On Optimal Currency Areas: Common Shocks Versus Common Persistence of Shocks

Grimm, Louisa; Steinkamp, Sven; Westermann, Frank Article — Published Version On Optimal Currency Areas: Common Shocks Versus Common Persistence of Shocks International Journal of Finance & Economics Provided in Cooperation with: John Wiley & Sons Suggested Citation: Grimm, Louisa; Steinkamp, Sven; Westermann, Frank (2024) : On Optimal Currency Areas: Common Shocks Versus Common Persistence of Shocks, International Journal of Finance & Economics, ISSN 1099-1158, John Wiley & Sons, Ltd., Chichester, UK, Vol. 30, Iss. 4, pp. 3825-3837, https://doi.org/10.1002/ijfe.3093 This Version is available at: https://hdl.handle.net/10419/329786 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. 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If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by/4.0/ International Journal of Finance & Economics, 2025; 30:3825–3837 https://doi.org/10.1002/ijfe.3093 3825 International Journal of Finance & Economics RESEARCH ARTICLE OPEN ACCESS On Optimal Currency Areas: Common Shocks Versus Common Persistence of Shocks LouisaGrimm | SvenSteinkamp | FrankWestermann Osnabrück University, Institute of Empirical Economic Research, Osnabrück, Germany Correspondence: Sven Steinkamp ([email protected]) Received: 13 March 2023 | Revised: 1 November 2024 | Accepted: 11 November 2024 Funding: This work was supported by Bundesbank's Regional office in Bremen, Lower Saxony and SaxonyAnhalt, as well as the SievertFoundation. Keywords: codependent business cycles| exchange rate regime choice| optimum currency area| serial correlation common feature ABSTRACT The Optimal Currency Area (OCA) literature has been focusing on the comovement of business cycle shocks as a key policy criterion. We document in a simple Barro–Gordon framework that, in addition to a high correlation of shocks, a common persistence of shocks is a relevant OCA criterion. The model provides a conceptual underpinning for empirical studies that have used the Serial Correlation Common Features (SCCF) test to evaluate common currency areas. We apply the SCCF test to a set of countries that could potentially introduce the Euro and find for the period from 1999 (Q1) to 2019 (Q3) only little evidence that the acceding countries share a common cyclical response pattern with the European Monetary Union (EMU) aggregate. JEL Classification: E52, F36, F41 1 | Introduction In the empirical literature on optimum currency areas, the most common approach has first been used in the classical article by Bayoumi and Eichengreen(1993). The authors conduct a trendcycle decomposition and analyse the contemporaneous correlation of shortterm shocks, interpreted as demand shocks.1 The approach draws its intuition from Mundell's(1961) work on optimum currency areas and it has more recently been formally illustrated by Berger, Jensen, and Schjelderup(2001). However, it neglects a key feature of macroeconomic data, the persistent and often complex serial correlation pattern of shocks. It thereby misses out on the potential spillover effects of the shock into subsequent periods. In a parallel strand of the literature, started by Beine, Candelon, and Hecq (2000) and summarised in De Haan, Inklaar, and JongAPin(2008), the persistence of the shocks is indeed the focus of the analysis. The authors employ the Serial Correlation Common Features (SCCF) test, initially developed by Engle and Kozicki (1993), to analyse whether the impulse response patterns to external shocks are similar across countries. Our contribution to this literature is to formally demonstrate that a common persistence of shocks—and not only their contemporaneous correlation—is indeed a necessary condition for minimising the costs associated with adopting a common currency. Building on the theoretical setups of Berger, Jensen, and Schjelderup(2001) and Bleaney(2000), we postulate a new criterion that provides an extension of the analytical framework by Mundell (1961). In our adaption of the model, shocks are identical across countries but autocorrelated with different persistence parameters. In this setting, we document that the studies relying on the SCCF test are indeed applying an appropriate complementary testing procedure.2 The topic of Optimal Currency Areas is a classic in the literature on international finance and there is a renewed interest in the topic as the European monetary union keeps expanding. Two potential new member countries, Bulgaria and Romania, have expressed their interest in EMU membership, and Croatia recently