Joakim Westerlund
email: joakim.westerlund@nek.lu.se.

Silika Prohl
email: silika.prohl@unisg.ch.

Panel Cointegration Tests of the Sustainability Hypothesis in Rich OECD Countries

Keywords: Fiscal Sustainability, Panel Cointegration, Structural Change JEL Classification: C22, C23, H60 Fiscal sustainability, Panel Cointegration, Structural Change JEL Classification: C22, C23, H60 Fiscal Sustainability, Panel Cointegration, Structural Change

This study reexamines the sustainability hypothesis by testing whether government revenues and expenditures for eight rich OECD countries between 1977Q1 and 2005Q4 are cointegrated. For this purpose, a nonstationary panel data approach is adopted, which is general enough to permit for cross-country dependence as well as structural breaks representing major shifts in fiscal policy. In contrast to many earlier studies, the results reported in this study suggest that the sustainability hypothesis cannot be rejected.

Introduction

The increased budget deficit and public debt experienced by many OECD countries raises the issue of sustainability of the government finance in the long run, and its potential effects on the economy as a whole. Fiscal policy is constrained by the need to finance the government deficit, which over the longer term implies that the market value of public debt must be offset by the present value of all discounted future budget surpluses. In other words, the fiscal policy is sustainable if the discounted value of debt is zero in the limit. This is the essence of the sustainability hypothesis. If the hypothesis holds, then the ongoing fiscal policy can, at least in principle, be maintained indefinitely, whereas if it fails, then there is a need for discretionary policy actions. In particular, a failure The second explanation is that the empirical relationship between public revenues and expenditures that is being estimated need not be invariant to policy regime changes, which may lead to structural shifts in both revenues and expenditures, and hence in the relationship between them, see for example [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF] and Martin (2000).

However, while very reasonable and potentially appealing, when analyzed separately, these explanations have been found to be empirically inadequate and far from convincing. This paper therefore offers an alternative route. The idea is that to be able to provide any robust evidence on the cointegration between revenues and expenditures, one needs to consider not the low power and the presence of structural change separately but simultaneously. The intuition is simple. On the one hand, while increasing the length of the sample may be justified from a power point of view, it also increases the probability of a break. On the other hand, modifying existing tests so as to accommodate for structural change is typically very costly in terms of power. Therefore, it is the joint consideration of both these aspects that it is likely to be key when testing the sustainability hypothesis.

One way to accomplish this is to resort to panel data, and the recent econometrical advances within this field that make it possible to construct powerful cointegration tools while simultaneously entertaining the possibility of structural change. Applying this approach to a panel of eight rich OECD countries between 1977Q1 and 2005Q4, in contrast to much of the earlier evidence, we are unable to reject the strong sustainability hypothesis. We also provide evidence suggesting that all countries have been subject to several structural breaks representing major changes in fiscal policy.

The remainder of this paper is organized as follows. In Section 2, we give the brief description of the theoretical model of fiscal sustainability, and of the empirical panel data framework that will be used to test it. Section 3 then reports the empirical results, while Section 4 concludes.

Testing the sustainability hypothesis

In this section, we begin with a brief account of the economic theory underlying the sustainability hypothesis, and then we go on to discuss the empirical method that we will use to test it.

Theoretical underpinnings

The theoretical model of sustainability of the fiscal policy starts with the budget constraint of the government at time t, which is given in nominal terms by where b t is the stock of public debt, i t is the nominal interest rate payable on the public debt, r t is the government revenue including revenue from seignorage, and g t is the government expenditure excluding interest payments. Of course, these variables are relatively uninteresting as they do not take into account the size of the economy. We therefore follow the conventional practice of rewriting (1) in terms of GDP ratios as

g t + (1 + i t )b t-1 = r t + b t , ( 1
g t y t + (1 + i t ) (1 + σ t ) b t-1 y t-1 = r t y t + b t y t ,
where y t is the nominal GDP, while σ t represents the nominal GDP growth rate. Using capital letters to denote the ratios of the corresponding upper-case variables to nominal GDP, we get

C t + (1 + i * t )B t-1 = R t + B t , ( 2
)
where C t = G t + (i * t -i * )B t-1 and i * is the mean of i * t = (i t -σ t )/(1 + σ t ), the growth adjusted interest rate. If we assume that the budget constraint in (2) holds continuously at each t, we can use forward substitution to obtain

B t-1 = ∞ j=t+1 1 1 + i * j-t (R j-1 -C j-1 ) + lim j→∞ 1 1 + i * j-t B j-1 . (3)
Now, consider taking expectations conditional on all the information available at time t. Since B t-1 is known at t, the hypothesis that the government obeys its intertemporal budget constraint can be expressed as

lim j→∞ E t 1 1 + i * j-t B j-1 = 0. ( 4
)
This transversality condition, also known as the no Ponzi game rule, says that the public debt-GDP ratio should grow no faster on average than the mean rate of interest, meaning that the principal repayments and interests cannot be financed indefinitely by issuing new debt. It then follows that the current stock of public debt is offset by all current and expected discounted future primary surpluses.1

A time series cointegration test

The empirical literature has developed several tests to investigate whether the transversality condition (3) holds. The particular test opted for in this paper is that of [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], who suggests testing the sustainability hypothesis by examining whether government revenues and expenditures are cointegrated or not. The intuition behind this test lies in first taking differences, and then

G t-1 -R t-1 = ∞ j=t+1 1 1 + i * j-t (∆R j-1 -∆C j-1 ) + lim j→∞ 1 1 + i * j-t ∆B j-1 .
(5)

As before, the sustainability hypothesis holds if the expected value of the second term on the right-hand side is zero. One way to test whether this is in fact the case, given that G t and R t possess unit roots, involves first estimating and then testing for cointegration in the following regression

R t = α + β G t + e t , ( 6
)
where e t is a mean zero disturbance term. To see what this means for the test of the sustainability hypothesis, note that ∆B t = G t -R t , which together with (5) implies that

∆B t = (1 -β) G t -α -e t . ( 7
)
As shown by [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], although the sustainability hypothesis holds regardless of the integratedness of ∆B t , the speed with which this happens does not. If ∆B t is stationary, then the second term in (5) vanishes at a much faster rate than if ∆B t is non-stationary. In the terminology of [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], the sustainability of the public deficit is said to be strong if ∆B t is stationary, whereas it is said to be weak if ∆B t is non-stationary.2

In terms of the regression in (6), by looking at (7), we see that cointegration with β = 1 is enough for strong sustainability, because only then will ∆B t be stationary. But since G t is non-stationary, the sustainability is weak if either β = 1 and there is no cointegration or 0 < β < 1. It follows that 0 < β ≤ 1 is both necessary and sufficient for sustainability, while cointegration is only sufficient. The distinction between strong and weak sustainability is made because although 0 < β < 1 is enough for the sustainability hypothesis to hold, the government is now spending more than it earns, thus making the public debt difficult to market in the long run. Finally, if β ≤ 0 the deficit is no longer sustainable because this would make ∆B t grow faster than the growth rate of the economy, as approximated by the mean interest rate. 3The above discussion suggests that testing for cointegration is key in this kind of sustainability analysis, not only because of its role in determining strong sustainability but also because we cannot do inference regarding β unless revenues and expenditures are cointegrated. The conventional way in which earlier studies have been trying to test the sustainability hypothesis within this framework involves first estimating (6) by ordinary least squares (OLS) and then testing whether the residuals from that equation can be treated as stationary or not by using any conventional cointegration test. This test is then repeated for every country in the sample, each time using only the sample information for that particular country. Studies based on this approach are generally unable to reject the null hypothesis of no cointegration, which is seen to imply that the strong form of the sustainability hypothesis should be rejected. In this paper, we argue that this result should not be taken at face value as a failure to reject the null may well be due to low power.

In fact, it is well known that tests that take no cointegration as the null hypothesis can have very little power against nearly cointegrated alternatives, especially if there are structural breaks present. In a situation like this, it is therefore essential to device tests with increased power. A natural approach to do this would be to combine the sample information obtained from the time series dimension with that obtained from the cross-sectional. This not only increases the power by taking the total number of observations and their variation into account, but also increases the precision of the test by effectively reducing the noise coming from the individual time series regressions. Therefore, one way to augment the power of univariate tests would be to subject the residuals from (6) to a panel data cointegration test.

Unfortunately, most existing tests of this kind rely critically on assuming that the countries are independent of each other, which is unlikely to hold in the present application because of strong intra-economy linkages. Another limitation of most panel cointegration tests is that they ignore the possibility of structural change, which is likely to be the rule rather than the exception in this kind of fiscal data. Thus, a first crucial step in testing the sustainability hypothesis using panel data is to employ tests that allow for structural breaks, and that do not rely to such a large extent on the countries being independent.

A panel cointegration test with breaks

The previous section suggests that testing for cointegration in cross-country dependent data with structural change is key in inferring the sustainability hypothesis. In this section, we outline a test that fits this description, and that is general enough to allow for both cross-country dependence and an unknown number of breaks that may be located at different dates for different countries. In so doing, we will use the index i = 1, ..., N to denote countries, while t again denotes time.

Consider the following panel version of the regression in ( 6)

R it = α ij + β i G it + e it , j = 1, ..., M i + 1, (8)
where β i is a country specific slope that is assumed to be constant over time, while α ij is a country specific intercept that is subject to M i structural breaks. In other words, there are M i + 1 regimes for each country i with the j th regime running form T ij-1 to T ij time series observations. Sustainability requires (8) being a cointegrated relationship. If there is no structural change, then this hypothesis can be readily tested by using the existing tests for cointegration in panel data. If there are breaks, however, then this test procedure is no longer valid since the relationship in ( 8) is now non-linear. This poses a serious problem for inference since conventional tests cannot be used to discriminate between cointegration with structural change and the absence of cointegration. This issue was recently addressed by Westerlund (2006), who develops a panel Lagrange multiplier test for cointegration that allows for multiple structural breaks.

