E Centrum výzkumu konkurenční schopnosti české ekonomiky Research Centre for Competitiveness of Czech Economy WORKING PAPER No. 10/2006 Czech Business Cycle Stylized Facts Miroslav Hloušek June 2006 B Centrum výzkumu konkurenční schopnosti české ekonomiky Research Centre for Competitiveness of Czech Economy Working Papers of the Research Centre for Competitiveness of Czech Economy are issued with support of MŠMT project Rresearch centres 1M0524. ISSN 1801-4496 Head: prof. Ing. Antonin Slaný, CSc, Lipová 41a, 602 00 Brno, e-mail: slany@econ.muni.cz, tel.: +420 549491111 Centrum výzkumu konkurenční schopnosti české ekonomiky Research Centre for Competitiveness of Czech Economy CZECH BUSINESS CYCLE - STYLIZED FACTS Abstract: This paper deals with identification of stylized facts of Czech business cycle. Empirical time series are decomposed into trend and cyclical component using bandpass filter. Cross-correlations between cyclical component of GDP and various time series are computed. The cyclical behaviour of the series is determined, leading and lagging indicators are identified. Finally, the Granger causality between GDP and other aggregate variables is tested. All these characteristics are presented in charts and commented. Several main conclusions about behaviour of variables over the cycle are summarized, which helps to judge implications of alternative economic theories. Distinctions between stylized facts in the Czech Republic and other developed countries are also discussed. Abstrakt: Tato studie se zabývá identifikací stylizovaných fakt českého hospodářského cyklu. Empirické časové řady jsou dekomponovány na trendovou a cyklickou složku pomocí bandpass filtru. Mezi cyklickými složkami HDP a různými časovými řadami jsou spočítány kroskorelace. Je určeno chování veličin během cyklu a jsou identifikovány veličiny, které cyklus předbíhají nebo se za ním zpoždují. Nakonec je testována Grangerova kauzalita mezi HDP a ostatními agregátními veličinami. Všechny tyto charakteristiky jsou prezentovány v tabulkách a komentovány. Jsou zhrnutý hlavní závěry o chování veličin během cyklu, což pomáhá posoudit implikace alternativních ekonomických teorií. Jsou rovněž diskutovány rozdíly mezi stylizovanými fakty v České republice a ostatních vyspělých zemí. Recenzoval: doc. Ing. Osvald Vašíček, CSc. B 1 INTRODUCTION* Stylized facts are empirical regularities which may not be rigorously exact always and everywhere, but they capture some important features in the economies we observe. This paper tries to identify some stylized facts of Czech business cycle. Comparison of model implications with stylized facts is useful for judgement of alternative economic theories and this paper contributes to it. Additionally, coincidence with stylized facts in other countries suggests that macroeco-nomic models or theories successfully applied to foreign economies can be used also for our economy. In the opposite case, when stylized facts differ, we can conclude that some institutional factors play important role and they are worth examining. The analysis is inspired primarily by work of Stock and Watson (1999) and Kydland and Prescott (1990) who used data of United States. Similar, but not so detailed analysis can be found in many textbooks of Macroeconomics, e.g. Barro (1997) or Williamson (2005). The paper is organized as follows. Section 2 introduces the reader into filtration of time series and discusses advantages and drawbacks of various filters. Section 3 briefly describes data used for analysis and their transformation and presents several statistics describing business cycle fluctuations. Section 4 deals with composition of GDP, while Section 5 focuses on behaviour of real and nominal variables over the cycle. The differences among theories and facts in other countries are outlined here. Final section discusses limitations of the analysis, summarizes main conclusions and suggests prospects for further research. *l thank to Ivo Burger, Jan Čapek, Hana Fitzová, Michal Kvasnička, Karel Musil, Jiří Polanský, Petr Sklenář and Osvald Vašíček for useful comments and suggestions. 4 2 ISOLATING THE CYCLICAL COMPONENT - FILTRATION The definition of business cycle fluctuations adopted in this paper is the deviation of actual time series from their long-run trends. These cyclical fluctuations are referred to as growth cycles.1 The linear filter is used to distinguish between the trend and cyclical components of economic time series. Here, I adopt the perspective of Baxter and King (1999) which draws on the theory of spectral analysis of time series data. The cyclical component can be thought of as those movements in the series associated with periodicities within a certain range of business cycle duration. I define this range of business cycle periodicities to be between six and thirty two quarters.2 The ideal filter would preserve these fluctuations but would eliminate all other fluctuations, both the high frequency fluctuations (periods less than six quarters) associated for example with measurement error and the low frequency fluctuations (periods exceeding eight years) associated with trend growth. This ideal filter cannot be implemented to finite data sets because it requires an infinite number of past and future values of the series. However, a feasible (finite-order) filter can be used to approximate this ideal filter. One widely used filter among macroeconomists is Hodrick-Prescott (1997) filter. However, this filter passes much of the high-frequency noise into the business cycle frequency band. The filter used in this study is bandpass filter designed by Christiano and Fitzgerald (1999) which mitigates this problem. Important problem of this filter (and univariate filters generally) is that data at the beginning and the end of time series are relatively poorly estimated.By contrast, multivariate filters, like Kaiman filter, reduce end-of-sample uncertainty3 Kaiman filter is an example of multivariate filters and is based on structural model. Essentially, it uses information from other time series such as inflation, real exchange rate, interest rate etc. For comparison, GDP gap estimated using three above mentioned filters is shown in Figure 1. The estimation by Hodrick-Prescott and bandpass filters differ only a little. Output gap estimated by the Kaiman filter has similar pattern but is shifted downwards and it implies that the Czech economy has been under its potential since 1997. It sharply contradicts estimation made by univariate filters. The main advantage of Kaiman filter is also its main disadvantage. It relies on structural (behavioural) equations and it makes it fragile against any error in the model structure. In addition, setting of parameters of the model, initial conditions of state variables and noise variances influence the resulting estimate. The reason why I do not use this filter is its complexity. I need 1For discussion between classical and growth business cycles see e.g. Stock and Watson (1998). 2This setting is in accordance with Stock and Watson (1998) for better comparison of the results. 3Kalman filter is successfully used in the Czech National Bank's Forecasting and Policy Analysis System. For more details see Beneš, Hlédik and Vlček (2005). 5 to estimate cyclical component of many variables and application of Kaiman filter thus requires to build many structural models. The time series are filtered by bandpass filter in spite of the fact that end-of-sample estimates are not reliable. Figure 1: Estimated output gap _5i------------------------1------------------------1------------------------1------------------------1------------------------1 1996 1998 2000 2002 2004 2006 Source: Data CSO, CNB, author's filtration 6 3 DATA AND SUMMARY STATISTICS I use data from the Czech National Bank and the Czech Statistical Office databases.4 The data series are seasonally adjusted using Kaiman smoother. Frequency of data is quarterly; sample period is from 1995Q1 to 2005Q4. Most of the series were transformed by taking logarithms. Because net exports and change in inventory stock can be negative (and taking logarithms is thus impossible) share to GDP was computed. Interest rate, unemployment rate and inflation rates are used without transformation. The cyclical components, usually referred to as gaps, are expressed as percentage deviations from trends. Although the business cycle is defined by comovements across many sectors and series, fluctuations in aggregate output are at the core of the business cycle. The cyclical component of real GDP is a useful proxy for the overall business cycle and is a useful benchmark for comparisons across series. The comovement between each series and real GDP is therefore examined. The cyclical component of each series is plotted along with the cyclical component of output in Figures 5 - 8 in Appendix. The cycle of output is always depicted by blue line, cyclical component of candidate variable is green. Note that the vertical scales of the plots differ. Relative amplitudes can be seen by comparing the series to aggregate output. The visual judgement provides some preliminary information of behaviour of the series.5 3.1 CROSS-CORRELATIONS The degree of comovement is quantitatively measured by cross-correlation of the cyclical component of each series with the cyclical component of real GDP. The magnitude of correlation coefficient indicates whether the variable is procyclical, countercyclical, or acyclical. The correlation is also calculated with phase shift up to five periods (forward and backward) which indicates if the variable is leading or lagging the cycle of GDP. Specifically, the correlation is computed between yt and xt+k, where yt is the gap of GDP and xt+k is the gap of relevant variable (both filtered by bandpass filter and expressed as deviations from trend values). A large positive correlation indicates procyclical behaviour of the series; a large negative correlation indicates countercyclical behaviour. A value of zero indicates absence of correlation: acyclical behaviour. For k < 0, the variable leads and for k > 0, the variable lags the cycle of output by k quarters. For example, if for some series the correlation is positive but maximum is at k = —2, it indicates that the variable is procyclical and tends to peak 2 quarters before the real GDP. 4Time series of German and Slovak GDP were obtained from Bundesbank and OECD Statistical database, respectively. specifically, the variables are positively correlated, when output is high (low) and the variable X is high (low) as well. In the case of negative correlation, when output is high (low) the variable X tend to be low (high). 