meeting maastricht 01 2008

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Meeting Maastricht:Nominal Convergence of the New Member States

Toward EMU

Pierre L. Siklos*Department of EconomicsWilfrid Laurier University

Viessmann European Research Centre

[August 2009]Please do not quote or cite without permission

* Part of the research for this paper was done while I was visited the European Commission under theDirectorate General Economic and Financial Affairs (DG-CFIN) Visiting Fellows program, January2008 (contract No. 309/2097/S12.483468), and held the Bundesbank Foundation Chair at the FreieUniversit t, Berlin, from October 2008-March 2009. Comments from seminar participants at DG-ECFIdetailed and constructive comments from four anonymous referees, as well as helpful discussions withLars Jonung and Istvn Szkely, also improved the paper. Additional results not presented in the paperrelegated to an Appendix available athttp://www.wlu.ca/sbe/psiklos.


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Abstract

This paper estimates whether the New Member States (NMS) that joined the EU in 20have achieved a form of inflation and long-term interest rate convergence. Using quarterly dfrom the mid-1990s, convergence is evaluated through a series of unit root and cointegrattests. Both univariate and panel tests are performed, including tests for a large number combinations of inflation and interest rates satisfying the Maastricht inflation and long-teinterest rate criteria. It is generally found that nominal convergence in inflation has been attaiamong the NMS. There is, however, less evidence of convergence in long-term interest ra

Possible exceptions include Estonia and the Czech Republic and, to a lesser extent, Slovawhich has since joined the euro area. There is also a large degree of consistency between various unit root and cointegration tests in both the univariate and panel variations.

Keywords: convergence, unit root, cointegration, new Member StatesJEL Codes: E31, E42, E58, C22, C23Pierre Siklos, e-mail: [email protected], Home Page:www.wlu.ca/sbe/psiklos


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1. Introduction

The Maastricht Treaty, notably the inflation criterion1, has been viewed as critical to the

successful launch of the European Monetary Union (EMU), and the euro. A drop in inflat

worldwide, as well as the political will to carry out the project of monetary unification, a

tipped the balance in favour of success. As 2009 began, the euro area expanded to 16 countr

with six of ten accession countries (new member states, or NMS) that joined in 2004 still in

euro adoption planning stages, with many likely to remain in that state for some time.2 Adoption

of the euro is mandated by the enlargement process.3

Other than Cyprus, Malta, and Slovakia, which entered the euro area in 2008 and 200intended EMU membership dates of almost all new EU members have proven to be ove

optimistic. von Hagen and Traistaru-Siedschlag (2006, Table 1) suggest euro adoption da

ranging from 2008 to 2010 for all but one of the accession countries.4 However, on both

economic and political grounds, euro adoption by the 7 remaining new EU members may

delayed.5

1 The macroeconomic, or convergence, criteria are specified in Article 109(j) of the Maastricht Treaty(http://www.eurotreaties.com/maastrichtec.pdf ). A brief background on the history of the Treaty can also be foundin Siklos (2008).2 For convenience, this study refers to the EMU-13 as the euro area member countries as of December 31, 2007.they are: Austria, Belgium, Finland, France, Germany, Greece, Ireland, Italy, Luxembourg, the Netherlands,Portugal, Slovenia, and Spain. Denmark and the U.K. have relied on an opt-out clause to remain outside the euroarea while Sweden has apparently exploited a loophole (De Grauwe 2007), as well as having politically rejectethe euro (Jonung 2004), to stay out of the euro area. The new EU members consist of : the Czech Republic, EstonCyprus, Hungary, Latvia, Lithuania, Malta, Poland, Slovakia, and Slovenia. Bulgaria and Romania, both joined tEU in January 2007, are not considered in this study due to data limitations.3

Once membership in the exchange rate mechanism (or ERM II, as it is called) has lasted for two years without adevaluation. ERM II describes the exchange rate regime for EU members outside the euro area in preparation foradoption of the euro. The latest agreement, in 2006, can be found athttp://www.ecb.int/ecb/legal/pdf/c_07320060325en00210027.pdf .4 Poland has no official intended date for adoption. Hungary and the Czech Republic have not officially joined ERII.5 The decision by the European Central Bank (ECB) and the European Commission (EC), to deny entry into the earea to Lithuania, in part because of a failure to meet the inflation criterion by 0.1% may also have discouragedentry into the euro area among the NMS. In reaching this decision the responsible bodies excluded episodes of negative inflation thus artificially raising the countrys reference inflation rate.


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There continues to be an outpouring of research on the general question of convergen

The present study follows a purely statistical approach in order to focus attention on the proc

of meeting two of the key convergence criteria named in the Treaty, namely the inflation a

interest rate thresholds. Ultimately, both the ECB and the EC will also focus on the question

nominal convergence, for good or ill, as these are the only criteria that open the door to e

adoption.6 Using quarterly data from the mid-1990s, nominal convergence is assessed through

series of unit root and cointegration tests. It is found that nominal convergence in inflation

been achieved among the NMS. There is somewhat less evidence of convergence in long-t

interest rates. Although not, strictly speaking, comparable to the Convergence Report proced(see below), the time series approach does provide an indication of the likely success at mee

the salient Maastricht criteria.

The rest of the paper is organised as follows. Section 2 provides some background abo

the scope of the study and a brief review of the related literature. Section 3 describes

methodology of the paper. The data and empirical results are discussed in Section 4. Sectio

includes a summary and concluding remarks.

2. Scope of the Study and Related Literature

This paper focuses exclusively on the following two Maastricht Treaty criteria applied

the NMS:

Inflation rates must not exceed 1.5% of the average of the three best performing member

countries with respect to price stability;

6 Arguably, real economic convergence is of greater concern for purely economic reasons. Lein et.al. (2008)consider the progress made in real convergence along one dimension, namely productivity growth. However, thealso point out that EU membership, combined with the prospect of entry into the EMU, produces offsettingimplications regarding price level convergence. Mixed evidence is generated regarding the current state of realconvergence for the NMS. Clearly, the decision to join the euro area indirectly involves real convergence. Formahowever, only nominal convergence matters.


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Long-term interest rates must not exceed 2% of the average of the three best performing

member countries with respect to price stability.

