry three tests were used: Mills, Mira and Sichel tests. Findings: Weaker evidence of deepness asymmetry was found in Cyprus, Montenegro and Turkey cycles where all three tests statistics for both filters have negative sign. However, only for one of the tests in each country the result was statistically significant. For two other countries, Germany and Sweden, four of six tests indicated deepness asymmetry, but only one of these tests results was statistically significant. Most of the cycles show steepness asymmetry, with exception of Ireland business cycles and to certain extent cycles of Poland, Malta, Montenegro and Spain. Introduction One of the business cycle stylised facts is that recessions are shorter than expansions, but less persistent, more volatile and therefore asymmetric. Investigating existence and type of business cycles asymmetry is important for analysis of economic policy and statistical modeling. Economic implication of business cycles asymmetry is that economic policy should be conditional on the stage of the cycle. Statistical implication is that linear models of business cycles cannot capture this stylised fact and therefore would be inefficient when applied. The main objective of this study is to explore whether European business cycles are asymmetric. More specifically the time series from the Eurostat database were used to achieve the following objectives:  extend the literature on the business cycles asymmetry by testing data from 36 European countries including countries never been analysed before  test robustness of the results to extraction methods and asymmetry tests used. Research Methodology There are three methodological problems that have to be addresses when conducting research on business cycle asymmetry. They are related to preparation of time series, selection of cycle extraction methods and selection of asymmetry tests. The quarterly time series of GDP at market prices (chain linked volumes, index 2010 = 100) seasonally unadjusted are extracted from the Eurostat Database. The sample period for most of the GDP series used in this study runs from 2000q1 to 2016q3. For Bosnia & Herzegovina and Montenegro quarterly GDP time series were not available, so the quarterly index of industrial production was used instead. Series were prepared by removing seasonal component using X13-ARIMA procedure. The logarithm of seasonally adjusted real GDP was used, so that the deviations around trend are expressed as percentages. Cycle extraction methods In order to assess how robust are the asymmetry tests results on using different extraction methods two filters were applied: Hodrick-Prescott (hereafter HP) and Corbae-Ouliaris (hereafter FD) filters. When applying HP filter the two-step procedure was used. For the smoothing parameter 𝜆𝜆=1600 was used. Since the extracted cycles still contain random component HP filter was applied for the second time. This time smoothing parameter 𝜆𝜆=10 was used. The other cycle extraction method used is FD filter (Corbae & Ouliaris, 2006). The advantage of FD filter over other filters is that it can handle series with nonstationarity (e.g. unit root