joined the EMU in 2023. In an empirical assessment, DeskarŠkrbić, Kotarac, and Kunovac(2021) argue that the candidate countries are indeed in a good position to join the common This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited. © 2024 The Author(s). International Journal of Finance & Economics published by John Wiley & Sons Ltd. 3826 International Journal of Finance & Economics, 2025 currency, using an advanced version of the classical empirical method proposed by Bayoumi and Eichengreen(1993).3 In our empirical application of the SCCF test, we take a fresh look at the evidence. Taking the persistence of shocks into account, we find much more limited evidence supporting an Optimal Currency Area for the majority of EMUcandidate countries. Among the countries analysed, Sweden comes closest to forming an Optimal Currency Area with the current EMU countries. For Sweden, using the Cubadda(2001) approach, we indeed cannot reject the null hypothesis of a common cycle in our benchmark regression. For Croatia, Hungary and the Czech Republic, we reject the null of a common cycle, but we do find some common cyclical elements when considering a less strict version of the common features test—the test for codependence that allows for an initially asymmetric response in the first quarter. Finally, all countries exhibit some higherorder codependence of order two or three, which, however, is hardly relevant in practice, given the overall shortlived cyclical nature of GDP shocks in quarterly data. In Section 2, we present our conceptual model framework. Section 3 generalises our main findings to higherorder ARprocesses and discusses why the SCCF test is indeed a modelconsistent test of OCAs. Section 4 covers preliminary tests, including visual inspections of the correlograms and assessments of the seasonal unit root and cointegration properties. Section5 details our main findings on common cyclical features and the sensitivity analysis, while Section6 concludes. 2 | Relationship to the Existing Literature The comovement of business cycles in the context of the literature on Optimal Currency Areas is one of the most extensively explored fields of empirical macroeconomics. Before presenting our model and main results, we would like to highlight how our approach is different from some key references in the literature. For the theoretical part, the most closely related paper is by Berger, Jensen, and Schjelderup(2001) on exchange rate regime choice. Their model is static and therefore, it only finds that the contemporaneous correlations matter for the decision to join a common currency (or, more broadly, fix the exchange rate to another country). Our paper uses their setup of a Barro–Gordon model of monetary policy and follows their approach of doing the welfare comparisons. The new aspect in our paper is that the error term, that is, the shocks, can be autocorrelated. For simplicity, we assume that the contemporaneous shocks are identical, which allows us to focus on the dynamic reactions only. This way, we are able to highlight that a high contemporaneous correlation is not sufficient, and additional tests of the type presented in this paper are needed. We are not the first authors, however, to add an autocorrelated error term to a Barro–Gordon setup. The paper by Bleaney(2000) has done so and has already reported the impact of autocorrelation on the inflation bias, which is the main focus of monetary models on the timeinconsistency of monetary policy. Our Lemma1 will replicate the result of their model. The difference between our theoretical model and the one of Bleaney(2000) is that we take the analysis one step further and conduct welfare comparisons. That is, we compare—under the assumption of perfectly correlated shocks—the welfare losses from the two choices of joining or not joining the monetary union, and document that the difference between the two welfare levels depends on the persistence parameters. If the persistence is not identical, we find that there is an additional welfare loss that has not been reported in either Berger, Jensen, and Schjelderup(2001) or Bleaney(2000). Regarding the empirical literature, the most closely related article is the one by Beine, Candelon, and Hecq(2000).4 This paper is the first that has used an early version of the common features test and interpreted it in the context of the literature on optimal currency areas. Our contribution to this paper is to provide a theoretical underpinning to the argument these authors have made. A further empirical contribution is to use a more elaborate version of the