The null hypothesis is formulated as that all the countries in the panel are cointegrated, while the alternative is formulated as that there is at least some country for which cointegration does not hold. The test statistic for this particular hypothesis can be written as

Z(M ) = 1 N N i=1 Mi+1 j=1 Tij t=T ij-1 +1 S 2 it /(T ij -T ij-1 ) 2 σ 2 i ,
where

S it = t s=Tij-1+1
e is and e it is the regression residual obtained by using any efficient estimator of the cointegration vector such as the conventional fully modified OLS (FMOLS) estimator. Given that the countries are independent, and some technical conditions regarding the persistency of the individual time series, Westerlund (2006) shows that Z(M ) reaches the following sequential limit as T → ∞ and then N → ∞ under the null hypothesis

√ N (Z(M ) -E(Z(M ))) var(Z(M )) ⇒ N (0, 1),
where the mean and variance adjustment terms E(Z(M )) and var(Z(M )) are defined in Westerlund (2006). Thus, by standardizing Z(M ) by its mean and standard deviation, we obtain a new test statistic that has an asymptotic standard normal distribution under the null hypothesis. Under the alternative hypothesis, the statistic diverges to positive infinity suggesting that the right tail of the normal distribution should be used to reject the null.

For the estimation of the number of breaks and their locations, Westerlund (2006) suggests using the Bai and Perron (2003) procedure, which can be implemented in two steps. In the first, the breakpoints are estimated by minimizing the sum of squared residuals for all permissable values of M i . In the second, the estimated breakpoints are used together with the associated sum of squares to estimate the number of breaks using an information criterion. These steps are then repeated N times to obtain the estimated number of breaks and their locations for each country. The fact that both the number of breaks and their locations are treated as unknown here is a clear advantage in comparison to other approaches. For example, most studies that allow for structural change, see [START_REF] Wilcox | The sustainability of government deficits: implications of the present-value borrowing constraint[END_REF] and Hakkio and Rush (1991), often maintain that the breaks are known, which means that they are likely to suffer from pre-test bias. Other studies such as Haug (1995) and [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF] allow for unknown breakpoints but restrict the number of breaks to one, which is not likely to be the case.

To handle the impact of cross-country dependence Westerlund (2006) suggests using the bootstrap approach. The particular bootstrap scheme opted for in this paper uses the sieve approach of Psaradakis (2003), who proposes a bootstrapped stationarity test for pure time series. The advantage with this scheme is that it can be modified to preserve not only the cross-country correlations but also the serial correlations.

Empirical results

In this section, we first briefly describe the data, and then we present the empirical unit root and cointegration test results. Finally, we present some results of the estimated cointegration vectors.

Data

The sustainability hypothesis is tested by using quarterly data that covers eight rich OECD countries over the period 1977Q1 to 2005Q4. The countries included in the panel are Canada, Finland, France, Ireland, Japan, Sweden, the United Kingdom, and the United States. The data are taken from the OECD Economic Outlook Database Inventory, updated in February 2006, and include general government receipts and disbursement, and GDP at market prices. As in Section 2, the variables used in the analysis were converted into GDP ratios.

Graphical analysis

In order to get a feeling of the behavior of the fiscal debt situation in the OECD area, we begin with a graphical inspection of the data. To foreshadow the more formal treatment in the next two sections, Figure 1 plots the deficit-GDP ratios of the eight countries in the sample. The figure clearly illustrates that while individually quite dispersed, the series tend to revert back towards a common mean value, which seem to have become more positive in recent years. Thus, if sustainability is to be interpreted as the mean reversion, or stationarity, of the public deficit, it appears that there is some indication of sustainability among the countries.

It is also interesting to consider Figure 1 is increased deficit-GDP ratios in the first half of the sample, which originated with public reforms based on tight monetary and loose fiscal policy (OECD, 2002). These deficits made it impossible for governments to compensate the spiraling debt interest payments. Hence, in order to stabilize and restore public finances, and to enhance output growth in the long-run, new fiscal rules was put in place in the United States, and the European Union member countries introduced stricter budget deficit and fiscal debt criteria. These reforms have in recent years made it possible for governments to move away from a strategy of controlling unstable debt dynamics, and towards policy actions designed to strengthen the fiscal stance. This improvement in the overall debt-GDP stance in the latter half of the sample is clearly visible in the figure.

Stationarity tests

We begin by considering the integratedness of the government revenue and expenditure series using the panel stationarity test of Carrion-i-Silvestre et al. 2005), which is very similar to the Westerlund (2006) cointegration test in the sense that it permits for both cross-country dependence and structural breaks. This is therefore an appropriate test for our purposes. Another similarity with the cointegration test is that the breaks are estimated using the Bai and Perron (2003) procedure and that the bootstrap is of sieve type. In applying the Carrion-i-Silvestre et al. ( 2005) test, we follow the recommendation of Newey and West (1994) and use the Bartlett kernel, where the bandwidth parameter is permitted to grow with T at the rate T 1/3 . In estimating the number of breaks, we allow for a maximum of five shifts for each country, which seem sufficient to capture most of the breaks in the data. The exact number of breaks for each country is estimated using the Schwartz information criterion. Also, to ensure that the break date estimator work properly, we set the minimum length of each regime equal to 0.1T . The sieve bootstrap is implemented using a lag length of five and we make 1,000 replications.

As for the deterministic specification, since all variables are expressed in GDP ratios, no time trends are required. Two models are considered. The first assumes a fixed mean while the second allows for up to five breaks in the mean of each series. Among these models, since most of the literature indicates the presence of breaks, the latter stands out as the most natural one.

Table 1 shows the results of panel stationary test for each variable. For each model, the first row represents the test value, the second row contains the asymptotic p-values, and the third row contains the bootstrapped p-values. The results from the asymptotic p-values suggest that the null hypothesis of stationary can be safely rejected. However, these values assume that the countries are independent, which is unlikely to hold. In order to account for this dependence, we use the bootstrapped p-values instead. Except for revenues in the structural break model, the conclusions are not altered by taking the crosscountry correlations into account. Thus, since the overall evidence in favor of a rejection is quite overwhelming, we choose to proceed as if the variables are in fact non-stationary.

Cointegration tests

The second step in our analysis is to test whether the variables are cointegrated using the Z(M ) test. The results are presented in the rightmost column of Table 1. It is seen that the p-values for the model with a fixed constant provide very little support of cointegration. However, these results do not take into account the possibility of structural breaks, and are therefore prone to erroneous conclusions. Indeed, if we allow for structural shifts and cross-country correlation, the null hypothesis of cointegration cannot be rejected at the 5 percent level. We therefore conclude that the variables appear to be cointegrated around a broken intercept.

Table 2 reports the estimated breakpoints obtained from the Bai and Perron (2003) procedure. It is seen that there are at least three breaks for each coun- try, which is indicative of structural instability. 4 This evidence seems consistent with the gradual shift towards increased business cycles synchronization among the OECD countries, which has substantially affected the fiscal position of many governments, see Fatas and Mihov (2003). The first break period in the 1980's reflects the effect of the Great Depression, during which the synchronized recession coincided with an increase in real interest rate. This caused a substantial deterioration of the fiscal stance of of governments of rich OECD countries, as the deficits created by the spiralling interest payments could not be offset, see OECD (2002).

Later, following the Maastricht Treaty and the Stability and Growth Pact in the early 1990's, the fiscal stance of many OECD countries were driven primarily by an increased coordination of both fiscal and monetary policy within the European Monetary Union, see Darvas et al. (2005). This period is also clearly visible in the table, as indicated by the concentration of breaks in the early 1990's, and seems consistent with the results reported in many earlier studies, see for example Afonso (2005). The many breaks in the late 1990's are most likely due to the formation of the European Monetary Union in January 1999.

To further illustrate the importance of accounting for structural change, Figures 2 and 3 plot the revenues-GDP ratio, the dependent variable, together with the fitted trend functions for the models with and without breaks. In the figures, the solid line represents revenues measured as a fraction of GDP, the dashed line represents the model with breaks and the dotted line represents the model without any breaks. It can easily be seen that nearly all revenue series exhibit several level breaks, most of which seem to reflect the effect of economic fluctuations, and changes in the monetary and fiscal policy objectives in the individual countries. Interestingly, it is seen that the revenues-GDP ratio of most countries have been rising during the first half of the sample and falling during the second half, which reflects a more flexible response of the recent fiscal policy of most OECD governments to the economic downturn.

More importantly, we see that the trend lines for the model with breaks seem to provide a very good fit to the revenues for all eight countries. By contrast, the trend lines for the model without breaks are generally incapable of accounting for the all variation in revenues, thus leading to a poor fit. This effect is particularly striking for the United States.

Cointegration estimation

Since the variables appear to be cointegrated, it is possible to estimate and test whether the cointegrating slope is indeed equal to one as required by sustainability hypothesis.

It is well known that the OLS estimator is consistent under fairly general conditions when applied to the cointegrated regression in (6). Unfortunately, if the regressor is endogenous, then this estimator suffers from nuisance parameter dependencies even asymptotically, which makes it a poor candidate for inference. To account for this, in addition to using OLS, we employ both FMOLS and dynamic OLS (DOLS) panel estimation techniques, see Kao and Chiang (2000). All three estimators are based on pooling along the cross-sectional dimension, and are appropriate for testing the null hypothesis that β i = 1 for all i against the alternative hypothesis that β i is equal to some common slope value, which is different from unity.

