Measuring Synchronisation and Convergence of Business
Cycles with an Application to the Euro Area
Master’s Thesis by Mark Mink
April 2007
Abstract
Table of contents
Abstract 1
Table of contents 2
1. Introduction 3
2. Discussion of the literature 6
3. Method 11
3.1 Bivariate synchronicity and proximity 11 3.2 Multivariate synchronicity and proximity 12
4. Data 15
5. Empirical analysis 17
5.1 Synchronicity and proximity towards the euro area’s reference cycle 17
5.2 Synchronicity and proximity towards the business cycle of the USA 19
5.3 Synchronicity and proximity towards the euro area’s aggregate cycle 20
5.4 Characteristics of the euro area’s reference cycle 22
6. Conclusion 23
References 25
Appendix 1: Decomposition of the proximity measure 27
Appendix 2: Lead/lag-relationships with the USA and within the euro area 29
Appendix 3: Tables 31
1. Introduction
With the start of Europe’s Economic and Monetary Union in 1999, monetary policy in the euro area has been delegated to the European Central Bank. In doing so, countries gave up the possibility to use national monetary policy as a macroeconomic stabilisation instrument. The economic considerations underlying this decision are derived from the literature on optimum currency areas, which was initiated by Mundell (1961). He argues that it can be beneficial for a group of countries to adopt a fixed exchange rate if their business cycles are sufficiently similar or if country-specific economic shocks can easily spill over to the rest of the region through high international mobility of capital and labour. Under such circumstances, the benefits of reduced exchange rate uncertainty can outweigh the costs of giving up a national macroeconomic stabilisation instrument by handing over monetary autonomy to a supranational policy maker. In an extension of the theory, Frankel and Rose (1998) claim that adopting a common currency automatically increases trade between countries, which in turn will promote shock spillover throughout the region and thus increases business cycle similarity as well. Krugman (1993), however, argues that higher international mobility of capital and labour will lead to specialisation in production along the lines of countries’ comparative advantages, which will lead to more idiosyncratic shocks and thus to decreasing business cycle similarity.
First, we note that business cycles can converge towards each other not only because the coincidence of their fluctuations increases over time, i.e. because they become more synchronous, but also because these fluctuations become more similar in magnitude. The economic literature, however, usually focuses only on the synchronicity component of cycle convergence while the other one, which we will refer to as the amplitude similarity component, has generally been overlooked. Nonetheless, as was discussed above, dissimilarities with respect to the magnitude of cyclical fluctuations across countries can hamper the implementation of a common monetary policy in a comparable manner as dissimilarities with respect to the timing thereof. Therefore, we develop a measure of business cycle proximity, an increase of which will be called convergence, which is decomposed in a synchronicity as well as an amplitude similarity component. Second, our proximity and synchronicity measures can easily be extended to a multivariate context and are therefore well suited for application to larger country groupings. Third, our approach does not require the ex
ante definition of a reference cycle, such as for instance the German cycle or an euro area
aggregate, but instead derives the region’s reference cycle from the data as part of the analysis. Fourth, our measures are computed on a per-observation basis rather than being calculated as averages over a longer time interval. This can prove especially valuable in regression analyses into the determinants of synchronisation and convergence processes, which currently rely on explaining output gap correlations over a limited number of
sub-sample periods.1
We apply our method to examine synchronisation and convergence patterns amongst countries in the euro area during the 1970-2005 time period. We find that changes in cycle synchronicity have only marginally contributed to developments in cycle convergence. As a result, synchronisation and convergence patterns are often fairly different from one another. Although several countries have experienced persistent synchronisation and convergence towards the area’s reference cycle, for the region as a whole synchronicity and proximity have not changed substantially over time. This finding casts doubt on the widespread belief that the optimum currency area criterion is endogenous. Since the establishment of the monetary union, business cycles of France, Germany, the Netherlands, and Spain exhibit above average similarities with the area’s reference cycle. However, we also find that business cycle’s of perceived core EMU members Belgium and Italy are relatively different from this cycle, while in addition these dissimilarities tend to increase towards the end of the sample period. If
these inter-countries differences increase over time, it could become more difficult for the ECB to implement a common monetary policy that suits all member states.
2. Discussion of the literature
As was mentioned in the introduction, many authors have examined the stance of business cycle synchronisation in the euro area. Table 1 presents a selection of these studies and indicates some of their methodological characteristics. By providing a more in depth discussion of these approaches and their shortcomings we create a point of departure for the next section where our proposed method is developed. For a more general and more extensive overview of the literature we refer to De Haan et al. (2007).
[insert Table 1 here]
The second column in the table shows that two definitions of the business cycle are used: classical cycles and deviation cycles. The classical cycle considers fluctuations in a country’s total economic activity, which is usually measured in terms of real GDP. The deviation cycle reflects fluctuations of these real GDP levels around their potential value. Usually, potential GDP is estimated by means of a production function, or by fitting a trend through the original GDP series, for instance using the procedure described by Baxter and King (1999).
crucial importance in determining whether they could benefit from a common monetary policy. Therefore, if the researcher’s objective is to analyse whether a region can be considered an optimum currency area, fluctuations in deviation cycles, i.e. in output gaps, are to be examined.