and heteroscedasticity) without prior testing for type of nonstationarity. Asymmetry tests Sichel (1993) considers two different types of asymmetric patterns of cycle, i.e. deepness (business cycle troughs are deeper than peaks are tall) and steepness (business cycle contractions are shorter and sharper than expansions). Deepness asymmetry of business cycle is illustrated in Figure 1(a) and cycle highness on panel (c). Boxplots on panels (b) and (d) illustrate how asymmetric distributions are when there is deepness or highness in business cycles. Figure 1. Deepness and Highness in business cycles (a) Left/Negative skewness (b) (c) Right/Positive skewness (d) Steepness asymmetry is illustrated in Figure 2. The first difference of the cycle series would have the same graph as the graph in Figure 1(a). The null hypothesis in these tests is that a given distribution is symmetric about some unknown median, against a very broad class of asymmetric alternatives. More specifically, null hypothesis is that the business cycles have no deepness/steepness asymmetry against the alternative that cycles do have deepness/steepness asymmetry. Figure 2. Steepness in business cycles Sichel test The asymmetry test proposed by Sichel (1993) is based on skewness of a cyclical series: 𝑆𝑆= 1 𝑁𝑁∑(𝑐𝑐𝑡𝑡−𝑐𝑐)3 𝑁𝑁 𝑡𝑡=1 𝜎𝜎(𝑐𝑐)3=𝜇𝜇3 𝜇𝜇2 3/2 (1) where 𝑐𝑐𝑡𝑡 is a cyclical component of time series; 𝑁𝑁 is the length of time series; 𝑐𝑐 and 𝜎𝜎(𝑐𝑐) are mean value and standard deviation of a cyclical component 𝑐𝑐𝑡𝑡 respectively and 𝜇𝜇𝑗𝑗 is j-th central moment of series 𝑐𝑐𝑡𝑡. When calculating the standard error of the test statistic (1) Sichel addressed the issue of possible autocorrelation and heteroscedasticity by using the following variable in the regression on a constant: 𝑧𝑧𝑡𝑡=(𝑐𝑐𝑡𝑡−𝑐𝑐)3 𝜎𝜎(𝑐𝑐)3 (2) Estimated regression coefficient is identical to S statistic, and for testing its significance Newey-West standard error was used. Though, as pointed out by Mills (2001), this adjustment still does not adjust variance for non- normality. Such modified t statistic follows an asymptotic normal distribution. Mills test Mills (2001) suggested two corrections in the Sichel’s test. The first correction addresses the problem of non-normality, and the variance of the test statistics is: 𝜎𝜎𝑆𝑆 2=1 𝑁𝑁�𝜇𝜇6 𝜇𝜇2 3−6𝐾𝐾+ 9 + 𝑆𝑆2 4(9𝑘𝑘+35)−3𝜇𝜇5𝜇𝜇3 𝜇𝜇2 4� (3) where S is the measure of skewness and 𝐾𝐾=𝜇𝜇4 𝜇𝜇2 3/2 is the measure of kurtosis. The second correction addresses the problem of autocorrelation by using the Newey-West adjustment. The variance of the test statistic S at lag 𝑙𝑙 is: 𝜎𝜎𝑆𝑆 2(𝑙𝑙)=𝜎𝜎𝑆𝑆 2�1 + 2 𝑁𝑁∑𝜔𝜔𝑗𝑗𝜌𝜌𝑗𝑗 𝑙𝑙 𝑗𝑗=1 � (4) where 𝜌𝜌𝑗𝑗 is the j-th autocorrelation of series 𝑐𝑐𝑡𝑡 3 (𝜇𝜇2)3/2 and 𝜔𝜔𝑗𝑗 is the weight 𝜔𝜔𝑗𝑗= 1 −𝑗𝑗 𝑙𝑙+1, with 𝑙𝑙= 4 �𝑁𝑁 100�2/9. Statistic 𝑍𝑍𝑆𝑆=𝑆𝑆 𝜎𝜎𝑆𝑆(𝑙𝑙) has an asymptotic normal distribution. Statistically significant negative value of this statistic indicates deepness, while positive value indicates highness of the business cycle. Mira test Mira (1999) proposed the test based on the following statistic: 𝑍𝑍𝑔𝑔=𝑔𝑔 𝜎𝜎𝑔𝑔 (5) with 𝑔𝑔=𝑐𝑐−𝑐𝑐𝑚𝑚𝑚𝑚𝑚𝑚, where 𝑐𝑐 and 𝑐𝑐𝑚𝑚𝑚𝑚𝑚𝑚 are mean and median respectively. Mira shown that 𝑍𝑍𝑔𝑔 statistic