Moreover, as when testing for stationarity and cointegration in panel data, the presence of cross-country dependence makes inference based on the asymptotic normal distribution inappropriate, in which case bootstrap inference might be better. The particular bootstrap opted for this section is taken from Chang et al. (2006), who propose a sieve resampling scheme that preserves the serial correlation properties of the errors, and that can be generalized along the lines of Westerlund (2006) to also accommodate cross-country dependence. As an indication of the severity of this problem, we applied the Pesaran (2004) test of cross-section correlation to the OLS residuals of the estimated cointegrated regression. 5 The computed test value was 4.98, which, when compared to the right tail of the asymptotic normal distribution, lead to a clear rejection of the no correlation null at all conventional significance levels. Thus, cross-country correlation is indeed a problem that needs to be addressed.

The results from the OLS, FMOLS and DOLS estimators are reported in Table 3 together with the double-sided p-values for the null hypothesis of a unit slope. The first thing to notice is that the estimated slopes lie very close to their hypothesized values of one. Indeed, the range of the estimated slopes is 0.909 to 0.934. The closeness of these estimates to their expected value based on the sustainability hypothesis is supported by the p-values.

Indeed, by looking at the p-values based on the asymptotic normal distribution, we see that the null hypothesis of a unit slope cannot be rejected even at the most generous 10 percent level. The results from the bootstrapped p-values, which allow for cross-country dependence, are even more supportive of the unit slope null, and are all well above 0.6. Thus, based on this evidence we cannot reject the null hypothesis of a unit slope in the panel. Thus, in contrast to much of the earlier evidence regarding the sustainability of fiscal policy, we are unable to reject the sustainability hypothesis for the panel as a whole.

Concluding remarks

Earlier empirical research based on testing for stationarity of public debt and budget deficit has tended to reject the hypothesis of fiscal sustainability. As a response to this, recent work within this field has turned towards more flexible testing approaches based on cointegration. The idea is that if fiscal policy is sustainable, then government revenues and expenditures should be cointegrated with a unit slope on expenditures. Unfortunately, the results of the earlier studies have not been very convincing.

In this paper, we provide some insights suggesting that the weak empirical support of the sustainability hypothesis may be due to inadequate econometric methods. In particular, we argue that a failure of accounting for structural breaks and the poor precision of commonly applied time series tests may well result in a rejection of the sustainability hypothesis. To circumvent these problems, we resort to some recent advances in the area of non-stationary panel data. These methods are more powerful than conventional time series methods, and are general enough to allow for cross-country dependence and an unknown number of structural breaks in the cointegrating relationship.

Based on data covering eight rich OECD countries over the period from 1977Q1 to 2005Q4, we show that revenues and expenditures are non-stationary and cointegrated. We also provide evidence suggesting that the null hypothesis of a common unit slope on expenditures cannot be rejected, suggesting that the sustainability hypothesis cannot be rejected. The results on the estimated structural breaks are suggestive of strong structural instability, and are compatible with the findings of many earlier studies such as [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], Martin (2000) and Afonso (2005). Some of the estimated breaks are related to the increased business cycle synchronization among the OECD countries, while others are related to the policy interventions resulting from the increased coordination of the monetary and fiscal policy within the European community.

Thus, although there is a growing concern about increased budget deficits within the OECD area, our results indicate that after taking into account structural change and economic growth, the budget of the eight rich countries considered in this study has in fact been balanced, at least intertemporally over the sample considered. In other words, for these countries the sequence of primary surpluses has been sufficient to cover the marked value of public debt. Thus, from an historical point of view, there is no reason to be concerned about the public debt situation.

This finding is in agreement with the results reported by [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF] for the United States, and is particularly interesting in view of the recent discus- sion regarding the effect of the projected increase in future public liabilities to age-related public spending and health care on public finances during the demographic transition of OECD countries to older societies. Our results imply that if governments are able to raise revenues at the same rate as the expected increase in spending, so that revenues and expenditures are one-to-one in the long run, then one need not worry about the future public debt situation. long run, and its potential effects on the economy as a whole. Fiscal policy is constrained by the need to finance the government deficit, which over the longer term implies that the market value of public debt must be offset by the present value of all discounted future budget surpluses. In other words, the fiscal policy is sustainable if the discounted value of debt is zero in the limit. This is the essence of the sustainability hypothesis. If the hypothesis holds, then the ongoing fiscal policy can, at least in principle, be maintained indefinitely, whereas if it fails, then there is a need for discretionary policy actions. In particular, a failure implies that the government will inevitably run into problems in managing its debt, thus requiring compensation in terms of higher interest rates leading to a slowdown in the economic growth.

Thus, from a policy point of view, the issue of whether the sustainability hypothesis holds or not is indeed an important one. Because of this, and because of the growing concern regarding the debt situation in many OECD countries, sustainability analysis has received much interest in recent empirical research. Most of the earlier work in this field focused on the stationarity of public deficit and debt as a way to empirically test the sustainability hypothesis. Prominent examples include, among others, [START_REF] Wilcox | The sustainability of government deficits: implications of the present-value borrowing constraint[END_REF], MacDonald (1992), Hakkio and Rush (1991) and [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF] for the United States, [START_REF] Smith | Persistent deficits and the market value of government debt[END_REF] for Canada, Baglioni and Cherubini (1993) for Italy, Olekalns (2000) for Australia, and perhaps most recently Kirchgaessner and Prohl (2006) for Switzerland. The overall picture being that the sustainability hypothesis does not hold.

As a response to this, more recent work has moved away from examining the stationarity of debt, and towards more flexible testing strategies based on cointegration. In particular, as shown by [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], given that public revenues and expenditures are non-stationary, sustainability requires these variables to be cointegrated with a unit slope on expenditures. In the terminology of [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF] lies between zero and one, regardless of whether revenues and expenditures are cointegrated or not. In this case, although the deficit is sustainable, the government is expected to have difficulty in marketing its debt, thus requiring fiscal reforms. Finally, if the slope on expenditures is equal to zero, then the deficit is not sustainable, in which case the sustainability hypothesis is refuted. Payne (1997) applies this approach to the G7 countries between 1950 and 1990, and rejects the sustainability hypothesis. Similarly, using the same approach to a sample of five EU countries between 1961 and 1995, Papadopoulos and Sidiropoulos (1999) only find evidence of cointegration for Greece and Spain. However, the cointegrating slope on government expenditures is estimated significantly lower than one, suggesting that only the weak form of the sustainability hypothesis is supported. Apparently, despite the strong theoretical appeal of the sustainability hypothesis, most empirical studies tend to reject it.

Although there are many explanations for why the sustainability hypothesis does not hold, this paper focuses on two that might potentially go a long way towards explaining the weak empirical evidence on the cointegration between revenues and expenditures. The first explanation is that conventional time series cointegration tests may have low power against persistent alternatives because of the short sample periods usually employed, see Afonso (2005).

The second explanation is that the empirical relationship between public revenues and expenditures that is being estimated need not be invariant to policy regime changes, which may lead to structural shifts in both revenues and expenditures, and hence in the relationship between them, see for example [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF] and Martin (2000).

However, while very reasonable and potentially appealing, when analyzed separately, these explanations have been found to be empirically inadequate and far from convincing. This paper therefore offers an alternative route. The idea is that, to be able to provide any robust evidence on the cointegration between revenues and expenditures, one needs to consider not the low power intuition is simple. First, while increasing the length of the sample may be justified from a power point of view, it also increases the probability of a break. On the other hand, modifying existing tests so as to accommodate for structural change is typically very costly in terms of power. Therefore, it is the joint consideration of both these aspects that it is likely to be key approach when testing the sustainability hypothesis.

One way to accomplish this is to resort to panel data, and the recent econometrical advances within this field that make it possible to construct powerful cointegration methods while simultaneously entertaining the possibility of structural change. Applying this approach to panel of eight rich OECD countries between 1977Q1 and 2005Q4, in contrast to much of the earlier evidence, we are unable to reject the strong sustainability hypothesis. We also provide evidence suggesting that all countries have been subject to several structural breaks representing major changes in fiscal policy.

The remainder of this paper is organized as follows. In Section 2, we give the brief description of the theoretical model of fiscal sustainability and the empirical panel data framework that will be used to test it. Section 3 then reports the empirical results, while Section 4 concludes.

Testing the sustainability hypothesis

In this section, we begin with a brief account of the economic theory underlying the sustainability hypothesis, and then we go on to discuss the empirical method that we will use to test it.

Theoretical underpinnings

The theoretical model of sustainability of the fiscal policy starts with the budget constraint of the government at time t, which is given in nominal terms by course, these variables are relatively uninteresting as they do not take into account the size of the economy. We therefore follow the conventional practice of rewriting (1) in terms of GDP ratios as

g t + (1 + i t )b t-1 = r t + b t , ( 1
g t y t + (1 + i t ) (1 + σ t ) b t-1 y t-1 = r t y t + b t y t ,
where y t is the nominal GDP, while σ t represents the nominal GDP growth rate. Using capital letters to denote the ratios of the corresponding upper-case variables to nominal GDP, we get

C t + (1 + i * t )B t-1 = R t + B t , ( 2
)
where

C t = G t + (i * t -i * )B t-1 and i * is the mean of i * t = (i t -σ t )/(1 + σ t )
, the growth adjusted interest rate. If we assume that the budget constraint in (2) holds continuously at each t, we can use forward substitution to obtain

B t-1 = ∞ j=t+1 1 1 + i * j-t (R j-1 -C j-1 ) + lim j→∞ 1 1 + i * j-t B j-1 . (3)
Now, consider taking expectations conditional on all the information available at time t. Since B t-1 is known at t, the hypothesis that the government obeys its intertemporal budget constraint can be expressed as

lim j→∞ E t 1 1 + i * j-t B j-1 = 0. ( 4
)
This transversality condition, also known as the no Ponzi game rule, says that the public debt-GDP ratio should grow no faster on average than the mean rate of interest, meaning that the principal repayments and interests cannot be financed indefinitely by issuing new debt. It then follows that the current stock of public debt is offset by all current and expected discounted future primary surpluses.