The above conclusion is in sharp contrast with the view of Harding and Pagan (2006, p.60), who state that “synchronisation [in classical cycles] is of interest … when countries are considering forming a monetary union”. They implement this concept by means of a concordance index that indicates the fraction of time during which a pair of cycles contemporaneously goes through the same phase, being either an upswing or a downturn. Figure 1, however, illustrates another argument why deviation cycles rather than classical cycles should be studied
[insert Figure 1 here]
From the shaded area in the left of the figure it becomes clear that concordance between the depicted pair of classical cycles is perfect even though their trend components are markedly different from one another. Hence, if one is looking for a synchronicity measure which takes into account similarities between cycles’ trend components, applying the concordance statistic to classical cycles is equally inadequate as is focusing on deviation cycles. More importantly, however, the shaded area in the right of the figure shows that turning points in the corresponding deviation cycles, and therefore upswings and downturns therein, are very different as well. Hence, if one is interested in similarities between cycle’s output gap components, focusing on deviation cycles should actually be preferred over analysing concordance in classical cycles. After all, since dissimilar trends can be combined with asynchronous output gaps to yield perfectly synchronous classical cycles, the concordance statistic becomes difficult to interpret from an economic perspective. This might also explain why Camacho et al. (2005) do not find a clear relation between business cycle concordance and similarities in other cycle characteristics.
output gaps are positive or negative. Moreover, focusing on upswings and downturns in deviation cycles, as is done by Altavilla (2004), is undesirable from a practical perspective as well. After all, while the level of the output gap is relatively persistent over time, the (quarterly) change therein generally tends to behave like a white noise series. As a result, it is substantially less informative about the stance of the business cycle than the output gap’s level. In fact, when Artis et al. (2004) try to identify prolonged periods of upswings and downturns in deviation cycles, they have to use a modified version of the Harding and Pagan (2006) dating algorithm. However, as they also encounter the problem that deviation cycles are substantially less persistent than the classical cycles the original algorithm was developed for, they have to formulate additional censoring rules. Since these censoring procedures necessarily introduce an arbitrary element in the analysis, and because Camacho et al. (2005) show that dating algorithms produce rather unstable results when a limited amount of observations is available for analysis, we consider it an advantage that by focusing on output gap levels, we are able to avoid their application.
As is indicated in the table, many other authors have focused on synchronicity in output gap levels, namely by calculating correlations between deviation cycles. However, again by means of a simple graphical example, it can be shown that the degree of output gap correlation is not necessarily informative in an analysis of business cycle synchronisation. [insert Figure 2 here]
Although both deviation cycles in Figure 2 are perfectly synchronous, i.e. positive and
negative output gaps coincide exactly, correlation between them only equals 0.53.2 Figure 3
illustrates that this low degree of correlation is not a reflection of the fact that amplitude differences between contemporaneous output gaps are larger than zero.
[insert Figure 3 here]
Here, correlation is equal to unity while, although synchronicity is perfect, differences in cycles amplitudes are substantial. In fact, the problem in figure 2 is caused by the fact that correlations do not simply indicate whether contemporaneous output gaps have identical
signs, but attach separate weights to each pair of output gaps on the basis of these gaps’ deviations from their series’ mean value. As a result, correlations are sensitive to heteroskedasticity of the output gap series since alternative pairs of observations are given different weights even though they are equally important from a synchronicity perspective. A related issue is identified by McDermott and Scott (2000, p. 19), who point out that “correlation, as scaled covariance, mixes the concepts of duration and amplitude into one measure. The statistic is therefore not easily interpreted: a high number may be the result of significant co-movement through time, or … the result of a single large event that is common to the two series.” Hence, correlation coefficients are difficult to interpret as they are partially driven by events that are irrelevant to inferences about cycle synchronicity.
From the above, it has become clear that in the literature synchronicity is generally defined either as coincidence in upswings and downturns, or as coincidence between positive and negative output gaps. What is usually overlooked however, is that being able to conclude that cycles are converging towards a common, for instance European, business cycle, requires more than establishing that synchronisation processes are taking place between them. After all, for a common cycle to have emerged, national cycles do not only need to be identical with respect to the signs of their output gaps (or the timing of upswings and downturns), but also with respect to the amplitudes thereof. The latter is also of particular importance for a supranational monetary policy maker trying to decide to what extent cyclical fluctuations in the currency area are to be dampened. From the third column in the table, however, it becomes clear that many researchers have only examined the synchronicity component of cycle convergence while they ignore the component reflecting amplitude similarity. Furthermore, those few authors that did pay some attention to this issue have only analysed broad measures of cycles volatility rather than explicitly examining differences between cycles’ amplitudes for individual observations in the sample. Hence, by focusing on synchronisation alone, the literature has overlooked an important component of the emergence of a common euro area business cycle.
region-wide synchronicity, namely to analyse all individual country pairs in the region, is not without problems either. After all, when authors examine the average or the spread of all bilateral distances, the results are difficult to interpret and do not lead to the identification of a reference cycle either. Alternatively, Camacho et al. (2006) examine whether a country can be identified which is relatively ‘close’ to all other countries in the currency union and who’s business cycle can therefore be regarded the region’s reference cycle. This however, still presupposes that this cycle is identical to one country’s individual cycle instead of being some sort of meta-cycle that is not bounded by artificial national borders. Hence, the current research on the identification of a European business cycle formulates restrictive assumptions on this cycle’s characteristics before having even established whether it actually exists.