It has now become conventional wisdom to argue that a price stability objective

synonymous with good monetary policy while the interest rate objective is supposed to signal

durability of the existing inflation regime since changes in long rates reflect changes

inflationary expectations.

Convergence is defined here by relying on the well-known and widely used concepts of u

roots and cointegration. Hence, convergence amounts to asking whether there exists a sin

stochastic trend shared by all series. For example, if all 10 of the most recently admittmembers into the EU share a common stochastic trend in inflation rates and interest rates, the

finding of nine cointegrating vectors implies a single common trend. This means that the lin

combination of these series is mean zero stationary. A single stochastic trend is, therefore, o

possible interpretation consistent with the notion of convergence. However, as we shall see, c

must be taken in identifying unit root and cointegration behavior with the convergence prope

Moreover, it is not at all obvious that all the NMS should be treated as a single block.

Unit root tests are used to determine if the resulting time series are stationary, based

the differential between each countrys inflation or interest rate and the reference value manda

by the Maastricht Treaty that are pre-conditions for membership in the EMU.7 More

importantly, some of the unit root tests reported below are based on the use of covaria

(Hansen 1995). Covariates are variables chosen according to economic theory, and presuma

correlated with the time series under investigation. After all, it comes as no surprise that succ

at meeting the Maastricht Treaty criteria depends on the behaviour of a constellation

7 The fact that the hypothesis is expressed in terms of inflation has implications for the time series properties of th price level. We return to this issue below.


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macroeconomic aggregates that influence inflation and interest rates.8 For this reason, the search

for structural breaks is eschewed in the present study.

Unit root tests using covariates have been shown to possess more power, and may also

more economically useful for the question whether certain aggregates can better explain the t

series properties of inflation or interest rates. To complement the univariate analysis, tests i

panel setting are also considered. Clearly, there is a possibility that the currently exclu

members of the euro may join temporally closely to each other, perhaps by virtue of the fact t

they all lie to the east of the existing EMU-13. Also, many of the countries in question sh

common borders not to mention a common entry date into the EU. While the span of the datais comparable published tests of this kind (e.g., see Lein et.al. 2008) panel tests also assist

establishing the robustness of the results. Finally, we turn to cointegration testing. Siklos a

Wohar (1997) and, more rigorously, Pesaran (2007a), show that convergence requires that

pairs of time series be cointegrated.

A variety of approaches have been adopted to study nominal convergence. Studies th

estimate the determinants of inflation, or inflation differentials, via cross-section or panel stud

come closest to the approach followed here. Another strategy is to examine either the persiste

properties of inflation (e.g., see Galati and Melick 2006, Franta, Saxa and mdkov 2007,

references therein), or assess the cross-sectional determinants of inflation differentials as in,

example, Hammermann and Flanagan (2007).9

8 Needless to say, this approach is far from being the only one. For example, one could instead ask whether the tiseries in question have a unit root, or are cointegrated, subject to some kind of structural break that upsets thestationarity property. However, there is a continuing controversy over the ability of existing tests to precisely datthe location of the break, not mention the possibility that there may be multiple breaks (e.g., see Bai and Perron2006). This aspect of the problem of testing for convergence is left for future research.9 Related to this question is the extent to which domestic versus global factors drive inflation differentials. See, foexample, Mody and Ohnsorge (2007), and Borio and Filardo (2007).


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Busetti et al (2007) consider inflation convergence among the first 12 countries

introduce the euro in 1999. They split their sample into two groups: pre-1997 and post-19

which is the year that the Maastricht criteria had to be met to qualify for euro adoption. Th

apply a variety of unit root tests to inflation differentials for each pair of countries to test

absolute convergence (i.e. inflation differentials converging to zero) and find evidence

converging inflation rates between 1980 and 1997. When performing the unit root tests,

intercept term is omitted since this is believed to increase the power of the tests largely beca

the test equation (see below) contains one less coefficient. As such, the test is for absol

convergence so that the inflation differential would be zero (on average) under the convergehypothesis. The authors conclude that the countries in the sample can be sub-divided i

clusters of low, mid, and high inflation groups. Accordingly, there is not complete convergen

especially after the exchange rate mechanism was changed.

Camarero et al (2002) analyse the convergence properties of interest rates using quarte

data from 1980-1996 for the original countries that joined the EU, including the UK, Sweden

Denmark, which did not to adopt the euro. They identify and test for two forms of convergen

namely long-run convergence and catching-up. Long-run convergence means that the count

have already converged, whereas catching-up refers to the narrowing of the interest r

differentials, that is, countries are in the process of converging. The degree of convergenc

determined by testing for the presence of both a stochastic and a deterministic trend, using

root tests of interest rate differentials. Camarero et al (2002) define the inflation differential

relation to the interest rate criterion set out in the Maastricht Treaty, as well as vis--v


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Germany.10 They find that long-run convergence exists for five countries, while six countries a

in the process of catching-up, and three are not converging at all (Finland, Portugal, and Italy)

Siklos and Wohar (1997) also resort to the cointegration methodology to consider t

convergence property of the data. However, they clarify the link between cointegration a

convergence. Most notably, convergence is consistent with a particular cointegrating vect

namely (1,-1) in the bivariate case. This is the statistical equivalent of stationarity in inflat

differentials.11 Moreover, in a multivariate setting, convergence has a common trend

representation. That is, if convergence betweenn countries is investigated, convergence requires

n-1 cointegrating vectors or one common trend. Siklos and Wohar (1997) consider thconvergence of inflation rates and interest rates in seven EU countries (five of which a

currently EMU member countries) as well as Canada, the U.S. and Japan. With respect

interest rate convergence, the cluster of countries that were among the first wave of EM

members show evidence of one or two cointegrating vectors for the 1981-1995 sample. Th

results are not indicative of convergence.

Relatively less empirical work has been done on the convergence properties of data fro

the NMS. Data limitations pose a significant problem. Holz (2006) tests for interest r

convergence in Central and Eastern European (CEE) countries using an error correction mo

The CEE countries include all the so-called accession countries that joined the EU, with

exception of Malta and Cyprus. Estonia and Slovenia are also excluded since no long-te

interest rates data were available for Estonia, while data for Slovenia are only availab

beginning in 2002. Slovakia is the only country to show evidence of cointegration with

10 However, they do not specifically identify how the Maastricht long-term interest rate criterion is actuallycalculated in their study.11 Horvath and Watson (1995) demonstrate that tests for cointegration have relatively more power when thecointegrating vector is specified a priori.