common features test, developed by Cubadda(2001), who in his research has highlighted the importance of using nonseasonallyadjusted data when analysing common cycles. Additionally, we also take a much more recent data set and apply the testing approach to a set of countries that currently indeed face the policy decision on whether or not to join a monetary union.5 A third key reference is the article of DeskarŠkrbić, Kotarac, and Kunovac(2021): The authors study three Eurocandidate countries (Bulgaria, Croatia and Romania), but only focus on contemporaneous correlations. The contribution of DeskarŠkrbić, Kotarac, and Kunovac (2021), however, is not only to apply the basic setup of the classic article of Bayoumi and Eichengreen(1993). Instead, they use stateoftheart Bayesian techniques to illustrate that shocks in the candidate countries and the Euro Area are quite similar. Based on their analysis, they conclude that the countries are ‘ready to join’ the EMU, a policy statement which in light of our findings and the additional OCA criterion postulated in this paper may be too strong, or at least incomplete from the important perspective of dynamic response patterns. 3 | A Conceptual Framework To motivate the use of a Serial Correlation Common Features test, we set up a very simple model in the classical Barro and Gordon(1983) framework. This model builds on Berger, Jensen, and Schjelderup(2001) who have analysed the optimal exchange rate regime choice in the presence of contemporaneous countryspecific shocks. The decision on the exchange rate regime in this model is based on the difference in expected losses in both regimes. We also build on the research of Bleaney(2000), who has expanded the Barro–Gordon framework to include autocorrelated shocks. The basic findings in this literature can be replicated in our setup. Our contribution is to highlight the implications of autocorrelated shocks for the exchange rate regime choice and to trace their effects on the inflation bias, output and welfare. First, we analyse the case of flexible exchange rates. We start with a stochastic version of the Lucassupply schedule: 3827 where yt is output, 𝜋t the inflation rate and 𝜋e t is expected inflation. 𝜀t is an error term, which we assume to follow an AR(1) process, 𝜀t=𝛾𝜀t−1+vt . vt is a white noise shock, and 𝛾 measures the degree of persistence of the shock. We assume 0<𝛾<1 , that is, 𝜀t is positively autocorrelated but the stochastic process is stationary. The central bank minimises the following quadratic loss function: subject to the inflation rate.6 For simplicity, we assume that the central bank can control the inflation rate directly. The timestructure of the model is as follows: 𝛼,𝜆 , as well as foreign inflation and the output target, 𝜋∗,y∗ , are predetermined. At the beginning of the period, workers form inflation expectations. The central bank then chooses the optimal inflation rate after observing the shock vt , which has zero mean and a variance of 𝜎2 v . Thereafter yt and L follow from the Philips curve based on 𝜋t and 𝜋e t . Equilibrium values for 𝜋 and y are then given by: and y=𝛾𝜀t−1+ 1 1+𝛼 2 𝜆 vt . These expressions simplify to the familiar expressions in the literature when setting the persistence parameter 𝛾 equal to zero. Lemma 1. The persistence of shocks affects the inflation bias. Proof. E [𝜋] 𝛾≠0 =𝛼𝜆 ( y∗−𝜀 t−1 𝛾 ) .E[𝜋] 𝛾≠0 −E[𝜋] 𝛾=0 =−𝜀 t−1 𝛼𝜆𝛾.■ . Depending on the sign of the shock in the previous period, this effect can either strengthen or reduce the inflation bias, that is, higherthanoptimal inflation rates due to the timeinconsistency problem. This preliminary result is known from Bleaney(2000), who derives the implications for inflation persistence, which is shown to depend on the degree of shocks' autocorrelation and the exchange rate regime. More importantly in the context of our overall question on the impact of persistence on the optimal exchange rate regime choice is the following finding that can be derived by plugging the values for 𝜋 and y into the loss function. Lemma 2. The shock persistence does not affect expected losses in a flexible exchange rate case. Proof. L 𝛾>0 flex −L𝛾=0 flex =−𝜆𝛾𝜀t−1 ( 𝜆𝛼2+1 )( 2y−𝛾𝜀t−1 ) and E [ L𝛾≠0 flex ] −E [ L𝛾=0 flex ] =0. ■ It is important to keep in mind that while the central bank chooses the optimal inflation rate after observing the shock, the shock is still a stochastic variable when the exchange rate regime is decided upon. Therefore, its meanzero characteristic needs to be taken into account when computing the expected aggregate welfare loss. Under flexible exchange