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DYNAMIC ECONOMETRIC MODELS 
Vol. 9 – Nicolaus Copernicus University – Toruń – 2009 

Dorota Górecka, Dominik  Śliwicki 
Nicolaus Copernicus University in Toruń 

Application of Panel Data Models to Exchange Rates’ 
Modeling for Scandinavian and Central  

and Eastern European Countries 

A b s t r a c t. In the paper the purchasing power parity (PPP) theory for 6 states belonging to 
OECD, namely Denmark, Norway, Sweden, Poland, Czech Republic and Hungary, was ex-
amined. In order to do that the IPS panel unit root test was employed. After establishing that the 
exchange rates permanently deviate from the long-term equilibrium rate and the PPP theory is at 
variance with the data, two panel models were estimated to identify factors that influence ex-
change rates of Scandinavian and CEFTA countries. 

K e y w o r d s: purchasing power parity, long-term equilibrium exchange rate, panel models with 
fixed individual effects. 

1. Introduction 
 Literature referring to the exchange rates and calculation of their real equili-
brium levels is very rich. A methodology related to this problems is depicted in 
the work of Hinkel and Montiel (1999) while a review of the results of the em-
pirical investigations can be found in the article of Edwards and Savastano 
(1999). At least three concepts have been used so far in the analyses to deter-
mine the equilibrium exchange rate, namely: Purchasing Power Parity theory 
(Johansen, Juselius, 1992; MacDonald, Nagayasu, 1998), fundamental theory 
(Williamson, 1983, 1994) and behavioral theory (Clark, MacDonald, 1998, 
2004). Development of the econometric estimation methods for the non-
stationary panel data has caused that cointegration models for this kind of data 
are used in many works (Habermeier, Mesquita, 1999; MacDonald, Ricci, 
2001). Into this stream an empirical investigation described in the article may be 
included. The investigation constitutes an attempt to determine dependencies 
between exchange rate and macroeconomic factors for three Scandinavian 
(Denmark, Norway and Sweden) and three CEFTA countries (Czech Republic, 
Hungary and Poland) by means of panel data models. Such set of countries was 



Dorota Górecka, Dominik Śliwicki 

 

52

selected in order to check if some differences concerning the exchange rate 
modeling between the developed and the developing European countries that 
have not adopted a common currency will occur.  

2. Purchasing Power Parity Theory and The Foreign Exchange 
Rate of OECD Countries 

 Investigation concerns the inverse real exchange rate of the euro in relation 
to the currencies of three Scandinavian countries (Danish krone, Norwegian 
krone and Swedish krone) and in relation to the currencies of three CEFTA 
countries (Czech krone, Polish zloty, Hungarian forint). The analysis is based 
on the data spanning the period from the first quarter of 1999 to the fourth quar-
ter of 2008 (40 observations)1. The real exchange rate RERdc is calculated on the 
basis of formula:  

,
d

fdc
dc P

PE
RER =  (1) 

where:  

dcE represents a simple nominal exchange rate,  

dP  denotes a domestic price level,  

fP  denotes a foreign price level. 

As price deflators the Producer Price Indices (PPI) have been used.   
 Verification of the non-stationarity of the foreign exchange rates has been 
performed on the panel data2 (the first panel comprised Scandinavian countries 
and the second one – Central and Eastern European Countries) with the aid of 
IPS unit root test (Im, Pesaran, Shin, 1997, 2003) that has a relatively high 
power and satisfactory properties for short time series and small number of 

                                                 
1 Quarterly data are used because the data concerning GDP (used in further analysis) are not 

available in monthly frequency. 
2 Until the moment of proposing the non-stationarity examination techniques for panels the 

analyses of bilateral exchange rates have provided very little evidence on the PPP theory. For 
instance the literature review made by Edwards and Savastano (1999) shows that in the case of 
developing countries the hypothesis that the real exchange rate series contain (at least) one unit 
root could not be rejected in 40 out of 54 individual country tests of RER stationarity. In turn, in 
the case of the empirical study of real effective exchange rates for the 51 largest economies in the 
world for the 1971-1997 period the relative version of the PPP theory was confirmed only for 14 
countries at 10% significance level and merely for 2 at 1% significance level. Research carried 
out for the panel data with the help of IPS test have shaken the previous conclusions in favor of 
the PPP theory – at 5% significance level the null hypothesis of non-stationarity was rejected for 
all 51 countries (Habermeier, Mesquita, 1999). Utilization of the panel non-stationarity examina-
tion techniques enables data range extension by adding the observations of the variables from 
other states and decreases ipso facto the risk of structural changes occurring.  



