First draft: April 2003 Last revised: September 13, 2007

Real Exchange Rate Adjustment In European Transition Countries *

Florin G. Maican ** Department of Economics, School of Economics and Commercial Law, Göteborgs University Richard J. Sweeney *** McDonough School of Business Georgetown University

This paper presents unit-root test results for real exchange rates in ten Central and Eastern European transition countries relative to the Euro during 1993:01-2005:12. Because of the shift from controlled to market economies and the accompanying crises, failed policy regimes and changes in exchange rate regimes, appropriate tests in transition countries require allowing for both structural changes and outliers. Single-equation tests reject the unit-root null for nine of ten countries. Accounting for structural breaks (and in some cases, outliers) gives much faster mean-reversion speeds than otherwise. Keywords: Purchasing power parity; real exchange rate; Monte Carlo; unit root; transition countries; panel data. JEL Classification: C15, C22, C32, C33, E31, F31. * Thanks are due to Erik Hjalmarsson, Lennart Hjalmarsson, Sorin Maruster, Eugene Nivorozhkin, Violeta Piculescu, Jesper Rangvid, Cătălin Stărică, Rick Wicks and Finn Østrup, and to participants of a seminar in the Finance Institute at the Copenhagen Business School.

** Box 640 SE 405 30, Göteborg, Sweden. Phone: +46-31-773-4866. Fax: +46-31-773-4154. E-mail: florin.maican handels.gu.se *** 37th and "O" Sts., NW, Washington, DC 20057. Phone: 1-202-687-3742. Fax: 1-202-687-4031. E-mail: sweeneyr georgetown.edu

Real Exchange Rate Adjustment In European Transition Countries

Abstract: This paper presents unit-root test results for real exchange rates in ten Central and Eastern European transition countries relative to the Euro during 1993:01-2005:12. Because of the shift from controlled to market economies and the accompanying crises, failed policy regimes and changes in exchange rate regimes, appropriate tests in transition countries require allowing for both structural changes and outliers. Single-equation tests reject the unit-root null for nine of ten countries. Accounting for structural breaks (and in some cases, outliers) gives much faster mean-reversion speeds than otherwise.

1. Introduction Purchasing power parity (PPP) is one of the oldest, most studied topics in international finance. Many models of exchange-rate determination include the assumption that PPP holds at least in the long run. Many papers present tests of PPP in developed countries, and more recently a number of papers present tests of PPP in developing countries. Little work, however, deals with PPP in the transition countries of Central and Eastern Europe (CEE), which are moving from communist planning to free market economies, with some mostly free market but others with far to go. All of the ten CEE economies discussed here have joined the European Union: the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia and Slovenia joined in 2004, Bulgaria and Romania in 2007. Many observers argue that stable longrun real exchange rates are important for real convergence of CEE economies to the rest of the EU and thus for successful integration. This paper investigates whether long run PPP holds for these ten CEE countries by testing the unit-root hypothesis for their real exchange rates relative to the Euro for the sample period 1993:01-2005:12. Beyond the intrinsic interest of the CEE economies, the unit-root tests reported below are methodologically interesting because important shifts in the underlying economic processes in these economies require careful test-equation specification. All of these CEE countries switched from controlled to market economies, with the switch more or less prolonged and often subject to major lurches, reversals and slow downs. Further, many of these CEE countries experienced financial or political crises, abandoned economic-policy regimes that appeared to be failing and adopted other regimes. (Fischer and Sahay 2000 perceptively discuss twenty-five transition economies’ problems, including the ten countries considered here). In particular, these countries often relied heavily on exchange rates as a stabilization tool, using a range of exchange-rate regimes from managed floats to currency boards; the majority of CEE countries changed exchange-rate regimes at least once in response to economic difficulties, as Table 1 1

shows. As an example, because of hyperinflation Bulgaria switched in July, 1997, from a managed float to a currency board against the Deutsche mark. As expected, such changes in exchange-rate regimes affected real exchange rates, often substantially. Furthermore, several countries experienced periods of strong real appreciation, which their policy makers attributed to capital-account liberalization, catch-up price rises as non-tradable goods were gradually decontrolled, fiscal imbalances and productivity gains. In Figure 1 these turbulent histories appear to be associated with structural shifts in real exchange rates for a number of countries (for example, Bulgaria, Estonia, Latvia and Lithuania,) and with outliers (for example, Bulgaria, Romania and perhaps Slovakia). Tests in this paper allow for structural shifts and outliers. Results below support the view that CEE economies’ real exchange rates revert to long-run equilibrium levels; the data show mean reversion for nine of ten CEE countries against the Euro. Further, the results show that failure to allow for parameter shifts—or for a few countries failure to allow for outliers—biases test results against mean reversion for CEE economies. In addition, the results show that even if tests with mis-specified equations correctly reject the unit-root null, failure to take adequate account of parameter shifts and of outliers may cause substantial under-estimates of real exchange rates' adjustment speeds. These results are quite different from those in the few previous unit-root tests of CEE economies’ real exchange rates. For Hungary and Poland’s real exchange rates, Dibooglu and Kutan (2001) cannot reject the unit-root null for real exchange rates in standard single-equation augmented Dickey-Fuller (ADF) tests that do not allow for structural shifts or outliers. Kim and Korhonen (2002) present panel unit-root tests (based on Hadri 2000) for real exchange rates for the Czech Republic, Hungary, Poland, Slovakia and Slovenia, and the data reject the null of stationarity; however, their models do not allow for structural shifts or outliers. Results below focus on real exchange rates with the Euro as the base currency, because this is the most

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important for EU members, but results for the USD are also presented. Other discussions of real-exchange-rate movements in CEE economies do not investigate whether PPP holds, but focus on demand or supply effects (De Broeck and Sløk 2001 and Coricelli and Jazbec 2001). Égert (2004) gives a comprehensive review of work on transition economies’ real exchange rates. (Kočenda 2005 studies breaks in nominal-rate trends in CEE countries.) Perron (1989) and later papers show that failure to account for structural shifts in mean or in time trend biases tests against rejection of the unit-root null hypothesis. Related, Franses and Haldrup (1994) and Perron and Rodríguez (2003) show that failure to account for outliers biases tests against rejection of the unit-root null. Beyond these size and power issues, this paper addresses the fact that even if the data reject the unit-root null in a misspecified model, the misspecifiation causes bias in the estimate of key parameters—in this paper, misspecification reduces the real exchange rates' adjustment speeds. For ten CEE countries' real exchange rates, this paper presents the first unit-root tests that allow for shifts in means and time trends as well as for outliers, using three sets of models. The first set is based on models proposed by Zivot and Andrews (1992) and Perron (1997) to allow for shifts in means and time trends, where the investigator searches for when the shifts occur. These models are generalizations of Perron (1989), where the dates of shifts were pre-specified. As noted above, because of changes in exchange-rate regimes, financial or political crises, and the large structural changes the CEE countries have had to make, some of their real exchange rates appear to show such shifts. Second, the sharp disturbances that rocked many CEE countries suggest using Perron and Rodríguez's (2003) approach to pre-test for the presence of important additive outliers; the unit-root tests in Zivot and Andrews (1992) and Perron (1997) models are then modified to allow for any outliers detected by the Perron and Rodríguez (2003) pre-testing procedure. Third, for comparison to panel tests on developed countries’ real exchange rates, and in some cases developing countries real rates, this paper uses panel unit-

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root tests based on SUR techniques with the constraint that adjustment speeds are the same across countries. From this paper's discussion of tests and results, the practical suggestion for researchers is to apply the battery of tests, rather than trying to select a particular model to test based on examining the data or reading discussions of the data and the period under review. As reported below, experience with the data used here argues that the break model that appears appropriate a priori is often not the one that best fits the data, even if some break model best fits the data— the researcher cannot be very confident in selecting just one test from the battery. The cost of using the battery of tests is that this increases the size of the test. This cost is mitigated by a number of considerations. First, the researcher avoids the substantial gamble of choosing which test in the battery is the appropriate one. Second, in this paper, data for nine out of ten countries reject the null for at least one of the tests in the battery. Though the size of the battery of tests is larger than the size for any one test, the probability of the battery rejecting for nine out of ten countries is extremely small. The researcher with multiple series can “afford” to use the battery of tests. This paper presents unit-root test results for five models: The augmented Dickey-Fuller model and four models that allow parameter shifts. The reader may well ask the following questions: In practice, which is the "best" model to use, and how can the researcher decide on a particular model? Is it perhaps wiser to use the battery of five tests rather than just using one test? And what are the consequences of using the battery of tests? The practical suggestion from the paper's discussion is for researchers to apply the battery of tests rather than trying to select a particular model to test based on examining the data, reading discussions of the sample period's history or using "preliminary" regressions to explore the data. From the results reported below, the break model that appears appropriate a priori is often not the one that best fits the data, even if some break model fits best—the researcher cannot be very confident in selecting

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just one test from the battery; further, examining the data or reading discussions of the sample period's history use degrees of freedom, just as using "preliminary" regressions do. Using the battery of tests, however, increases the size of the test. This cost is mitigated by a number of considerations. First, the researcher avoids the substantial gamble of choosing which test in the battery is the appropriate one. Second, in this paper, data for nine out of ten countries reject the null for at least one of the tests in the battery. Though the size of the battery of tests is larger than the size for any one test, the probability of the battery rejecting for nine out of ten countries is extremely small: The researcher with multiple series can "afford" to use the battery of tests. (Section 3 discusses these issues in some detail.) In the remainder of this paper, Section 2 presents illustrations of the importance of using specifications that allow for structural shifts and outliers in unit-root tests of CEE economies’ real exchange rates, and also gives a survey of the literature on mean-reversion tests of real exchange rates. Single-equation unit-root tests for real exchange rates are discussed in Section 3, and Section 4 discusses panel unit-root tests. Section 5 describes the data and presents test results for monthly data on CEE real exchange rates with the Euro the base currency and CPIs the price levels. (For comparison, this section also briefly discusses results for CEE real exchange rates with the USD as the base currency and both CPIs and PPIs used as price levels.) Section 6 discusses the real-rate speeds of adjustment in these economies. Section 7 summarizes and draws conclusions. 2. Parameter Shifts and Outliers in CEE Economies; Previous Real-Rate Tests This paper presents unit-root test results for a battery of test-equation specifications. As Perron (1989), Zivot and Andrews (1992), Perron (1997), Perron and Rodríguez (2003) and others demonstrate, if a unit-root test is to have the stated size and optimized power, the researcher must use the specification the data require, including allowing for parameter shifts and outliers. In contrast, conventional unit-root tests—for example, augmented Dickey-Fuller

5

(ADF) tests—assume that the process’s mean and time-trend coefficient are constant, and any outliers are insufficiently important to distort the tests. Consider two illustrations. The data in Figure 1 suggest that there was a sharp change in Bulgaria’s mean real exchange rate relative to the Euro at approximately the start of 1997, and just after, a large outlier. In fact, in the face of a grave economic and financial crisis “the socialist government resigned in December 1996, and a reform-minded caretaker government was established to resolve the crisis….” (IMF 2004, p. 8, point 10), which suggests a structural shift and an outlier. Otherwise, the real exchange rate appears to show mean reversion on either side of the shift and outlier. As Section 5 shows, if unit-root tests do not allow for a structural change, the data reject the unit-root null at the 10% level (Table 4), but if the tests allow for a mean shift, the data reject the null at the 1% level (Tables 5, 6 and 8); conditional on the mean shift, Bulgaria’s real exchange rate shows mean reversion. In no test, however, do Bulgaria data require inclusion of an outlier: this illustrates a general point discussed below; the researcher cannot rely on visual examination of the data or examining the written record to select the appropriate model. In Figure 1 the data for Estonia appear to show a substantial negative mean rate of change in the real exchange rate (or real appreciation, as the real exchange rate is defined in Section 3) until say 1997, with perhaps a zero mean rate of change thereafter; otherwise deviations appear to be mean-reverting. In fact, in June, 1991, when Estonia adopted the kroon and pegged it to the Deutsche Mark through a currency board (and then to the Euro when it was introduced), Estonia central bank officials expected a period of real-rate appreciation as gradual decontrol of non-tradable prices caused the domestic price level to rise. As seen in Section 5, in ADF tests that do not allow for parameter shifts, the data can nevertheless reject the unit-root null at the 1.0% level (Table 4) against the Euro. The estimated speed of adjustment is very slow as compared to estimates in other specifications that allow for parameter shifts (Tables 5, 6 and 8), where the data also reject the null at the 1% level; the estimated speed of adjustment is 6

substantially faster, 6.80% or 6.70%/month in Table 5 (depending on the model) versus 2.2%/month for the ADF in Table 4. Previous Tests of Mean-Reversion in Real Exchange Rates. For developed-country data from the post-Bretton Woods era and using single-equation methods, Meese and Rogoff (1988) and Mark (1990) cannot reject the unit-root null for real exchange rates. Largely because of the low power of single-equation techniques when the root is close to unity, much of the later literature focuses on panel tests. Abuaf and Jorion (1990), Jorion and Sweeney (1996), Papell (1997), Sarno and Taylor (1998) and Higgins and Zakrajek (1999) find developedcountry data can reject the unit-root null in panel tests with SUR techniques.1, 2 Using panel methods with GLS techniques on developed-country data, Papell and Theodoridis (1998) find weak but increasing evidence in favor of PPP as the sample period lengthens. In contrast, O’Connell (1998) cannot reject the unit-root null using GLS techniques on panels that include both developed- and developing-country data. These papers make no allowance for structural shifts or large outliers.3 Some papers, however, detect the need to allow for parameter shifts in real exchange rate processes. Hegwood and Papell (1998) examine long annual data series—from 90 to 200 years, the Lee (1976) and Lothian and Taylor (1996) data sets—and find that the real exchange rate is stationary around a mean that experiences occasional structural shifts. Related to this paper's results, Hegwood and Papell also estimate substantially faster adjustment speeds in specifications that allow for mean shifts. Some economists argue that real exchange rate time-series models may require inclusion of time trends. Papell and Prodan (2003) find evidence of mean reversion around time

1

Some papers, for example, Wu (1996) and MacDonald (1996), use fixed-time effects rather than SUR methods. Fixed-time effects are not adequate, however, for real exchange rate data. 2 Sweeney (2007) applies SUR to G-10 countries’ log nominal exchange rates relative to the dollar during the current float and rejects the unit-root null with significance levels from the 0.5% to 15% across sample periods. 3 In panel tests, Jorion and Sweeney (1996) allow for mean and trend shifts in monthly data for G-10 countries from 1974 to 1993, but find that the shifts are usually not significant or are not needed to reject the unit-root null.

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trends in four of 18 countries’ real exchange rates. Obstfeld (1993) models such trends as arising from the Balassa-Samuelson effect (Balassa 1964, Samuelson 1964).4 In results below, inclusion of time trends sometimes reduces the standard error of the regression and increases the estimated speed of adjustment of a given currency. 3. Single-Equation Unit-Root Tests for Real Exchange Rates The real exchange rate is calculated as (1) where

denotes the natural logarithm of the nominal exchange rate (the domestic-currency

price of the base currency, either the Euro or the USD) at time , and

and

are the logs of

foreign and domestic price levels.5 Testing for PPP is equivalent to testing for a unit-root in the real exchange rate against a stationary alternative. In the simplest unit-root tests, the estimating equation is based on (2) where

is a sequence of independent identically distributed random variables with mean zero

and variance

or

. Under the unit-root null,

and

; if

,

then the real exchange rate is a random walk with drift, or contains a time trend with slope . Under the alternative hypothesis of mean reversion, rate is

and

holds in the long run if

, the long-run real exchange

is the real rate’s adjustment speed to its long-run level. PPP shows mean reversion, or permanent shocks do not drive .

A more general model allows for trend stationarity, as in

4

A number of economists investigate Balassa-Samuelson effects in transition economies, though they report mixed evidence regarding the size of the effect; Égert (2004) provides a survey of the arguments and evidence. 5 Engel (2000) and Ng and Perron (2002) use a somewhat different approach to analyze the real exchange rate. They decompose the real exchange rate into two components: . is the traded-goods component; captures the bilateral differences between the relative price of traded to nontraded goods. Engel (2000) and Ng and Perron (2002) investigate how non-stationarity of affects real-rate stationarity.

8

(3) ; if

Under the alternative,

, the equilibrium real rate contains a time trend,

but the real rate reverts to the trend equilibrium rate. Furthermore, serial correlation in allowed for by including k lagged values of

is

, giving an augmented Dickey-Fuller

regression, (4) k can be determined using the selection procedure Perron (1989) suggests (see also Ng and Perron 1995): Choose some maximum value for

and then reduce

until the t-statistic

exceeds 1.6 in absolute value. but either

Perron (1989) shows that if

or

shifts one time in (2), (3) or (4)

and the shift is not accounted for in estimation, then conventional tests are biased against rejecting the unit-root null. To allow for one shift in the intercept or time trend, re-write (4) as

(5) is a dummy, equal to zero for which the intercept shifts. where

and to unity for

is a dummy, equal to zero for

, where

is the time at

and to unity for

,

is the time at which the trend coefficient shifts. This is the general model nests the

models Zivot and Andrews (1992) investigate. Specialized versions of the general model in (5) are tested below. In Break Model 1, the time-trend parameters are, and

, but one mean shift

is allowed, and , , ,

are fit freely.6 Break Model 2 allows for one shift in the mean , but includes a constant

time trend,

6

and

, which does not shift,

. Break Model 3 allows for one shift in the trend

Papell (1997) and others argue, however, that real rates should not contain time trends.

9

parameter

but no shift in the mean . Break Model 4 allows for one shift in

at the same time, denoted Perron (1989) finds

and one shift in

. ,

, or

by identifying events before experimenting with

estimation (for example, the Great Depression and the oil shock of 1973-74). Most often, economists now find

,

and

(and the date of outlier h,

) as part of the estimation

procedure. Zivot and Andrews (1992) and Perron (1997) extend Perron’s (1989) methods for unit-root tests by developing procedures for detecting the date at which structural change most likely occurs. They endogenously estimate one breakpoint for each series considered.7 Zivot and Andrews (1992) suggest running OLS regressions for (5), where the breakpoint for

or

(1992),

is obtained for

,

. Following Zivot and Andrews

, is chosen such that (6)

Zivot and Andrews (1972) assume that any shift in process occurs only if the alternative hypothesis is true. Perron (1997), however, allows for a unit-root series where there is a oneperiod shift that has a permanent effect on the series. Under the null,

where

is a parameter and

is a dummy variable with value unity at time

and

zero otherwise. Under this general alternative,

(5') A process similar to that described around (6) is used to find break points. In addition to possible shifts in mean or trend, some CEE real rates appear to contain outliers. Franses and Haldrup (1994) and Shin et al. (1996) show that the presence of additive 7

Lumsdaine and Papell (1997) extend these tests to allow for two breaks.

10

outliers in a univariate time series affects the limiting distribution of ADF test statistics. Before the researcher performs unit-root tests, Perron and Rodríguez (2003) suggest s/he use a pre-test detection-procedure based on the regression 8 (7) , otherwise 0. The presence of an additive outlier can be tested for

where using

. If

exceeds the critical value, then an outlier is detected where

. (Perron and Rodríguez give critical values for

in their Table IV.)

The outlier-dates found from applying (7) are then used to augment the various break models to allow for outliers, giving the general model (8) (Unless the data strongly demand multiple outliers, Perron and Rodríguez suggest stopping with one outlier to preserve degrees of freedom.) If additive outlier the model requires a unit dummy for

occurs at time

and the next k periods because of the

ADF lag structure, with the dummy zero otherwise. An appendix available from the authors provides the details of how exact critical values from simulation were found for the various single-equation models. Discussion of Using a Battery of Tests. Papers on unit-root tests often present results for several break models, either for the same or different series. Perron's (1989) seminal paper uses BM2 on annual real GNP, nominal GDP, and interest rate data for the U.S., BM3 for quarterly real GDP, and BM4 for common stock prices and real wages. Perron chooses break points a priori, making use of history—for example, the Great Crash of 1929—to choose the break point for real GNP. Zivot and Andrews (1992) )suggest that

8

Vogelsang (1999) proposes two procedures for unit-root testing when additive outliers may be present. Perron and Rodríguez’s (2003) simulations show that the method used here has considerably more power.

11

researchers are most often likely to choose break points endogenously, at a date where some test statistic is maximized (or minimized), and they present critical values for break points thus chosen. Most papers presenting unit-root test results do not discuss how the model discussed was chosen. "Eyeballing" the data, or even deciding a priori as Perron did based on history, uses degrees of freedom. For an unknown number of papers, the researcher tries more model specifications than he reports. Researchers seldom examine the implications of using, say, all five of the models in Table 1. Maican and Sweeney (2007), however, examine this case using methods closely related to Zivot and Andrews' (1992) and Perron's (1997). If the researcher uses the 5.0% significance level for each model on the same random walk series, simulation results show that the size of the battery of tests that the null cannot be rejected at the 5% level in any model is approximately 17%. By themselves, these results make the rejections reported below in Tables 4-11 less impressive. The same is true, of course, in the unknown number of papers where the researcher tries more model specifications than he reports. Five considerations mitigate the fact that size increases when using a battery of tests. First, the battery of tests rejects the unit-root null for nine of the ten CEE countries. The size of a battery of tests on multiple series will depend on the cross correlations of test rejections (and these are only weakly related to the cross correlations of the increments). Results in the appendix suggest that if the cross-correlation of the increments is 0.50, then under the null the probability of rejecting for nine of ten real rates is 10-5 2.64%.9 Thus, with a number of series, the researcher has the "luxury" of using a battery of tests that has a larger size than the size for each series.10 Second, though less important, in the appendix’s simulation results for power, 9

Intuitively, the probability of not rejecting for the first real rate is 0.82953 and thus the probability of rejecting for the second real rate is 0.17047. Conditional of rejection for the second real rate, the probability of rejecting for any of other eight real rates is 0.1923. Then the probability for rejecting in nine out of ten cases is (0.82953) (0.17047) (0.1923)8 = 10-7 2.64 or 10-5 2.64%. 10 For example, if the cross-correlation of the increments is 0.50, then under the null the probability that five of the ten series reject is approximately 0.0003457 or 0.03475%. If the researcher has only five series, but two reject, the probability under the null is approximately 7.45% percent. Indeed, with only four series, rejection of two has a

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rejections tend to cluster across models. For example, if the true model is among BM2, BM3 and BM4, then rejection by one model tends to be associated with rejection by another of these three models. This clustering is observable in Tables 3-8. Third, the reader can make her own decision if all the results are reported (or summarized), rather than only the best results with no mention of the number and specifications of tests tried. Fourth, if the researcher tries to preserve the nominal size by choosing only one test, he may do so by inspecting the data with great care, reading discussions of the history of the time period the data cover or even trying "preliminary" regressions. Of course this uses up degrees of freedom. Fifth, and related, as illustrated below with CEE data the researcher may well focus on a sub-optimal model and thus draw erroneous conclusions about significance and the speed of adjustment. 4. Panel Models Panel data methods are frequently used in unit-root tests of real exchange rates, because they can ameliorate the low-power problem against near-unit-root alternatives in standard single-equation tests for short data spans. It is useful to use panel methods with this paper’s data, though in univariate model results reported below, the data reject the unit-root null in at least one of the models for 9 out of 10 countries. Nonetheless, using panel methods on this paper’s data is valuable because the panel results illustrate how sensitive the estimated speed of adjustment can be to the common assumption that the slope on the lagged log real exchange rate is the same across countries, αi = α. Imposing this constraint adds power at no cost in bias if the constraint αi = α holds in the DGP, and adds power at little cost in bias if deviations of (αi - α) from zero are all quite small. For the CEE data used in this paper, the estimates of αi vary substantially from the cross-country mean in single-equation estimates.11 Imposing (αi - α) probability under the null of approximately 9.23%. 11 Here are the smallest estimated slopes: Country Bulgaria Czech Republic

Model BM2 BM2

αˆ -0.548 -0.294

Country Lithuania Romania

13

Model BM1 BM4-O

αˆ -0.043 -0.319

causes the speeds of adjustment estimated for panel models to be notably slower than for univariate models. Put another way, unless the researcher has good reason to believe that the deviations of (αi - α) from zero are all quite small, estimated speeds of adjustment from panel tests are likely biased towards being too slow.12 In Levin and Lin’s (1992) panel unit-root tests,

, for all ,

where root null,

; under the alternative,

, and

is the identity matrix. The unit-

, or innovations decay at the rate - .13

Because real exchange rates display substantial contemporaneous cross-correlations, Levin and Lin’s (1992) panel unit-root test suffers from substantial upward size-distortion (as O’Connell’s 1998 discusses). To avoid this problem, a number of researchers use SUR panel techniques, as Section 2 discusses. Though few researchers have done so (but see Jorion and Sweeney 1996), SUR techniques can be extended to systems of ADF equations with one shift in mean or trend for each country. This extension is applied below to the ten CEE countries’ real exchange rates. This paper uses the following ADF systems, based on (5) above,

Estonia Hungary Latvia

BM2 BM2 ADF

-0.093 -0.264 -0.033

Slovakia Slovenia

BM4 BM3

-0.412 -0.339

The range of the estimates is from -0.548 to -0.033, a difference of -0.515. The range of the implied roots is thus 0.452 and 0.967, for a difference of 0.515 [note that Poland’s root is not statistically significant]. These results strongly suggest that using panel tests with the constraint αi = α is problematical. In experiments, the best approach for panel tests seems to be to choose for each country the break model indicated by the Akaike information criterion or the Bayes information criterion tests in the univariate case. 12 It is well known that univariate unit-root tests have a downward bias in the estimate of α and hence an upwards bias in the estimated speed of adjustment. The panel unit-root tests discussed here are biased compared to the estimates from univariate models. 13 See also Levin, Lin and Chu (LLC 2002). LLC, a revision of Levin and Lin (1992, 1993), give a more elegant proof and a superior discussion, with references to important results in Phillips and Moon (1999) for the case where T → ∞ and n → ∞ simultaneously, rather than the more common and tractable case where T → ∞ and then n → ∞ sequentially. Note that instead of using the asymptotic t-statistic in the text above (from LL), LLC normalize it to make it N(0, 1).

14

(9) Note that this model does not take account of outliers.14

denotes the time-series of the

logarithm of the real exchange-rate for country ,

for all , and

. This approach is a generalization of Levin and Lin (1992) and Levin, Lin and Chu (2002). Furthermore, SUR is more efficient than ordinary least squares, because it takes into account the correlation of the errors. The ADF estimating-systems proposed here allow for country-specific intercepts ( ) and different higher-order dynamics (

,

).

Following Levin and Lin (1992), however, a common speed-of-adjustment coefficient is imposed across countries,

.

If the DGP for real exchange-rates in transition countries contain linear trends, then the unitroot null implies alternative implies

> / < 0, but with

= 0, ,

,

, and

= 0, and

for all ;15 the stationary

possibly non-zero. In the present case, under

the alternative hypothesis the CEE real exchange rates are stationary around country-specific deterministic trends (possibly non-zero) with structural changes (

and

possibly non-zero).

Using the SUR panel test, all the parameters in the system of ten equations are estimated simultaneously, including the parameters in the contemporaneous cross-sectional covariancematrix

. Sweeney (2007) proves that the asymptotic results in Levin and Lin (1992) hold

under SUR, though he does not consider mean or time-trend shifts. Specialized versions of the general model in (9) are tested below as Panel Break Models 14, analogous to the univariate break models discussed above. The panel tests use the break points found from the univariate regressions discussed in Section 3. In some experiments the 14

In preliminary estimates of these panels, tests often rejected the null that the residuals were normal. Dummy variables were parsimoniously introduced to make the residuals approximately normal in order to satisfy panel unit-root test assumptions. After this procedure, there was no need to allow for outliers. Introducing dummies to make the residuals approximately normal had little effect on the t-value of the slope on the lagged real rate. 15 As discussed above, Perron (1997) allows a one-time shift under the null.

15

are forced to be the same for all series; in others (see the individual and IM) specifications in Table 13), the

are those found in the univariate experiments.

Critical values for SUR estimates were found by Monte Carlo simulation. The data generating process for errors in (9) is assumed

, where

is non-

diagonal and positive definite. The literature suggests three possible DGPs for

under the

unit-root null:

and

where

are estimated values for each country . Im et al. (1997) suggest

,

, and Sarno and Taylor (1998) suggest

O’Connell (1998) and Papell (1997) suggest

. Sweeney (2007) discusses the choices in terms of size and power; based on his is used here. Furthermore, the sample covariance-matrix of

discussion,

is used as an estimator of

,

,

.16

Simulations were done as follows. First, the variance-covariance matrix of the firstdifferences of the

time-series,

, were computed. Then

random numbers

were drawn using the variance-covariance matrix from the sample. Third, the generated random numbers

,

,

, were added to obtain

random walks with

observations

each. Fourth, the systems (9) for Panel Break Models 1-4 were estimated using simulated timeseries and the distribution of

were computed. Repeating steps 1-4 for 5,000 replications yielded the under the null hypothesis

.

5. Empirical Results for Real Exchange Rates in the CEE-10 This section presents empirical results for CEE countries for unit-root tests of real exchange rates constructed from monthly nominal exchanges rates against the Euro and consumer price 16

The asymptotic estimate of α is the same for any estimator of ΩSUR that is consistent, as ΩSample is for T → ∞.

16

indexes (CPIs). Results for the USD and also for PPIs are briefly discussed for comparison; complete results are available from the authors. The methods are described in Sections 3 and 4. The ten CEE countries included are: Bulgaria, the Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Romania, Slovakia and Slovenia. CPI, PPI and USD data are from International Financial Statistics (CD-ROM, August 2006); Euro exchange rates are from the Reuters database and are checked against national central bank statistics.17 The sample period generally starts in 1993:01 and always ends in 2005:12.18 Figure 1 illustrates the evolution of real exchange rates during the sample period for CPIs with the Euro as the base currency. Descriptive statistics for levels and first differences of real exchange rates are in Table 2 for CPIs with the Euro as the base currency and the German CPI as the base price level.19 Table 3 gives a summary of which single-equation models have significant slopes on the lagged log real exchange rate. For purposes of convergence and stability, Euro real rates are most important for the ten CEE countries: Results for the Euro case are shown in tables and are discussed in some detail. In the five models without outliers in Table 3, in the Euro case the data reject the unitroot null for nine of ten countries in at least one model, and 25 of 50 models have slopes significant at the 10% level or better. For CPIs when the USD is the base currency, in the five models without outliers the data reject the unit-root null for five of the ten countries, and 13 of the 50 models have significant slopes. (For the 40 break models with outliers, there are three significant cases for the Euro and five for the USD.) 5.1.a. Single-Equation Unit-Root Tests for Real Exchange Rates—The Euro Each country’s real exchange rate was tested for a unit root with five single-equation models discussed in Section 3: The ADF model and the four break models. For Bulgaria, the Czech Republic, and Romania, the Perron and Rodríguez (2003) pre-test indicated the presence 17

European Monetary Union currencies were locked into the Euro on January 1, 1999. Before that date, the Euro exchange rates are calculated as weighted averages of the EMU-country exchange rates. 18 For Euro experiments, data begin in 1995:01 for Latvia and Romania, and 1994:01 for Lithuania and Poland. For PPI experiments, data begin in 1995:01 for Bulgaria, and 1994:01 for Estonia and Latvia. 19 An alternative approach is to use a weighted average of the EMU-country CPIs.

17

of an outlier, and break models with one outlier were estimated for these countries.20 Table 3 summarizes the results. In the ADF model, the data cannot reject the unit-root null for six of the ten countries. For the four break models without outliers, in at least some of these models the data reject the null for eight of the ten CEE countries—Bulgaria, the Czech Republic, Estonia, Hungary, Lithuania, Romania, Slovakia and Slovenia. Three break models with outliers reject the null for Romania. For Poland, the data cannot reject the null in any of the nine models considered. In different sample periods, the data reject the null for Poland in some models; this illustrates that the models can be sensitive to the sample period used. Consider results for the ADF and the four break models. For Bulgaria the data reject the null for all five models, for Estonia, Romania and Slovenia in four models each, for the Czech Republic, Lithuania, and Slovakia in two models, and for Latvia and Hungary in only a single model. For a given country, however, comparisons across Tables 4 – 8 show that the various models differ substantially in how adequately they fit the data. For purposes of discriminating across models, focus on the estimated slope of the lagged real exchange rate [Note: The standard error of the regression (SER) tells much the same story]. In the ADF model without shifts, the data cannot reject the null for six countries—the Czech Republic, Hungary, Poland, Romania, Slovakia, and Slovenia—implicitly a zero speed of adjustment for all. For Bulgaria, the slope is largest in absolute value for Break Model 2, where a shift in mean is allowed for and a trend is included. For the Czech Republic, the adjustment speed is fastest for a shift in mean with a time trend included. The data demand a mean shift for Estonia (Break Model 1), but the speed of adjustment is faster if a time trend and shift in trend are also included (Break Model 4). The single model that works for Hungary is 20

For the Euro as the base currency, the pre-test detects an outlier for Bulgaria, the Czech Republic and Romania; three of the four break models with an outlier are significant for Romania, but no break model is significant for the other two countries. For the USD as the base currency, the pre-test detects an outlier for Bulgaria, the Czech Republic, Latvia and Romania. For Bulgaria and Latvia, two break models with an outlier are significant, and one is significant for Romania. Despite the pre-test results for the Czech Republic, no break model with outlier is significant. Thus, in seven cases break models with an outlier are fit, and in four of the cases the results are significant for at least one break model with an outlier.

18

Break Model 2. Only one model works for Latvia—the ADF. For Lithuania, the ADF and Break Model 1 work, but Break Model 1 gives the higher speed of adjustment (4.3%/month versus 3.0%/month). For Romania Break Model 3 (a shift in time trend but no shift in mean) gives the largest slope in absolute value [For the models with outliers, Break Model 2 is very close and Break Model 4 gives a slightly faster adjustment speed. Models with outliers are discussed in more detail below]. For Slovakia, Break Model 4 gives the fastest speed of adjustment, but for Slovenia Break Model 3 gives the fastest speed by far. No model works for Poland at even the 10% significance level. Break Models with Outliers. It is worthwhile to spell out how outliers are handled in this analysis. As mentioned above, in Perron and Rodríguez (2003) pre-tests the data reject the null of no outliers in the data for Bulgaria, the Czech Republic and Romania. The dates found in outlier pre-tests were saved. The break models were then run for the three countries, without outliers, and for each model the date that gave the t-value largest in absolute value was saved. The twelve equations (three countries by four models) were estimated including an outlier and break at the dates previously detected. The figures for Bulgaria and Romania's real rates show evidence of outliers, but only models for Romania reject the null of a slope of zero on the lagged real rate. The figure for the Czech Republic does not give clear indication of an outlier, and no model including a break is significant. These results suggest that the researcher cannot rely on intuition from visual examination of the data or from pre tests. Baltic Country Results. The figures for the Baltic countries—Estonia, Latvia and Lithuania—appear qualitatively similar (though the latter two are more volatile). All three appear to require a break model. Nevertheless, the data reject the null for Estonia for the ADF and three out of four models; the data for Latvia reject the null only for the ADF; and the data for Lithuania reject the null under the ADF at the 1% level and under Break-Model 1 at the 2.5% level. These results suggest that the researcher cannot rely on intuition from visual

19

examination of the data. 5.1.b. Single-Equation Unit-Root Tests for Real Exchange Rates—The USD In contrast to the Euro case, when the USD is the base currency the data can reject the null for only five of the ten countries—Bulgaria, Estonia, Latvia, Lithuania, and Romania. For Estonia, Latvia, and Lithuania, the data reject the null in the ADF model with no outliers. But note that allowing for parameter shifts and outliers gives substantially faster adjustment speeds for all five countries. Note further that Break Models with outliers "work" for only three countries, but for Bulgaria and Romania they give notably faster adjustment speeds (though not for Latvia). 5.2. Panel Models Table 13 presents SUR panel test results, as measured by the processes’ half lives (discussed below), for the sample period 1995:01 to 2005:12. Results are reported for the ADF model and for all four Break Models. In four cases the same number of lags is imposed on each country, k = 0, 3, 6, 9; in the IL (Individual Lags) column, the each series has the kj estimated in the univariate models shown in Tables 4-8. [In the IM (Individual Model) column, for the four given k the model used is the one that gives the fastest adjustment speed in Tables 4-8.] The null hypothesis α = 0 can be rejected at the 1% significance level in all break models for all k. On the one hand, as k increases, the t-statistic of

decreases in absolute value, as might be

expected with the increases in the number of estimated parameters. On the other hand, an increase in k is associated with a rise in the estimate of | α |, and thus with an increase in the estimated speed of adjustment, as shown by the decrease in the half life of adjustment. (The half-life varies inversely with the speed of adjustment | α |, as Section 6 discusses.) Break Models 2 and 3 give very roughly the same half lives. Break Model 1 gives the largest half lives and Break Model 4 the smallest. As discussed above, the possibility of outliers is not considered for these SUR panel unit-root tests.

20

The IL column in Table 13 presents SUR panel test results where the k is chosen separately for each country. For each Break Model the null can be rejected at the 1% significance level. The half lives are sometimes larger, sometimes smaller in the IL column versus the case where k = 9 for all countries. The smaller half-lives is given by the SUR model that uses the best break univariate model for each country (see IM column). We used AIC and BIC tests to choose the models for each country to use in SUR estimation. Are Some Real Exchange Rates I(1)? Karlsson and Löthgren (2000) emphasize that in panel tests, rejecting the unit-root null is not sufficient to conclude that all series are stationary. From above, however, in single-equation tests for the EUR as the base currency, all currencies save Poland’s appear stationary, and for the USD as the base currency five currencies appear stationary.21 6. Half Lives The half life of a process is an intuitive measure of the speed of adjustment; originally from physics, it measures the decay of a substance comprised of a large number of identical particles. Half life is the time it takes for any amount of the substance to decay to half. The half life in the models considered here is (10) Univariate Models: Half Lives with Euro Exchange Rates. The results reported above illustrate that failure to allow for structural shifts and outliers, when the data demand them, causes downward bias in estimated speeds of adjustment, that is, upwards bias in estimated half

21

Another approach to investigating the number of rates which are I(0) is to use a Johansen (1988) Likelihood Ratio (JLR) test. Sarno and Taylor (1998), for example, use a JLR test for this purpose on four real exchange rates, but their models do not contain shifts in mean or trend, or outliers, nor does Johansen (1988) allow for these. Tests in papers by Johansen, Mosconi and Nielsen (2000), Saikkonen and Lütkepohl (2000) and Lütkepohl, Saikkonen and Trenkler (2004) allow for the case where the data contain shifts in trend or level, or outliers, but are too rigid to be appropriate for present purposes. These papers’ models assume that a mean shift, say, in one country must be parameterized as showing up in all countries, and similarly with trend shifts or outliers; this leads to disastrous collinearity if more than one or two shifts or outliers are allowed, and hence very imprecise model estimates.

21

lives.22 Table 12 reports on half-lives for single-equation-models with significant results for nine countries in Tables 4 – 11. Across all significant univariate models in Section 5, the lowest minimum half life (0.87 months) was estimated for Bulgaria in Break Model 2, and the highest minimum (15.63 months) for Lithuania in Break Model 1. Table 12 shows that half lives estimated by the standard ADF unit-root test (Table 4) tend to be high relative to half lives in other models; in ADF estimates real exchange-rate shocks take between 31.05 months to be reduced to half for Estonia, and 5.21 months for Bulgaria. Across this paper's univariate estimates, the average of minimum half life is 3.89 months.23 This is much faster than other research finds for developed countries where real-exchange-rate shocks generally take 3-5 years to be reduced by half. Univariate Models: Half-Lives with Dollar Exchange Rates. For CPIs the average of the minimum half-lives is 4.95 months, as opposed to 3.89 months for the Euro. For PPIs the average minimum half-life is 3.30 months. 18 models reject for the dollar with CPIs (Table 3), and 17 for the dollar with PPIs. Five break models with outliers reject for the USD with CPIs, and seven for the USD with PPIs. Panel Models: Half Lives with the Euro. Table 13 presents half lives implied by SUR panel estimates. For ADF models, without time trends, half lives range from 22.02 months to 13.50 months. Estimates for Panel Break Models all imply lower half lives. For k = 9 for each country, and also for k chosen individually for each country, the half lives are very roughly the same for Break Models 1 – 4. The difference between half lives in panel models and the average half life for singleequation models is striking. Intuitively, this appears to arise for two reasons. First, univariate estimates suggest that the constraint imposed in panel estimation, that αi = α, is very far from 22

As is well known, the estimated speed of adjustment from unit-root test equations is biased down. Failure to allow for structural shifts and outliers, when the data contain them, causes greater downward bias in the estimated speed of adjustment, and thus greater upward bias in estimated half life. 23 It might be noted that in the absence of the three Baltic countries, the average half-life is 3.19 years.

22

the truth. Second, and less important, most of the panel models require each currency to have the same model, but the single-equation models show that the data demand very different models across currencies. 7. Summary and conclusions This paper reports single-equation and panel unit-root tests for real exchange rates of ten Central and Eastern European (CEE) economies. It makes three main contributions. First, the unit-root tests presented here differ from the previous empirical literature on CEE real exchange rates by allowing for structural changes and outliers in the transition-country real exchange rates. Second, the study presents both single-equation and panel test results for CEE countries. Third, this paper documents the way that incorrect model specification biases downward the estimated speed of real rate adjustment and biases upwards real rates’ half-lives. In previous single-equation unit-root tests on non-CEE countries, many studies report the data are unable to reject the unit-root null; researchers commonly note, however, that standard single-equation unit-root tests have low power against local-stationarity alternatives in small samples. In this paper, when single-equation-test specifications allow for structural shifts and for outliers, the data reject the unit-root null for nine of ten CEE countries, often at the 1% significance level. If neither structural changes nor outliers are taken into account, the unit-root hypothesis is rejected in some of this paper’s single-equation tests. In these cases, however, the estimated speed of mean reversion is relatively slow; using test-equation specifications that allow for structural shifts and for outliers, the estimated speeds of adjustment are substantially faster. Note that these CEE adjustment speeds are much faster and the half lives much smaller than results in previous work that finds mean reversion in real exchange rates in major industrialized countries. This paper also reports on SUR panel unit-root tests for transition-country real exchange

23

rates. Some tests do not allow for structural shifts but others do. In all sets of panel tests, the data reject the unit-root null at the 1% significance level. Constraining all countries to have the same break model of the same number of real-exchange rate lags often substantially biases down the estimated speed of adjustment. This paper's use of a battery of tests has pros and cons. On the one hand, if the researcher uses only one test from the battery discussed in this paper, he runs an important risk of choosing model that fails to reject the null because of misspecification. Even if a misspecified model rejects the null, the estimated speed of adjustment is likely to be substantially slower than that for the correct specification. On the other hand, the battery of tests has a larger size than that of any single test; for example, if the size of any single test is 0.050, the size for the battery is 0.170. Four considerations mitigate the costs of this increase in size. First, the reader can make her own decision if all the results are reported (or summarized), rather than only the best results with no mention of the number and specifications of tests tried. Second, if the researcher tries to preserve the nominal size by choosing only one test, he may do so by inspecting the data with great care, reading discussions of the history of the time period the data cover or even trying "preliminary" regressions. Of course, these methods also use up degrees of freedom and increase the test's size, though by an unknown amount. Third, power studies indicate that across the second, third and fourth break models, rejections of the null show important positive correlations; the researcher who observes such correlations may then have more confidence than otherwise. Fourth, the increase in size for any one series may be more than offset if the researcher has a number of series as in this paper.

24

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27

Table 1: Exchange-rate regimes Regime Bulgaria

Managed float from February 1991, Currency board with DEM (subsequently EUR) from July 1997.

Czech Republic

Fixed peg against basket 65% DEM, 35% USD from January 1991, Managed float against Euro from March 1997.

Estonia

Currency board with DEM (subsequently EUR) from June 1992, ERM II from June 2004.

Hungary

Peg to basket 50% ECU, 50% USD, Basket changed to 50% DEM, 50% USD from August 1993, Basket changed to 70% ECU, 30% USD from May 1994, Crawling peg/band to basket from March 1995, Basket changed to 70% EUR, 30% USD from January 1999, Basket changed to 100% EUR from January 2000.

Latvia

Managed float from July 1992, Fixed peg to SDR basket. Central Bank margin +/-1% from February 1994, Fixed peg to EUR. Central Bank margin +/-1% from January 2005, ERM II from May 2005.

Lithuania

Managed float from July 1992, Currency board with USD from April 1994, Currency board with EUR from February 2002, ERM II from June 2004.

Poland

Fixed to USD from January 1990, Fixed to basket (45% USD, 55% DEM+GBP+FF+CHF) from May 1991, Crawling peg to (same) basket, Basket changed to 55% EUR, 45% USD from January 1999, Free float (but Central Bank reserves extraordinary right to intervene) from April 2000.

Romania

Managed float, various degrees of tightness from August 1992.

Slovakia

Fixed peg against basket 60% DEM, 40% USD, Central Bank intervention band +/-1.5% from January 1991, Crawling band, band currency board with DEM (subsequently EUR) from June 1992, Managed float from October 1998, core inflation target, ERM II from November 2005.

Slovenia

Managed float with no pre-announced exchange rate path from 1992, annual M3 growth target, ERM II from June 2004.

NOTE: Source: IMF, National Cenral Banks, Koˇ cenda (2005), Halpern and Wyplosz (2001).

28

Table 2: Basic statistics of logs of real exchange-rates and of the first differences of logs of real exchange-rates The first difference of Log of real exchange-rate EUR

EUR

Corr(S,r)

Mean

St.Dev.

Bulgaria

0.830

0.338

-0.637

Czech Republic

3.615

0.181

Estonia

2.904

Hungary

log of real exchange-rate Corr(P,r)

EUR

EUR

Mean

St.Dev.

-0.854

-0.006

0.193

0.595

-0.972

-0.004

0.019

0.311

-0.403

-0.963

-0.008

0.013

5.552

0.149

-0.659

-0.922

-0.002

0.017

Latvia

-0.440

0.131

0.738

-0.724

-0.003

0.018

Lithuania

1.502

0.296

0.839

-0.967

-0.007

0.023

Poland

1.485

0.150

-0.515

-0.884

-0.003

0.027

Romania

0.812

0.207

-0.771

-0.804

-0.004

0.044

Slovakia

3.798

0.201

-0.356

-0.985

-0.004

0.018

Slovenia

5.355

0.066

-0.849

-0.885

-0.001

0.012

NOTE: S is the nominal exchange-rate; P is domestic CPI relative to German CPI; and r is log of the real exchange rate. The sample period generally starts in 1993:01 and always ends in 2005:12. Data begin in 1995:01 for Latvia and 1994:01 for Lithuania.

29

Table 3: Univariate Unit-Root Test Results A. Real Exchange Rates: Euro Base, Consumer Price Indices Country

ADF

BM1

BM2

BM3

BM4

BM1-O

BM2-O

BM3-O

BM4-O

Bulgaria

10%

1%

1%

10%

1%

N

N

N

N

Czech Republic

N

N

2.5%

10%

N

N

N

N

N

Estonia

1%

1%

1%

N

1%

N

N

N

N

Hungary

N

N

5%

N

N

N

N

N

N

Latvia

10%

N

N

N

N

N

N

N

N

Lithuania

1%

2.5%

N

N

N

N

N

N

N

Poland

N

N

N

N

N

N

N

N

N

Romania

N

2.5%

1%

10%

1%

1%

10%

N

1%

Slovakia

N

N

5%

N

1%

N

N

N

N

Slovenia

N

10%

1%

1%

1%

N

N

N

N

N

1%

N

10%

N

B. Real Exchange Rates: USD Base, Consumer Price Indices Bulgaria

N

N

N

N

Czech Republic

N

N

N

N

N

N

N

N

N

Estonia

1%

1%

1%

5%

N

N

N

N

N

Hungary

N

N

N

N

N

N

N

N

N

Latvia

1%

1%

1%

2.5%

1%

N

N

1%

1%

Lithuania

1%

1%

10%

N

1%

N

N

N

N

Poland

N

N

N

N

N

N

N

N

N

Romania

N

N

N

N

N

N

N

10%

N

Slovakia

N

N

N

N

N

N

N

N

N

Slovenia

N

N

N

N

N

N

N

N

N

NOTE: Significance of the slope on lagged log real exchange rate is indicated at the 10%, 5%, 2.5% and 1% levels. N indicates that the slope on the lagged log real exchange rate is not significant at even the 10% level. The models are specializations of the Break Model 4 with Outliers:

∆rt = [µ + θDµ,t ] + [βt + φDβ,t (t − Tb )] +

p X

δi Dao,t−i + αrt−1 +

i=0

k X

γi ∆rt−i + εt ,

i=1

where Dµ,t is a dummy, equal to zero for t < Tb and equal to unity for t ≥ Tb , where Tb is the time at which the intercept shifts. Dβ,t is a dummy, equal to zero for t < Tb and equal to unity for t ≥ Tb , where Tb is the time at which the trend coefficient shifts. DTp is a dummy variable with value unity at time Tp at which the break in trend occurs and zero otherwise (see Perron 1997). The models are as follows. ADF : Augmented Dickey-Fuller - θ = β = φ = δi = 0. BM 1: Break Model 1 - β = φ = δi = 0. BM 2: Break Model 2 - φ = δi = 0. BM 3: Break Model 3 - θ = δi = 0. BM 4: Break Model 4 - δi = 0. BM 1 − O: Break Model 1 with Outliers - β = φ = 0. BM 2 − O: Break Model 2 with Outliers - φ = 0. BM 3 − O: Break Model 3 with Outliers - θ = 0. BM 4 − O: Break Model 4 with Outliers. The sample period generally starts in 1993:01 and always ends in 2005:12. For Euro experiments, data begin in 1995:01 for Latvia and Romania, and 1994:01 for Lithuania and Poland.

30

Table 4: Tests for unit roots in real exchange rates, using the standard Augmented-Dickey-Fuller equation: ∆rt = µ + αrt−1 + k Bulgaria

Estonia

Latvia

Lithuania

k=1

k=3

k=1

k=4

Pk

i=1 γi ∆rt−i

µ ˆ

+ εt

α ˆ

0.096

-0.124

(2.402)

(−2.771)∗

0.058

-0.022

(5.177)

(−5.311)∗∗∗∗

-0.017

-0.033

(-3.088)

(−2.753)∗

0.037

-0.030

(3.408)

(−4.044)∗∗∗∗

S(ˆ e)

0.00008

0.00029

0.00047

NOTE: r is the log of the real exchange rate for CPIs, with the EUR as the base currency. t-statistics are in parentheses. The t-statistics for α ˆ is for testing α=0. The symbols ∗, ∗∗, ∗ ∗ ∗ and ∗ ∗ ∗∗ denote significance of the test for α=0 at the 10%, 5%, 2.5% and 1% levels, using critical values from simulation. The sample period generally starts in 1993:01 and always ends in 2005:12. Data begin in 1995:01 for Latvia and 1994:01 for Lithuania.

31

Table 5: Tests for unit roots in real exchange rates, using Break Model 1: ∆rt = [µ + θDµ,t ] + αrt−1 +

Bulgaria

Estonia

Estonia

Lithuania

Lithuania

Romania

Romania

Slovenia

Slovenia

Pk

i=1 γi ∆rt−i

+ εt α ˆ

Tˆµ1

k

µ ˆ

θˆ

1997-01

k=4

0.509

-0.275

-0.392

(6.452)

(-6.518)

(−6.184)∗∗∗∗

0.158

0.020

-0.067

(6.343)

(4.233)

(−6.913)∗∗∗∗

0.158

0.022

-0.068

( 6.324)

(4.181)

(−6.915)++++

0.087

-0.033

-0.043

(4.264)

(-2.863)

(−5.035)

0.084

-0.029

-0.043

(-5.732)

( -2.358)

(−5.033)+++

0.185

-0.084

-0.148

( 5.256)

(-5.363)

(−5.069)∗∗∗

0.158

-0.069

-0.131

(5.387)

(-5.199)

(−5.363)+++

0.483

-0.023

-0.086

(4.556)

(-4.990)

(−4.491)∗

0.483

-0.023

-0.086

(4.534)

(-4.916)

(−4.467)+

1996-07

1996-06

1994-10

1994-09

1997-02

1996-12

1994-02

1994-01

k=12

k=12

k=4

k=4

k=2

k=2

k=0

k=0

S(ˆ e) 0.02280

0.00005

0.00005

0.00045 ∗∗∗

0.00045

0.00148

0.00126

0.00013

0.00126

NOTE: r is the log of the real exchange rate for CPIs, with the EUR as the base currency. Dµ,t is a dummy, equal to zero for t < Tˆµ1 and equal to unity for t ≥ Tˆµ1 , where Tˆµ1 is the time at which the intercept shifts. The Perron model used is ∆rt = [µ + θDµ,t ] + ηDTµ + αrt−1 +

Pk

i=1

γi ∆rt−i + εt ,

where DTµ is a dummy variable with value unity at time Tˆµ1 and zero otherwise. t-statistics are in parentheses. k is determined as described in Section 2. The t-statistic for α ˆ is for testing the null α=0. The symbols ∗, ∗∗, ∗ ∗ ∗, and ∗ ∗ ∗∗ denote significance of the test of α=0 at 10%, 5%, 2.5%, and 1% levels, using critical values for Zivot and Andrews (1992)’s test statistics from simulation. The symbols +, ++, + + +, and + + ++ denote significance of the test of α=0 at 10%, 5%, 2.5%, and 1% levels, using the critical values for Perron (1997)’s test statistics from simulation. Tˆµ1 is the estimated time date at which µ shifts in Model 1. The sample period generally starts in 1993:01 and always ends in 2005:12. Data begin in 1995:01 for Romania, and 1994:01 for Lithuania.

32

Table 6: Unit-root tests for real exchange rates, using Break Model 2: ∆rt = [µ + θDµ,t ] + βt + αrt−1 +

Bulgaria

Czech Republic

Czech Republic

Estonia

Estonia

Hungary

Hungary

Romania

Romania

Slovakia

Slovakia

Slovenia

Slovenia

-0.150

-0.002

-0.548

(5.760)

(-2.564)

(-2.955)

(−5.995)∗∗∗∗

1.160

0.024

-0.001

-0.294

( 4.863)

(3.419)

(-4.758)

(−4.885)∗∗

1.159

0.023

-0.001

-0.294

(4.844)

(3.314)

(-4.722)

(−4.885)++

0.242

0.020

-0.0001

-0.093

(7.563)

(4.261)

(-3.881)

(−8.025)

0.238

0.023

-0.0001

-0.093

(7.473)

(4.601)

(-3.734)

(−8.056)++++

1.529

-0.031

-0.001

-0.264

(4.964)

(-3.926)

(-4.517)

(−4.968)∗∗

1.538

-0.032

-0.001

-0.266

(4.959)

(-3.914)

(-4.501)

(−4.963)++

0.267

-0.086

-0.0004

-0.213

( 5.527)

(-5.587)

(-2.433)

(−5.428)∗∗∗∗

0.236

-0.068

-0.0004

-0.193

(5.731)

(-5.287)

(-2.627)

(−5.751)++++

1.219

0.031

-0.002

-0.292

(4.806)

(4.182)

(-4.944)

(−4.817)∗∗

1.223

0.031

-0.002

-0.293

(4.796)

(4.166)

(4.933)

(−5.042)++

1.366

-0.032

-0.0002

-0.246

(6.763)

(-6.587)

(-4.931)

(−6.736)∗∗∗∗

1.337

-0.034

-0.0002

-0.241

µ ˆ

1998-01

k=2

0.692

2003-04

1996-08

1996-07

2001-04

2001-03

1997-02

1996-12

1998-05

1998-04

1994-03

1994-02

k=7

k=7

k=12

k=12

k=12

k=12

k=2

k=2

k=12

k=12

k=1

k=1

+ εt α ˆ

k

θˆ

i=1 γi ∆rt−i

βˆ

Tˆµ2

2003-05

Pk

(6.592)

(-6.702)

(-4.775)

S(ˆ e) 0.02790

0.00030

0.00030

0.00005 ∗∗∗∗

0.00005

0.00025

0.00025

0.00142

0.00120

0.00024

0.00024

0.00012

0.00012 ++++

(−6.556)

NOTE: r is the log of the real exchange rate for CPIs, with the EUR as the base currency. Dµ,t is a dummy, equal to zero for t < Tˆµ2 and equal to unity for t ≥ Tˆµ2 , where Tˆµ2 is the time at which the intercept shifts. t is the time trend. The Perron model used is ∆rt = [µ + θDµ,t ] + ηDTµ + βt + αrt−1 + DTµ

Pk

i=1

γi ∆rt−i + εt , where

is a dummy variable with value unity at time Tˆµ2 and zero otherwise. t-statistics are in parentheses. k is

determined as described in Section 2. The t-statistic for α ˆ is for testing the null α=0. The symbols ∗, ∗∗, ∗ ∗ ∗, and ∗ ∗ ∗∗ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values from Table 2A of Zivot and Andrews (1992). The symbols +, ++, + + +, and + + ++ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values from Table 1(a) of Perron (1997). Tˆµ2 is the estimated time date at which µ shifts in Model 2. The sample period generally starts in 1993:01 and always ends in 2005:12. Data begin in 1995:01 for Romania.

33

Table 7: Unit-root tests for real exchange rates, using Break Model 3: P ∆rt = µ + [βt + φDβ,t (t − Tˆβ3 )] + αrt−1 + ki=1 γi ∆rt−i + εt

Bulgaria

Bulgaria

Czech Republic

Czech Republic

Romania

Romania

Slovenia

Slovenia

Tˆβ3

k

2000-12

k=8

2000-12

2002-04

2002-04

2002-01

2002-01

1994-08

1994-08

k=8

k=7

k=7

k=12

k=12

k=11

k=11

βˆ

µ ˆ

φˆ

α ˆ

S(ˆ e)

0.726

-0.004

0.003

-0.503

0.02829

(4.052)

(-3.747)

( 2.023)

(−4.125)∗

0.726

-0.004

0.003

-0.503

(4.052)

(-3.747)

( 2.023)

(−4.125)+

0.966

-0.001

0.001

-0.245

(4.265)

(-4.119)

(2.580)

(−4.291)∗

0.966

-0.001

0.001

-0.245

(4.265)

(-4.119)

(2.580)

(−4.291)+

0.391

-0.003

0.002

-0.303

(4.026)

(-3.386)

(4.850)

(−4.368)∗

0.391

-0.003

0.002

-0.303

(4.026)

(-3.386)

(4.850)

(−4.368)+

1.958

-0.006

0.006

-0.339

(6.342)

(-4.120)

(3.990)

(−6.401)

1.958

-0.006

0.006

-0.339

(6.342)

(-4.120)

(3.990)

(−6.401)++++

0.02829

0.00031

0.00031

0.00162

0.00162

0.00006 ∗∗∗∗

0.00006

NOTE: r is the log of the real exchange rate for CPIs, with the EUR as the base currency. t is the time trend. Dβ,t is a dummy, equal to zero for t < Tˆβ3 and equal to unity for t ≥ Tˆβ3 , where Tˆβ3 is the time at which the trend coefficient shifts. The Perron model used is ∆rt = µ + [βt + φDβ,t (t − Tˆβ3 )] + ηDTβ + αrt−1 + where DTβ is a dummy variable with value unity at time

Tˆβ3

Pk

i=1

γi ∆rt−i + εt ,

and zero otherwise. t-statistics are in parentheses.

k is determined as described in Section 2. The t-statistic for α ˆ is for testing α=0. The symbols ∗, ∗∗, ∗ ∗ ∗, and ∗ ∗ ∗∗ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values from Table 3A of Zivot and Andrews (1992). The symbols +, ++, + + +, and + + ++ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values from Table 1(g) of Perron (1997). Tˆβ3 is the estimated time date at which β shifts in Model 3. The sample period generally starts in 1993:01 and always ends in 2005:12. Data begin in 1995:01 for Romania.

34

Table 8: Unit-root tests for real exchange rates, using Break Model 4: P ∆rt = [µ + θDµ,t ] + [βt + φDβ,t (t − Tˆb4 )] + αrt−1 + ki=1 γi ∆rt−i + εt Country

Tˆb4

k

µ ˆ

θˆ

βˆ

φˆ

α ˆ

S(ˆ e)

Bulgaria

1997-01

k=4

0.493

-0.003

0.007

-0.008

-0.546

0.00620

( 4.441)

(-0.045)

(4.272)

(-4.762)

(−6.405)∗∗∗∗

0.008

-0.002

0.0003

-0.081

(0.427)

(-2.897)

(-0.231)

(−6.675)∗∗∗∗

0.003

-0.0001

0.0003

-0.081

(6.459)

(0.017)

(-2.779)

( -0.261)

(−6.647)++++

0.283

-0.056

0.002

-0.003

-0.258

(6.150)

(-2.662)

(1.749)

(-2.175)

(−6.492)

0.250

-0.060

0.0002

-0.0007

-0.214

(6.184)

(-2.976)

(0.208)

(-0.594)

(−6.317)++++

0.072

-0.002

-0.0005

-0.411

(4.858)

(-5.181)

(-3.308)

(−5.705)∗∗∗∗

0.072

-0.002

-0.0005

-0.412

(5.677)

(4.803)

(-5.196)

(-3.141)

(−5.696)++++

1.550

-0.051

-0.003

0.002

-0.276

(6.929)

(-6.393)

(-7.069)

(6.835)

(−6.568)∗∗∗∗

1.536

-0.052

-0.002

0.002

-0.274

(6.877)

(-6.514)

(-7.201)

(6.966)

(−6.539)++++

Estonia

2003-01

k=12 0.234 (6.518)

Estonia

Romania

Romania

Slovakia

2002-05

1997-02

1997-01

1998-07

k=12 0.237

k=1

k=1

k=12 1.700 (5.684)

Slovakia

Slovenia

Slovenia

1998-06

1995-07

1995-06

k=12 1.703

k=1

k=1

0.00006

0.00006

0.00140 ∗∗∗∗

0.00122

0.00022

0.00022

0.00011

0.00011

NOTE: r is the log of the real exchange rate for CPIs, with the EUR as the base currency. Dµ,t is a dummy, equal to zero for t < Tˆb4 and equal to unity for t ≥ Tˆb4 , where Tˆb4 is the time at which the intercept shifts. t is the time trend. Dβ,t is a dummy, equal to zero for t < Tˆb4 and equal to unity for t ≥ Tˆb4 , where Tˆb4 is the time at which the trend coefficient shifts. The Perron model used is ∆rt = [µ+θDµ,t ]+[βt+φDβ,t(t− Tˆb4 )]+ηDTb +αrt−1 + where DTb is a dummy variable with value unity at time

Tˆb4

Pk

i=1

γi ∆rt−i +εt ,

and zero otherwise. t-statistics are in parentheses. k is

determined as described in Section 2. The t-statistic for α ˆ is for testing the null α=0. The symbols ∗, ∗∗, ∗ ∗ ∗, and ∗ ∗ ∗∗ denote significance of the test for α=0 at the 10%, 5%, 2.5% and 1% levels, using the critical values from Table 4A of Zivot and Andrews (1992). The symbols +, ++, + + +, and + + ++ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values from Table 2(d) of Perron (1997). Tˆb4 is the estimated time date at which both µ and β shift in Model 4. The sample period generally starts in 1993:01 and always ends in 2005:12. Data begin in 1995:01 for Romania.

35

Table 9: Unit-root tests for real exchange rates, using Break Model 1 with outliers:

Romania

Romania

∆rt = [µ + θDµ,t ] +

Pp

Tˆµ1

Tˆao

p

k

µ ˆ

θˆ

1997-02

1997-03

p=1

k=1

0.208

-0.091

-0.169

(5.696)

(-5.714)

(−5.499)∗∗∗∗

0.183

-0.077

-0.154

(5.875)

(-5.613)

(−5.835)++++

1997-01

1997-03

i=0 δi Dao,t−i

p=1

k=1

+ αrt−1 +

Pk

i=1 γi ∆rt−i

+ εt α ˆ

S(ˆ e) 0.00152

0.00129

NOTE: r is the log of the real exchange rate for CPIs, with the EUR as the base currency. Dµ,t is a dummy, equal to zero for t < Tˆµ1 and equal to unity for t ≥ Tˆµ1 , where Tˆµ1 is the time at which the intercept shifts. Dao,t−i is a dummy, equal to zero for t >< Tˆao + i, and equal to unity for t = Tˆao + i; the outlier occurs at time Tˆao , and p is the number of dummy variables. The Perron model used is ∆rt = [µ + θDµ,t ] + variable with value unity at time

Tˆµ1

Pp

δD i=0 i ao,t−i

+ ηDTˆµ + αrt−1 +

Pk

i=1

γi ∆rt−i + εt , where DTˆµ is a dummy

and zero otherwise. t-statistics are in parentheses. k is determined as described in Section

2. The t-statistic for α ˆ is for testing α=0. The symbols ∗, ∗∗, ∗ ∗ ∗, and ∗ ∗ ∗∗ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values for Zivot and Andrews (1992)’s test statistics from simulation. The symbols +, ++, + + +, and + + ++ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values for Perron (1997)’s test statistics from simulation. Tˆµ1 is the estimated time date at which µ shifts in Model 1. The sample period starts in 1995:01 and ends in 2005:12.

36

Table 10: Unit-root tests for real exchange rates, using Break Model 2 with outliers: ∆rt = [µ + θDµ,t ] + βt +

Romania

Pp

i=0 δi Dao,t−i

+ αrt−1 + θˆ

Tˆµ2

Tˆao

p

1997-02

1997-03

p=1 k=11 0.382

µ ˆ

k

(6.066) Romania

1997-01

1997-03

Pk

p=1 k=11 0.326 (6.221)

i=1 γi ∆rt−i

+ εt

βˆ

α ˆ

-0.101

-0.001

-0.303

(-5.512)

(-3.767)

(−6.060)∗∗∗∗

-0.072

-0.001

-0.269

(-4.494)

(-3.991)

(−6.446)++++

S(ˆ e) 0.00143

0.00118

NOTE: r is the log of the real exchange rate for CPIs, with the EUR as the base currency. Dµ,t is a dummy, equal to zero for t < Tˆµ2 and equal to unity for t ≥ Tˆµ2 , where Tˆµ2 is the time at which the intercept shifts. t is the time trend. Dao,t−i is a dummy, equal to zero for t >< Tˆao + i, and equal to unity for t = Tˆao + i; the outlier occurs at time Tˆao , and p is the number of dummy variables. The Perron model used is ∆rt = [µ+θDµ,t ]+βt+ where DTµ is a dummy variable with value unity at time

Tˆµ2

Pp

δD +ηDTµ +αrt−1 + i=0 i ao,t−i

Pk

i=1

γi ∆rt−i +εt ,

and zero otherwise. t-statistics are in parentheses. k is

determined as described in Section 2. The t-statistic for α ˆ is for testing α=0. The symbols ∗, ∗∗, ∗ ∗ ∗, and ∗ ∗ ∗∗ denote significance of the test for α=0 at the 10%, 5%, 2.5% and 1% levels, using the critical values for Zivot and Andrews (1992)’s test statistics from simulation. The symbols +, ++, + + +, and + + ++ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values for Perron (1997)’s test statistics from simulation. Tˆµ2 is the estimated time date at which µ shifts in Model 2. The sample period starts in 1995:01 and ends in 2005:12.

37

Table 11: Unit-root tests for real exchange rates, using Break Model 4 with outliers: P P ∆rt = [µ + θDµ,t ] + [βt + φDβ,t (t − Tˆb4 )] + pi=0 δi Dao,t−i + αrt−1 + ki=1 γi ∆rt−i + εt

Romania

θˆ

Tˆb4

Tˆao

p

1997-02

1997-03

p=1 k=11 0.300

k

µ ˆ

(3.997) Romania

1997-01

1997-03

p=1 k=11 0.336 (4.470)

βˆ

φˆ

α ˆ

S(ˆ e)

-0.001

0.004

-0.005

-0.319

0.00139

(-0.009)

(1.666)

(-1.957)

(−6.381)∗∗∗∗

-0.081

-0.001

0.0005

-0.269

(-1.388)

(-0.414)

(0.175)

(−6.736)++++

0.00120

NOTE: r is the log of the real exchange rate for CPIs, with the EUR as the base currency. Dµ,t is a dummy, equal to zero for t < Tˆb4 and equal to unity for t ≥ Tˆb4 , where Tˆb4 is the time at which the intercept shifts. t is the time trend. Dβ,t is a dummy, equal to zero for t < Tˆb4 and equal to unity for t ≥ Tˆb4 , where Tˆb4 is the time at which the trend coefficient shifts. Dao,t−i is a dummy, equal to zero for t >< Tˆao + i, and equal to unity for t = Tˆao + i; the outlier occurs at time Tˆao , and p is the number of dummy variables. The Perron model used is ∆rt = [µ + θDµ,t ] + [βt + φDβ,t (t − Tˆb4 )] + is a dummy variable with value unity at time

Tˆb4

Pp

δ D i=0 i ao,t−i

+ ηDTb + αrt−1 +

Pk

i=1

γi ∆rt−i + εt , where DTb

and zero otherwise. t-statistics are in parentheses. k is determined as described in

Section 2. The t-statistic for α ˆ is for testing α=0. The symbols ∗, ∗∗, ∗ ∗ ∗, and ∗ ∗ ∗∗ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values for Zivot and Andrews (1992)’s test statistics from simulation. The symbols +, ++, + + +, and + + ++ denote significance of the test for α=0 at the 10%, 5%, 2.5%, and 1% levels, using the critical values for Perron (1997)’s test statistics from simulation. Tˆb4 is the estimated time date at which both µ and β shift in Model 4. The sample period starts in 1995:01 and ends in 2005:12.

38

Table 12: Half Lives for transition countries; estimates from univariate models: CPIs, EUR as Base Currency Model Country

ADF

BM1

BM2

BM3

BM4

BM1-O

BM2-O

BM3-O

BM4-O

Bulgaria

5.21

1.39,-

0.87,-

0.98,0.98

1.24,1.24

-,-

-,-

-,-

-,-

Czech Republic

-

-,-

1.98,1.98

2.46,2.46

-,-

-,-

-,-

-,-

-,-

Estonia

31.05

9.92,9.87

12.79,16.97

-,-

8.18,9.45

-,-

-,-

-,-

-,-

Hungary

-

-,-

2.25,2.23

-,-

-,-

-,-

-,-

-,-

-,-

Latvia

20.63

-,-

-,-

-,-

-,-

-,-

-,-

-,-

-,-

Lithuania

22.36

15.63,15.61

-,-

-,-

-,-

-,-

-,-

-,-

-,-

Poland

-

-,-

-,-

-,-

-,-

-,-

-,-

-,-

-,-

Romania

-

4.32,4.91

2.87,3.22

1.91,1.91

2.32,2.87

3.74,4.14

1.92,2.20

-,-

1.80,2.20

Slovakia

-

-,-

2.01,1.99

-,-

1.31,1.31

-,-

-,-

-,-

-,-

Slovenia

-

7.67,7.67

2.44,2.51

1.67,1.67

2.14,2.16

-,-

-,-

-,-

-,-

NOTE: -,- gives the half-live estimates from models following Zivot and Andrews (1992) and Perron (1997). The models are as follows. ADF : Augmented Dickey-Fuller. BM 1: Break Model 1. BM 2: Break Model 2. BM 3: Break Model 3. BM 4: Break Model 4. BM 1 − O: Break Model 1 with Outliers. BM 2 − O: Break Model 2 with Outliers. BM 3 − O: Break Model 3 with Outliers. BM 4 − O: Break Model 4 with Outliers. The sample period generally starts in 1993:01 and always ends in 2005:12. Data begin in 1995:01 for Latvia and 1994:01 for Lithuania.

39

Table 13: Panel Unit-Root Test Results: CPIs, EUR as base currency Number of Lags 0

3

6

9

Individual

t-value

-10.713

-6.728

-6.166

-5.257

-5.432

half life

13.501

20.200

20.522

22.024

19.516

t-value

-8.398

-7.845

-8.061

-7.537

-7.483

half life

9.356

10.598

10.033

9.779

9.463

t-value

-11.540

-11.094

-11.165

-10.430

-10.836

half life

4.208

4.674

4.681

4.000

3.441

t-value

-10.181

-9.445

-9.719

-8.925

-8.358

half life

4.736

5.227

4.984

4.179

4.698

t-value

-13.453

-11.367

-11.738

-11.860

-12.216

half life

2.898

3.391

3.263

2.753

2.567

t-value

-13.391

-11.817

-11.617

-11.384

-12.124

half life

2.760

3.064

2.989

2.702

2.503

Model ADF

BM1

BM2

BM3

BM4

IM

NOTE: The models are as follows. ADF : Augmented Dickey-Fuller. BM 1: Break Model 1. BM 2: Break Model 2. BM 3: Break Model 3. BM 4: Break Model 4. IM : for each country the model specification is chosen according to AIC and BIC tests. Individual : The lag structure for each country is chosen as the structure found in univariate tests above. The sample period starts in 1995:01 and ends in 2005:12.

40

3.8

4.0

3.2

3.7

2.5 1.5

2.6

0.5

3.4 1994 1998 2002 2006 Czech Republic−log of real exchange−rate of koruna per EUR

1.6

−0.3

1.2

−0.6

5.5 5.3

1996 2000 2004 Latvia−log of real exchange−rate of lat per EUR

1994 1998 2002 2006 Lithuania−log of real exchange−rate of lita per EUR

3.8 1996 2000 2004 Romania−log of real exchange−rate of leu per EUR

1994 1998 2002 2006 Slovakia−log of real exchange−rate of koruna per EUR

5.30

5.45

1994 1998 2002 2006 Poland−log of real exchange−rate of zloty per EUR

3.4

1.2

0.6

1.5

1.0

1.8

1.4

1994 1998 2002 2006 Hungary−log of real exchange−rate of forint per EUR

1994 1998 2002 2006 Estonia−log of real exchange−rate of kroon per EUR

2.0

5.7

1994 1998 2002 2006 Bulgaria−log of real exchange−rate of leva per EUR

1994 1998 2002 2006 Slovenia−log of real exchange−rate of koruna per EUR

Figure 1: Logarithm of Real Exchange-rates per EUR in Ten Transition Economies

41