rates, when a central bank can fully respond to positive and negative shocks, the autocorrelation does not constitute an additional welfare loss to the economy.7 Next, we consider the case of fixed exchange rates, or equivalently a small country that joined a monetary union (permanently fixed exchange rates). We have the same autocorrelated output function, yt =𝛼 ( 𝜋 t −𝜋 e t) +𝜀 t with 𝜀t=𝛾𝜀t−1+vt , but, in this case, inflation is determined by the purchasing power parity, which is given by where 𝜃t is the shock from the foreign country, which we also assume to be autocorrelated: where ut is a white noise shock and 𝛿 captures the degree of persistence of shocks in the foreign country. The output of the home country is, therefore: yt=𝛼ut+𝛾𝜀t−1+vt . We can plug both expressions into the loss function: As the central bank has fixed its exchange rate and is importing the inflation rate from abroad, the inflation rate is no longer a choice parameter. To focus on asymmetric persistence and its implications for welfare and exchange rate regime choice, we now set u=v . That is, the stochastic elements of the timeseries process are identical and any differences are only driven by the persistence parameters δ and γ . In the terminology of the OCA theory, this captures the case of symmetric shocks with asymmetric effects.8 Proposition 3. When joining a monetary union, there is an additional welfare gain/loss from asymmetric persistence. Proof. E[ L𝛿≠𝛾 fix ] −E [ L𝛿=𝛾 fix ] =var ( 𝜃t )( 𝛿2−𝛾2 ) , with var ( 𝜃t ) = 𝜎2 v ( 1−𝛿2 ) . The expression is zero if, and only if, 𝛿=𝛾.■ Note that the expression for the additional welfare effect can get negative if shocks are more persistent in the joining country than in the monetary union (𝛾>𝛿 ) . That is, there is always an argument to anchor unilaterally against a stable country. It follows that common persistence in two countries forming a monetary union is a new criterion for Optimal Currency Areas that so far has not been postulated formally in the literature. Corollary 4. The only symmetric equilibrium where two countries find it optimal to form a monetary union is when 𝛿=𝛾 . 4 | From Model to Data The empirical implication from the conceptual framework discussed above is that the persistence of shocks in two countries forming a monetary union should be identical. A typical way to measure the persistence is looking at estimates of the halflifes of the real GDP growth rates, which for the set of acceding countries to the EMU are reported in Figure1. This preliminary inspection of the data suggests that the countries may indeed form an Optimal Currency Area, as the persistence in the yt =𝛼 ( 𝜋 t −𝜋 e t) +𝜀 t (1) L flex =E [ 𝜆 ( 𝛼 ( 𝜋t−𝜋e t ) +𝛾𝜀t−1+vt−y∗ ) 2+𝜋2 t ] 𝜋 =𝛼𝜆 ( y∗−𝜀t−1𝛾 ) − 𝛼𝜆 ( 1+𝛼2𝜆 ) vt 𝜋t=𝜋∗+𝜃t, 𝜃t=𝛿𝜃t−1+ut, (2) L fix =E [ 𝜆 ( 𝛼ut+𝛾𝜀t−1+vt−y∗ )2 + ( 𝜋∗+𝛿𝜃t−1+ut )2] 3828 International Journal of Finance & Economics, 2025 candidate countries is not statistically different from that of the monetary union. This simplified approach, however, has two shortcomings. First, the standard errors of halflife estimates are known to be large. Thus, it is hardly a reliable source of information. Second, it abstracts from the possibility of higherorder autoregressive processes, which are common in quarterly macroeconomic data. Most time series on GDP typically display both a partial autocorrelation function that is significant for about four to six quarters, as well as a strong seasonal pattern. When extending Proposition3 to higherorder AR(p) processes of the same order for 𝜃 and 𝜀 , we get the following expression for the additional welfare loss under asymmetric persistence: Thus, not only the persistence parameters of the AR(1)- term but all coefficients in the AR(p) process need to be identical for this expression to be zero, that is, ∣𝛿i ∣= ||𝛾i||, ∀ i. Intuitively, Equation(3) can be interpreted as the expected squared deviation of the two processes.9 The empirical approach of a serialcorrelationcommonfeature test (SCCF), which was first developed by Engle and Kozicki(1993), thus indeed constitutes a modelconsistent empirical approach to assess the existence of an Optimal Currency Area. It tests for a common higherorder AR(p) process in different time series by identifying the existence of a linear combination of two variables that is free of autocorrelation. An alternative interpretation of the SCCF is that the impulse response patterns of two variables, when faced with a common exogenous shock, need to be identical. Concretely, the test for codependence assumes that two time series follow an AR(p) process of the same order: Xt,Yt∼AR(p) and the strategy is to search for a linear combination of the two time series such that: Z=Xt−𝛽Yt∼AR(0) . In order to find this linear combination, we first estimate the following regression equation: where Xt,Yt symbolise growth rates of equal AR processes. In a second step, we examine the estimated residual 𝜔 t via an Ftest that is evaluated using a: 𝜒2 - distribution: If the two countries follow a common response pattern, the coefficients in the second regression should jointly be insignificant. Our null hypothesis is H0 : There is a SCCF. That is, if the lagged growth rates exert no influence on the residual of the regression above, there is a SCCF. The alternative is H1 : There is no SCCF. In practice to safeguard against possible endogeneity issues in the two time series, the regression is typically estimated following a twostage least squares approach using Xt−k,Yt−k , with k=1, …,p , as the instruments. A somewhat weaker test than the strict SCCF is the test for codependence of higher order. Codependence exists if a linear combination of Xt and Yt , each following an AR(p) process, can shorten that process to AR(pj). In this approach, the time series do not have to immediately return to their equilibrium in the same way after a shock. In the empirical analysis below, we report both approaches but note that only the strict SCCF is consistent as a test for the OCA criterion developed in the previous section. Furthermore, both tests can be conducted with a twostage least squares regression or with a GMM approach. In the tables below, we report the results of both estimation techniques. Since the first proposal of the SCCF by Engle and Kozicki(1993) and Vahid and Engle(1993, 1997), there have been several advancements in the testing procedure that are relevant to our dataset. First, as shown by Cubadda(1999) the coexistence of seasonality and autocorrelation requires an integrated approach to modelling the data. The usage of deseasonalized data may lead to an incorrect finding of common cycles. As all countries in our dataset indeed have a seasonal component, this point is particularly relevant for our analysis. In the following empirical section, we first consider the longterm trend dynamics before finally conducting the Serial Correlation Common Features test. We perform both the strong form of the SCCFtest, as well as the less restrictive test for codependence, which was first discussed in Vahid and Engle(1997).10 5 | Preliminary Analysis The quarterly real GDP series' (1999Q1–2019Q3) were extracted from Eurostat and are displayed in Figure2 in seasonal differences. Eyeballing the data, we see immediately some commonalities across countries, such as the boom period in the mid2000s, the cyclical downturn after the global financial crisis in 2007/8, as well as a rebound and a renewed recession after the onset of (3) var (𝜃t) P ∑ p=1 (𝛿2 p−𝛾2 p)+2var(𝜃t) P−1 ∑ p=1 P ∑ q=p+1 𝜑q−p(𝛿p𝛿q−𝛾p𝛾q ) Xt=c+𝛿Yt+𝜔t, 𝜔 t=c+ ∑p k=1 𝛼kXt−k+ ∑p k=1 𝛽kYt−k+e t FIGURE 1 | Halflife estimates [quarters]. This figure depicts halflife estimates (± 2 standard errors) based on the impulse response of an univariate vector autoregressive model with 4 lags. 3829 the sovereign debt crisis in 2010 and again a rebound thereafter. Since roughly 2012, most countries have displayed a relatively steady growth path. A standard response to an exogenous shock is then displayed in Figure3. For each country, we show the correlograms that display the autocorrelation of each time series. Contemporaneous correlations are reported in Table1. It can be interpreted as the cyclical response pattern of each country to an exogenous shock. In this representation of the data, we already see that the response patterns can be quite different across countries—despite the similarities of the halflifes reported in the previous section. FIGURE 2 | Graphical analysis of (seasonal) real GDP growth rates. This figure depicts seasonal growth rates of real GDP for Bulgaria (BGR), Czech Republic (CZE), Croatia (HRV), Hungary (HUN), Poland (POL), Romania (ROU), Sweden (SWE), the 12 founding euro area members (EA12), consisting of Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands, Portugal and Spain. 3830 International Journal of Finance & Economics, 2025 Each of the acceding countries in this figure is displayed together with the correlogram of the EA12 countries—the set of countries for which we have a consistent dataset of 83 observations as full Eurozone members.11 The EA12 aggregate is characterised by a typical positive autocorrelation for about 4–5 quarters and a negative, but somewhat smaller, autocorrelation, for the 4–8 quarters thereafter. Thus, when accumulating these impulse response patterns in the GDP growth rates, one gets the typical upanddown swing patterns in the associated levels of GDP around its trend. Thereafter, there are further ups and downs, which, however, are statistically insignificant (we omit the standard errors in this graph for a better visual illustration of commonalities and differences in the point estimates). FIGURE 3 | Autocorrelogram. This figure shows estimated sample autocorrelation functions of real GDP growth rates (seasonal differences of logged values) over 36 quarters. 3831 The correlograms of the acceding countries, by contrast, are quite different. Except for Poland and Sweden, most countries display a much longer positive autocorrelation and a delayed cyclical rebound. Cumulatively, this would imply a much longer cycle. While this first pass gives a visual impression of the data, a formal test on the colinearity of impulse response patterns needs to be conducted to precisely pin down which country may fulfil the OCA criterion postulated in the previous section and which countries do not. An integral part of the analysis of common cycles is the consideration of trends and seasonal elements in the data. We, therefore, start the formal regression analysis by conducting the respective tests needed for the subsequent analysis of common cycles. Table2 reports the seasonal unit root tests (HEGY),12 which shows that the time series of all countries are integrated at the zero frequency, a plausible finding as all data are in logged levels. At the frequency π/2, all countries including the EA12 except Bulgaria and Croatia are stationary. The Czech Republic and Sweden are further stationary at frequency π. We take these stationarity properties into account when testing for cointegration in the next step. Table3 shows that all countries except for Romania, Hungary and the Czech Republic indeed are cointegrated, and thus share a common longterm trend with the EA12. Regarding the cointegration at frequency π, we find that Bulgaria and Poland also share a common stochastic seasonal trend with the EA12. While not directly relevant to the OCA literature, it is very important to take account of these characteristics of the data when performing the test for common serial correlation in the next section. We will—wherever necessary—include the error correction term in the list of instruments when conducting the common features tests. 6 | Codependence and Common Cycles We now get to the main part of the analysis—the test for the existence of common cyclical patterns across countries, that is, a common impulse pattern to an exogenous shock. The results are summarised in Table4. There are in principle two different approaches to conduct a test for a common serial correlation feature, one is regressionbased and one is based on canonical correlation analysis, similar to the EngleGranger twostep and the Johansen multivariate approach to the cointegration test. In our exercise, we take the latter approach and estimate the parameters with OLS as well as with GMM.13 When starting with the strict form of identical impulse response patterns, we need to consider the first column of test statistics and associated pvalues, labelled ‘codependence of order zero’. This table illustrates that indeed most of the countries do not share a common impulse response pattern, not even Poland, which appeared to be quite similar to the EA12 when initially eyeballing the data. The only country which indeed shares a common impulse response pattern appears to be Sweden. A somewhat weaker definition of a common cycle could be used where the initial response (at lag 1) is allowed to be different, but all subsequent lags would be required to be identical. This is considered to be a codependent cycle of order one and may also be of relevance for the OCA case, although it does not follow TABLE 1 | Correlation coefficients. BGR ROU HRV HUN POL CZE SWE EA12 0.307*** 0.442*** 0.730*** 0.760*** 0.515*** 0.810*** 0.880*** [2.90] [4.43] [9.13] [10.54] [5.41] [12.44] [16.65] Note: Table1 reports (Pearson) correlation coefficients between countries' real GDP growth rates (seasonal differences). tStatistics for the null of the coefficient being unequal to zero are given in parenthesis. *** indicates statistical significance at the 1% level. The sample period is 1999Q1–2019Q3. TABLE 2 | HEGYseasonal unit root tests for loglevels (seasonally unadjusted). Country Frequency 0π π/2 All seasonal frequencies EA12 −2.455 −2.179 14.803*** 12.010*** BGR −1.919 −2.537* 3.240 4.910 ROU −1.996 −1.747 7.308** 6.173** HRV −2.305 −1.878 1.250 2.004 HUN −1.699 −2.653* 13.402*** 12.517*** POL −2.403 −2.658* 11.690*** 10.321*** CZE −2.202 −3.890*** 10.252*** 11.714*** SWE −3.286* −2.939** 14.022*** 11.974*** Note: *, **, *** indicate statistical significance at the 10%, 5%, and 1% level, respectively. Regressors include, intercept, trend and seasonal dummies. Optimal lag order between 1 and 7 is derived from the Akaike Information Criterion. 