 Application of Panel Data Models to Exchange Rates’ Modeling … 

 

53

cross-section data as the results of separate analysis of the currency exchange 
rate for each of six investigated OECD countries have not provided much evi-
dence on the PPP theory – at 10% significance level there was no basis for re-
jection the null hypothesis of non-stationarity of the examined foreign exchange 
rates3. 

Table 1. The results of the panel stationarity test (1999 1st quarter – 2008 4th quarter) 
Countries Deterministic component LM statistic p-value 

Scandinavian Constant 0.104 0.504 
constant + trend 0.604 0.727 

Central and Eastern European Constant -1.358 0.087 
constant + trend -0.405 0.343 

On the basis of values of statistics presented in Table 1 one may say that at 5% 
significance level there is no basis for rejection the null hypothesis of non-
stationarity of the investigated foreign exchange rates. It may be treated as an 
evidence of the fact that Purchasing Power Parity theory is false in the cases of 
Scandinavian and CEFTA countries4. 
In order to verify if the global financial crisis has contributed to the failure of 
the PPP hypothesis the analysis has been carried out for datasets containing 32 
and 36 observations. 

Table 2. The results of the panel stationarity test (1999 1st quarter – 2006 4th quarter) 
Countries Deterministic component LM statistic p-value 

Scandinavian Constant -0.985 0.162 
constant + trend 0.337 0.633 

Central and Eastern European Constant -1.253 0.105 
constant + trend 0.238 0.594 

Table 3. The results of the panel stationarity test (1999 1st quarter – 2007 4th quarter) 
Countries Deterministic component LM statistic p-value 

Scandinavian Constant -0.623 0.267 
constant + trend -0.459 0.323 

Central and Eastern European Constant -1.459 0.072 
constant + trend -0.010 0.496 

                                                 
3 Analysis has been also performed for monthly data and it has not provided much support for 

the PPP theory – the null hypothesis of non-stationarity was rejected only in the case of Hunga-
rian forint exchange rate (at 1% significance level). In the case of the monthly and quarterly data 
concerning the inverse real exchange rate of the U.S. dollar in relation to the currencies of six 
investigated OECD countries the null hypothesis was not rejected (at 10% significance level) 
even once. 

4 Empirical research with the help of the IPS test has been also carried out for monthly data 
concerning the inverse real exchange rate of the euro and for monthly and quarterly data concern-
ing the inverse real exchange rate of the U.S. dollar in relation to the currencies of six examined 
OECD countries. The PPP theory has not received much support from these studies as at 5% 
significance level the null hypothesis of non-stationarity was rejected only once (in the case of 
monthly exchange rates of Central and Eastern European Countries against the euro). 



Dorota Górecka, Dominik Śliwicki 

 

54

On the basis of values of the statistics presented in Tables 2 and 3 one may say 
that the structural change that occurred at the end of the time series had no in-
fluence on the results of the research - at 5% significance level there is no basis 
for rejection the null hypothesis of non-stationarity of the investigated foreign 
exchange rates. 

3. Reasons of the Exchange Rate Volatility 
 In connection with the conclusion presented in the previous part of this ar-
ticle the question of the reasons of the exchange rate deviations from the PPP 
should be raised.  
 One of the most known conceptions explaining behavior of the real ex-
change rates in the long-run is so-called Balassa-Samuelson effect (Balassa, 
1964). The essence of the B-S effect is that the increase of the productivity in 
the tradable goods sector causes inflation in the non-tradable goods sector and 
raises ipso facto overall price index, which – in turn – leads to an appreciation 
of the real exchange rate. The B-S hypothesis concerns the catching-up econo-
mies, including transition countries entering the European Union. The pheno-
menon occurring has been confirmed in many researches (Rogoff, 1996), in 
which the significant positive influence of the economic growth on the real ex-
change rate has been demonstrated.  
 Another potential exchange rate determinant is government expenditure.  
It moves the internal demand towards the non-tradable items causing the in-
crease of their prices and the real exchange rate appreciation (Habermeier,  
Mesquita, 1999).   
 A different factor influencing the real exchange rate is terms of trade de-
fined as a ratio between export and import prices. The rise of this index value 
(caused either by the increase of the export prices or by the decrease of the im-
port prices) means a decline of the domestic products competitiveness and leads 
to a depreciation of the exchange rate (Baffes, Elbadawi, O’Connell, 1997;  
Habermeier, Mesquita, 1999). 
 The real exchange rate changes may be also explained by the behavior of 
the real interest rate. Relatively higher national rate of interest, boosting the 
foreign currency supply, contributes to the drop of the national currency rate, 
that is its appreciation (Brook, Hagreaves, 2001; Chortareas, Driver, 2001). 



