(Since When) Are East and West German Business Cycles Synchronised?


 We analyze whether, and since when, East and West German business cycles are synchronised. We investigate real GDP, unemployment rates and survey data as business cycle indicators and we employ several empirical methods. Overall, we find that the regional business cycles have synchronised over time. GDP-based indicators and survey data show a higher degree of synchronisation than the indicators based on unemployment rates. However, synchronisation among East and West German business cycles seems to have become weaker again recently.


Introduction
Almost 30 years after German reunification, there is substantial evidence that the East German economy is still structurally different from the West German economy in terms of GDP per capita, productivity and unemployment (see, e.g., Maseland, 2014). For instance, GDP per capita in East Germany is still, on average, 20% lower compared to total Germany. From 2014-16, the East German economy has largely benefited from the current expansion of the German economy with annual GDP growth being higher compared to growth rates in West Germany. However, this special situation was mainly driven by the "Berlin-effect" with a rapidly rising services sector. Currently, the East German growth rates are again below their West German counterparts. Based on the existence of a common monetary policy and labor mobility between East and West Germany, it is an open question whether and to what degree regional business cycles are synchronized. 1 Analyses of European business cycles synchronization grew, particularly in the light of the EU enlargement and with regard to the question whether the new EU member states are eligible to join the monetary union (see, e.g. Artis and Zhang, 1997;Fidrmuc and Korhonen, 2006;Darvas and Szapáry, 2008;Belke et al., 2017). Recently, the synchronization literature analyzes in more detail the effects of trade and financial integration on business cycle synchronization (e.g. Gong and Kim, 2018) and the role of Animal Spirits (De Grauwe and Ji, 2017). Recently, studies show evidence that after the Great Recession synchronization, has weakened, both within Europe and between Europe and the US, although synchronization among business cycles was high prior to 2008 (Grigoraş and Stanciu, 2016;Belke et al., 2017). The European business cycle was constantly enforced by formal or informal cohesion between EU member states prior to the Great Recession.
All these studies focus on synchronization at the national level -besides European Monetary Union (EMU) as a whole, Germany is often used as benchmark. However, business cycle analyses at a regional level are rare. Some studies analyze synchronization across European NUTS regions (Montoya and de Haan, 2008;Bierbaumer-Polly et al., 2016;Gomez-Loscos et al., 2018) or German states (Schirwitz et al., 2009a,b,c). 2 For Germany, Inklaar et al. (2008) and Ferreira-Lopes and Sequeira (2011) had analyzed synchronization of business cycles across German Laender and find stronger synchronization inside West German Laender and East German Laender, respectively. 3 1 The traditional theory of optimum currency areas (OCA) states that a high degree of business cycle synchronization is an important criterion for participation in a monetary union (Mundell, 1961). 2 Recently, regional business cycle analyses for US states have been conducted by Aguiar-Conraria et al. (2017), for provincial business cycles in Canada by Lange (2017) or for Australian states by Dixon and Shepherd (2013). 1 It is important to get deeper insights into the different regional business cycle developments which provide the basis for (regional) fiscal policy decisions and related federal subsidies. Regional analyses are also highly relevant at the European level with regard to regional policies dealing with diminishing interregional differences ("Cohesion Policy"). Therefore, it is of the utmost importance for policy makers to know the extent to which business cycles between East and West Germany become similar -given that the German states have their own responsibility for federal fiscal policy. In addition, this is essential because policy decisions at the national level could affect the East and West differently. Therefore, we analyze whether the cyclical economic development in East Germany is similar to that in West Germany, and, hence, whether Germany exhibits a single synchronized business cycle or if separate regional business cycles exist. Our analysis builds on a variety of business cycle indicators and makes use of a new data set provided by the Halle Institute for Economic Research for quarterly GDP data at the regional level. In addition to static analyses of business cycle co-movements, we allow for time-varying analyses.
The structure of the paper is as follows: Section 2 describes the relevant economic indicators, Section 3 provides the empirical analysis and Section 4 concludes and summarizes the main findings.