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EMU. The validity of these tests is clearly in question, as cointegration tests require a long s

of data and only five years of data were employed. Other studies, such as Koenda (2001), Kutan

and Yigit (2004), Koenda, Kutan, and Yigit (2006), also examine the convergence properties o

macroeconomic data for a variety of NMS. No firm conclusions are reached. Again,

benchmarks used are either Germany, or some combination of EU member states.

Weber and Beck (2005) test for convergence in inflation rates among six EMU countri

Using data for the 1995-2004 period, they report that once a country has met the Maastri

criteria, it will loosen the policies in place and converge at a slower rate.

3. MethodologyAccording to the Maastricht Treaty, EMU membership requires comparison with t

performance of the average of the three Member States with the best inflation record and lo

term interest rates.12 For example, the May 2007 convergence report relies on the April 2006 t

March 2007 period to arrive at an inflation reference value of 3%, which is 1.5% above

arithmetic average value of inflation in Finland, Poland, and Sweden, then the three count

with the lowest inflation rates.13 As such, when testing for convergence, it follows that each

country should be compared to the EMU criterion.

3.1 Unit Root and Panel Unit Testing

The existence of a unit root in the differential between the series indicates that there is

convergence since the two variables do not then share a common trend. Therefore, the abse

of a unit root implies convergence in the sense just described.

12 There is no certainty as to the timing of convergence reports. The ECB is required to report to the Council of thEuropean Union at least once every two years, or at the request of a Member State. The European Commission (Eis given the same mandate, and two reports are submitted to the Council in parallel. Convergence reports have be published since 1998, with the last three in May 2006, December 2006, and May 2007, and again in 2008 which a convergence report that led to a recommendation that led to Slovakias entry into the euro area in 2009. Seewww.ecb.int/pub/convergence/html/index.en.html.13 When no long-term interest rate data are available, a broad analysis of financial markets is conducted.. (EC2007, p. 13).


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The most frequently used unit root test is based on the Augmented Dickey Fuller (AD

specification. Nevertheless, a large variety of unit root tests exist, owing to the relatively l

power of the ADF test, among several statistical issues that have been raised in connection w

unit root testing (e.g., see Maddala and Kim 2003). In its most parsimonious form the ADF

equation is written

11

p

t t i t i t i

y y y (1)

where yt is the time series under investigation, defined as inflation in a country relative to t

Maastricht Treaty mandated reference value,is the differencing operator (i.e., 1t t t y y y ),

and the distributed lag of the dependent variable captures remaining serial correlation in the t

series. Schwarzs Info Criterion (AIC) is one of several available criteria that may be used

select the lag length in the augmented part of the test equation (see below) and is the prefer

choice under the circumstances, in large part to economize on degrees of freedom.14 Equation

(1) has no constant or deterministic terms. The possibility of a trend contaminating t

convergence test is another complication (e.g., see Pesaran 2007a).15 The role of the constant

can also be problematic. If the series in question is stationary, then is statistically

insignificant, and there is convergence in the time series sense of the word. As previously no

a test of absolute convergence (e.g., as in Busetti et. al. 2007) would exclude an interce

14 In most instances, relying on the Akaike Information Criterion (AIC) produced the same lag lengths (results noshown).15 Elliott, Rothenberg and Stock (1996) propose the DF-GLS (and point optimal) test wherein the series detrended using GLS and the ADF test is applied to an auxiliary equation shown below.

11

k

t t i t i t i

y y y u (2)

where t y is the demeaned time series being investigated. More precisely,

21 2 1 1, 1, ( )( ), (1,(1 ),...,(1 )) ', ( ,( ),...( )) ', 1 , 7,t t t t t t t t T T

c y y z z z zy z y y y y y y c T

T

is the number of observations. Test results (not shown )based on this procedure did not qualitatively change theconclusions in the overwhelming number of cases.


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Clearly, however, there can be a form of convergence such that there is a constant differen

between the Maastricht criterion and a NMSs inflation rate. A negative shift, for examp

relative to the minimum acceptable inflation rate, would be consistent with the Trea

convergence requirement.16 The existence of this tolerance factor in the inflation criterion

suggests that absolute convergence, as defined above, is not the only condition that comp

with the Treaty requirements. A form of convergence, conditional on a constant differential, m

also be consistent with convergence.

Beyond the well-known limitations of the ADF test, perhaps the most striking is that on

the past history of the time series is used to make inferences about the unit root property of data. Hansen (1995) augments the ADF test with information from (stationary) covariates (a

see Elliott and Jansson (2003), and Caporale and Pittis 1999). The result is the so-called

Covariate ADF or CADF test, which adds a correlated stationary variable to the test equation

and this is shown by Hansen (1995), and Elliott and Jansson (2003), to considerably increase

power of the ADF test. Hence, equation (1) becomes (again, omitting a constant,

deterministic components)

11

p

t t t i t i t i

y y x y (4)

where (0)t x I .

There is intuitive appeal to the CADF test since covariates should be economica

relevant variables that would be incorporated, for example, into a structural VAR type model

16 However, both the sign and the size of the constant may matter. Some of the tests considered do include anintercept and it turns out that the role of the constant does not change any of the conclusions reported below. If, fexample, there is a permanent shift in the inflation rate this will bias the test towards the rejection of stationarity in favour of the unit root null hypothesis. Another possibility not considered below, is that there exists an asymmaround some equilibrium value. This extension requires testing in the univariate framework (e.g., see Enders andGranger 1998, Enders and Siklos 2001). Extensions to the panel setting have not yet been developed. This extensis also left for future research.


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the context of a test for convergence in the spirit of the Maastricht framework, there are clear

number of excellent candidates that can serve as covariates. Romer (1993), and Gruben

McLeod (2004), argue that openness is correlated with inflation, and is therefore an obvi

covariate candidate. The openness variable is usually defined as:

( ) Exports ImportsOpen

GDP(5)

where Exports is the flow of the value of goods and services exported, Imports is the flow

of the value of goods and services imported, andGDP is nominal GDP. Other candidates as

covariates include of a measure of output growth (or the output gap), and a real exchange r

The latter is relevant in the present study owing to the impact of the Balassa-Samuelson effec

the NMS (e.g., see gert et.al. (2006), Lein et.al. 2008). The CADF test, applied to the long-t

interest rate, would consider inflation or, rather, expected inflation, as a covariate. This is ea

motivated by the Fisher equation that captures the wedge between nominal and real interest ra

Other covariates include the long-term interest rate in the euro area.

Panel unit root tests are considered next. Since all NMS joined in 2004, it is likely ththere will be some cross-sectional correlation in the behaviour of the time series und

investigation. Of course, the extent of the correlation may vary as there is potential variation

the anticipated euro adoption dates. Pesaran (2004) proposes a simple test statistic to meas

cross-sectional dependence. In the present context, pair-wise correlations between the residu

of individual ADF type specifications which omit a cross-sectional element can also be use

derive the appropriate test statistic.17 A version of a panel test performs an ADF test on each

17 Specifically, the following estimate of the average of the pair-wise correlations is obtained from1

1 1 (2 / ( ( 1))

N n

jk j k I

N N , where is the pair-wise correlation of the residuals across the countries (total =


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country individually, and Im, Pesaran and Shin (2003; IPS) provide the critical values. The A

tests tend to have a downward bias, which is corrected for when a panel test is used. Genera

if all independent parameter estimates are unbiased, then the mean of these estimates is a

unbiased (Enders 2004, p. 225). This version of the panel unit root test generates a test stati

for each cross-section, as well as a country specific lag augmentation term. In contrast, if

hypothesis that ' j j , where ' j j , represent the unit root test statistic for two different

countries, and it cannot be rejected then an alternative formulation of the test specification

where (as well as in equation (1)) are fixed across all countries results in the more

restrictive Levin, Lin, and Chu (2002; LLC) panel unto root test.18

These tests are the standard ones used in the literature but they all have in common t

fact that the tests are designed for cross-sectionally independent panels. This could be a stro

assumption since all new EMU countries must meet the reference inflation rate prior to entr19

In the panel setting, there have similarly been several developments addressing the role of cr

sectional dependence. Pesaran (2007) is a recent contribution that provides a brief overview

the literature (also see reference therein). Assuming that there is a single common factor that

be represented by the cross-section mean, he shows that the following specification tends to

perform other similar panel unit root tests in terms of power. The resulting test, called the cro

sectional ADF test statistic (CS-ADF) is written as follows (omitting deterministic factors):

, 1 1 jt j j j t j t t t y y y y (6)

N) in the data set. The statistic for cross-sectional dependence (CD), is then evaluated as 1/2 ( ( 1) / 2)TN N whereT is the total number of observations in the panel. The formula is slightly different if the panel is unbalanced.18 LLC advocate removing the overall mean of the series (i.e., y ) prior to running the test. It is not immediatelyobvious that this is necessary when the series under investigation is a differential between two existing series.19 Since the timing of entry can be different this can have the effect of reducing cross-sectional dependence but mnot eliminate it entirely. Karlsson and Lthgren (2000) show that the power of the IPS and LLC tests is affected bthese considerations.


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where the resemblance to the ADF specification should be clear except for the additional ter

that capture the cross-sectional mean and change in the mean, both lagged one period.

continue to be interested in the ( , ) jt N T on the parameter j as an indication of whether there is

a unit root in the panel that consists of N cross-sections and T observations. Pesaran (200

Table II) derives critical values and these are shown to depend on T/N. In the present applicat

T/N ranges between 20 and 76.

3.2 Cointegration and Panel Cointegration Testing

The Johansen cointegration test is employed on each individual country and the EM

variable, as well as in a panel, with all ten NMS pooled together. However, it is also sensiblconsider separate tests where Cyprus, Malta, Slovenia, and Slovakia, all recently admitted i

the EMU, are treated as belonging to one cluster (cluster #1) while the remaining NMS

relegated to a second cluster of countries (cluster #2). The tests are run on the full samp

because the convergence process is assumed to have begun well before entry into the EU.

with the unit root tests, the cointegration tests are run with an intercept only, and the Schw

criterion is used to select the lag lengths. The specification for the Johansen cointegration te

written:

... jt j0 jECt 1 1 jt 1 p 1 jt p 1 jt (7)

where jt is the inflation/interest rate of country j at timet , jECt 1 is the error correction term, p is

the number of lags, s arem x m matrices of unknown parameters and jt is an error term. In

order for a country to be converging with the EMU benchmark, results must indicate evidenc

one cointegrating vector.

4. Data and Empirical Results

4.1 Data


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The data, unless otherwise stated, are from Eurostat and are sampled or were converted

to the quarterly frequency. This includes data for the covariates (exports, imports, nominal GD

real exchange rates, debt to GDP ratio). All statistical tests cover the 1995.1-2007.4 peri

However, data limitations required generating some additional results for shorter samples (e

1996.1-2007.4). It is not straightforward to pinpoint an appropriate start date for unit root a

cointegration type tests. Ideally, cointegration testing requires a long span of data but th

ultimately depends on how quickly euro adoption is expected. When the 10 accession count

considered in this study joined the EU in May 2004 the expectation was that euro adopt

would take place as soon as possible as this was viewed as arguably the most desirable elemof euro area entry. It is also known that negotiations for accession began soon after the candid

countries began to liberalize their economies and modified legislation to conform to the EU

acquis communautaire . Therefore, a mid-1990s start data appears reasonable as it excludes th

ERM crisis and avoids, though not entirely, the era of administered pricing. Inflation w

constructed from the raw Harmonized Index of Consumer Prices (HICP).20 The annual inflation

rate is defined as:

12100*(log log )t t t HICP HICP (9)

As several of the covariates (e.g.,Open, output gap) are only available at the quarterly

frequency, the monthly inflation figures were converted into quarterly data by arithme

averaging.21 Since the Eurostat HICP data begin in 1996 data from the IMFs International

Financial Statistics (IFS) CD-ROM (December 2007 edition) for the calendar years 1994 and

1995 were used to supplement the price series. A check of the series (not shown) from the

20 It is also worth pointing out that most time series studies of convergence rely on the IMFs CPI data, which is nidentical to the HICP that is used in the convergence reports.21 Inflation estimates based on measurement at the quarterly frequency do not change the conclusions.


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sources suggest few differences in the early part of the sample (e.g., 1996-1997).22 Long-term

interest rate data, namely the yield on government bonds maturing in 10 years, were obtai

from the ECBs website because these are the rates used in evaluating whether member sta

have achieved the relevant convergence criterion, as well as because one country, Estonia, d

not have comparable long-term interest rate data. Hence, the relevant proxy was constructed

the ECB for this purpose (http://www.ecb.int/stats/money/long/html/index.en.html). These are

available since January 2001. Additional data from the IMFs IFS were spliced with the ECB

series to extend the sample back to 1997.

As the CADF test requires stationary covariates, either differencing or Hodrick-Presc(H-P) filtering was used.23 Gaps were generated for the real exchange rate and real GDP using

the standard 1600 smoothing parameter. The real exchange rate variable is based on unit la

costs as this was the definition available for the widest possible number of countries. There w

no comparable real exchange rate data for Slovenia. For the openness and debt to GDP r

covariate differencing was used to generate stationary series.

It was, of course, necessary to create a series that represents the inflation criterion in t

Maastricht Treaty. The following procedure was adopted. From the monthly HICP inflat

figures an annual inflation rate was created via simple arithmetic averaging. While converge

reports can, in principle, occur at any time during a calendar year it is unlikely that more t

one will be published in one year. Next, the three lowest inflation rates in a given calendar y

were used to create the reference rate. To arrive at the reference values, negative inflation ra

were removed. In addition, only the EU-15 member countries inflation rates were used in

period 1995-2003, inclusive. Thereafter, the sample of countries included in the calculation

22 This appears less true in subsequent years though no formal statistical comparison was carried out.23 The H-P filter has well-known deficiencies but is widely used. Alternative filters (e.g., band pass, Beveridge- Nelson) have their own drawbacks.


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expanded to the EU-25. If we take the ECBs reference inflation rate from the May 20

convergence report, that is 3% (ECB 2007, p. 8), the procedure adopted here selects the sa

countries (Finland, Poland, and Sweden) and produces a reference value of 2.85%. Ot

reference values were also considered for the sake of comparison since there is inher

uncertainty about which countries and what inflation rates will prevail in future. One obvi

alternative is the ECBs own inflation objective of below 2% in the rate of change of the HI

Alternatively, I took the three lowest values from the highest inflation rates on a monthly ba

recorded for each member state in a given calendar year to construct a maximum refere

value for inflation. I also constructed a minimum inflation reference value where the thlowest monthly inflation rates within a calendar year for each country was the norm used aga

which inflation rates across member states were compared. Finally, all of the above referen

values were also constructed using euro area wide data.

Figure 1 plots a variety of reference values together with the resulting convergen

criterion estimates for the long-term interest rate. By way of comparison, the shaded a

displays a range of 1-3% that is typical of inflation targets in many industrialized economies.

ECBs 2% rule is meant to reflect the ceiling for its price stability objective. The Maastri

criterion approaches but never quite reaches the ECBs objective. Only the minimum versio

the Maastricht definition reaches the ECBs goal but only on three occasions (1999, 2000, 200

Interestingly, 2004 marks the year when the NMS considered in this study joined the EU. All

other alternatives produce substantially worse inflation outcomes. This is most clearly seen in

third part of the Figure which shows that a euro area based calculation appears to result i

permanently higher reference value relative to the ECBs own price stability objective.


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Tests are based on the differential between the NMS inflation or interest rate outcom

and the appropriate reference values, the series tested are defined as

M jt jt t d y y (10)

where jt d is the difference either between inflation( ) jt or the long-term interest rate( ) jt r in

country j, at timet , and the reference values denoted M t y .24 For the panel tests, the results

reported below are based on two clusters of countries. This is done mainly to differenti

between countries that recently joined the euro area, namely Slovenia (2007), Cyprus and M

(2008), and Slovakia (2009). Figure 2 plots the inflation and interest rate differentials defin

above arranged according to the cluster definitions provided above. One sees the sha

downward movement in the inflation differentials across all countries in the second half of

1990s, although it is interesting to note that progress toward the Maastricht criterion appe

more pronounced among the second cluster of countries. At least half of the NMS in the f

cluster were achieving inflation records that were consistently around the reference value,

indication perhaps of the sustainability requirement highlighted in the Maastricht Tre

protocols. It is also the case that for the NMS in the second cluster of countries there i

noticeable rise in annual inflation toward the end of the sample. This is also apparent, though

lesser extent, for the cluster 1 group of countries while, as Figure 1 reveals, average euro a

inflation is fairly stable after 2002. Turning to the interest rate differentials, we see that these

almost all below the Treaty requirement.25

4.2. Empirical Results

24 To economize on space only results pertaining to the Maastricht defined convergence rules are presented.25 A particularly important problem with interest rate data is that while long-term rates are supposed to reflectdomestic inflationary expectations, in practice here are other factors that affect such rates including, of course,liquidity and risk considerations but perhaps also the expectation that all the NMS are eventually required to joinEMU.


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Table 1 provides test results concerning the univariate properties of the series o

differentials (i.e., it d ). When openness is the covariate, 3 of the 4 member states inflation rat

differentials are found to contain a unit root.26 In contrast, for only half of the second cluster of

countries (i.e., the last six countries listed in the Table; all are first Cluster countries) is ther

non-rejection of the unit root null, though it is worth pointing out that these non-rejections

overturned when the DF-GLS version of the same test is applied (not shown). Since this

applies a form of detrending which might be important under the circumstances (e.g., see Fig

2) it is still reasonable to conclude that while inflation differentials are I(0), reasonable dou

can be raised for certain countries (e.g., Slovakia). Roughly, the same conclusion holapproximately when the output gap is used as a covariate.27 Similarly, other covariates, such as

the real exchange rate gap, produce some contradictory results relative to the standard,

statistically less powerful, unit root tests (results not shown). It is likely that the stationar

property is less a feature of the data for the Czech Republic, Estonia, Slovakia, and, poss

Poland, than for the other NMS examined. Finally, it is instructive that when a shorter sam

that begins in 2000 is used, permitting the use of the debt to GDP ratio, the unit root hypothe

cannot be rejected for six of the ten countries examined. The only rejections are to be found

two of the four cluster 1 group of countries that have joined the euro area in 2008, nam

Cyprus and Malta. Since the debt to GDP ratio involves a shorter sample, the remaining te

were also carried out again for the post 2000 period (not shown). The case against a unit roo

inflation is once again confirmed for all members of the first four countries listed in Table

26 The case of Slovakia is overturned when the DF-GLS version of the unit root test is applied.27 In principle it is possible to rely on more than one covariate at a time but owing to the span of the sample it islikely statistically inadvisable to do so. Moreover, as these covariates are likely to be somewhat endogenous, it isunclear that the simultaneous addition of several covariates will improve on the precision of the test.


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Hence, it is possible that convergence is indeed a feature of the data for the countries that h

joined the euro area, and Slovakia, but this is not the case for the six remaining NMS countrie

Turning to the interest rate series, the results are overwhelmingly in favour of the findi

of a unit root in the interest rate differential. This implies lack of convergence. It should

emphasized that this lack of convergence need not arise because jt d is too high in the NMS but,

as Figure 2 suggests, long-term rates may be too low relative to the Maastricht criterion.28

Table 2 considers the test for cointegration based on pairs of series. In other words, t

test asks whether the linear combination of ( , ) M jt t y y is I(0) rather than directly testing the

stationarity property of the differential series. If cointegration is found, we can then test whet

the cointegrating vector has the (1,-1) property. If the cointegration tests are to be consistent w

the unit root tests then the pairs of series should be cointegrated in the case of inflation and no

the case of the long-term interest rate. For countries in cluster #1, this conclusion holds up w

the exception of Cyprus inflation rate.29 In cluster #2 cointegration is rejected for Lithuania,

Latvia and Poland. In a few instances the cointegration hypothesis was overturned when one

the covariates in the unit root test was added as an exogenous variable in the cointegration te30

The convergence property of inflation is more apparent than in the long-term interest rate ser

Additional cointegration tests, also displayed in the Table, this time asking how many comm

trends there are among the NMS clusters considered in this paper, suggest that the number

common trends is sensitive to the inclusion of covariates. For example, there is evidence

28 I also considered other covariates with no impact on the conclusions. I tried the long-term interest rate in the euarea as well as well as a dummy set to zero prior to 2004Q2, and then set to 1 for the first year the NMS weremembers of the EU, 2 for the second year, and so on. The conclusions reported in Table 2 are unchanged (resultsshown).29 Before estimating each VAR, a test was conducted to determine the appropriate lag length. This was limited to,most, three lags due to data availability.30 Once again, in order to economize on degrees of freedom, only one lag of the covariate in question was added the VAR.


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convergence as defined in this paper, when the debt to GDP ratio is added. As noted previou

this case applies to a shorter sample (i.e., post 2000). Otherwise, the results reveal relatively

cointegration among the second cluster of countries which is a result compatible with

previous cointegration and unit root test results. In contrast, there is a single cointegrating ve

among the first cluster of countries so that there is no interest rate convergence in this gro

However, the opposite conclusion is reached for the second cluster of NMS since fi

cointegrating vectors are found, an indication that there is one common trend in long-te

interest rates among, the Czech R., Estonia, Hungary, Lithuania, Latvia, and Poland. Wh

cointegration is found, the estimates of cointegrating vectors return a (1, -1) verdict only Cyprus, Malta, Lithuania, and Poland.31

Table 3 considers the above tests as before but in a panel setting.32 The panel unit root

tests for inflation confirm the findings based on univariate tests, the panel tests. The CS-A

tests reveal a clear rejection of the unit root null indicating non-convergence for interest ra

while, interestingly, convergence is a feature only of the first cluster of countries. There is

convergence for the second cluster of countries.33 The panel cointegration tests also support the

earlier findings of inflation convergence. Similarly, the results of the panel cointegration te

echo the univariate tests with three of the four cases considered consistent with non-converge

in long-term interest rates.

7. Conclusions

31 Error correction terms suggest a fairly quick speed of adjustment for Cyprus and Malta (roughly 2 quarters), anconsiderably longer adjustment (e.g., 8 to 13 quarters) for Lithuania and Poland (not shown).32 A panel of all ten countries was also considered but the conclusions are not fundamentally changed, for reasonthat will soon become apparent.33 The results tend to hold up even if the panel tests are run for a run or a sub-sample beginning in 2000 (results nshown).


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This study examines the time series properties of inflation rates and interest rates of t

New Member States that joined the European Union in 2004. Since the Maastricht Treaty

set specific guidelines that countries must meet before entering the EMU, it is useful

investigate whether these countries are in fact converging to the euro area member countr

Moreover, since four of the ten NMS have recently joined the euro area the procedures used

this paper can be judged against the much broader examination that all prospective EM

members must go through before being admitted into the euro area. The approach taken in

study asks whether each of the NMSs inflation and long-term interest rates has converged to

reference value mandated by the Maastricht Treaty on the basis of a series of statistical tests. Trelevant tests are conducted in both the univariate and panel settings.

Overall, the results are suggestive of convergence in inflation but not of interest rat

There is some question about whether inflation in the Czech R., Estonia, and possibly Pola

violate the inflation convergence criterion. Nevertheless, what is clear is that the test

stationarity is illuminated by including covariates, that is, economic variables that a

theoretically linked to the time series of interest. It is important to emphasize that the finding

inflation convergence is a somewhat weaker requirement than the finding of convergence

non-divergence, in interest rates. Moreover, the non-convergence of long-term interest rates n

not imply that the NMS have not satisfied the requisite criterion as the evidence simply sugg

that long-term interest rates are, for the time being, permanently below the Maastricht Tre

requirement. Whether this reflects what some believe to be the peculiar global behavior inte

rates in recent years is, of course, unclear. Nevertheless, and this is a salient conclusion of

study, proper time series tests of convergence can serve as a useful short-hand expression of

prospects of the remaining NMS joining the euro area.