1 1 Note that 1/(1 + i * ) = (i + σ)/(1 + i)
, where i and σ are the mean values of it and σt, respectively. Thus, if i < σ, then the transversality condition is satisfied automatically.

A time series cointegration test

The empirical literature has developed several tests to investigate whether the transversality condition (3) holds. The particular test opted for in this paper is that of [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], who suggests testing the sustainability hypothesis by examining whether government revenues and expenditures are cointegrated or not. The intuition behind this test lies in first taking differences, and then

rewriting (2) in terms of G t = G t + i * t B t-1
, the total expenditure including interest payments, as

G t-1 -R t-1 = ∞ j=t+1 1 1 + i * j-t (∆R j-1 -∆C j-1 ) + lim j→∞ 1 1 + i * j-t ∆B j-1 .
(5)

As before, the sustainability hypothesis holds if the expected value of the second term on the right-hand side is zero. One way to test whether this is in fact the case, given that G t and R t possess unit roots, involves first estimating and then testing for cointegration in the following regression

R t = α + β G t + e t , ( 6
)
where e t is a mean zero disturbance term. To see what this means for the test of the sustainability hypothesis, note that ∆B t = G t -R t , which together with (5) implies that

∆B t = (1 -β) G t -α -e t . ( 7
)
As shown by [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], although the sustainability hypothesis holds regardless of the integratedness of ∆B t , the speed with which this happens does not. If ∆B t is stationary, then the second term in (5) vanishes at a much faster rate than if ∆B t is non-stationary. In the terminology of [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], the sustainability of the public deficit is said to be strong if ∆B t is stationary, whereas it is said to be weak if ∆B t is non-stationary.

In terms of the regression in (6), by looking at (7), we see that cointegration stationary. But since G t is non-stationary, the sustainability is weak if either β = 1 and there is no cointegration or 0 < β < 1. It follows that 0 < β ≤ 1 is both necessary and sufficient for sustainability, while cointegration is only sufficient. The distinction between strong and weak sustainability is made because although 0 < β < 1 is enough for the sustainability hypothesis to hold, the government is now spending more than it earns, thus making the public debt difficult to market in the long run. Finally, if β ≤ 0, then the deficit is no longer sustainable, because this would make ∆B t grow faster than the growth rate of the economy, as approximated by the mean interest rate.2

The above discussion suggests that testing for cointegration is key in this kind of sustainability analysis, not only because of its role in determining strong sustainability but also because we cannot do inference regarding β unless revenues and expenditures are cointegrated.

The conventional way in which earlier studies have been trying to test the sustainability hypothesis within this framework involves first estimating (6) by ordinary least squares (OLS) and then testing whether the residuals from that equation can be treated as stationary or not by using any conventional cointegration test. This test is then repeated for every country in the sample, each time using only the sample information for that particular country. Studies based on this approach are generally unable to reject the null hypothesis of no cointegration, which is seen to imply that the strong form of the sustainability hypothesis should be rejected. In this paper, we argue that this result should not be taken at face value as a failure to reject the null may well be due to low power.

In fact, it is well known that tests that take no cointegration as the null hypothesis can have very little power against nearly cointegrated alternatives, especially if there are structural breaks present. In a situation like this, it is therefore essential to device tests with increased power. A natural approach to do this would be to combine the sample information obtained from the time series dimension with that obtained from the cross-sectional. This not only increases the power by taking the total number of observations and their variation into account, but also increases the precision of the test by effectively reducing the noise coming from the individual time series regressions. Therefore, one way to augment the power of univariate tests would be to subject the residuals from ( 6) to a panel data cointegration test.

Unfortunately, most existing tests of this kind rely critically on assuming that the countries are independent of each other, which is unlikely to hold in the present application because of strong intra-economy linkages. Another limitation of most panel cointegration tests is that they ignore the possibility of structural change, which is likely to be the rule rather than the exception in this kind of fiscal data. Thus, a first crucial step in testing the sustainability hypothesis using panel data is to employ tests that allow for structural breaks, and that do not rely to such a large extent on the countries being independent.

A panel cointegration test with breaks

The previous section suggests that testing for cointegration in cross-country dependent data with structural change is key in inferring the sustainability hypothesis. In this section, we outline a test that fits this description, and that is general enough to allow for both cross-country dependence and an unknown number of breaks that may be located at different dates for different countries. In so doing, we will use the index i = 1, ..., N to denote countries, while t again denotes time.

Consider the following panel version of the regression in ( 6)

R it = α ij + β i G it + e it , j = 1, ..., M i + 1, (8)
where β i is a country specific slope that is assumed to be constant over time, while α ij is a country specific intercept that is subject to M i structural breaks.

In other words, there are M i + 1 regimes for each country i with the j th regime running form T ij-1 to T ij time series observations. 8 The null hypothesis is formulated as that all the countries in the panel are cointegrated, while the alternative is formulated as that there is at least some country for which cointegration does not hold. The test statistic for this particular hypothesis can be written as

Z(M ) = 1 N N i=1 M i +1 j=1 T ij t=T ij-1 +1 S 2 it /(T ij -T ij-1 ) 2 σ 2 i ,
where

S it = t s=T ij-1 +1
e is and e it is the regression residual obtained by using any efficient estimator of the cointegration vector such as the conventional fully modified OLS (FMOLS) estimator. Given that the countries are independent, and some technical conditions regarding the persistency of the individual time series, [START_REF] Westerlund | Testing for panel cointegration with multiple structural breaks[END_REF] shows that Z(M ) reaches the following sequential limit as T → ∞ and then N → ∞ under the null hypothesis

√ N (Z(M ) -E(Z(M ))) var(Z(M )) ⇒ N (0, 1),
where the mean and variance adjustment terms E(Z(M )) and var(Z(M )) are defined in [START_REF] Westerlund | Testing for panel cointegration with multiple structural breaks[END_REF]. Thus, by standardizing Z(M ) by its mean and standard deviation, we obtain a new test statistic that has an asymptotic standard normal distribution under the null hypothesis. Under the alternative hypothesis, the statistic diverges to positive infinity suggesting that the right tail of the normal distribution should be used to reject the null.

For the estimation of the number of breaks and their locations, Westerlund (2005) suggest using the Bai and Perron (2003) be implemented in two steps. In the first, the breakpoints are estimated by minimizing the sum of squared residuals for all permissable values of M i . In the second, the estimated breakpoints are used together with the associated sum of squares to estimate the number of breaks using an information criterion. These steps are then repeated N times to obtain the estimated number of breaks and their locations for each country.

The fact that both, the number of breaks and their locations are treated as unknown here is a clear advantage in comparison to other approaches. For example, most studies that allow for structural change, for example [START_REF] Wilcox | The sustainability of government deficits: implications of the present-value borrowing constraint[END_REF] and Hakkio and Rush (1991), often maintain that the breaks are known, which means that they are likely to suffer from pre-test bias. Other studies such as Haug (1995) and [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF] allow for unknown breakpoints but restrict the number of breaks to one, which is not likely to be the case.

To handle the impact of cross-country dependence [START_REF] Westerlund | Testing for panel cointegration with multiple structural breaks[END_REF] suggests using the bootstrap approach. The particular bootstrap scheme opted for in this paper uses the sieve approach of Psaradakis (2003), who proposes a bootstrapped stationarity test for pure time series. The advantage with this scheme is that it can be modified to preserve not only the cross-country correlations but also the serial correlations.

Empirical results

In this section, we first briefly describe the data, and then we present the empirical unit root and cointegration test results. Finally, we present some results on the estimated cointegration vectors.

Data

We test the sustainability hypothesis by using the quarterly data that covers

Stationarity tests

We begin by considering the integratedness of the government revenue and expenditure series using the panel stationarity test of Carrion-i-Silvestre et al.

(2005), which is very similar to the [START_REF] Westerlund | Testing for panel cointegration with multiple structural breaks[END_REF] cointegration test in the sense that it permits for both cross-country dependence and structural breaks.

This is therefore an appropriate test for our purposes. Another similarity with the cointegration test is that the breaks are estimated using the Bai and Perron (2003) procedure and that the bootstrap of the sieve type.

In applying the Carrion-i-Silvestre et al. ( 2005) test, we follow the recommendation of Newey and West (1994) and use the Bartlett kernel, where the bandwidth parameter is permitted to grow with T at the rate T 1/3 . In estimating the number of breaks, we allow for a maximum of five shifts for each country, which seem sufficient to capture most of the breaks in the data. The exact number of breaks for each country is estimated using the Schwartz information criterion. Also, to ensure that the break date estimator work properly, we set the minimum length of each regime equal to 0.1T . The sieve bootstrap is implemented using a lag length of five and we make 1,000 replications.