The empirical results on the stance of cycle synchronicity in the euro area have been rather mixed. For instance, Artis and Zhang (1997, 1999) conclude that since 1979, when the Exchange Rate Mechanism (ERM) of the European Monetary System (EMS) took off, a euro area business cycle has emerged that exhibits strong similarities with the German cycle while it has become detached from the business cycle in the USA. Inklaar and De Haan (2001), however, cast doubt on this finding by showing that during the last eight years of the pre-ERM period cycle synchronicity was higher than during the first eight years of the post-pre-ERM period. Massmann and Mitchell (2004) use a moving window approach and find that synchronicity levels tend to fluctuate substantially over time. However, they also observe an upward trend in these levels from the start of the 1990s onwards. Similar increases in synchronicity are observed by Altavilla (2004) and Artis et al. (2004). Darvas and Szapáry (2005) are the most optimistic as they find significant increases in synchronicity during the 1990 – 2002 period, which they consider as evidence for the endogeneity of the optimum currency area criterion. Camacho et al. (2006), however, strongly disagree with this conclusion as they find no evidence for the emergence of a euro area reference cycle while in addition they show that synchronicity was already fairly high prior to the establishment of the monetary union. In a literature survey covering many more articles than the ones discussed here, De Haan et al. (2007) conclude that although many authors seem to agree that cycle synchronicity in the euro area has increased from the 1990s onwards, the evidence is mixed and depends on the time periods examined. Also in light of these empirical findings, it would be preferable to have available measures of synchronicity and proximity that do not require ex
ante selection a fixed set of countries on the basis of which the euro area’s perceived
3. Method
3.1 Bivariate synchronicity and proximity
On the basis of the discussion above, we define the degree of synchronicity between business cycles as the percentage of time that contemporaneous output gaps have identical signs. In light of this definition, a natural measure of synchronicity at time t is
( ) ( ) ( ) ( ) ( ) .
ij t g t g ti j g t g ti j
ϕ = (1.1)
Here, ϕij( )t denotes synchronicity between ( )g t and i g t , which are the output gaps of j( ) deviation cycles i and j observed at time t. They are measured in percentages of potential GDP. Since synchronicity is calculated as the product of both output gaps scaled by this product’s absolute value, it equals 1 when both gaps have the same sign, and –1 if their signs are opposite. As a result, if the measure is transformed to a (0,1) rather than a (-1,1) scaling, its average value over a particular time interval precisely indicates the fraction of time during which both cycles have equally signed output gaps. Hence, computing synchronicity using equation (1.1) produces easily interpretable outcomes.
To analyse cycle proximity we need to go beyond measures of cycle synchronicity as we also need to take into account differences between cycles’ amplitudes (i.e. volatility). To this end, we could simply define cycle proximity as the mean absolute difference between
( )
i
g t and g t . Doing so, however, raises two problems. First, if both cycles’ volatility j( ) decreases by an equal percentage while synchronicity remains constant, the absolute
difference between ( )g t and i g t declines as well due to the decrease in cycle’s variances. j( )
This, however, is not to be interpreted as an increase in cycle proximity, i.e. as cycle convergence, since cycle’s relative positions have remained unchanged. Second, when pairs of cycles are ranked simply on the basis of the mean absolute difference between them, no inferences can be made on which pair has converged the most. After all, absolute differences between a pair of highly volatile cycles will, everything else equal, be larger than absolute differences between cycles with lower variances. Therefore, cycle proximity at time t can be quantified as
( ) ( ) ( ) ( ).
ij t g ti g tj g t
The numerator of Equation (1.2) simply indicates the absolute difference between the observed output gaps preceded by a minus sign. As a result, a decrease of this difference is
reflected by an increase in cycle proximity. The denominator consists of a scaling factor ( )g t ,
which is set equal to the median of the absolute values of ( )g t and i g t .j( ) 3 As a result, the proximity measure expresses the (negative value of the) distance between a pair of output gaps relative to these output gap’s absolute value.
Differences between contemporaneous output gaps can decrease because cycles become more synchronous, or because both cycles variances become more similar over time. Hence, cycle proximity as formulated in Equation (1.2) can be decomposed in a cycle synchronicity component as well as a component reflecting amplitude similarity. As is shown in Appendix 1, the share of cycle proximity that is to be attributed to the fact that cycles are not perfectly synchronous can be quantified as
(
( ) ( ) 2( ) 2( ) 2 ( ) ( ))
( ),ij g ti g tj g ti g tj g t g ti j g t
ϕ
γ ≈ − − − + − (1.3)
while the share that is to be ascribed to deviations from perfect amplitude similarity equals
2 2
( ) ( ) ( ) 2 ( ) ( ) ( ).
ij t g ti g tj g t g ti j g t
σ
γ ≈ − + − (1.4)
It is easy to see that Equations (1.3) and (1.4) add up to the proximity measure defined in Equation (1.2).
3.2 Multivariate synchronicity and proximity
The bivariate synchronicity and proximity measures in the previous section can easily be modified to deal with larger country groupings. For instance, consider the case where one is interested in examining similarities between individual countries and the cycle in aggregate euro area GDP. Such an exercise would be relevant if the researcher’s aim is to examine whether individual countries will benefit from a central bank implementing a common
monetary policy on the basis of this aggregate cycle. In this case, synchronicity of the region towards this aggregate cycle can be calculated as
(
)
1 1 ( ) n ( ) ( ) ( ) ( ) . emu i r i r i t g t g t g t g t n ϕ = =∑
(1.5)Here, n is the number of countries in the sample and g t is the output gap of the reference r( )
cycle, which is set equal to the euro area aggregate. Likewise, region-wide cycle proximity towards this aggregate cycle can be computed as
1 1 ( ) n ( ) ( ) ( ). emu i r i t g t g t g t n γ = = −
∑
− (1.6)In this case, the scaling factor is computed as the absolute value of the aggregate cycle’s output gap rather than as the median of all countries’ output gaps. This makes sense because the degree with which differences between output gaps across the region hamper the implementation of the common monetary policy depends on the magnitude of these differences relative to the output gap on the basis of which this policy is determined. Just as before, a lower bound of a quarter of a percentage point is imposed when calculating the scaling factor. Furthermore, the definition of the synchronicity and volatility components of proximity towards this aggregate cycle can be obtained in a similar manner as was used to derive Equations (1.5) and (1.6) from their bivariate counterparts. Similarities between individual countries and this cycle can be examined using the measures defined in Equations (1.1) to (1.4).