Data
Instead of focusing on individual German states, we distinguish between two regions -East Germany and West Germany. The former consists of Brandenburg, Saxony, Saxony-Anhalt, Thuringia, Mecklenburg-West Pomerania and Berlin. The remaining states cover West Germany. We refer to common business cycle indicators, such as GDP and (un)employment rate. Since quarterly GDP data for East Germany is not provided by the German Federal Statistical Office, we make use of a new data set on quarterly regional GDP series provided by the Halle Institute for Economic Research (IWH). 4 We assess quarterly, seasonally adjusted GDP growth for the period 1991 to 2017. 5 As a measure for the cycle, we calculate the deviation from a trend (output gap). Trend GDP is based on a full sample asymmetric band-pass (frequency) filter by Christiano and Fitzgerald (2003) 4 See Claudio et al. (2018) for description of the data. Data is available at http://www.iwh-halle.de/en/ research/data-and-analysis/macroeconomic-reports/macro-data-download/ 5 In contrast to Ferreira-Lopes and Sequeira (2011) we do not consider the per capita indicators.
2 that eliminates both high and low frequency fluctuations. 6 Figure 1 shows the year-on-year GDP growth rates in East and West Germany and the corresponding output gap. Year-on-year percentage changes for GDP growth. The output gap is based on an asymmetric band-pass filter (Christiano and Fitzgerald, 2003). Sources: German Federal Statistical Office and own calculations.
Data for unemployment is provided by the Federal Employment Agency (BA) for East and West Germany at monthly frequency. First differences of seasonally adjusted unemployment rates are used for the period 1991M1 to 2017M12. The unemployment rate can be divided into a component linked to the business cycle (cyclical component of unemployment rate) and a longer-term component (structural component). The first is obtained by using the asymmetric band-pass filter of Christiano and Fitzgerald (2003). Unemployment rates and cyclical component of unemployment rates are shown in Figure 2.
Both figures indicate that the pattern between East and West data become more similar. While annualized GDP growth was substantially higher in East Germany than in West Germany at the beginning of the 1990's, the year-on-year growth rate is currently about 2.2%, which is in line with the corresponding rates in West Germany. 7 During the financial crisis, the East German economy was less affected in terms of economic slump. However, also the subsequent recovery was lower than in West Germany. In 2017, the regional actual growth rates exceeded the corresponding trends and, hence, result in a positive output gap. The unemployment rate in East Germany is much higher over the whole sample, with peak values in 2006 above 19%. In the subsequent years, both the 6 Although the Hodrick-Prescott (HP) filter is heavily criticized in the literature (Hamilton, 2017), e.g. for spurious dynamic relations and spurious dynamics, we apply this filter for robustness. However, the results for the empirical analysis are relatively similar. Note: 12 months moving averages for unemployment. The cyclical component of the unemployment rate is calculated with asymmetric band-pass filter (Christiano and Fitzgerald, 2003). Sources: Federal Employment Agency and own calculations.
implemented labor market reforms and a huge migration from East to West Germany contributed to an ongoing decrease of the East German unemployment rate. In recent years, the unemployment rate in West Germany has stabilized at around 5%. Although there was a huge decline in East German rates to around 7% at the end of 2017, there is still a gap between East and West German unemployment rates of about two percentage points. Also, with regard to the cyclical component, there are still huge differences among East and West German rates. In addition to the hard indicators presented above, we make use of the ifo business survey indicators for business situation and business expectations in trade and industry ( Figure 3) published 4 by the ifo institute in Munich. A shortcoming of this indicator is that the ifo business surveys for East Germany do not include data for Berlin. Seasonally adjusted values are considered at a monthly frequency. In the 1990's, the survey results were different in East Germany compared to West Germany; however, in recent years, both the business situation and business expectations for East and West Germany have become aligned with each other with regard to direction, not amplitude. This development is even more prominent for business expectations. Moreover, both indicators are less pronounced at their turning points for East Germany.
In addition to the visual analysis, Table 5 in the Appendix summarizes the business cycle statistics. In line with Figure 1, average GDP growth in East Germany is slightly higher. However, the average unemployment rate in East Germany is almost twice as much as in West Germany ( Figure   2). The ifo business situation indicator is, on average, higher in West Germany, the expectation indicator is higher in East Germany. The latter is mainly distorted by high expectations in the 1990's. Standard-deviations (volatility) figures show that data for East Germany is much more volatile, with the exception of ifo business situation. Persistence -measured by autocorrelations coefficients -is not very high, and is slightly higher in West Germany. 8