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Borio, C., and A. Filardo (2007), "Globalization and Inflation: New Cross-Country Evidencethe Global Determinants of Domestic Inflation," Bank for International Settlements work paper no. 227, May.

Busetti, F., Forni, L., Harvey, A. and Venditti, F. (2007) Inflation Convergence and Divergenwithin the European Monetary Union. International Journal of Central Banking , 3 (June), 95-121.

Camarero, M., Ez, J., and Tamarit, C.(2002) Tests for Interest Rate Convergence and StructuBreaks in the EMS: Further Analysis. Applied Financial Economics 12, 447-456.

Caporale, G., and N. Pittis (1999), "Unit Root Testing Using Covariates: Some Theory aEvidence",Oxford Bulletin of Economics and Statistics 61(4): 583-95.

De Grauwe, P. (2007), The Challenge of Enlargement of the Eurozone, SUERF AnnuLecture 2007, Vienna, June.

gert, B., K. Lommatzsch, and A. Lahrche-Rvil (2006), Real Exchange Rates in Small OOECD and Transitional Economies: Comparing Apples with Oranges?, Journal of Banking and Finance 30(12): 3393-3406.

Elliott, G and Jansson, M. (2003), Testing for Unit Roots with Stationary Covariates Journalof Econometrics 115: 75-89.

Elliott, G., T.J. Rothemberg, and J.H. Stock (1996), "Efficient Tests for an Autoregressive URoot", Econometrica 64: 813-36.

Enders, Walter.(2004), Applied Economic Time Series , Second Edition. (New York: John Wiley& Sons).

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Enders, W., and P. L. Siklos (2001), Cointegration and Threshold Adjustment, Journal of Business and Economic Statistics 19 (April): 166-76.

European Central Bank (2007),Convergence Report May 2007, available atwww.ecb.int/pub/pdf/cpnrep/cr200705en.pdf .


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Franta, M., B. Saxa, and K. midkov (2007), Inflation Persistence: Euro Area and NMember States, ECB working paper 810, September.

Galati, G., and W. Melick (2006), The Evolving Inflation Process: An Overview, BIS work paper No. 196, February.

Gruben, W. and McLeod, D. The openness-inflation Puzzle Revisited. Applied Economics Letters , 11, 465-468, 2004.

Hammermann, F., and M. Flanagan (2007), What Explains Persistent Inflation DifferentiAcross Transition Economies?, IMF working paper 07/189, July.

Hansen, B. (1995), "Rethinking the Univariate Approach to Unit Root Testing UsiCovariates to Increase Power", Econometric Theory 11: 1148-1171.

Holz, M. (2006), Interest Rate Convergence in CEE Countries towards EMU Levels, Bo

Market Performance and the Perspective of EMU Membership, Universit

t Trier, January.Horvath, M., and M.Watson (1995), Testing for Cointegration When Some of the Vectors Prespecified, Econometric Theory 11 (December): 984-1014.

Im, H.M. Pesaran, and Y. Shin (2003), Testing for Unit Roots in Heterogeneous Panel Journal of Econometrics 115 (July): 53-74.

Jonung, L. (2004), To Be or Not to Be in the Euro: Benefits and costs of monetary unificatas perceived by voters in the Swedish euro referendum 2003, paper presented at the 4th AnnualViessmann European Research Centre Conference, available fromwww.wlu.ca/viessmann.

Karlsson,S. and M. Lthgren (2000), On the Power and Interpretation of Unit Root Test Economics Letters 66 (March): 249-55.

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Lein, S.M., M. A. Lon-Ledesma, and C. Nerlich (2008), How is Real Convergence Driv Nominal Convergence in the New EU Member States?, Journal of International Money and Finance 27: 227-248.

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Table 1 Unit Root TestsCountry Inflation Long-term interest rate

Open ygap Debt REERgap Open ygap Debt Cyprus -3.92* -4.13* -3.39* -4.35* -1.19 -1.17 -0.87Malta -1.14 -2.70* -2.74* -3.39* -0.61 -0.52 -0.38Slovenia -2.05 -1.65 -2.03* N/A -1.17 -1.09 -0.99Slovakia -2.12 -2.09 -3.40* -1.98 -0.80 -0.77 -2.07Czech R -2.12 -1.99 -1.86 -1.66 0.13 -0.02 -0.29Estonia -2.07 -1.79 -0.50 -2.33 -1.79 -2.12 -2.90Hungary -3.93* -3.53* -1.27 -3.80* -2.46 -2.20 -1.47Lithuania -4.94* -4.91* -0.56 -4.80* -0.80 -0.86 -0.72Latvia -5.05* -4.42* 1.05 -4.32* -0.87 -0.37 -0.70Poland -3.88* -4.04* -2.48 -3.47* -1.23 -1.19 -2.14

Notes: The unit root null is tested, and * indicates rejection of the null. The test statistic forspecific covariate shown. They are: the openness of the economy (OPEN), the output gap (ygreal exchange rate gap (REERgap). The critical value is from Hansen (1995, Table 1) and is -that expresses the relative contribution of each one of the covariates to the ADF type test equa provided but they are available on request and range from a low of 0.88 to a high of .999. Sein the main body of the paper. The inflation and long-term interest rate series are expressreference value whose calculation is described in the text.


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Table 2 Cointegation Tests

A. Pairwise Tests

Country Inflation With Covariate Long-termInterest Rate

With Covariate

Cyprus 17.76 (.01)* 3.00 (.85)Malta 7.28 (.30) 16.12 (.01; ygap)*

14.65 (.02; Debt)*4.42 (.65)

Slovenia 3.76 (.74) 24.66 (.00)*Slovakia 7.78 (.25) 12.15 (.05; Debt)* 4.86 (.59)Czech R. 4.32 (.66) 10.93 (.08) 14.92 (.02; Debt)*Estonia 11.27 (.07) 12.62 (.04; Open)* 6.95 (.33)Hungary 9.21 (.16) 18.10 (.01)* 8.42 (.21; Debt)Lithuania 15.70 (.01)* 19.51 (.003)*

Latvia 12.32 (.03)* 9.04 (.17)Poland 13.84 (.03)* 3.26 (.81)

Notes: Cluster # 1 consists of: Cyprus, Malta, Slovenia, Slovakia; Cluster # 2: Czech R., Estonia, Hungary,Lithuania, Latvia, Poland. The number of cointegrating vectors in parenthesis are shown for cases where theaddition of an exogenous variables changes the number of vectors found above. The test statistic is for the null ozero cointegrating vectors between pairs of series consisting of either inflation or the long-term interest rate and tMaastricht reference value. Tests rely on the Johansen VAR methodology, as shown in the main body of the papeExcept when the test statistic is in italics, in which case a VAR(1) is estimated, all other test statistics are based oVAR(2), based on a variety of lag length selection criteria (e.g., AIC, SIC). The column headed by Withcovariates provides the test statistic when a single lagged value of the covariate shown is added to the estimatedVAR. The critical values used are not, strictly speaking, appropriate under the circumstances, however. * indicaterejection of the null that r=0 with p-values in parenthesis.