in the region. As a result, calculating Equations (1.5) or (1.6) in this case does not provide information on whether countries in the region have converged or synchronised towards each
other over time, it only indicates whether countries have converged or synchronised towards a
particular business cycle constructed in advance by the researcher.
Intuitively, the degree of synchronicity within a region is proportional to the size of the largest fraction of countries with equally signed output gaps (which can range between 50% and 100%). For instance, if all gaps have equal signs then synchronicity is perfect, while if half of the gaps are positive and half of them is negative, synchronicity is at its minimum value. Likewise, the degree of proximity within the region should be proportional to the minimum absolute distance between all countries. On the basis of this, the region’s reference cycle can be defined as the cycle that maximizes Equations (1.5) and (1.6) simultaneously. This implies that the reference cycle’s output gap at time t has to be set equal to the median of all output gaps (still expressed as percentages of trend GDP) observed across the region at this time. After all, the median maximizes synchronicity as it has the same sign as the majority of the individual country’s gaps, while it maximizes proximity through minimizing the sum of the absolute distances towards them. Therefore, if the reference cycle is derived from the data in this manner, it can be interpreted as the cycle that lies the ‘closest’ to all individual countries’ cycles. This cycle is not pre-defined by the researcher, but is obtained as a by-product of simultaneously maximizing synchronicity and proximity between all countries in the region. Furthermore, it is not necessarily identical to one of the individual countries’ cycles, but can be interpreted as some sort of latent cycle which might be driving the cycles of individual countries in the region. When calculating proximity towards this reference cycle, the scaling factor again is to be calculated analogous to the bivariate case, i.e. as the median
of the absolute output gaps observed at time t.4
4. Data
In the empirical analysis we use volume indices on quarterly GDP in the EMU-11 countries (Luxembourg had to be excluded from the sample) which in general cover the 1970.01 – 2005.04 time period. The statistics are predominantly obtained from the online version of the
IMF International Financial Statistics database.5 The 1991.01 level-shift in German GDP,
caused by the unification, is removed from the data by means of ratio splicing using the first annual overlap. All series are seasonally adjusted by means of the U.S. Census Bureau’s X12 seasonal adjustment program, which is standard available in the EViews 4.1 software package. Table 2 provides a more detailed overview of the data used in the analysis.
[insert Table 2 here]
In order to compute the output gaps required for the analyses below, potential GDP has to be estimated. Many authors do this by fitting a trend through the original data using nonparametric filtering methods such as the high-pass filter developed by Hodrick and Prescott (1997), or the band-pass filters proposed by Baxter and King (1999) and Christiano and Fitzgerald (2003). These last type of filters can be configured to remove higher frequency fluctuations as well. In the literature, it is generally decided to follow Baxter and King (1999) and to extract only fluctuations with a duration between 1.5 and 8 years. We do not follow this approach, however, since even if it were true that higher frequency fluctuation are not part of the business cycle, and even though monetary policy is set on the basis of structural rather than temporary developments in economic activity, the answer to the question whether the impact of this policy is the same for all countries in the currency union depends on all asymmetries between them, no matter whether these are of a transitory nature. Hence, if cycle synchronisation and convergence processes could only be detected in smoothed cycles, while between fluctuations in actual economic activity such developments cannot be identified, their relevance would be rather limited.
Therefore, we aim to stay close to the original GDP statistics and only remove a trend component from the data. Although it would be preferable to do so by means of the method proposed by Koopman and Wong (2006), who develop an approach to estimate time-varying
5. Empirical analysis
In this section, changes in cycle synchronicity and proximity in the euro area are examined using the measures developed in the previous section. First, an analysis is performed into synchronicity and proximity between countries and the euro area’s reference cycle. Thereafter, to put the results into perspective, it is examined to what extent euro area countries have synchronised and converged towards the USA’s business cycle. This way, it can be inferred whether any increases of integration within the euro area have come at the cost of detachment from the USA’s economy. Finally, an analysis on the basis of the euro area’s aggregate cycle is performed in order to examine whether a common monetary policy can successfully be implemented in the region.
5.1 Synchronicity and proximity towards the euro area’s reference cycle
In figure 4, for each individual country graphs are presented indicating synchronicity and proximity towards the region’s reference cycle. The separate synchronicity and amplitude similarity components of cycle proximity are depicted as well. All graphs present eight-year moving averages of the computed statistics.
[insert Figure 4 here]
Several observations can be inferred from the graphs. First, with a minor exception for Portugal during the pre-1992 period, synchronicity is always positive for each country in the sample, which implies that their output gaps have the same sign as the output gap of region’s reference cycle for at least fifty percent of the time. Moreover, in case of Spain, France, and Portugal, synchronicity has increased substantially over time. Currently, Germany, Spain, France, and the Netherlands are almost perfectly synchronised with the reference cycle. Interestingly, this finding can be established despite the fact that higher frequency fluctuations were not filtered from the output gap series. Moreover, the high synchronicity levels for France and Germany are not caused by a size bias due to their larger weight in the euro area’s economy since all countries’ output gaps are treated as equals in deriving the region’s reference cycle.