As for the deterministic specification, since all variables are expressed in GDP ratios, no time trends are required. Two models are considered. The first assumes a fixed mean while the second allows for up to five breaks in the mean of each series. Among these models, since most of the literature indicates the presence of breaks, the latter stands out as the most natural one. The results from the asymptotic p-values suggest that the null hypothesis of stationary can be safely rejected. However, these values assume that the countries are independent, which is unlikely to hold. In order to account for this dependence, we use the bootstrapped p-values instead. Except for revenues in the structural break model, the conclusions are not altered by taking the cross-country correlations into account. Thus, since the overall evidence in favor of a rejection is quite overwhelming, we choose to proceed as if the variables are in fact non-stationary.

Cointegration tests

The second step in our analysis is to test whether the variables are cointegrated using the Z(M ) test. The results are presented in the rightmost column of Table 1. It is seen that the p-values for the model with a fixed constant provide very little support of cointegration. However, these results do not take into account the possibility of structural breaks, and are therefore prone to erroneous conclusions. Indeed, if we allow for structural shifts and crosscountry correlation, the null hypothesis of cointegration cannot be rejected at the 5 percent level. We therefore conclude that the variables appear to be cointegrated around a broken intercept. in the early 1990's, the fiscal stance of many OECD countries were driven primarily by an increased coordination of both fiscal and monetary policy within the European Monetary Union, see Darvas et al. (2005). This period is also clearly visible in the table, as indicated by the concentration of breaks in the early 1990's, and seems consistent with the results reported in many earlier studies, see for example Afonso (2005). The many breaks in the late 1990's are most likely due to the formation of the European Monetary Union in January 1999.

Figure 1: Revenues-GDP ratio with fitted trend functions.

To further illustrate the importance of accounting for structural change,

Cointegration estimation

Since the variables appear to be cointegrated, it is possible to estimate and test whether the cointegrating slope is indeed equal to one as required by sustainability hypothesis.

It is well known that the OLS estimator is consistent under fairly general conditions when applied to the cointegrated regression in (7). Unfortunately, if the regressor is endogenous, then this estimator suffers from nuisance parameter dependencies even asymptotically, which makes it a poor candidate for inference. To account for this, in addition to using OLS, we employ both FMOLS and dynamic OLS (DOLS) panel estimation techniques, see Kao and Chiang (2000). All three estimators are based on pooling along the crosssectional dimension, and are appropriate for testing the null hypothesis that β i = 1 for all i against the alternative hypothesis that β i is equal to some common slope value, which is different from unity.

Moreover, as when testing for stationarity and cointegration in panel data, the presence of cross-country dependence makes inference based on the asymptotic normal distribution inappropriate, in which case bootstrap inference might be better. The particular bootstrap opted for this section is taken from Chang et al. (2006), who propose a sieve resampling scheme that preserves the serial correlation properties of the errors, and that can be generalized along the lines of Westerlund (2006) to also accommodate cross-country dependence. As an indication of the severity of this problem, we applied the Pesaran (2004) test of cross-section correlation to the OLS residuals of the estimated cointegrated regression. The computed test value was 4.98, which, when compared to the right tail of the asymptotic normal distribution, lead to a clear rejection of the no correlation null at all conventional significance levels. Thus, cross-country correlation is indeed a problem that needs to be addressed.

The results from the OLS, FMOLS and DOLS estimators are reported in to their hypothesized values of one. Indeed, the range of the estimated slopes is 0.909 to 0.934. The closeness of these estimates to their expected value based on the sustainability hypothesis is supported by the p-values.

Indeed, by looking at the p-values based on the asymptotic normal distribution, we see that the null hypothesis of a unit slope cannot be rejected even at the most generous 10 percent level. The results from the bootstrapped p-values, which allow for cross-country dependence, are even more supportive of the unit slope null, and are all well above 0.6. Thus, based on this evidence we cannot reject the null hypothesis of a unit slope in the panel. Thus, in contrast to much of the earlier evidence regarding the sustainability of fiscal policy, we are unable to reject the sustainability hypothesis for the panel as a whole.

Concluding remarks

Earlier empirical research based on testing for stationarity of public debt and budget deficit has tended to reject the hypothesis of fiscal sustainability. As a response to this, recent work within this field has turned towards more flexible testing approaches based on cointegration. The idea is that if fiscal policy is sustainable, then government revenues and expenditures should be cointegrated with a unit slope on expenditures. Unfortunately, the results of the earlier studies have not been very convincing.

In this paper, we provide some insights suggesting that the weak empirical support of the sustainability hypothesis may be due to inadequate econometric methods. In particular, we argue that a failure of accounting for structural Based on data covering eight rich OECD countries over the period from 1977Q1 to 2005Q4, we show that revenues and expenditures are non-stationary and cointegrated. We also provide evidence suggesting that the null hypothesis of a common unit slope on expenditures cannot be rejected, suggesting that the sustainability hypothesis cannot be rejected. The results on the estimated structural breaks are suggestive of strong structural instability, and are compatible with the findings of many earlier studies such as [START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF], Martin (2000) and Afonso (2005). Some of the estimated breaks are related to the increased business cycle synchronization among the OECD countries, and the policy interventions resulting from the increased coordination of the monetary and fiscal policy within the European community. 17 1979Q4 1983Q4 1987Q1 1993Q1 1998Q2 Sweden 5 1983Q1 1986Q4 1992Q1 1996Q2 2001Q2 United Kingdom 4 1980Q3 1986Q4 1992Q2 1998Q1 -United States 5 1980Q3 1987Q2 1994Q2 1997Q3 2002Q1 Notes: The breaks are estimated using the Bai and Perron (2003) procedure with a maximum number of five breaks for each state. The minimum length of each break regime is set to 0.1T . The p-values for the between and within estimates are for the null of a unit slope against the alternative that the slope is different from unity.

a The p-value is based on the asymptotic normal distribution.

b The p-value is based on the bootstrapped distribution. The number of lags in the sieve approximation is five and we make 1,000 bootstrap replications.

  Figure 1: Deficit-GDP ratios.

Figure 2 :

 2 Figure 2: Revenues-GDP ratio with fitted trend functions.

Figure 3 :

 3 Figure 3: Revenues-GDP ratio with fitted trend functions.

Page

  with β = 1 is enough for strong sustainability, because only then will ∆B t be 6

  Sustainability requires (8) being a cointegrated relationship. If there is no structural change, then this hypothesis can be readily tested by using the existing tests for cointegration in panel data. If there are breaks, however, then this test procedure is no longer valid since the relationship in (8) is now non-linear. This poses a serious problem for inference since conventional tests cannot be used to discriminate between cointegration with structural change and the absence of cointegration. This issue was recently addressed by[START_REF] Westerlund | Testing for panel cointegration with multiple structural breaks[END_REF], who develops a panel Lagrange multiplier test for cointegration that allows for multiple structural breaks.

Page

  eight rich OECD countries over the period 1977Q1 to 2005Q4. The countries included in the panel are Canada, Finland, France, Ireland, Japan, Sweden, the United Kingdom, and the United States. The data are taken from the 10 Database Inventory, updated in February 2006, and include general government receipts and disbursement, and GDP at market prices. As in Section 2, the variables used in the analysis are defined in terms of GDP ratios.

Figures 1 and 2 Figure 2 :

 22 Figures 1 and 2 plot revenues-GDP ratio, the dependent variable, together with the fitted trend functions for the models with and without breaks. In the figures, the solid line represents revenues measured as GDP ratio, the dashed line represents the model with breaks and the dotted line represents the

  breaks and the poor precision of commonly applied time series tests may well result in a rejection of the sustainability hypothesis. To circumvent these problems, we resort to some recent advances in the area of non-stationary panel data. These methods are more powerful than conventional time series methods, and are general enough to allow for cross-country dependence and an unknown number of structural breaks in the cointegrating relationship.

Table 1 :

 1 Panel stationarity and cointegration tests. All test results allow for up to five structural breaks for each state. To handle the serial correlation, the Bartlett kernel is used with a bandwidth parameter of T 1/3 .

			Stationarity tests
	Specification	Test	R it	G it	Z(M )
	Fixed constant	Value	20.147	18.684	16.661
		p-value a	0.000	0.000	0.000
		p-value b	0.000	0.002	0.028
	Constant with breaks Value	2.192	5.114	1.416
		p-value a	0.014	0.000	0.078
		p-value b	0.242	0.008	0.678
	Notes:

a

The p-value is based on the asymptotic normal distribution. b The p-value is based on the bootstrapped distribution. The number of lags in the sieve approximation is five and we make 1,000 bootstrap replications.

Table 2 :

 2 Estimated breaks. The breaks are estimated using theBai and Perron (2003) procedure with a maximum number of five breaks for each state. The minimum length of each break regime is set to 0.1T .