3832 International Journal of Finance & Economics, 2025 directly from our model. When applying this less strict criterion, Table4 shows that the Czech Republic and Croatia also display some similarity in the sense of a common, but not perfectly synchronised common cycle. Finally, when considering higher orders up to three, we find a common feature for all countries for at least one of the two testing procedures. To further explore the robustness of the limited finding on a common seasonal pattern, we first consider the choice of lag length in the common features test. In our baseline specification, the lag length was determined by the Akaike Information Criterion (AIC). However, underspecification of the lag length might lead to an overrejection of the null hypothesis of ‘no common serial correlation feature’ as any remaining autocorrelation in the residuals would be picked up in the second stage of the test. We, therefore, also explored other lag structures to illustrate this point. Table5 shows the results when adding or dropping one lag, compared to the one indicated by the AIC. We indeed find that with a shorter lag length, there is an even stronger rejection of the null hypothesis, while at a larger lag length, we cannot reject a common serial correlation feature for the case of the Czech Republic at the conventional 5% significance level anymore, when using the 2SLS procedure that leads to a pvalue of 0.068. We nevertheless keep the AIC as our benchmark. This is because the alternative Schwarz Information Criterion indicates the same or fewer lags to be included in the exercise. Also, when using the 10% level, the result of the Czech Republic would be negative, and the GMM test even rejects the common feature at 5%. As another robustness check, Table6 reports the results of the earlier canonical correlationbased version of the common features test of Tiao and Tsay(1989), of which the previously reported test can be seen as a generalisation. Schleicher(2007) showed that the optimal GMM estimator tends to slightly underreject and the Tiao and Tsay test tends to slightly overreject at sample sizes comparable to those in our analysis. When using this test, however, we confirm most of the findings above, except for Sweden, which according to the strict common features test does not constitute an Optimal Currency Area with the EMU countries. Overall, the evidence of common persistence and the similarity of autoregressive coefficients between the EU12 and the TABLE 3 | Seasonal cointegration tests for loglevels (unadjusted) with trend/bivariate against EA12. 0 𝝅 Lags r = 0 r ≤ 1 r = 0 r ≤ 1 BGR 723.073*** 0.217 16.342*** 6.761 ROU 58.485 0.532 7.793* 3.103 HRV 618.462*** 2.112 8.017* 2.320 HUN 611.625* 0.251 6.119 0.568 POL 521.180*** 0.022 15.258*** 0.754 CZE 57.885 0.000 — — SWE 714.640** 3.334 — — Note: Trace statistics. *, **, *** indicates the rejection of the null based on linearly interpolated critical values of Lee and Siklos (1995). Optimal lag order between 1 and 7 is derived by Akaike Information Criterion of the bivariate VAR incl. deterministic trends and seasonal dummies. TABLE 4 | Optimal GMM test. Cointegration at frequency Codependence of order 0 1 2 3 Lags Null Stat. Prob. Stat. Prob. Stat. Prob. Stat. Prob. BGR 0, 𝜋 7GMM 46.26 0.000 39.02 0.001 32.24 0.006 24.79 0.053 2SLS 28.59 0.018 26.41 0.034 13.07 0.597 ROU — 5 GMM 72.60 0.000 56.05 0.000 44.22 0.000 32.63 0.000 2SLS 34.80 0.000 33.56 0.000 12.63 0.180 HRV 0 6 GMM 31.70 0.002 27.26 0.007 24.67 0.016 19.12 0.086 2SLS 18.75 0.095 16.59 0.166 9.94 0.621 HUN — 6 GMM 43.42 0.000 34.26 0.000 28.20 0.003 16.08 0.138 2SLS 21.14 0.032 19.93 0.046 7.73 0.737 POL 0, 𝜋 5GMM 77.16 0.000 62.86 0.000 45.12 0.000 28.88 0.002 2SLS 42.15 0.000 39.28 0.000 11.66 0.390 CZE — 5 GMM 19.35 0.022 10.41 0.319 5.92 0.747 4.75 0.855 2SLS 7.61 0.574 7.60 0.575 2.70 0.975 SWE 0 7 GMM 17.24 0.244 12.85 0.538 9.82 0.775 10.11 0.754 2SLS 9.75 0.780 7.60 0.909 7.77 0.901 Note: Optimal GMM/2SLS χ2 test statistics and relative pvalues. Lag order selection, see Table3.