Finland stands out in this respect as for this country synchronicity has been relatively low over the entire time period considered. More or less the same can be said for Austria, while during the later years of the sample also Greece, Italy and Belgium become more detached from the reference cycle. Hence, membership of the currency union apparently does not automatically increase business cycle synchronicity amongst member states. This can also be inferred from the graph that depicts average developments in the area as a whole. Since the mid-1980s, synchronicity within the region has increased only marginally and in fact was somewhat higher at the start of the sample period than at the end of it. Since average synchronicity within the region as a whole cannot fall below zero (the reference cycle is by construction always synchronised with at least half of the countries in the sample), the synchronicity level of 0.57 observed for 2005 implies that about 75% of the countries is synchronised with the region’s reference cycle. Interestingly, eyeballing the bottom right graph in the figure suggests that this reference indeed has the characteristics of an ‘actual’
business cycle.6
When looking at developments in cycle proximity across the region, three findings are worth mentioning. First, one of the countries for which synchronicity levels are rather low and volatile, i.e. Greece, has substantially and persistently converged towards the euro area’s reference cycle. As a result, at the end of the sample period it experiences below average cycle synchronicity while it at the same time performs above the region’s average with respect to cycle proximity. Furthermore, also Portugal and the Netherlands have experienced a net increase in proximity over time. Although fluctuations in all other countries have been substantial, their proximity level does not show a tendency to persistently rise or fall. This also holds for the euro area average, which has not experienced a net increase or decrease over time. However, just as when cycle synchronicity was considered, proximity has gradually increased since the mid-1980s. Despite this resemblance between synchronicity and proximity patterns at the aggregate level, at the level of individual countries, these patterns differ substantially amongst each other. In fact, correlation between them ranges from –0.68 (Italy) to 0.89 (France), with an average value of 0.02. Hence, cycle synchronicity and cycle proximity are different concepts also from an empirical perspective.
The reason for the observed difference between synchronicity and proximity mainly lies in the role for the amplitude similarity component of cycle proximity. After all, when correlations between synchronicity patterns and the synchronicity component of cycle proximity are examined, we find values ranging from 0.38 (Finland) to 0.98 (Portugal) with an average equal to 0.79. Correlations of synchronicity with the amplitude similarity component lie between –0.76 (Italy) and 0.83 (France) with an average value equal to –0.16. In addition, the graphs indicate that the share of cycle proximity that is to be attributed to the synchronicity component is substantially smaller than the share corresponding to the amplitude similarity component. As a result, the majority of the observed changes in cycle proximity are caused by the fact that similarities between business cycles’ amplitudes change over time. Changes in synchronicity between cycles were only of minor importance in this respect.
5.2 Synchronicity and proximity towards the business cycle of the USA
To put the results presented above into perspective, synchronicity and proximity between business cycles of individual countries and the US cycle was analysed. This was done using the same analysis as performed above, although this time the United States’ output gap series
was used instead of the euro area’s reference cycle.7 The scaling factor in the proximity
measure was computed on the basis of the US cycle as well. In figure 5 the results from the analysis are reported.
[insert Figures 5 here]
To start with, synchronicity with the US cycle is generally lower and more volatile than synchronicity with the euro area’s reference cycle. In fact, for all countries synchronicity is negative for several observations in the sample. Interestingly, however, since the start of the currency union in Europe, a substantial increase in synchronicity with the US cycle is observed for all countries in the region. Such an increase was absent when the euro area’s reference cycle was examined. Nonetheless, as becomes clear from the middle graph in the bottom row, synchronicity in 2005 equals 0.40 and is therefore not only lower than at the start
of the sample period, but also lower than average synchronicity with the region’s reference cycle.
The observed proximity patterns are again rather different from those reflecting cycle synchronicity. Correlation between them ranges from –0.16 (Greece) to 0.93 (France) with an average value of 0.59. Moreover, just as when the region’s reference cycle was examined, the synchronicity component of cycle proximity is rather small compared to the amplitude similarity component. In general, fluctuations in the proximity patterns are rather large, especially for Finland, Greece, and Belgium. However, since the currency union was established, an increase in proximity is observed amongst all countries, which is similar to the increase in cycle synchronicity that was reported above. Nonetheless, at the sample end average proximity towards the US cycle equals –1.37, which is lower than the value of –0.85 reported for the region’s reference cycle.
As it is often believed that the US economy leads economic activity in the euro area, Appendix 2 extends the analysis of contemporaneous synchronicity and proximity by allowing for lead/lag-relationships between countries and the US cycle. Although in several cases synchronicity and proximity improve when such a relationship is taken into account, the phase shifts that are found between countries and the US cycle tend to vary in length as well as in direction (i.e. lead or lag) over time and across countries. Apart from the fact that the German cycle consistently lags behind the US cycle, we do not find any structural lead/lag-relationships. When the same analysis is applied to the euro area, the results are markedly different and show that lead/lag-relationships within the region are virtually nonexistent. Hence, also these findings suggest that economic integration within the euro area is larger than integration between countries and the USA.
5.3 Synchronicity and proximity towards the euro area’s aggregate cycle
the region’s reference cycle.8 As the reason for carrying out this part of the analysis lies in examining whether it is feasible to successfully implement a common monetary policy in the area, we only report the results for the period after the establishment of the monetary union. Therefore, table 3 reports synchronicity and proximity levels for the last eight-year period in
our sample, which ranges from 1998 to 2005 (to be exact, the ECB was established on June 1st
1998 while the common monetary policy was implemented from the start of 1999 onwards). For comparison, the results obtained from the analysis of the euro area’s reference cycle are reported as well.
[insert Table 3 here]
From the table, it becomes clear that the weighted average of countries’ synchronicity with the aggregate euro area cycle is equal to 0.67, which is somewhat higher than the value of 0.57 reported for synchronicity with the reference cycle. This is the result of the fact that especially the larger countries, i.e. France, Germany, and Spain, are strongly synchronised with aggregate euro area GDP. However, the country with the highest value for cycle synchronicity is the Netherlands. As this value is equal to 0.94, the Dutch business cycle is almost perfectly synchronous with the euro area aggregate. In the analysis of the area’s reference cycle, this position was taken by Spain, also with a value of 0.94. In terms of proximity towards the aggregate cycle, the Netherlands does reasonably well either, although it is outperformed by France and Germany. Furthermore, diversity within the region is fairly large since some of the countries experience very low synchronicity and proximity levels. Especially Finland and Greece perform badly in this respect, while Ireland and Italy are clear underperformers as well. Hence, although until now the ECB has seemingly been able to implement the common monetary policy without being hampered too much by this type of asymmetries, it remains to be seen whether future developments in cycle convergence and
synchronisation will turn out favourable.9
8 These aggregate statistics were calculated as a weighted average of individual countries’ GDP volume indices, using as weights the countries’ real GDP levels. The data was obtained from the January 2007 version of the Total Economy Database maintained by The Conference Board and the Groningen Growth and Development Centre. See http://www.ggdc.net.
5.4 Characteristics of the euro area’s reference cycle.
Figure 9 illustrates an interesting finding regarding the characteristics of the euro area’s reference cycle. Here, again within a moving window, coefficient estimates are reported that are obtained from regressing the euro area’s reference cycle and the individual countries’ cycles on their AR(1) terms. The magnitude of the reported coefficients can be interpreted as a measure of business cycle persistence. A large AR(1) coefficient therefore implies that the cyclical pattern is to a lesser extent affected by random shocks and is more strongly driven by its own past.
[insert Figure 9 here]
In the graph, the persistence pattern for the reference cycle is printed in bold, while the individual countries’ patterns are reported in the background for comparison. As can be seen, persistence in the euro area’s reference cycle has increased substantially after an initial
decline at the start of the sample.10 Interestingly, the turning point around the mid-1980s
coincides almost perfectly with the start of the prolonged increase in average synchronicity and proximity that was depicted in Figure 4. Hence, not only have countries on average experienced (moderate) synchronisation and convergence towards the reference cycle over the last two decades, the reference cycle itself has become more pronounced as well during this period. Nonetheless, persistence is not higher in 2005 than it was at the start of the sample period, which again closely resembles the findings for average synchronicity and proximity that were reported before. Interestingly, however, especially at the sample end persistence in the reference cycle is in many cases larger than persistence in the cycles of individual countries. Hence, this result confirms what could already be inferred from the bottom right graph in Figure 4, namely that the somewhat abstract concept of the European reference cycle turns out to have the characteristics of an ‘actual’ business cycle rather than being merely a white noise series. Furthermore, loosely speaking it also suggests that although individual countries can be hit by idiosyncratic shocks that interfere with their business cycle fluctuations, the reference cycle ‘underlying’ these fluctuations remains fairly stable and can still be extracted from the data.
6. Conclusion
If national business cycles within a currency union diverge considerably, a common monetary policy will not be optimal for all countries concerned. At a point in time, some countries could prefer a monetary contraction, while others would require a more expansionary monetary policy. Whether such problems are likely to occur depends on to what extent adopting a common currency strengthens economic relationships between countries, for instance through increasing trade integration in the union. The latter could automatically induce national business cycles to become more similar within the region through increased facilitation of idiosyncratic shock spillovers between countries. Therefore, it has often been suggested that the optimum currency area criterion might in fact be endogenous. The foundation of the Economic and Monetary Union in Europe has intensified this debate and has inspired many researchers to examine business cycle synchronisation in the euro area.
This research adds to this literature in several ways. To start with, we recognize that the successful implementation of a common monetary policy not only requires business cycles to be identical with respect to the timing of upswings and downturns, but also with respect to the amplitudes thereof. Therefore, we develop a measure of business cycle convergence that can be decomposed in a synchronicity and an amplitude similarity component. While doing so, we show that current methodologies adopted to address the synchronicity component of cycle convergence suffer from several shortcomings that either involve the way they define the concept of synchronicity, or concern the accuracy with which this concept is measured. Furthermore, our synchronicity and convergence measures are of a multivariate nature and can therefore easily be applied to groups of more than two countries. In addition, our approach does not require specifying a reference cycle in advance, but instead derives the region’s reference cycle from the data as part of the analysis. Finally, the measures can be computed on a per-observation basis rather than being calculated as average values over a longer time interval (as is the case when output gap correlations are computed).
component. In other words, changes in cycles’ relative volatility have had a much more pronounced impact on changes in the ‘closeness’ of euro area business cycles than changes in synchronicity did. This is also reflected by the finding that correlation between synchronisation and convergence patterns amongst countries in the currency union is on average equal to zero.
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Appendix 1: Decomposition of the proximity measure
The proximity measure that was defined in Equation (2.1) is given by
( ) ( ) ( ) ( ).
ij t g ti g tj g t
γ = − − (A.1)
To decompose this proximity measure in a synchronicity and an amplitude similarity
component, we have to answer the question: “how large would the difference between ( )g t i
and ( )g t have been if synchronicity between cycles i and j would have been perfect?” j
Subtracting this difference from the numerator of Equation (A.1) would yield the amplitude similarity component of cycle proximity, while the remainder is to be attributed to the synchronicity component. A complication involved in answering the above question, however, is that the difference between both output gaps partially depends on both cycle’s variance, which is not constant over time but could in fact be different for each observation in the sample. As a result, one could say that for each time t the observed output gaps are generated on the basis of a different, i.e. time dependent, distribution. Assuming that this is a normal distribution (which holds for all countries in our sample, although for some of them this requires the removal of a limited amount of extreme observations from the output gap series), we can write
(
2)
( ) ~ 0, ( ) for , ,
k k
g t N σ t k i j=
where we use σk( )t to denote the standard deviation of the distribution that generated the
output gap of cycle k at time t. Now, in order to deal with this time-dependent variance, we rephrase the question formulated above and instead ask ourselves: “how large would the
difference between cycles generated on the basis of the distributions that generated ( )g t and i
( )
j
g t have been if synchronicity between these generated cycles would have been perfect?”
Denoting the output gap series corresponding to the generated cycles as gk( )τ , we can write
(
2)
( ) ~ 0, ( ) .
k k
As is shown by Patel and Read (1982, p.34), it follows that the absolute values of these output gaps are generated by half-normal distributions with expected values given by
( ) ( ) 2 ,
k k
E g τ =σ t π (A.2)
where E denotes the expectations operator. Likewise, the absolute distance between the output gaps is given by
(
2 2)
(
)
( ) ( ) ( ) ( ) 2 ( ) ( ) ( ) 2 ,
i j i j ij i j
E g τ −g τ = σ t +σ t − ρ τ σ t σ t π (A.3)
where the first term between brackets corresponds to the standard deviation of the difference
between both output gap series. Furthermore, ρ τij( ) denotes correlation between output gap
series ( )gi τ and gj( ).τ If we now substitute Equation (A.2) into Equation (A.3), we obtain
(
2 2)
( ) ( ) ( ) ( ) 2 ( ) ( ) ( ) .
i j i j ij i i
E g τ −g τ = E g τ +E g τ − ρ τ E g τ E g τ (A.4)
Since the actual values for E gi( )τ and E gi( )τ are unknown, Equation (A.4) cannot
directly be computed. However, we do have an estimate of these expected values, namely
their realisations which are given by g ti( ) and g t Furthermore, since the output gap j( ) .
series in Equation (A.4) are homoskedastic, perfect synchronicity now implies perfect
correlation (as was shown in Figure 3), yielding ϕ τij( )=ρ τij( ) 1.= Therefore, the answer to
the question “how large would the expected difference between cycles generated on the basis
of the distributions that generated ( )g t and i g t have been if synchronicity between these j( )
generated cycles would have been perfect?”, can be approximated by
2 2
( ) ( ) ( ) ( ) 2 ( ) ( ) .
i j i j i j
E g τ −g τ ≈ g t +g t − g t g t (A.5)
Appendix 2: Lead/lag-relationships with the USA and within the euro area
In order to find out whether individual business cycles lead or lag begin the reference cycle, we could examine by how many quarters and in what direction these individual cycles need to be shifted versus the reference cycle in order to maximize synchronicity between them. This approach is adopted by Artis and Zhang (1997) and Darvas and Szapáry (2005). The latter authors, however, only check for leads or lags with a maximum length of three quarters in order to avoid finding occasional matches at relatively large and implausible lead or lag lengths. In the present analysis, we do not impose such relatively arbitrary restrictions, and instead require that if a country leads (lags behind) the reference cycle with k quarters, synchronicity between this reference cycle and the country’s cycle should increase gradually when the lead (lag) length is increased from zero to k. Furthermore, although the concept of a lead/lag-relationship is essentially related to cycle synchronicity, we additionally require that cycle proximity does not decrease when the length of the lead (lag) is increased towards k. More explicitly, if we define ϕir t j,± and γir t j,± as synchronicity and proximity between the output gap of the reference cycle at time t and the output gap of country i at time t±j, we conclude that country i leads this reference cycle by k quarters if it holds that
, , 1 and , , 1 for 1,..., .
ir t j ir t j ir t j ir t j j k
ϕ + >ϕ + − γ + ≥γ + − =
Likewise, country i lags behind the reference cycle by k quarters if it holds that
, , 1 and , , 1 for 1,..., .
ir t j ir t j ir t j ir t j j k
ϕ − >ϕ − + γ − ≥γ − + =
Obviously, we cannot compute these lead/lag-relationships for each individual observation, but instead determine the leads and lags over a prolonged time period, namely within an eight year moving window. If leading as well as lagging a country’s cycle both lead to an improvement in synchronicity with the reference cycle, we select the relationship that increases synchronicity by the largest amount. The results obtained from the analysis of lead/lag-relationships towards the US business cycle are presented in Figure 5.
As can be seen, for several countries leads and lags with the US cycle can be substantial. Nonetheless, the relationships are not very stable as leads and lags tend to alternate over time. Only Germany seems to consistently lag behind the US cycle with an average lag length of 1.75 quarters. Hence, these results suggest that in general there are no structural lead/lag-relationships between euro area countries and the USA. For comparison, a similar analysis was performed using the euro area’s reference cycle instead of the US cycle. The results are reported in Figure 6.