Factor analysis of business cycle indicators
The literature has shown that is ambiguous to rely on a single indicator to determine the dating of the business cycle and to assess synchronization. For instance, the NBER's Business Cycle Dating Committee uses various measures of broad economic activity, such as real GDP -both on the production and income side -, economy-wide employment, real income and also indicators that do not cover the entire economy, such as real sales and industrial production. To incorporate all the indicator information on GDP, ifo expectations, ifo situation and unemployment, we construct a coincident index determined by an inverse standard deviation weighting for all indicators i (see Stock and Watson, 2014): where X it is the level data in native units. Using the standard deviation s i of the logged differences y it , we determine the parameter α = s −1 i / 4 j=1 s −1 j . 8 Only output gap and cyclical component of unemployment show high persistence for both regions.
5 Furthermore, we estimate a factor model of the indicators (see, e.g. Stock and Watson, 2002) where the indicators are represented by two unobservable components: the common component (factor) χ t and the idiosyncratic component t :

Econometric analysis
For assessing synchronization between business cycles, various methods have been applied in the literature, e.g. correlations, synchronization indices and historical decompositions. Using these techniques, we conduct the analysis for the East and West German cycle.

Correlations
Starting with a benchmark analysis, we are determining the degree of synchronization of the East and West German business cycle using correlations of quarterly GDP growth, output gap, first  The correlation coefficients are larger for the second sub-sample as compared to the first subsample (ρ 1 and ρ 2 ) for all considered variables. This implies that the correlation and, hence, synchronization has increased over time. For robustness, the third column of panel A presents the results of the correlation coefficients for the last 8-years which allows an assessment on how the great recession and the subsequent recovery has affected the correlation pattern in recent years. The coefficients of the last 8-years window (ρ 3 ) are smaller compared to the second sub-sample (ρ 2 ) for The null hypotheses are rejected for almost all indicators which implies that correlation coefficients of the second sub-sample are significantly larger from those of the first sub-sample.
This implies that the correlation of all indicators has increased over the considered time period and thus indicates that the business cycle of East and West Germany has become more synchronized.
To assess the degree of business cycle correlation between East and West Germany, we take into account a number of lagging or leading periods (quarters or months, respectively) to measure phase shifts and analyze whether the correlation coefficient increases (Artis and Zhang, 1997). Table 2a shows that the correlation pattern did not improve if a particular lead or lag of the respective indicator is considered for the full sample. However, it might be that a non-contemporaneous 10 Belke et al. (2017) find that peripheral countries decreased synchronization with regards to the core, non-EMU countries and among themselves.
8 relationship between the two cycles exists, if various leads/lags are taken into account. We follow the approach of multiple correlation suggested by Ferreira-Lopes and Sequeira (2011), where the East indicator y East t is explained by various lead and lags of the West German counterpart, and the vice versa. The (multiple) correlation coefficient between both indicators can be calculated as square root of the R 2 of regression (eq.3). The results in Table 2b   Note: Correlation coefficients for seasonally adjusted series are shown for 1991-2017. a Given negative R 2 -values, the sample is adjusted to 1993-2017. GDP and output gap at quarterly frequency. Unemployment indicators and survey data at monthly frequency. The grey line refers to contemporaneous correlation (see Table 1). The columns lag and lead indicate that West German variables lag or lead n quarters/months behind its East German counterpart. For the multiple correlation analysis, line East / West(±t) indicates the coefficient of correlation of East German indicators with various leads and lags for West Germany, and vice versa.
Analyzing the correlations of different consecutive sub-samples, the results of the correlation coefficients in Table 1 have already revealed first evidence that the business cycle between East and West Germany has converged over time. However, correlation coefficients are prone to potential outliers biasing the results. Therefore, we conduct a rolling window correlation analysis which allows us to analyze the evolution of the correlation coefficients for each point in time for the full sample. For this analysis, we choose a rolling window of eight years that covers at least one cycle; additionally, we also provide results for a six-year rolling window as robustness check.

11
The correlation coefficient for GDP growth in 1993-2017 is 0.30.  Overall, our results indicate that the synchronization of the business cycle has increased over time and in particular, the results referring to the rolling correlation analysis reveal strong evidence.
Moreover, the results show that the business cycle synchronization is more pronounced for GDP variables and less for indicators based on unemployment rates and business confidence indicators.
However, all indicators indicate that synchronization has weakened since 2014.