			Breakpoint
	Country	No.	1	2	3	4	5
	Canada	5	1981Q1 1987Q2 1990Q2 1996Q2 2001Q3
	Finland	4	1984Q3 1988Q2 1999Q4 2002Q4	-
	France	5	1979Q4 1992Q1 1996Q2 1999Q1 2002Q1
	Ireland	3	1983Q1 1987Q4 2001Q1	-	-
	Japan	5	1979Q4 1983Q4 1987Q1 1993Q1 1998Q2
	Sweden	5	1983Q1 1986Q4 1992Q1 1996Q2 2001Q2
	United Kingdom	4	1980Q3 1986Q4 1992Q2 1998Q1	-
	United States	5	1980Q3 1987Q2 1994Q2 1997Q3 2002Q1
	Notes:

16 Page 16 of 42 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 3 :

 3 Panel cointegration slope estimates.The increased budget deficit and public debt experienced by many OECD countries raises the issue of sustainability of the government finance in the * Westerlund gratefully acknowledges financial support from the Jan Wallander and Tom

	Estimator	Value p-value a p-value b
	OLS	0.925	0.594	0.708
	DOLS	0.934	0.689	0.718
	FMOLS	0.909	0.444	0.602

Notes: All results allow for up to five structural breaks for each state. The p-values for the between and within estimates are for the null of a unit slope against the alternative that the slope is different from unity. a The p-value is based on the asymptotic normal distribution. b The p-value is based on the bootstrapped distribution. The number of lags in the sieve approximation is five and we make 1,000 bootstrap replications. 17 Page 17 of 42 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK 1 Page 21 of 42 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

) 4 Page 24 of 42 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

  where b t is the stock of public debt, i t is the nominal interest rate payable on the public debt, r t is the government revenue including revenue from seignorage, and g t is the government expenditure excluding interest payments. Of

	Submitted Manuscript
	F o r
	P
	e
	e r
	R e v
	i e
	w

Table 1

 1

	shows the results of panel stationary test for each variable. For
	each model, the first row represents the test value, the second row contains the
	asymptotic p-values, and the third row contains the bootstrapped p-values.
	11

Table 2

 2

	reports the estimated breakpoints obtained from the Bai and Per-
	ron (2003) procedure. It is seen that there are at least three breaks for each
	country, which is indicative of structural instability. This evidence seems con-
	sistent with the gradual shift towards increased business cycles synchroniza-
	tion among the OECD countries, which has substantially affected the fiscal
	position of many governments, see Fatas and Mihov (2003). The first break
	period in the 1980's reflects the effect of the Great Depression, during which
	the synchronized recession coincided with an increase in real interest rate. This
	caused a substantial deterioration of the fiscal stance of of governments of rich
	OECD countries, as the deficits created by the spiralling interest payments
	could not be offset, see OECD (2002).
	Later, following the Maastricht Treaty and the Stability and Growth Pact
	12

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

Table 3

 3 together with the double-sided p-values for the null hypothesis of a unit slope. The first thing to notice is that the estimated slopes lie very close

	15

Table 2 :

 2 Estimated breaks.

			Breakpoint
	Country	No.	1	2	3	4	5
	Canada	5	1981Q1 1987Q2 1990Q2 1996Q2 2001Q3
	Finland	4	1984Q3 1988Q2 1999Q4 2002Q4	-
	France	5	1979Q4 1992Q1 1996Q2 1999Q1 2002Q1
	Ireland	3	1983Q1 1987Q4 2001Q1	-	-
	Japan	5

Table 3 :

 3 Panel cointegration slope estimates. All results allow for up to five structural breaks for each state.

	Estimator	Value p-value a p-value b
	OLS	0.925	0.594	0.708
	DOLS	0.934	0.689	0.718
	FMOLS	0.909	0.444	0.602
	Notes:

19 Page 39 of 42 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

	Submitted Manuscript
	F o r F o r F o r
	P P P
	e e e
	e r e r e r
	R e v R e v R e v
	i e i e i e
	w w w

Note that 1/(1 + i * ) = (i + σ)/(1 + i), where i and σ are the mean values of it and σt, respectively. Thus, if i < σ, then the transversality condition is satisfied automatically.

[START_REF] Bergman | Testing government solvency and the No Ponzi Game condition[END_REF] extends the results of[START_REF] Quintos | Sustainability of the deficit process with structural shifts[END_REF] by showing that sufficient condition for government solvency is that government debt is integrated of any finite order.

Note that the case with β > 1 is not consistent with a deficit, since revenues are growing faster than expenditures.5

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Note that for five of the eight countries we end up estimating the maximum number of breaks. This is in agreement with the results of[START_REF] Ahamada | Detecting multiple breaks in time series covariance structure: a non-parametric approach based on the evolutionary spectral density[END_REF] and[START_REF] Perron | L'estimation de modèles avec changements structurels multiples[END_REF], who point out that the type of information criteria used here cannot directly take into account the effect of different distributions of the data and possible serial correlation in the regression errors. In fact, as[START_REF] Perron | L'estimation de modèles avec changements structurels multiples[END_REF] showed in simulations, although most criteria perform reasonably well when the errors are not correlated, they have a strong tendency to overestimate the number of breaks when serial correlation is present. Of course, the purpose in this paper is not the correct estimation of the number of breaks per se but rather the accounting of the effects of these breaks. Thus, overestimation is not a serious problem in the sense that the model is still free to estimate the associated break parameters to zero.11

ThePesaran (2004) test is basically the average pair-wise correlation coefficient of the regression residuals, which has an asymptotic normal distribution under the null hypothesis of no cross-correlation.

Note that the case with β > 0 is not consistent with a deficit, since revenues are growing faster than expenditures.

Westerlund gratefully acknowledges financial support from the Jan Wallander and Tom Hedelius Foundation, research grant number W2006-0068:1.

To handle the serial correlation, the Bartlett kernel is used with a bandwidth parameter of T 1/3 .

a The p-value is based on the asymptotic normal distribution.

b The p-value is based on the bootstrapped distribution. The number of lags in the sieve approximation is five and we make 1,000 bootstrap replications.

18


Leigh Drake
email: leigh.drake@nottingham.ac.uk

Terence C Mills

CYCLES IN EURO AREA REAL GDP

Keywords: E32 -Business Fluctuations|Cycles &lt, E3 -Prices, Business Fluctuations, and Cycles &lt, Euro Area, Business Cycle, Band Pass Filter Euro Area, Business Cycle, Band Pass Filter JEL Categories: E32, F15

come

Introduction

The countries within the European Union (EU) have become increasingly integrated in recent decades. Following the inception of the Common Market under the Treaty of Rome in 1957 we have witnessed: the introduction of the European Monetary System (EMS) in 1979; the onset of the Single Market in 1992 (covering goods, services, labour and capital); the signing of the Maastricht Treaty in 1992, and the introduction of the single currency, the Euro, in January 1999. Although the EU has certainly become more integrated in recent years, there is a continuing debate over the extent of convergence across the EU countries, and most especially across the countries participating in the single currency. Furthermore, this debate has intensified recently with the accession of a further ten countries into the EU and the expectation that they will ultimately join the single currency, the Euro zone.

Following the seminal contribution of the theory of Optimal Currency Areas (OCAs) by Mundell (1961), business cycle convergence and the absence of asymmetric shocks has been considered as an important pre-requisite for a successful monetary union. Subsequent analysis, such as [START_REF] Frankel | The Endogeneity of the Optimal Currency Area Criterion[END_REF], however, has stressed that OCAs may be endogenous, in the sense that a group of countries adopting a single currency may be more likely to satisfy the OCA criteria ex-post rather than ex-ante. This is also the view of the European Commission (1990), who have argued that real macroeconomic convergence is more likely ex-post given the stimulus to intra-industry trade provided by the adoption of the single currency. A contrary view has been proposed by [START_REF] Krugman | Geography and Trade[END_REF], however, who argues that the combination of trade integration and economies of scale is likely to result in industrial concentration and clustering, as in the U.S., which may well exacerbate asymmetric shocks and hence undermine real macroeconomic convergence.

A further contentious issue is the potential impact of the adoption of the Euro on growth in the Euro zone economy. Once again, there is an ex-ante and ex-post aspect to this issue. From an ex-ante perspective, there is the possibility that, for many of the countries wishing to participate in the single currency, the nominal convergence criteria set out in the Maastricht Treaty imposed a severe deflationary policy bias which may have acted to reduce economic growth. There is also the possibility that the continuing imposition of the Stability and Growth Pact, and the consequent restriction on Government fiscal deficits relative to GDP, may have It is also possible that the alleged benefits of monetary unions (such as the elimination of transactions costs, the boost to intra-industry trade, the potential reduction in real interest rates and the stimulation of investment expenditure, etc.) may have acted to enhance economic growth ex-post.

The main purpose of this paper, therefore, is to examine the time series properties of real GDP in the Euro area as a whole, both prior to and after the adoption of the Euro in January 1999. The sample period is 1980Q1 to 2005Q4 and covers the EU-11 countries which were the initial adopters of the Euro. Of particular interest is the decomposition of the real GDP series into trend and cyclical components. This is a key issue in respect of any business cycle convergence analysis as the aggregate Euro zone cycle provides an ideal benchmark for comparison against the cycles of individual countries. To date, most of the convergence analysis has consisted of comparing the cycles of individual countries (for example, Dickerson et al, 1998, andWynne andKoo, 2000) or comparing these cycles with benchmark countries such as Germany (see, for example, Artis andZhang, 1997, 1999). Given that the European Central Bank (ECB) sets monetary policy in the context of the Euro zone economy as a whole, however, it can be argued that it is the extent to which individual countries' business cycles are converged with that of the Euro zone as a whole which is of paramount importance from an OCA perspective. Hence, although the analysis of Euro zone convergence is beyond the scope of this current paper, a thorough analysis of the time series properties, and in particular the trend and cycle decomposition of the Euro zone real GDP series, is of great policy relevance.

In addition, by offering a fresh perspective on the decomposition of Euro area real GDP into trend and business cycle components, we aim to provide a perspective on whether the adoption of the Euro has had any impact on trend real GDP growth in the Euro area, both ex-ante and ex-post.