 Application of Panel Data Models to Exchange Rates’ Modeling … 

 

55

4. Panel Data Models for the Real Exchange Rates of the OECD 
Countries  

 Below two panel data models will be presented5. The first of them concerns 
Scandinavian countries (Denmark, Norway and Sweden) and the second one – 
Central and Eastern European Countries (Czech Republic, Hungary and Pol-
and). In both cases an explained variable is the real exchange rate of the ex-
amined countries against the euro (the nominal rate deflated by the Producer 
Price Index – PPI). Among the explanatory variables are: relative economic 
growth6 (representing the B-S effect), trade balance in relation to GDP (evi-
dencing the competitiveness of a given economy) and relative real interest rate. 
It is expected that in accordance with the above-mentioned mechanisms the 
signs of the parameter estimates for all three explanatory variables will be nega-
tive.  

Table 4. The results of the model estimation for the group of Scandinavian countries  
Variable Parameter estimate Student’s t-statistic p-value R2 
constant 8.801 68.79 0.0000*** 

80.12% interest rate 0.128 4.058 0.0000*** 
trade balance/GDP -6.682 -5.021 0.0000*** 

 The results of estimation of the panel data model with fixed individual ef-
fects for developed Scandinavian countries point to the existence of the signifi-
cant relationship between real exchange rate and both the trade balance and the 
relative real interest rate. In the case of the relative real interest rate the sign of 
the parameter estimate is at variance with the predictions, which can be ex-
plained among other things by the influence of the world interest rates or differ-
ent kinds of expectations. On the other hand, in accordance with the predictions 
the impact of the relative economic growth on the exchange rate in the case of 
Scandinavian countries turned out to be statistically insignificant.  
 In the case of the panel data model with fixed individual effects for develop-
ing countries belonging to CEFTA a direction of influence of the explanatory 
variables is in accordance with the earlier formulated expectations: the increase 
of the relative GDP as well as the trade surplus contribute to the decrease of the 
exchange rate, that is its appreciation.  Moreover, the influence of the relative 
real interest rate on the exchange rate is also negative, albeit statistically insigni-
ficant, which leads to the conclusion that in the case of Central and Eastern 
European Countries behavior of the interest rates affects the exchange rate 
much more weakly than behavior of other macroeconomic factors.  

                                                 
5 Panel data models, contrary to the time series models, allow one to investigate general rela-

tionships for fixed groups of chosen countries.    
6 The term ‘relative’ means in this case comparison with the euro area.  



 

 

 

 

 
Figure 1. Fitted and actual values of the exchange rate of the Danish krone (1999 1st 

quarter – 2008 4th quarter) 

 
Figure 2. Fitted and actual values of the exchange rate of the Swedish krone (I quarter 

1999 1st quarter – 2008 4th quarter) 
 

6,9
7

7,1
7,2
7,3
7,4

7,5

7,6
7,7
7,8
7,9

8

I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

fitted actual

7

7,5

8

8,5

9

9,5

10

I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

fitted actual



 

 

 

Figure 3. Fitted and actual values of the exchange rate of the Norwegian krone (1999 1st 
quarter – 2008 4th quarter) 

Table 5. The results of the model estimation for the group of Central and Eastern Euro-
pean Countries   
Variable Parameter estimate Student’s t-statistic P-value R2 
constant 12.615 71.86 0.0000*** 

99.07% relative economic growth -0.754 -3.607 0.0005*** 
trade balance/GDP -24.800 -5.507 0.0000*** 

 
Figure 4. Fitted and actual values of the exchange rate of the Polish zloty (1999 1st quar-

ter – 2008 4th quarter)  

0

2

4

6

8

10

12
I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

fitted actual

0

1

2

3

4

5

6

7

I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

fitted actual



Dorota Górecka, Dominik Śliwicki 

 

58

 

Figure 5. Fitted and actual values of the exchange rate of the Czech krone (1999 1st 
quarter – 2008 4th quarter) 