is asymptotically standard normal with 𝜎𝜎𝑔𝑔= �4𝜎𝜎 �2+𝐷𝐷2−4𝐷𝐷𝐷𝐷� 4𝑁𝑁 , with 𝜎𝜎�2=∑(𝑐𝑐𝑡𝑡−𝑐𝑐)2 𝑁𝑁 𝑡𝑡=1 (𝑁𝑁−1), 𝐸𝐸=𝑐𝑐− 2 𝑁𝑁∑𝑐𝑐𝑡𝑡𝐼𝐼(𝑐𝑐𝑡𝑡≤ 𝑐𝑐𝑚𝑚𝑚𝑚𝑚𝑚) 𝑁𝑁 𝑡𝑡=1 and 𝐷𝐷=𝑁𝑁1/5�𝑐𝑐1/2�𝑁𝑁+𝑁𝑁4/5�−𝑐𝑐1/2�𝑁𝑁−𝑁𝑁4/5+2��. The first difference of business cycles would show negative skewness if the cycle shows steepness. So, the same three tests could be used to test the hypothesis of steepness asymmetry by simply replacing 𝑐𝑐𝑡𝑡 with its first difference, i.e. ∆𝑐𝑐𝑡𝑡. Results Table 1 shows the results of the deepness asymmetry tests conducted for 36 European countries plus cycles of European Union (EU28) and Euro Area (EA19). Results vary across the tests and filters used. Negative values of the test statistics are in bold font. Only a few countries has all negative values for both filters and for all three tests. They are Cyprus, Montenegro and Turkey. For two other countries (Germany and Sweden), four of six tests indicated deepness asymmetry. However, as the p-values in parenthesis show, not all of these tests results are statistically significant. For instance, significant results were observed for the following countries: Cyprus (Mills test & HP filter), Germany (Mills & HP), Montenegro (Mira & FD), Portugal (Mills & HP) and Turkey (Mira & HP). Overall, we can conclude that the business cycles for majority of European countries exhibit cycle symmetry and that the evidence of deepness asymmetry is very weak, depending on the tests and filters used. Table 2 shows the results of the steepness asymmetry tests where negative values of the test statistics are in bold font. With a few exceptions (most prominent case is Ireland) a majority of European countries have a negative sign for all three tests and for both filters. That would strongly support the claim that European cycles exhibit steepness asymmetry. However, such claim should be made with caution because not all these negative values are indicating statistically significant result. For example, Sichel test for both filters shows that none of the results are significant. This could be a result of the test weakness and its sensitivity to outliers. As pointed out by Mills (2001) less evidence of asymmetries of Sichel test could be the result that the variance in the test statistic is not adjusted for non-normality. Overall, Mills test does not reject the null hypothesis of symmetric distribution in 19% (FD filter) and 11% (HP filter) cases, while this percentages raise to 83% in case of Mira’s test for both filters. Two tests (Mills and Mira) yielded for both filters statistically significant result indicating steepness asymmetry only for Czech Republic, Macedonia FRY and Turkey cycles. Table 1. Deepness asymmetry tests of the business cycles (2000q1-2016q3) Country Mills test Mira test Sichel test FD HP FD HP FD HP Austria 2.68 (0.00) 15.52 (0.00) -0.61 (0.54) 1.05 (0.30) 0.23 (0.89) 0.33 (0.91) Belgium 15.40 (0.00) 5.05 (0.00) 1.13 (0.26) 1.78 (0.07) 0.34 (0.83) 0.35 (0.87) Bosnia & Herz. 0.43 (0.33) -1.31 (0.10) 1.05 (0.29) 1.37 (0.17) 0.27 (0.79) -0.47 (0.51) Bulgaria 2.73 (0.00) 52.18 (0.00) 3.20 (0.00) 2.64 (0.01) 0.77 (0.84) 1.31 (0.74) Croatia 5.85 (0.00) 801.5 (0.00) 