Data

The univariate analysis conducted in this paper relates to real GDP (seasonally

Trend-Cycle Decompositions of Real GDP

In this section we consider trend-cycle decompositions of real GDP of the form

t t t t c q + + =
, where t , t c and t are the trend, cycle and irregular (short-run) components of t q , assumed to be independent of each other. As is now common in the business cycle literature, we require that t c captures those components of t q that have frequencies in the range of 1.5 to 8 years (6 to 32 quarters). This component can be estimated by a band pass filter: the filter that we actually use is the 'optimal approximation' of Christiano and Fitzgerald (2003), which has been shown to be superior to the traditional Hodrick and Prescott (1997) filter and the Baxter and King (1999) band pass filter in several respects. In particular, the asymmetric version employed here is better at estimating the cycle in real time, i.e., at and near the end of the sample period, which is important when attention is focused on identifying recent and current cyclical movements, as would be the case here.

Of course, construction of any cyclical filter requires assumptions about the behaviour of the trend component. We construct our cyclical component under two very different assumptions about the trend behaviour of t q . First, we consider that t q follows an ARIMA process, so that the underlying trend is stochastic. andFitzgerald (2003, section 2) is approximately optimal. Figure 2 shows the stochastic trend that is obtained from this filter (the cycle is discussed later). The trend is seen to evolve over time in line with the discussion above.

An alternative trend assumption is that it evolves as a deterministic function.

Given our earlier discussion of the evolution of t q , a simple linear (or indeed higher order polynomial) trend is unappealing. However, a segmented linear trend of the type originally analysed by Fuller (1976, chapter 9.2) produces a satisfactory fit:

( ) ( ) ( ) ( ) ( ) t t t t t t e q + + + =
= i i i it t t t , 0 , 4 , , 1 K = i where Q1 1983 1 Q1 1992 2 1 Q 1993 3 4 Q 2000 4
Here five segments are fitted and their selection follows the evolution of the series discussed above. The fitted trend is shown in Figure 3. Trend growth is zero until 1983Q1 and then 0.73% per quarter (3% per annum) until 1992Q1. The downturn during 1992 is then modelled as a trend change, with a decrease of 0.5% per quarter (2% per annum). From 1993 to 2001Q1 trend growth was 0.59% per quarter (2.3% per annum), after which growth declined to 0.34% per quarter (1.4% per annum).

Hence, the evidence provided in Figure 3 annum, in contrast to 3% between 1983Q1 and 1992Q1. Furthermore, the trend growth rate declined further to only 1.4% per annum in the post-2001Q1 period.

In the context of the segmented linear trend, the innovations to the trend are modelled by a stationary first order autoregressive process. Since the residuals, defined as

t t t t t c q e + = =
, are by definition stationary, the cyclical component The fact that the two alternative methods produce very similar cycles in the post-1994 period gives us some confidence that we have identified a robust and

Summary and Conclusions

In this paper we employ the 'optimal approximation' band pass filter developed by Christiano and Fitzgerald (2003) to identify a Euro-zone business cycle in real GDP.

We also utilise two alternative assumptions regarding the behaviour of the trend With respect to the cyclical behaviour of Euro zone real GDP, there are considerable differences between the cycles from the segmented and stochastic trend models during the earlier part of the sample period, most especially during 1992.

From 1994, however, the two cycles are very closely synchronised.

ABSTRACT

This paper examines the time series properties of real GDP in the Euro area as a whole, both prior to and after the adoption of the Euro in January 1999. We employ the relatively recent "optimal approximation" band pass filter developed by Christiano and Fitzerald (2003) in order to identify a Euro-zone business cycle. We also utilise two alternative assumptions regarding the behaviour of the trend component of Euro area real GDP. The empirical results suggest that the single currency experiment appears to have reduced trend growth in the Euro zone, both ex-ante during the Maastricht nominal convergence phase, and also ex-post, during the period 2001Q1 to 2006Q1. With respect to cyclical behaviour, we identify a very robust measure of the Euro zone business cycle in the post 1994 period which does not appear to be sensitive to the particular assumption made regarding the trend rate of growth of real GDP.

Key words: Euro Area; Business Cycle; Band Pass Filter

JEL Categories: E32; F15 Introduction

The main purpose of this paper is to examine the time series properties of real GDP in the Euro area as a whole, both prior to and after the adoption of the Euro in January 1999. Of particular interest is the decomposition of the real GDP series into trend and cyclical components. This is a key issue in respect of any business cycle convergence analysis as the aggregate Euro zone cycle provides an ideal benchmark for comparison against the cycles of individual countries. To date, most of the convergence analysis has consisted of comparing the cycles of individual countries (for example, Dickerson et al, 1998, andWynne andKoo, 2000) or comparing these cycles with benchmark countries such as Germany (see, for example, Artis andZhang, 1997, 1999). Given that the European Central Bank (ECB) sets monetary policy in the context of the Euro zone economy as a whole, however, it can be argued that it is the extent to which individual countries' business cycles are converged with that of the Euro zone as a whole which is of paramount importance from an Optimal Currency Area (OCA) perspective (see Mundell, 1961). Hence, although the analysis of Euro zone convergence is beyond the scope of this current paper, a thorough analysis of the time series properties, and in particular the trend and cycle decomposition of the Euro zone real GDP series, is of great policy relevance.

In addition, by offering a fresh perspective on the decomposition of Euro area real GDP into trend and business cycle components, we aim to provide a perspective on whether the adoption of the Euro has had any impact on trend real GDP growth in the Euro area, both ex-ante and ex-post.

Data

The univariate analysis conducted in this paper relates to real GDP (seasonally 2 the logarithms of this series, denoted t q , is shown in Figure 1 and shows several features that are of interest and importance in any decomposition of the series into trend and cyclical components. While the series exhibits a secular increase with an average rate of growth per quarter of 0.5% (approximately 2% per annum), this growth rate is by no means constant. In the early years of the 1980s growth was nonexistent but picked up quite rapidly during the later years of the decade. There was a pronounced downturn during 1992, whereupon growth picked up once again, remaining fairly stable until the Euro-zone entry of Greece in 2001Q1 produced both an immediate jump in real GDP followed by a growth slowdown.

Trend-Cycle Decompositions of Real GDP

In this section we consider trend-cycle decompositions of real GDP of the form

t t t t c q + + =
, where t , t c and t are the trend, cycle and irregular (short-run) components of t q , assumed to be independent of each other. As is now common in the business cycle literature, we require that t c captures those components of t q that have frequencies in the range of 1.5 to 8 years (6 to 32 quarters). This component can be estimated by a band pass filter: the filter that we actually use is the 'optimal approximation' of Christiano and Fitzgerald (2003), which has been shown to be superior to the traditional Hodrick and Prescott (1997) filter and the Baxter and King (1999) band pass filter in several respects. In particular, the asymmetric version employed here is better at estimating the cycle in real time, i.e., at and near the end of the sample period, which is important when attention is focused on identifying recent and current cyclical movements, as would be the case here.

Of course, construction of any cyclical filter requires assumptions about the behaviour of the trend component. We construct our cyclical component under two very different assumptions about the trend behaviour of t q . First, we consider that t q follows an ARIMA process with an additive outlier at 2001Q1 to model the inclusion of Greece into the Euro-zone, so that the underlying trend is stochastic. The model so identified is a random walk with drift ( ) ( ) t q q t t t then follows a pure random walk with drift, for which the filter proposed in Christiano and Fitzgerald (2003, section 2) is then optimal. Figure 2 shows the stochastic trend that is obtained from this filter (the cycle is discussed later). The trend is seen to evolve over time in line with the discussion above.

t t t a q + + =
An alternative trend assumption is that it evolves as a deterministic function.

Given our earlier discussion of the evolution of t q , a simple linear (or indeed higher order polynomial) trend is unappealing. However, a segmented linear trend of the type originally analysed by Fuller (1976, chapter 9.2) produces a satisfactory fit: From 1993 to Greek entry in 2001Q1 trend growth was 0.58% per quarter (2.3% per annum), after which growth declined to 0.43% per quarter (1.7% per annum). Hence, the evidence provided in Figure 3 reinforces the finding from the stochastic trend specification that the adoption of the Euro appears to have reduced the trend rate of growth of the Euro zone economies, both ex-ante and ex-post. Specifically, annual trend growth during the Maastricht convergence period was only around 2.3% per annum, in contrast to 3% between 1983Q1 and 1992Q1. Furthermore, the trend growth rate declined further to only 1.7% per annum in the post-2001Q1 period.

( ) ( ) ( ) ( ) ( ) ( ) t t
In the context of the segmented linear trend, the innovations to the trend are modelled by a stationary first order autoregressive process. Since the residuals, defined as

t t t t t c q e + = =
, are by definition stationary, the cyclical component The fact that the two alternative methods produce very similar cycles in the post-1994 period gives us some confidence that we have identified a robust and definitive Euro-zone business cycle for this period. Clearly, this should prove extremely useful in the context of subsequent business cycle convergence analysis, i.e., the extent to which individual countries or groups of countries have business cycles which are synchronised or converging with the Euro-zone business cycle.

With respect to business cycle chronology, both cycles suggest a business cycle peak in 1995 followed by a double dip recession during 1996/97 and 1998/99.

Interestingly, the launch of the single currency in January 1999 coincided with a strong cyclical upturn in the Euro-zone economies with a business cycle peak in early

2001. The subsequent downturn ended in mid-2003 and the Euro area is still experiencing a steady cyclical recovery which previous evidence suggests will probably be complete by mid-2006.

Summary and Conclusions

The evidence produced in this paper suggests that the single currency experiment appears to have reduced trend growth in the Euro zone relative to the period 1983 to 1992, both ex-ante during the Maastricht nominal convergence phase, and also expost, during the period 2001Q1 to 2006Q1.