Cycle synchronization index
In this section, we employ the concept of cycle synchronization index (CSI) for assessing the degree of business cycle synchronization (Gogas, 2013). The CSI counts the sum of sign concordance (k t ) of two indicators and relates this sum to the number of observations (N) of the time series. The cycle synchronization index of East Germany and West Germany is defined as follows: where x East,t and x W est,t are the values of the corresponding variables at time t of East and West Germany, respectively. The CSI value ranges between zero and one and can be interpreted as a percentage of quarters/months for which the specific variables indicate synchronization between the East and West German business cycle. The higher the sign concordance the stronger is the degree of business cycle synchronization. The results show that the CSI is larger in the second sub-sample (C) compared to those of the first sub-sample (B) for almost all variables except for the output gap. For GDP growth and first difference of unemployment rate, the test of difference shows that the CSI of second subsample is significantly larger from CSI of the first sub-sample at the 1% and 5% significance level, respectively. For the output gap, the cyclical component of unemployment rate and for the ifo business confidence indicators, the test of difference show insignificant results, which implies that the synchronization has not increased significantly from the first to the second sub-sample. Nevertheless, the degree of synchronization is already high for these indicators in both sub-samples. The CSI results for the common factors clearly confirm a high synchronization among business cycles phases. Note: *,**,*** denote rejection of the null at the 10%, 5% and 1% significance level, respectively.
Overall, our results indicate that the synchronization of the business cycle has increased over time and in particular, the results referring to the rolling correlation analysis reveal strong evidence.
Moreover, the results show that the business cycle synchronization is more pronounced for GDP variables and less for indicators based on unemployment rates and business confidence indicators.

Classifying booms and recessions
Official dating of business cycle turning points does not exist either for Germany as a whole or the German states. Therefore, several authors have proposed a business cycle chronology for the German economy (Fritsche and Kuzin, 2005;Schirwitz, 2009) and the German states (Schirwitz et al., 2009b). But none of them has distinguished between East and West Germany as aggregate.
Therefore, we apply the methodology of Bry and Boschan (1971), which is called the BB method for describing the business cycle. This method allows isolation of turning points in the time series and detection of periods of expansion and recession. Adopting the procedure for quarterly series by Harding and Pagan (2002) (BBQ), we can calculate the different states of the business cycle for East and West Germany and, hence, can determine the recession periods.   length. Synchronization appears to be large over the entire sample and differences in the degree of synchronization of the two consecutive sub-samples are hard to detect. Hence, we provide further analysis to address the question whether boom and recession periods have been aligned between East and West German business cycle indicators. Therefore, we apply the cycle synchronization index for GDP, for the unemployment rate and for ifo business confidence indicators of East and West Germany, respectively. However, we use the CSI in a different way as compared to the calculations in the previous section, i.e. the concordance of boom and recession periods for each of the considered business cycle indicators are investigated. 13 In this context, the CSI of the respective business cycle indicator demonstrates the share of quarters/months with business cycle concordance relative to the total number of quarters/months of the (sub-)sample. Hence, a high value of the CSI implies a high degree of synchronization of the business cycle phases in terms of GDP, the unemployment rate and the ifo business confidence indicators or among the common factors.
In Table 4, the results of the CSI calculations are illustrated. Column A reports the CSIs for the entire time period from 1991 to 2017. Column B and C report the CSIs for two sub-samples, which consist of the same time length as described in Table 2. Column D illustrates the CSIs for the last 8 years of the sample. The results show for all indicators that the CSIs are larger in the second sub-sample than the CSIs in the first sub-sample, except for the unemployment rate, where the indicator slightly decreases. This implies that the synchronization of phases has increased over the considered period from the first to the second sub-sample for GDP and the ifo business confidence indicators. Column E reports the difference of the CSIs of the two consecutive subsamples. Additionally, this column reports the results of the test of difference for the two CSIs for each of the four variables. For GDP the test of difference shows significant results at the 1% level which shows that the degree of synchronization of booms and recessions has significantly increased for GDP over the considered time period. For the unemployment rate and the ifo business situation indicator, the test of difference is insignificant but the degree of synchronization is high for both consecutive sub-samples. That the test of difference is significant for the ifo business expectations implies that the degree of synchronization has increased over time at the 10% significance level.
The results for the factors show similar results as the ifo survey indicators, since synchronization is on a high level in both sub-samples and the test of difference indicates that there is no significant increase of the degree of synchronization from the first to the second sub-sample.
We conclude from these results that the degree of synchronization of the business cycle with regard to common booms and recession has increased in terms GDP and unemployment rate. For ifo business confidence indicators and the factors, the degree of synchronization is already high for 13 The binary variable k t is one if both the East and West German indicator is in a boom or recession simultaneously; k t is zero otherwise.

Historical decomposition of business cycle fluctuations
In this section, we analyze how the contribution of the total German business cycle on the variability of the East German business cycle has changed. For this analysis, we conduct a forecast error variance decomposition, which measures the contribution of each type of shock on the forecast error variance. The analysis is based on a structural vector-autoregressive model (SVAR) with shocks which are identified by means of long-run restrictions where shocks of East German variables have no long-run effect on total German variables (Chow and Kim, 2003). This analysis allows us to measure the contribution of the specific total German business cycle indicator on the variability of the corresponding East German business cycle indicator. Moreover, we split the entire sample into three sub-samples of equal length which allows us to pursue this variance decomposition for three consecutive sample periods (1991-1999, 2000-2008, 2009-2017). The results of the forecast error variance decomposition analysis are illustrated in Figure 7, whereas the corresponding confidence bands are calculated by means of Monte Carlo simulations. For all indicators the explained variance increases considerably from the first to the second subperiod. After the Great Recession, the impact of the total German indicators on the variance of the East Germany indicators decreases compared to pre-crisis levels. For production and unemployment, the share that is explained is above 50%. For survey data German data explains about 30% of East German survey variation. In particular for the common factor based on the factor model (A2), there is a clear increase in the variance explained from about 10% in first sample to almost 70% in the last sample.
To provide more details, we conducted forecast error variance decomposition for GDP growth in East Germany and for all of Germany and measured the size of the variability in GDP growth of East Germany which is explained by the variability of GDP growth of total Germany ( Figure   7a). From 1991 to 1999, the contribution of entire German GDP growth to the variability of East German GDP growth is about 4% from the first quarter to the 10th quarter. From 2000 to 2008, the contribution of the entire German GDP growth to the variability of East German GDP growth is almost 50% in the first quarter and rises to about 80%, in the 10th quarter. Finally, from 2009 to 2017, the contribution of the entire German GDP growth to the variability of East German GDP growth is about 50% in the first quarter and drops slightly in the 10 quarters ahead. Hence, for GDP growth, we can conclude that the contribution of total German GDP growth to the variability of East German GDP growth has increased from the first to the third sample period, which indicates a higher impact of the total German business cycle on the East German business cycle.
The contribution of total German output gap to the variability of East German output gap from 1991 to 1999 is close to 10% (Figure 7b). In the second period, the contribution increases up to 80%. Finally, from 2009 to 2017, the contribution of total German output gap to the variability of East German output gap is almost 60%. Thus, for the output gap, we obtain nearly the same results as for GDP growth, since the contribution of total German output gap to the variability of East German output gap has increased over time, which suggests a higher impact of the total German business cycle on the East German business cycle.

Conclusions
In this paper we analyze the question of whether East and West German business cycles have become more synchronized over time. The results from the correlation analysis, synchronization indices, the variance decomposition and the analysis of business cycle turning points are robust and fit accurately with each other. We observe an increase in regional business cycle synchronization until 2014, although there are differences depending on the indicators considered. The business cycle indicator based on production data show larger evidence for business cycle synchronization as compared to the indicators based on unemployment rates and ifo indicators. However, the finding for the ifo surveys might be distorted by the fact that Berlin is not included in the East German survey data. Our findings also support that dissimilitudes decreased over time and in particular from the mid 2000's, synchronization has been relatively stable. However, labor market indicators still indicate differences, which arise mainly from different demographic structure and employment creation; the share of West German population to total population is 80.5%, while it it 19.5% in East Germany. In recent years, the degree of business cycle conformity between East and West seems to have abated, which is in line with international evidence after the Great Recession.
In contrast to Ferreira-Lopes and Sequeira (2011), our analysis is not based on per capita indicators, but given the similar development of GDP growth rates results might be relatively similar ( Figure  10). Furthermore, it might be the case that the synchronization pattern is different when sectorallevel data or state-level data is analyzed.