7 Further, the test of statistical significance of correlation coefficient is made.6 The results are presented in Tables 2-3. For better orientation, the largest absolute value of correlation coefficient is underlined, correlation coefficient that is statistically different from 0 is emphasized in bold. In next section, I also distinguish if the variable is weakly (\p\ < 0.5) or strongly (0.5 < \p\) correlated. This distinguishing is subjective and is not statistically tested. Standard deviations of the cyclical component of each of the series are used as a measurement of variability. These values are also shown in Tables 2 and 3. 3.2 CAUSALITY Finally, the Granger (1969) causality between the cyclical component of GDP and candidate variable is tested. The causality is examined in both directions. The test is based on adding of past values of explanatory variables into regression equation and testing if these variables improve explanatory power of the regression. Concretely, to test whether X causes Y, we proceed as follows. First, we test the null hypothesis "X does not cause Y" by running two regressions: Unrestricted regression Yt = «o + /, aiXt-i + /, ßi-^t-i + £t (1) i=i i=i m Restricted regression Yt = «o + / ct-iXt-i + £t (2) i=i and use the sum of squared residuals from each regression to calculate F statistic7 and test whether the group of coefficients ß\, ßi, ■ ■ ■,ßm is significantly different from zero. If they are, we can reject the hypothesis that "X does not cause Y". Second, test the null hypothesis "Y does not cause X" by running the same regressions as above, but switching X and Y and testing whether lagged values of Y are significantly different from zero. To conclude that X causes Y, we must reject the hypothesis "X does not cause Y" and accept the hypothesis "Y does not cause X." The number of lagged 6The hypothesis of uncorrelation of the variables (which is equivalent to p = 0) is tested. The test statistic follows i-distribution; the test is two-tailed with 95 percent confidence intervals: tstat = p \/n — 2, where p is correlation coefficient and n is number of observations. 7The F statistic is computed using the formula: _, , ., ESSfl — ESSc/fl Fstat = (n - k)------—------— m{tSSuR) where ESSr and ESSc/fl are the sums of squared residuals in the restricted and unrestricted regressions, respectively; n is the number of observations; k is the number of estimated parameters in the unrestricted regression; and m is the number of parameter restrictions. This statistic is distributed as F(rn,n — k). The significance level is 5 %. For more details about the test see e.g. Pindyck and Rubinfeld (1998). 8 variables (m) is set from one to five which corresponds to the phase shift calculated for correlations. It tells us if the result is sensitive to the choice of m. However, extra care must be taken when interpreting Granger causality test results. As Stock and Watson (1998) say: "Granger causality is not the same thing as causality as it is commonly used in economic discourse. For example, a candidate variable might predict output growth not because it is a fundamental determinant of output growth, but simply because it reflects information on some third variable which is itself a determinant of output growth. Even if Granger causality is interpreted only as a measure of predictive content, it must be borne in mind that any such predictive content can be altered by inclusion of a additional variables." In this study, I test only bivariate relationships. If the word "cause" occurs in text, bear in mind that better interpretation of this statement is "X helps to predict Y" and do not forget that some variable Z can be the "true" determinant of behaviour of Y. The results of Granger causality test are presented in Tables 4-7. Tested hypothesis Hq is quoted in the first column, the F statistic and p value respectively are presented for every lag in next columns, p value indicates at what level of significance the hypothesis Hq can be rejected. If its value is lower than 5% (which corresponds to rejection of the hypotheses Hq at 5 % significance level) it is emphasised in bold.8 8The rule of thumb is when bolded p value for one direction is followed by non-bolded value for opposite direction, the Granger causality is proved in the first direction. If both values are bolded or nonbolded the result is ambiguous and we can not talk about causal relationship between the variables. 9 4 GDP AND ITS COMPONENTS Before examination of cyclical behaviour of various time series, it is useful to look at the composition of real GDP. In Figure 2 is depicted real GDP and its components in accordance with national accounting identity Y = C+I+G+NX9 The data are in millions of CZK (constant prices of 1995). However, percentage shares of individual components to GDP provide more Figure 2: GDP & its components, 1995Q1-2005Q4 1994 1996 1998 2000 2002 2004 2006 time Source: Data CSO, author's calculation interesting view. They are depicted in Figure 3. Average shares over the whole period are quoted in Table l.10 Consumption comprises the largest part of GDP, its share is 52 %. This is common fact also in other countries. The share of investment is 33 %. Compared to e.g. United States where investment form only about 20 % it is quite large number. Government expenditures are 22 % of total GDP. Decrease of 9Output Y is the sum of consumption C, investment /, government expenditures G, and net exports NX. Here, the investment includes change in inventories and net acquisition of valuables; government expenditures include expenditures of nonprofit institutions. 