[insert Figure 6 here]
Appendix 3: Tables
Table 1: Literature
Measure of
Study Cycle synchronicity Amplitude similarity Reference cycle
Altavilla (2004) Concordance between
classical as well as deviation cycles
Comparison of average deepness and steepness of phases
EU aggregate cycle
Artis and Zhang
(1997, 1999) Correlation between deviation cycles German cycle
Artis, Krolzig and
Toro (2004) Concordance between classical cycles EMU component (MS-common
VAR) Camacho et al. (2006) Concordance between
classical cycles; correlations between frequency bands
Comparison of average deepness and curvature of phases
Cluster analysis with bivariate distances; distribution of bivariate distances
Croux et al. (2001) Correlations (on
frequency bands)
Weighted average of bivariate correlations Darvas and Szapáry
(2005) Correlation between deviation cycles Comparison of output gap variances EU aggregate / EU common factor Harding and Pagan
(2006) Concordance between classical cycles Distribution bivariate concordance of
statistics Inklaar and De Haan
(2001) Correlation between deviation cycles German cycle
Lumsdaine and Prasad (2003) Correlation between deviation cycles EU common component (time-varying weights) Massmann and
Mitchell (2004) Correlation between deviation cycles Distribution bivariate correlationsof
Wynne and Koo (2000)
Correlation between deviation cycles
Comparison of output gap variances
Table 2: Data sources
Country Period Source
Austria 1970.01 – 2005.04 IFS online version (downloaded March 2007)
Belgium 1980.01 – 2005.04 IFS online version (downloaded March 2007)
Finland 1970.01 – 2005.04 IFS online version (downloaded March 2007)
France 1970.01 – 2005.04 IFS online version (downloaded March 2007)
Germany 1970.01 – 2005.04 IFS online version (downloaded March 2007)
Greece 1970.01 – 2000.04
2001.01 – 2005.04
Eurostat (downloaded March 2007)
IFS online version (downloaded March 2007)
Ireland 1997.01 – 2005.04 IFS online version (downloaded March 2007)
Italy 1970.01 – 1979.04
1980.01 – 2005.04
Eurostat (downloaded March 2007)
IFS online version (downloaded March 2007)
Netherlands 1977.01 – 1998.04
1999.01 – 2005.04
IFS 2005, CD-ROM
IFS online version (downloaded March 2007)
Portugal 1977.01 – 2005.04 IFS online version (downloaded March 2007)
Table 3: Cycle proximity and synchronicity for the 1998 – 2005 period Aggregate cycle Reference cycle
Country Synchronicity Proximity Synchronicity Proximity
Austria 0.56 -1.55 0.56 -0.75 Belgium 0.38 -1.25 0.50 -0.81 Finland 0.25 -2.00 0.25 -1.28 France 0.75 -0.60 0.75 -0.32 Germany 0.88 -0.64 0.75 -0.62 Greece 0.13 -1.46 0.25 -0.82 Ireland 0.50 -2.79 0.63 -1.74 Italy 0.31 -1.02 0.19 -0.92 Netherlands 0.94 -0.72 0.81 -0.41 Portugal 0.63 -1.40 0.63 -1.04 Spain 0.81 -1.21 0.94 -0.67 Euro area 0.67 (0.56) -0.91 (-1.25) 0.57 (0.63) -0.85 (-0.81)
Appendix 4: Figures
Figure 1: Perfect concordance despite different trends and asynchronous deviation cycles G D P Lev el Time classical cycle 1 classical cycle 2
Figure 2: Imperfect correlation despite perfect coincidence of positive and negative output gaps G D P Level Time deviation cycle 1 deviation cycle 2
Figure 3: Perfect correlation despite differences in cycle volatility G D P Level Time deviation cycle 1 deviation cycle 2
Figure 4: Synchronicity and proximity towards the euro area’s reference cycle -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Austria -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Belgium -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Finland -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 France -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Germany -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Greece -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Italy -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Netherlands -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Portugal -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Spain -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005
Sy nchronicity Proximity Proximity : sy nchronicity component Proximity : amplitude similarity component Euro area av erage
-.03 -.02 -.01 .00 .01 .02 .03 1970 1975 1980 1985 1990 1995 2000 2005 Euro area ref erence cy cle
Figure 5: Synchronicity and proximity towards the USA’s business cycle -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Austria -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Belgium -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Finland -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 France -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Germany -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Greece -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Italy -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Netherlands -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Portugal -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005 Spain -3 -2 -1 0 1 1970 1975 1980 1985 1990 1995 2000 2005
Synchronicity Proximity Proximity: synchronicity component Proximity: amplitude similarity component Euro area average
-.06 -.04 -.02 .00 .02 .04 .06 1970 1975 1980 1985 1990 1995 2000 2005 USA cycle
Figure 6: Lead/lag-relationships with the US business cycle -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Austria -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Belgium -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Finland -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 France -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Germany -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Greece -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Italy -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Netherlands -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Portugal -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Spain
Figure 7: Lead/lag-relationships with the euro area’s reference cycle -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Austria -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Belgium -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Finland -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 France -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Germany -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Greece -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Italy -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Netherlands -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Portugal -8 -4 0 4 8 1970 1975 1980 1985 1990 1995 2000 2005 Spain
Figure 8: Persistence in the euro area’s reference cycle -0.2 0.0 0.2 0.4 0.6 0.8 1.0 1970 1975 1980 1985 1990 1995 2000 2005