0.89 (0.37) 3.71 (0.00) 0.89 (0.78) 1.40 (0.76) Cyprus -0.25 (0.40) -5.41 (0.00) -0.78 (0.44) -0.68 (0.50) -0.04 (0.97) -0.47 (0.93) Czech Republic 2.32 (0.01) 6.85 (0.00) 3.72 (0.00) 0.58 (0.56) 0.66 (0.83) 0.71 (0.84) Denmark 1.01 (0.16) 3.67 (0.00) 0.88 (0.38) 0.57 (0.57) 0.16 (0.93) 0.13 (0.96) Estonia 0.06 (0.48) 0.12 (0.45) 0.89 (0.37) 0.87 (0.38) 0.09 (0.98) 0.13 (0.98) Finland 1.11 (0.13) 2.90 (0.00) 0.60 (0.55) 1.97 (0.05) 0.32 (0.86) 0.41 (0.90) France 0.54 (0.30) 0.26 (0.40) 0.79 (0.43) 1.55 (0.12) 0.00 (1.00) 0.02 (0.99) Germany -0.55 (0.29) -1.68 (0.05) 1.06 (0.29) 0.37 (0.71) -0.09 (0.96) -0.07 (0.98) Greece 0.12 (0.45) -0.91 (0.18) 0.72 (0.47) 1.38 (0.17) 0.05 (0.98) -0.22 (0.96) Hungary 1.18 (0.12) 4.93 (0.00) 2.64 (0.01) 1.83 (0.07) 0.26 (0.85) 0.27 (0.92) Iceland 1.08 (0.14) 2.54 (0.01) 1.26 (0.21) 0.95 (0.34) 0.73 (0.81) 0.87 (0.82) Ireland 0.50 (0.31) -0.28 (0.39) 1.11 (0.27) 0.55 (0.58) 0.38 (0.83) -0.14 (0.97) Italy 1.70 (0.04) 8.49 (0.00) 0.72 (0.47) 0.51 (0.61) 0.10 (0.95) 0.15 (0.94) Latvia 0.33 (0.37) 0.51 (0.31) 2.44 (0.01) 2.05 (0.04) 0.47 (0.91) 0.53 (0.91) Lithuania 0.44 (0.33) 0.78 (0.22) 0.42 (0.67) 0.50 (0.62) 0.49 (0.87) 0.57 (0.89) Luxembourg 2.78 (0.00) 11.93 (0.00) 0.55 (0.58) 1.32 (0.19) 0.97 (0.74) 1.21 (0.77) Macedonia, FRY 1.80 (0.04) 5.22 (0.00) 0.95 (0.34) -1.04 (0.30) 0.64 (0.62) 0.72 (0.20) Malta 1.98 (0.02) 60.80 (0.00) 2.15 (0.03) 0.26 (0.79) 0.30 (0.82) 0.21 (0.93) Montenegro -0.29 (0.38) -0.06 (0.48) -1.68 (0.09) -1.36 (0.17) -0.44 (0.72) -0.05 (0.95) Netherlands 1.07 (0.14) 29.23 (0.00) 2.12 (0.03) 0.82 (0.41) 0.20 (0.90) 0.43 (0.83) Norway 12.89 (0.00) 3.25 (0.00) 0.32 (0.75) -0.74 (0.46) 0.24 (0.92) 0.24 (0.94) Poland 2.17 (0.02) 3.40 (0.00) 3.10 (0.00) 1.00 (0.32) 0.36 (0.86) 0.25 (0.90) Portugal 0.66 (0.25) -38.26 (0.00) 0.39 (0.69) -0.44 (0.66) 0.09 (0.95) -0.26 (0.91) Romania 0.77 (0.00) 43.74 (0.00) 1.41 (0.16) 1.92 (0.06) 0.51 (0.86) 1.47 (0.73) Serbia 1.39 (0.08) -1.12 (0.13) 1.86 (0.06) 0.36 (0.72) 0.49 (0.92) -0.11 (0.92) Slovakia 9.37 (0.00) 10.02 (0.00) 4.19 (0.00) 3.43 (0.00) 1.69 (0.68) 1.79 (0.73) Slovenia 3.01 (0.00) 8.74 (0.00) 1.35 (0.18) 1.65 (0.10) 1.05 (0.74) 1.15 (0.77) Spain 2.08 (0.02) 2.49 (0.01) -0.06 (0.95) 0.16 (0.88) 0.33 (0.90) 0.12 (0.99) Sweden -0.60 (0.27) -0.84 (0.20) 2.01 (0.04) 0.65 (0.51) -0.15 (0.94) -0.07 (0.98) Switzerland 3.57 (0.00) 26.31 (0.00) 1.38 (0.17) 1.36 (0.17) 0.33 (0.87) 0.34 (0.89) Turkey -0.27 (0.39) -1.01 (0.16) -1.19 (0.23) -3.08 (0.00) -0.19 (0.91) -0.38 (0.88) UK 4.06 (0.00) 11.35 (0.00) 2.10 (0.04) 2.69 (0.01) 0.49 (0.83) 0.40 (0.91) EU28 8.71 (0.00) 20.83 (0.00) 0.60 (0.55) 1.03 (0.30) 0.63 (0.79) 0.55 (0.86) EA19 6.19 (0.00) 28.55 (0.00) 0.76 (0.45) 0.61 (0.54) 0.48 (0.81) 0.47 (0.86) Note: Negative values (bold font) indicate the deepness asymmetry. In case of Bosnia and Herzegovina and Montenegro industrial cycles were used in period 2006q1-2016q3 and 2010q1-2016q3 respectively. In case of Poland quarterly GDP series was available in period 2002q1-2016q3. Test results with p-values within parenthesis are based on cycles extracted using Corbae-Ouliaris (FD) and Hodrick-Prescott (HP) filters.