B. Multivariate Cointegration TestsGroup of Countries Inflation Long-term Interest RateCluster # 1 (n=4) r=0, 37.69(.09)

r 1, 12.44 (.67)r 2, 6.41 (.65)r 3, 0.13 (.77)(r=1; Debt)(r=2; ygap)

r=0, 57. 55(.0004)r 1, 22.63 (.08)r 2, 12.32 (0.70)r 3, 4.13 (.72)

Cluster # 2 (n=6) r=0, 196.97 (.0004)r 1, 97.15 (.000)r 2, 56.51 (.001)r 3, 22.30 (.09)r 4, 7.55 (.27)r 5, 0.20 (.71)(r=4; Open)(r=4; ygap)(r=3; Debt)

r=0, 301.01 (.000)r 1, 138.98 (.000)r 2, 74.88 (.000)r 3, 40.32 (.0002)r 4, 17.10 (.01)r 5, 1.03 (.36)

Notes: see notes to Table 2A. r refers to the number of cointegrating vectors found (the number of common trendthenn-r ). For inflation and the long-term interest rate, the cointegration test is based onit d defined in the text, thatis, the inflation and interest rate differentials vis--vis the Maastricht reference value.Bold indicates the number of cointegrating vectors, p-values in parenthesis.


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Table 3 Panel Unit Root and Cointegration TestsA. Panel Unit Root

Group of Countries Inflation Long-term interest rateCluster # 1 LLC (DF-GLS): -8.87 (.00)

IPS (DF-GLS): -10.67 (.00)

LLC (DF-GLS): -2.02 (.02)

IPS (DF-GLS):-4.36 (.00)Cluster #2 LLC (DF-GLS): -8.50 (.00)IPS (DF-GLS): -8.29 (.00)

LLC (DF-GLS): -3.45 (.00)IPS (DF-GLS): -6.14 (.00)

Cluster # 1CS-ADF

CY: -3.43*MT: -4.91*SI : -3.88*SK: -4.98*

-4.93* CY: -1.93MT: -1.96*SI: -4.38*SK: -3.85*

-4.94*

Cluster # 2 CZ: -2.07EE: -3.38*HU: -3.74*LT: -6.64*

LV: -6.39*PL: -3.61*

-6.82* CZ: -1.62EE: -3.63*HU: 0.35LT: -1.75

LV: -1.88PL: -2.10

-3.18*

Notes: LLC is the Levin-Lin-Chu test, IPS is the Im-Pesaran-Shin test. CS-ADF is the crossectionally augmented DF test due to Pesaran (2007a; critical values in Table II), whileversions of the LLC and IPS tests based on the GLS detrending of Elliot, Rothenberg, andStock are the remaining tests given. P-values are given in parenthesis for the null of a unitroot in the panel. The text provides an explanation of the differences in the testspecifications.

B. Panel Cointegration Tests

Inflation Long-term interest rateCluster #1: 1.07 (.39)/2.00(.05)Cluster #2: 9.43 (.00)/12.21 (.00)

Cluster # 1: 1.19 (.20)/2.38 (.02)Cluster #2: 0.20 (.40)/1.80 (.08)

Notes: The test statistic is an Engle-Granger type test in a panel setting. The first set of tesimposes a common autoregressive parameter while the second set of test statistics assumesthat individual AR parameters are estimated for each cross-section in the panel. See Table for the definitions of the Clusters


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Figure 1 The Maastricht Inflation and Long-Term Interest Rate Criteria

0

1

2

3

4

5

1 996 1 998 2000 2002 2004 2006

Maast r i ch t ar t i c l e Eu r o ar ea av e r ageEuro are:best of hi ghest Euro ar ea:best of l ow estMaastricht article:best of highest Maastricht article:best of lowestECB 'target'

P e r c e n

t

Varieties of Inflation Cri eria:Annual Basis

0

1

2

3

4

5

6

7

8

9

1 998 2000 2002 2004 2006

Maastr icht arti cle Best of hi ghest Best of l ow est

Varieti es of Long-term interest rate cri teria:Annual Basis

P e r c e n

t

0

1

2

3

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5

1 998 2000 2002 2004 2006

Euro area averageEuro area Maxi mumEuro area Minimum

P e r c e n

t

Note: For a description of the sources of data and the detailed calculations, see the text.


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Figure 2 Inflation and Interest Rate Differentials Vis--vis Maastricht Reference Value

-5.0

-2.5

0.0

2.5

5.0

7 .5

10.0

12.5

15.0

1 994 1 996 1 998 2000 2002 2004 2006

Cy pr us Mal taSl ov eni a Sl ov ak ia

I n f l a t i o n D

i f f e r e n t i a l : P e r c e n t

-10

0

1 0

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30

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1 994 1 996 1 998 2000 2002 2004 2006

Czech R. Estoni a Hu ngar y Li thuani a Latv i a Pol and

I n f l a t i o n D

i f f e r e n t i a l : P e r c e n t

-3

-2

-1

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3

1998 2000 2002 2004 2006

Cy pr us Mal taSl ov eni a Sl ov ak ia

I n t e r e s t r a t e

d i f f e r e n t i a

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I n t e r e s t a t e

d i f f e r e n t i a

l : P e r c e n t

Note: Sources and calculations are described in the text. The vertical bar in the top two figureindicates the quarter in which the NMS became EU members.

meeting maastricht 01 2008

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