With respect to the cyclical behaviour of Euro zone real GDP, there are considerable differences between the cycles from the segmented and stochastic trend models during the earlier part of the sample period, most especially during 1992.

From 1994, however, the two cycles are very closely synchronised. This suggests that we have identified a very robust measure of the Euro zone business cycle in the post 1994 period which does not appear to be sensitive to the particular assumption made regarding the trend rate of growth of real GDP. This should facilitate a more accurate assessment of the extent to which individual countries and groups of countries are converged with respect to the Euro area business cycle. As the ECB makes monetary policy decisions with respect to the Euro zone as a whole, such analysis is important in the context of any analysis of Europe as an OCA.

  , at least in the short term, after the introduction of the Euro.

  reinforces the finding from the stochastic trend specification that the adoption of the Euro appears to have reduced the trend rate of growth of the Euro zone economies, both ex-ante and ex-post. Specifically, annual the Maastricht convergence period was only around 2.3% per

tc

  can be calculated by applying the stationary Christiano and Fitzgerald filter to t e .The cyclical components estimated by the two methods are shown in Figure4.Since 1994 the two cycles are very similar to each other. The cycles are very different to each other between 1992 and 1994 because the segmented trend model treats the decline of 1992 and subsequent rebound as a pair of trend shifts whereas the random walk model allocates this movement to the cycle. Less severe differences are also seen before 1992, again because the models allocate shifts to trend and cycle differently.The evidence presented in Figures 2 to 4 suggests that the deflationary impact of the Maastricht Treaty from early 1992 contributed to the very large cyclical downturn evident in the early 1990s, but also reduced the trend rate of growth during the 1990s relative to that which prevailed for most of the 1980s. With respect to the introduction of the Euro, the evidence suggests that the trend rate of growth from early 2001 has been reduced relative to the mid to late 1990s, and especially relative to the late 1980s. It is clearly inappropriate to attribute this recent slowdown in growth solely to the impact of the single currency. The initial growth slowdown is likely to be attributable in large part to the impact of the "high tech shock" and the subsequent general slowdown in the world economy after 2001. Nevertheless, it seems likely that many countries in the Euro-zone, faced with this general slowdown in world economic growth, were unable to allow their automatic stabilisers to work in the traditional fashion due to the imposition of the Stability and Growth Pact. Clearly, this will have compounded the loss of an independent monetary policy and exchange rate under the single currency and may well have transformed a cyclical downturn in the Euro zone economies into a further decline in trend growth.

  area real GDP. In both cases, it is evident that the single currency experiment appears to have been associated with reduced trend growth in the Euro zone relative to the period 1983 to 1992, both ex-ante during the Maastricht nominal convergence phase, and also ex-post, during the period 2001Q1 to 2005Q1.

  adjusted) for the aggregate Euro zone economies. The sample period is 1980Q1 to 2006Q1 and relates to the EU-11 economies until 2000Q4 and the EU-12 economies from 2001Q1, following the entry of Greece into the Euro zone. We utilise the official data produced by the ECB from 1990Q1. Prior to this date, we utilise the Euro area database constructed by Gollinelli, and we gratefully acknowledge the use of this data. This data has been constructed (and verified) to be consistent with the official ECB data (seeGollinelli and Pastorello, 2000, for further details). A plot of

  errors are shown in parentheses and a ˆ is the estimated standard error of the white noise t a .) Thus trend growth averages 0.48% per quarter (1.9% per annum), with the entry of Greece producing a one-off increase in the growth rate of 1

  segments are fitted (the fifth is equivalent to the additive outlier modelling the Greek entry) and their selection follows the evolution of the series discussed fitted trend is shown in Figure3. Trend growth is zero until 1983Q1 and then 0.74% per quarter (3% per annum) until 1992Q1. The downturn during 1992 is then modelled as a trend change, with a decrease of 0.5% per quarter (2% per annum).

tc

  can be calculated by applying the stationary Christiano and Fitzgerald filter to t e .The cyclical components estimated by the two methods are shown in Figure4.Since 1994 the two cycles are very similar to each other. The cycles are very different to each other between 1992 and 1994 because the segmented trend model treats the decline of 1992 and subsequent rebound as a pair of trend shifts whereas the random walk model allocates this movement to the cycle. Less severe differences are also seen before 1992, again because the models allocate shifts to trend and cycle differently.The evidence presented in Figures 2 to 4 suggests that the deflationary impact of the Maastricht Treaty from early 1992 contributed to the very large cyclical downturn evident in the early 1990s, but also reduced the trend rate of growth during the 1990s relative to that which prevailed for most of the 1980s. With respect to the introduction of the Euro, the evidence suggests that the trend rate of growth from early 2001 (after the entry of Greece into the Euro) has been reduced relative to the mid to late 1990s, and especially relative to the late 1980s. This may reflect the fact that many countries in the Euro-zone, faced with the general slowdown in the world economy after 2001, were unable to allow their automatic stabilisers to work in the traditional fashion due to the imposition of the Stability and Growth Pact. Clearly, compounded the loss of an independent monetary policy and exchange rate under the single currency.

  Figure 1Real Euro-GDP; 1980.1 -2006.1 (logarithms: t q )

  Standard errors are shown in parentheses and a ˆis the estimated standard error of the

	q	t	=	( 0 . 0007 0038 . 0	) ( ) + 094 . 0 226 . 0	q	t	1	+	a	t	ˆ= a	00489 . 0
	white noise t a . Thus trend growth averages	38 . 0	( 1	226 . 0	) =	0.49% per quarter
	(1.96% per annum) and the filter proposed in Christiano
				F o r
					P
					e
						e r
											R e v
												i e
													w
														The model so
	identified is an ARIMA(1,1,0) with drift
														4

  the context of subsequent business cycle convergence analysis, i.e., the extent to which individual countries or groups of countries have business cycles which are synchronised or converging with the Euro-zone business cycle.With respect to business cycle chronology, both cycles suggest a business cycle peak in 1995 followed by a double dip recession during 1996/97 and 1998/99. The latter may well be attributable to the deflationary impact of the Maastricht convergence criteria ahead of the decision on Euro eligibility in 1997. It is the case, for example, that, due to the construction of the inflation convergence requirements, the average inflation rate in the potential Euro zone countries was continually driven downwards until 1998/99. The very stringent fiscal convergence requirements, however, necessitated very tight fiscal as well as monetary policies and it was not until 1996, for example, that the Euro zone economies in aggregate managed to reduce the ratio of Government debt to GDP. Finally, conformation of the fact that the impact of the convergence process was most pronounced in the post-1996 period Aside from any positive benefits attributable to the single currency itself, this may also reflect the fact that the countries in the Euro zone were effectively freed from the deflationary constraints of the Maastricht convergence criteria after 1997 and hence the abortive economic recovery of 1996 / 97 belatedly materialised across the Euro zone. The subsequent downturn ended in mid-2003 and, during the latter part of the sample, the Euro area was still experiencing a steady cyclical recovery which previous evidence suggests will probably have been completed bymid-2006.

	extremely useful in
	F o r
	P
	e
	e r
	R e v
	i e
	w
	6

definitive Euro-zone business cycle for this period. Clearly, this should prove is confirmed by the fact that short term interest rates across the Euro-zone began to converge with those of Germany's over this period. Hence, the pronounced deflationary impact of the Maastricht nominal convergence requirements may well have been sufficient to "snuff out" the economic recovery evident during 1996 / 97 and produce the double dip recession during 1998 / 99. Interestingly, the launch of the single currency in January 1999 coincided with a strong cyclical upturn in the Euro-zone economies with a business cycle peak in early 2001.

TRENDS AND CYCLES IN EURO AREA REAL GDP Leigh Drake*

  This suggests that we have identified a very robust measure of the Euro zone business cycle in the post 1994 period which does not appear to be sensitive to the particular assumption made regarding the trend rate of growth of real GDP. This should facilitate a more accurate assessment of the extent to which individual countries and groups of countries are converged with respect to the Euro area business cycle. As the ECB makes monetary policy decisions with respect to the Euro zone as a whole, such analysis is important in the context of any analysis of Europe as an OCA.

	7.4
	.012
	7.4 7.3 .008	segmented trend cycle
	7.3 7.2 .004
	7.2 7.1 .000	Professor of Financial Economics Nottingham University Business School Trend	Actual
	7.1 7.0 -.004		and
	6.9 7.0 -.008		Terence C. Mills
	6.8 6.9 1980 6.8 1980 Figure 2 -.016 -.012 1980	F o r F o r 1985 F o r 1985 Band pass trend fitted to t 1990 1990 q . F o r 1985 1990 Professor of Applied Statistics and Econometrics 1995 2000 1995 2000 1995 2000 bandpass cycle F Department of Economics, Loughborough University Loughborough, LE11 3TU o r November 2006	2005 2005 2005
	Figure 4 5	P e P e P P Cyclical components from the two models. P e e e
	3 4 7.4		e r e r e r e r e r		0.34%
	1 2 7.2 7.3		R e v R e v R e v 0.59% R e v R e v
	0 7.1		-0.50%	i e i e i e i e i e
	-1 7.0	0.73%		w w w w w
	-2
	1980 6.9	1985	1990	1995	2000	2005
	0%
	6.8
	1980	1985	1990	1995	2000	2005
	Figure 1 Figure 3	Real Euro-GDP; 1980.1 -2005.4. Top panel: logarithms: t q . Bottom panel: annual growth rates, ( ) 4 100 t t q q . Segmented trend with growth rates.
						9 10 11

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript