OF~PURCHASING POWER PARITY ΙΝ ΤΗΕ TRANSITION EUROPEAN ECONOMIES:

ΕΠΙΒΕΩΡΗΣΗ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ - Τεύχος 5 (2009), 4-52 ΑΝ EMPIRICAL STUDY OF ΤΗΕ THEORY OF~PURCHASING POWER PARITY ΙΝ ΤΗΕ TRANSITION EUROPEAN ECONOMIES: ΤΗΕ CASE OF CZECH REPUBLIC Abstract The Theory of Purchasing Power Parity (ΡΡΡ), despite short -term deviations, is considered to be a structural tool of monetary model. Among the reasons for which this argument stands, is lack of a theory, which argues the invalidity of the theory of ΡΡΡ and hence there is ηο alternative theory to provide a relation between price levels. Moreover, a second reason and even more persuasive is the fact that all theories include certain assumptions that may not be correct. Thus according to Friedman and Schwartz (963), the theory of ΡΡΡ should be subject to criticisms having as a criterion the quality of the theory's predictions and not its assumptions. Α significant test that studies the short -terrn validity of ΡΡΡ, is the Augmented Dickey - Fuller (ADF) test that examines the hypothesis that the real exchange parity contains a unit root. The aim of this paper is to apply the Dickey - Fuller test ίη the case of Czech Republic. This test was used to examine the stationarity of the time seήes of the real exchange rates. For the application of this test monthly obsejύations of the nominal exchange rates were used. The calculation of the values of the real exchange rates was based οη the indicators of the consumers' prices. The application of Dickey - Fuller test resulted in the rejection of the unit root. Consequently, ίt is concluded the ηοη -stationarity of the time series and thus for the data used the ηοη -validity of ΡΡΡ. Περίληψη Eteni Zafelrlou Uniνerslty of Macedonla Spyrldon Soflos Unlνersity of Thessaly Garyfallos Arabatzls Democritus Uniνersity of Thrace Ελtνη Ζαφειρίου Πανεπιστήμιο Μακεδονίας Σπυρίδων Σόφιος Πανεπιστήμιο Θεσσαλίας Γαρύφαλλος Αραμπατζής Πανεπιστήμιο Θράκης Η Θεωρία Ισοδυν αμίας Αγοραστικών Δυνάμεων (Θ.Ι.Α.Δ.), παρά την ύπαρξη βραχυπρόθεσμων αποκλίσεων από αυτή, αποτελεί ένα δομικό λίθο του νομισματικού υποδείγματος. Ένας από τους λόγους για τους οποίους ισχύει αυτό, είναι η έλλειψη κάποιας θεωρίας η οποία να τεκμηριώνει τη μη ισχύ της Θ.Ι.Α.Δ. και άρα να μην υπάρχει εναλλακτικός τρόπο ς που να παρέχει τους συσχετισμούς μεταξύ του επmέδου των τιμών σε διεθνές επίπεδο. Επmλέον, ένας δεύτερος λόγος κα ι ίσως περισσότερο πειστικός, είναι το γεγονός ότι όλες οι θεωρίες περιλαμβάνουν κάποιες παραδοχές οι οποίες μπορεί να είναι και λανθασμένες. Συνεπώς, σύμφωνα με τους Friedman και Schwartz (963), η θεωρία πρέπει να κρίνεται όχι βάσει του ρεαλισμού των υποθέσεών της, αλλά βάσει της ποιότητας των προβλέψεων αυτής. Ο βασικότερος έλεγχος_ για την βραχυπρόθεσμη ισχύ της Θ.Ι.Α.Δ., είναι ο έλεγχος του επαυξημένου Dickey - Fuller, σύμφωνα με τον οποίο ελέγχεται η υπόθεση πως η πραγματική συναλλαγματική ισοτιμία περιέχει μία μοναδιαία ρίζα. Στην παρούσα εργασία, γίνε ται εφαρμογή του ελέγχου της μοναδιαίας ρίζας, η οποία εξετάζει τη στασιμότητα των χρονολογικών σειρών των πραγματικών συναλλαγματικών ισοτιμιών για τη Δημοκρατία της Τσεχίας. Χρησιμοποιήθηκαν μηνιαίε ς παρατηρήσεις της ονομαστικής συναλλαγματικής ισοτιμίας ενώ οι πραγματικές συναλλαγματικές ισοτιμίες καθορίστηκαν από τους δείκτες του επmέδου των τιμών καταναλωτή για τη Δημοκρατία της Τσεχίας σε συνάρτηση με του ς δείκτες τιμών των ΗΠΑ. Κατά την εφαρμογή του επαυξημένου ελέγχου του Dickey- Fuller, ήταν δυνατή η απόρριψη της ύπαρξης μοναδιαίας ρίζας. Οπότε, διαπιστώνεται η στασιμότητα των σειρών, και επομένως για τα δεδομένα του δείγματος η μη ισχύς της Θ.Ι.Α.Δ. JEL Classification: C2, 052, Ρ27. Key words: Augmented Dickey - Fuller Test, Transition Economies, Purchasing Power Parity, Czech Republic. 4

ΕΛ. ΖΑΦΕΙΡΙΟΥ, ΣΠ. ΣΟΦΙΟΣ, ΓΑΡ. ΑΡΑΜΠΑΤΖΗΣ - ΕΠΙθΕΩΡΗΣΗ ΟΙΚΟΙJΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ - Τεύχος 5 (2009), 4-52. Introduction 42 The theory of ΡΡΡ is not the oldest theory regarding the exchange rates. This theory is simple and describes the relation between two different currencies. Ιη particular, the nominal exchange rate between two currencies is equal to the ratio of the price levels between the two countries ίη order the same purchasing power parity to be ίη validity between the two countries (Taylor Μ., Taylor Α., 2004). This theory in its primitive form, was suggested by students of the University of Salamanca in the 6 h century. Furthermore, the theory of ΡΡΡ reappeared ίη the period extending from 920-940 under the concept of argument and related to the appropriate \evel of resetting of the international exchange rates. There are ηο bibliographic references referring to the theory of ΡΡΡ in the ancestry. Einzig (970), argues that even the Greeks or the Romans, had not used the concept of ΡΡΡ not even in a primitive form. The terminology of the Theory of ΡΡΡ was specified after the First World War during an argument related to the appropriate \evel of the nominal exchange rate among the industrial countries and after a period ίη which high inflation dominated (Cassel, 98). The vast majority of economists argues that the Theory of ΡΡΡ consists a turning point, while accounts for the behavior of the rea\ exchange rates (Dornbush, 976, Κrugman, 987). According to Cassel (922), the evaluation of foreign currency from the citizens of one country in terms of the currency of the domestic currency will be related to the relevant purchasing parity of the currencies of the two countries. As far as the empirical study of the ΡΡΡ is concerned ίη the short as well as ίη the long run appears to have shifted a number of times ίη the post - war period. Ιη particular ίη the period before the break down of the Bretton - Woods system the majority of the studies appeared to support the validity of ΡΡΡ, and thus the existence of a fairly stable rea\ exchange rate over the long run. Οη the other hand the high volatility ίη real exchange rates ίη the 970s' has \ed rapidly \ed to the view that ΡΡΡ has co\\apsed (Frenkel, 98). Α number of studies testing ΡΡΡ during the recent f\oat cannot reject the null hypothesis for the rea\ exchange rates of a\l the major industrialized countries and consequently come to the conclusion the series is ηοη - stationary suggesting that al\ deviations are permanent (Taylor, 988; Mark, 990). Ιη the last decade the usage of more data and the usage of the ηοη linear econometric methods have improved the methods used for estimation resulting in the limitation of the variations of the real exchange rates from those determined by ΡΡΡ, as wel\ as the limitation of the gap between the theory and the empirical surveys enhancing the theory under review (Zafeiriou, 2005). The aim of the present paper is the empirical test of the validity of the Theory of ΡΡΡ using the Augmented Dickey - Fuller method for the currency of the Czech Republic, one of the 0 new member states of the European Union (EU).

ELENH ZAFEIRIOU, SPIRIDON SOFIOS, GARYFALLOS ARABATZIS - REVIEW OF ECONOMIC SCIENCES - Νο 5 (2009), 4-52 2. Survey area The area under surνey as already mentioned above, is Czech Republic, a state with a medium inflation economy that became a member state of the EU οη May st of the year 2004, 3 years after the disbanding of Comecon and 5 years after the fall of Berlin Wall. The major economic and demographic data of the state under review are depicted οη Table. Table. Selected demographic and national accounts indicators for Czech Republic (CZ) Population on January2003 (thousands) Population compared to EU 5onJanuary2003 (%) Total labour force (thousands)l Share offemales in total labour force (%) Unemployment rate (%) GDP at market pήces (EUR million) GDP at market pήces (EUR per capita) Share ofgdp at market pήces in the EU 5 (%) Share of gross value added at basic pήces (% )2 Agriculture (Α and Β) lndustry (C to Ε) Construction (F) Trade, accommodation and transport (G to ) Financial and business services (J and Κ) Other services (L to Ρ) Central bank official deposit rate (% )3 Hannonised index of consumer prices, change 2002/200 (%) EUlS 378,988 00.0 76,427 43.5 7.6 9,70,34 24,060 00.0 2.0 2.5 5.5 2.4 27.4 22.2.8 2. CC3 cz 74,296 0,203 9.6 2.7-5,087-44.7-7.5 693,493 73,875 3,990 7,20 6.6 30.0 7. 3.7 25.7 3.9 5.9 6.6 29. 25.8 5. 6.6 7. 5.5 -.8 -.4 () Second quarter 2003, except for EU-5. (2) Candidate Countries, CC-3, 200. (3) Data for EU-5 refers to the euro-zone (EUR-2). Source: Eurostat, Demography, National accounts According to the indicators given in Table, Czech Republic is one of Central European countries characterized by important economic development and consequently could be one of the dynamic new member states of EU. 43

ΕΛ. ΖΑΦΕΙΡΙΟΥ, ΣΠ. ΣΟΦΙΟΣ, ΓΑΡ. ΑΡΑΜΠΑΤΖΗΣ - ΕΠΙθΕΩΡΗΣΗ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ -Τεύχος 5 (2009), 4-52 3. Empirical survey Ιη the following Table 2 are given the results of univariate test of unit roots using as reference country the United States of America. Ρ values provide the distribution ratio of Dickey - Fuller (979), located to the column next to τc values ( critical values determined by Dickey- Fuller). For the determination of the half life time was used the coefficient of the lag of the real exchange rate (0 _ ), that provides the percentage ίη which declined the disturbance that has occurred to the exchange rate ίη a year. Moreover according to Edison (987), the coefficient of the lag of the real exchange rate (0 _ ), determines the rate in which the nominal exchange rate tends to the level that figured out by the Theory of ΡΡΡ. Table 2. Unit root test using the augmented Dickey - Fuller method ίη real exchange rates Country τc p value Half time life (years) Czech Republic -.2 0.927 22 Source: IMF (992-2004), dala processing 44 Regarding the exchange rate of the national currency of Czech Republic "crown" or "koruna" as it is called otherwise, to dollar the regime of the fixed exchange rates was replaced by the regime of the flexible exchange rates. This process occurred gradually. Ιη particular οη J anuary sι of the year 995 the annual amount ίη evaluated in domestic currency that Czech citizens had the ability to exchange for a currency that is characterized by greater stability significantly increased from 2,000 to 00,000 crowns. Consequently, the band within the exchange rate of crown regarding to dollar becomes greater. Ιπ addition, οη October s of the year 995, a new regulation enacted, according to which complete conversion of the current account as well as the partial deregulation of capital exchange. Given the fact of a medium inflation, the alterations of the real as well as the nominal exchange rate is extremely smooth as shown in the following Figure. Furthermore, the existence of a unit root is obvious and consequently the series of real exchange rate is non-stationary. Smidkova (2004), has used the Fundamental Real Exchange Rates ίη order better performance to be achieved. These exchange rates are defined so as to be in line with some macroeconomic variables such as the External Public Debt, the growth of the domestic and the foreign country and others. Ιη that case the rates are presented in Figure 2. According to this Figure 2, the national currency of the Czech Republic, crown, is over estimated ίη the year 2002 with a rate of 5%, a tendency that persisted in the following years but with lower rates.

ELENH ZAFEIRIOU, SPIRIDON SDFIOS, GARYFALLOS ARABATZIS - REVIEW OF ECONOMIC SCIENCES - Νο 5 (2009), 4-52 Figure. The real and the nominal exchange rates for Crown and US Dollar ίη a logarithmic form 993-2004 ~.. i.c ~. i c '! ο c 3,3 3,2 "i f 3, 3 ;;;; ~ iii ~ ;::: a; i σ> σ> σ> σ> ~ ~ ~ ~ ~ ~ ~ Reference period Figure 2. The Fundamental Real Exchange Rates - -. - --- - -- -- - -------........ _...._.... -. -....... ιιιιu.~... ί...j - CRRER CRFER Notes: CRRER: Observed va lues of tle real effective Koruna exchange rates. CR FER: The basic estimate of the fιιn da m e n ta l exchange rates. Source: Srnidkova, (2004) 45

ΕΛ. ΖΑΦΕΙΡΙΟΥ, ΣΠ. ΣΟΦΙΟΣ, ΓΑΡ. ΑΡΑΜΠΑΤΖΗΣ - ΕΠΙθΕΩΡΗΣΗ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ -Τεύ χ ο ς 5 (2009), 4-52 4. Results Regarding the unit root test and ίη the case of the currency of Czech Republic monthly data were used for the period 993-2004. The presentation of the results of the augmented Dickey - Fuller test and having as aim the presentation of the process the residuals of the Dickey - Fuller equation follows the correlation as well as the partial autocorrelation is used. The graphical depict of those is given to the correlogram presented ίη Figure 3. Figure 3. The correlogram of the residuals of the estimated ADF equation Included observations: 42 Autocorrelation Partial Correlation AC PAC Q-Stat Prob 0.000 0.000 9. Ε-06 0.998 2-0.002-0.002 0.0007.000 3-0.008-0.008 0.005.000 *',. 4-0.06-0.06 0.5682 0.967.,. 5 0.00 0.00 0.5684 0.989 6 0.027 0.027 0.6770 0.995 7 0.029 0.028 0.806 0.997 8-0.007-0.0 0.8087 0.999 *.,'* 9 0.077 0.078.7262 0.995 According to Figure 3 partial autocorrelation is zero consequently an autoregressive of first order should be used. The results of the ADF test are given ίη Table 3 that follows. The given test was conducted with the econometric program Ε - Views 4.. 46

ELENH ZAFEIRIOU, SPIRIDON SOFIOS, GARYFALLOS ARABATZIS - REVIEW OF ECONOMIC SCIENCES - Νο 5 (2009), 4-52 Table 3: The results of ADF test ίη the case of Czech currency Null Hypothesis: Q has a unit root Exogenous: Constant Lag Length: Ο (Automatic based on SIC, MAXLAG= 3) Augmented Dickey-Fuller test statistic Test critical values: % level 5% level 0% level * MacΚinnon (996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(Q) Method: Least Squares fncluded observations: 43 after adjusting endpoints t-statistic -0.53093-3.476472-2.88685-2.57759 Variable Coefficient Std. Error t-statistic Q(-) c R-squared Adjusted R-squared S.E. of regression Sum squared resid Log likelihood Durbin-Watson stat -0.0848 0.037407 0.00996-0.005082 0.035757 0.80278 274.4328 2.088 0.022309-0.53093 0.078466 0.476722 Mean dependent var S.D. dependent var Akaike info criterion Schwarz criterion F-sta tistic Prob(F-statistic) Prob.* 0.8805 Prob. 0.5962 0.6343-0.004236 0.035667-3.80250-3.7688 0.282059 0.59690 Based on the results given above the null hypothesis is rejected and consequently the test should be repeated with the use of the linear trend. Those results are given ίη Table 4. 47

ΕΛ. ΖΑΦΕΙΡΙΟΥ, ΣΠ. ΣΟΦΙΟΣ, ΓΑΡ. ΑΡΑΜΠΑΤΖΗΣ - ΕΠΙθΕΩΡΗΣΗ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ - Τεύχος 5 (2009), 4-52 Table 4. ADF test with the use of linear trend Null Hypothesis: Q has a unit root Exogenous: Constant, Linear Trend Lag Length: (Fixed) Augmented Dickey-Fuller test statistic Test critical values: % level 5% Jevel 0% level *MacΚinnon (996) one-sided p-values. Augmented Dickey-Fuller Test Equation Dependent Variable: D(Q) t-statistic -.64-4.023975-3.44777-3.45474 Method: Least Squares Included observations: 42 after adjusting endpoints Variable Coefficient Std. Error t-statistic Q(-) - 0.03395 0.028242 -.64 D(Q(-)) -0.040538 0.086796-0.467047 c 0.4458 0.03267.08367 @TREND(993:0) -0.0009 9.02Ε-05 -.33406 R-squared 0.06773 Mean dependent var Adjusted R-squared -0.00460 S.D. dependent var S.E. of regression 0.035872 Akaike info criterion Sum squared resid 0.77579 Schwarz criterion Log likelihood 273.0867 F-statistic Durbin-Watson stat.986659 Prob(F-statistic) 0.504377 Prob.* 0.9227 Prob. 0.2682 0.642 0.2696 0.92-0.004275 0.035790-3.789953-3.70669 0.784735 48 According to the results given in Table 4 above the test should be interrupted with the result that the null hypothesis is rejected and thus the time series under preview has not a unit root, it is stationary and consequently every exogenous disturbance tends to have a permanent impact οη the exchange rate ( endogenous variable ). The small size of the sample accounts for the low interpretative ability of the test given the fact that the values are monthly and the period used is extremely small. Ιη particular the number of observations is 42 after the adj ustment. Durbin - Watson test does not show autocorrelation. The test under review is not credible because of the fact that lags of the endogenous variable are

ΕΛ. ΖΑΦΕΙΡΙΟΥ, ΣΠ. ΣΟΦΙΟΣ, ΓΑΡ : ΑΡΑΜΠΑΤΖΗΣ - ΕΠΙθΕΩΡΗΣΗ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ - Τεύχος 5 (2009), 4-52 5. Conclusions The aim of this paper, as an empirica\ survey, is the study of the existence of a unit root that states the non - stationarity of the time series of the real exchange rates for the currency of the Czech Republic. The application of the ADF test showed the rejectioπ of a uπit root. Thus the series is ποπ - statioπary aπd consequeπtly the theory of ΡΡΡ is ποt valid. These results are compatible with Figure that depicts the alterations of the real aπd the πomiπal exchange rates. Accordiπg to bibliographic references ADF test is characterized by low validity due to the small πumber of the monthly observatioπs. Ιπ additioπ the refereπce period is characterized by great alteratioπs ίπ the ecoπomic situatioπ of the Czech Republic, a fact that is reflected to the πominal exchange rates. What also must be mentioned is the fact that the validity of the test is not affected by the variation of the real exchange rates (Froot and Rogoff, 996). However, according to the used data the rejection of the πull hypothesis regarding the existence of a unit root was not possible. In sequence, the rejection of the stationarity of the time series was not possible. Another factor that has a powerful impact on the results of this method is the alteration ίπ the regime of exchange rates of Czech Republic that during the reference period (993-2004), turns to be floating. The half - lifetime is extremely high 22 years, a fact that can be accounted by smooth alterations of the income related to the alterations of the regime. Accordiπg to studies conducted till today the half - lifetime ranges from four to seven years. Another point that should be mentioned is the impact of the iπflation on the validity of the theory. The economy of the Czech Republic is characterized by medium inflation. The majority of the cases in which the validity of ΡΡΡ was examined concerned industrialized economies that are characterized by low inflations. In this survey, the differences in the inflations between the Czech Republic and the USA, amplified the nοπ - validity of the theory of ΡΡΡ. In addition, significant πonlinearities may account for the mean reversion ίπ real exchaπge rates, and thus the long half time lives. For the settlement of the validity problem the use of monthly data, referring to loπger period is necessary. Another method that overcomes the problems meπtioned above is the method of co - integratioπ. This method is uninhibited from the eπdogeneity and the participatioπ of the endogenous variables. Co - integration provides the ability of scouting the validity of ΡΡΡ eveπ in its weakest form. 50

ELENH ZAFEIRIOU, SPIRIOON SOFIOS, GARYFALLOS ARABATZIS - REVIEW OF ECONOMIC SCIENCES - Νο 5 (2009), 4-52 References Cassel G. (98). ' Άbnormal Deviations in International Exchanges". Economίc Joumal, 28, pp. 43-45. Cassel G. (922). Money and Foreίgn Exchange after 94. New York. Macmillan. Christou G. (2000). Introductίon to Econometrίcs. Athens. Gutenberg (in Greek). Dickey D. and W. Fuller (979). "Distribution of the estimators for autoregressive time series with a unit root". Journal of the American Statistical Association, 74, pp. 427-43. Dornbusch R. (976). 'Έxpectations and Exchange Rate Dynamics". Joumal of Polίtίcal Economy, 84 (December), pp. 6-76 Edison Η. (987). Purchasing Power Parity in the Long run: Α test of the dollar / pound exchange rate (890-78). Joumal of Money, Credίt and Bankίng, 9, pp. 367-387. Einzig Ρ. (970). The History of Foreign Exchange. London. Macmillan. Eurostat. Demography, Natίonal accounts. Frenkel J.A. (98). "The Collapse of Purchasing Power Parities during the 970's". European Economίc Reνίew, 6, pp. 45-65. Friedman Μ. and Α.. Schwartz (963). 'Ά Monetary Hίstory of the Unίted States: 867-960". Princeton N.J.: Princeton University Press for the National Bureau of Economic Research. Froot Κ. Α. and Κ. Rogoff (995). "Perspectives οη ΡΡΡ and Long-Run Real Exchange Rates". Handbook of Intematίonal Economίcs, vol. 3, edited by G. Grossman and Κ. Rogoff. Amsterdam: North Holland. IMF Database. Krugman Ρ. R. (987). "Prίcίng - to - Market when the Exchange Rate Changes" ίn S. W Ardnt and J. D. Rίchadrson, Real Εχ - Financial Linkages among Open Economies, Campridge, Mass. ΜΙΤ Press, pp. 49-70. Mark Ν. C. (990) "Real and Nominal Exchange Rates in the Long Run: An empirical lnvestigation". Joumal of Intematίonal Economίcs, 28, pp. 5-36. Smidkova Κ. (2004). 'Άdoption ofthe Euro: Why is the Czech Approach so cautious?" Atlantίc Economίc Joumal, 32, pp. 302-3. Taylor Μ. Ρ. (988). " An Empirical Examination of Long Run Purchasing Power Parity Using Cointegration Techniques" Applίed Economίcs, 20, pp. 369-38. 5

ΕΛ. ΖΑΦΕΙΡΙΟΥ, ΣΠ. ΣΟΦΙΟΣ, ΓΑΡ. ΑΡΑΜΠΑΤΖΗΣ - ΕΠΙθΕΩΡΗΣΗ ΟΙΚΟΝΟΜΙΚΩΝ ΕΠΙΣΤΗΜΩΝ - Τεύχος 5 (2009), 4-52 Taylor Α. and Μ. Ρ. Taylor (2004). "The Pυrchasing Power Parity Debade". NBER, W 0607. - Zafeirioυ Ε. (2005). Α Review of the Theory of Purchasing Power Parity. MSc Thesis that was sυbmitted to the University of Macedonia. Thessaloniki (ίη Greek with English abstract). 52