10The Czech Statistical Office uses the method of chain-linking of quarterly data with the annual overlap to compute real values of GDP and its components. This convention is adopted by all EU Member States. While this method brings more accurate description of economic developments, it involves the loss of additivity: chain-linked components of GDP will usually not sum to chain-linked GDP. That is the reason why the sum of percentage shares of the components is not 100 %. 10 Figure 3: Components of GDP, 1995Q1-2005Q4 (share in %) 1994 1996 1998 2000 2002 2004 2006 time Source: Data CSO, author's calculation Table 1: Components (average shares in %) C I G NX 52 33 22 -9 Source: Data CSO, author's calculation this ratio that is seen in last two years is caused mostly by rapid growth rate of GDP than by decrease of government expenditures. Average share of net exports (export minus imports) is —9 %. There is apparent increase of net exports in last two years that reflects improving current account deficit. An interesting fact is increasing openness of the Czech economy during the time. It is illustrated in Figure 4. At the beginning of observed period (in 1995), the share of imports and exports to GDP was 55 % and 51 % respectively. In recent years, imports and exports exceeded total GDP (with shares 109 % and 103 % respectively). Average shares during the whole period are 82 % for imports and 73 % for exports. These numbers indicate that the Czech republic is very open country and international trade plays important role in determining the growth of GDP. However, it also means that our country can be more vulnerable to external shocks and business cycle fluctuations can stem from world markets. 50 40 30 £ 20 10 0 -10 11 Figure 4: GDP, exports and imports 600 i. i ------------1--------------------1--------------------1--------------- 1994 1996 1998 2000 2002 2004 2006 time Source: Data CSO, author's calculation 12 5 BUSINESS CYCLE STYLIZED FACTS This section presents stylized facts about Czech business cycle. Cross correlations of real variables with real GDP are quoted in Table 2, nominal variables are presented in Table 3. Results of test of Granger causality can be checked in Tables 4 and 5 in Appendix. Conclusions about behaviour of variables over the cycle are summarized and distinctions between stylized facts in the Czech republic and other developed economies are mentioned.11 The relationship between economic theory and facts is discussed. 5.1 REAL FACTS First, we look at the behaviour of GDP gap. Value of first order autocorrelation coefficient is 0.92 which is quite high compared e.g. to the United States where this value is about 0.85. It indicates certain persistence and rigid behaviour of this variable. For example, when shock hits the economy, it takes more time for GDP to return to its potential level. Consumption and investment are both strongly procyclical and lag output by one quarter. Correlation of consumption with output is lower than it is usual in developed countries. Consumption is often more stable (measured by standard deviation) which is theoretically explained by smoothing behaviour of economic agents. In the case of the Czech republic, consumption is more volatile than output which again contradicts observations in other countries. Causality between consumption and output was not proved. Investment is much more volatile than output. Granger causality test shows weak predictive power from investment to output (only for one lag). Change of inventory stock (measured as share to GDP) is rather procyclical and lags output by one quarter. Its volatility is the smallest of all GDP components. GDP helps to predict change in inventory stock when five lags are considered (for lower significance level it was proved even for four lags). Government expenditures are acyclical variable (the correlation coefficient is not statistically significant), which corresponds with behaviour in other states. Apart from this statistical assessment, slight negative correlation occurs two or three quarters before the cycle of output. It means that when government increases its expenditures, GDP tends to fall half a year later. Taking opposite action, decrease of government expenditures is followed by expansion of output. Even if the correlation is weak, Granger causality test shows that government expenditures help to predict output for lags of two and four quarters (for other lags, the result is unclear). The question whether the government creates political business cycle cannot be resolved based on these results. This issue will be subject for further research. Exports are weakly positively correlated and leads the cycle of GDP by two quarters. Imports are strongly procyclical and coincide with the cycle. The behaviour of imports is in accordance with economic theory - the volume of 11United States are usually used as a reference economy. 13 23 O d f H fö fö fö o < o <1> Cr p O3 Ü o 3 3 ■ô, 3 P O o 3 o" -íl 3 3 o 5' p 2S H x Tí B TS O Ul H Q X o o 2 CC o o ?r o T? 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