 

 

Figure 6. Fitted and actual values of the exchange rate of 100 Hungarian forints (1999 
1st quarter – 2008 4th quarter) 

Summary 
 The main conclusion drawn from the analysis carried out in this paper is 
rejection of the hypothesis that the exchange rates of the examined Scandina-

0

5

10

15

20

25

30

35

40

I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

fitted actual

0

0,5

1

1,5

2

2,5

3

3,5

4

4,5

I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV I II II
I IV

1999 2000 2001 2002 2003 2004 2005 2006 2007 2008

fitted actual



 Application of Panel Data Models to Exchange Rates’ Modeling … 

 

59

vian and CEFTA countries in the years 1999-2008 were shaping according to 
the purchasing power parity theory. The results obtained indicate that the real 
exchange rate of six OECD countries is determined by such economic factors as 
economic growth, trade balance and interest rates.  
 Further research concerning exchange rates may, first of all, focus on wi-
dening the cross-section of the panels with other countries, for instance Bulga-
ria, Romania, Croatia and Ukraine in the case of Central and Eastern European 
Countries. Another possibility is taking into account in the models additional 
variables such as net foreign assets, real wages, private consumption, govern-
ment spending, budget deficit, public debt or foreign direct investments (Bęza-
Bojanowska, MacDonald, 2009). Finally, these models may be employed in 
forecasting. 

References  
Baffes, J., Elbadawi, I.A., O’Connell, S.A. (1997), Single-Equation Estimation of the Equilibrium 

Real Exchange Rate, WB Working Paper 08/20/97, World Bank, Washington. 
Balassa, B. (1964), The Purchasing Power Parity Doctrine: A Reappraisal, Journal of Political 

Economy, 72, 584–596. 
Bęza-Bojanowska, J., MacDonald, R. (2009), The Behavioural Zloty/Euro Equilibrium Exchange 

Rate, CESifo Working Paper Series No. 2568, University of Glasgow, Glasgow.  
Brook, A., Hagreaves, D. (2001), PPP-based Analysis of New Zealand’s Equilibrium Exchange 

Rate, Discussion Paper Series DP2001/01, Reserve Bank of New Zealand, Wellington. 
Cassel, G. (1918), Abnormal Deviations in International Exchanges, Economic Journal, Black-

well Publishers, Oxford, 413–415.  
Chortareas, G.E., Driver, R.L. (2001), PPP and the Real Exchange Rate – Real Interest Rate 

Differential Puzzle Revisited: Evidence from Non-Stationary Panel Data, Bank of Eng-
land, London. 

Clark, P.B., MacDonald, R. (1998), Exchange Rates and Economic Fundamentals: A Methodo-
logical Comparison of BEERs and FEERs, IMF Working Paper 98/67, International 
Monetary  Fund, Washington.  

Clark, P.B., MacDonald, R. (2004), Filtering the BEER: A Permanent and Transitory Decomposi-
tion, Global Finance Journal, 15, 29–56. 

Edwards, S., Savastano, M.A. (1999), Exchange Rates in Emerging Economies: What Do We 
Know? What Do We Need to Know?, NBER Working Paper No. 7228, National Bureau 
of Economic Research, Cambridge.  

Habermeier, K., Mesquita, M. (1999), Long-Run Exchange Rate Dynamics: A Panel Data Study, 
IMF Working Paper WP/99/50, International Monetary Fund, Washington.  

Hinkle, L., Montiel, P. (1999), Exchange Rates Misalignment. Concepts and Measures for Devel-
oping Countries, Oxford University Press, New York. 

Im, K.S., Pesaran, M.H., Shin, Y. (1997), Testing for Unit Roots in Heterogeneous Panels, Dis-
cussion Paper, University of Cambridge, Cambridge. 

Im, K.S., Pesaran, M.H., Shin, Y. (2003), Testing for Unit Roots in Heterogeneous Panels, Jour-
nal of Econometrics, 115, 53–74.  

Johansen, S., Juselius, K. (1992), Testing Structural Hypothesis in a Multivariate Cointegration 
Analysis of the PPP and the UIP for UK, Journal of Econometrics, 53, 211–244. 

MacDonald, R., Nagayasu, J. (1998), On the Japanese Yen-U.S. Dollar Exchange Rate: A Struc-
tural Economic Model Based on Real Interest Differentials, Journal of the Japanese and 
International Economies, 12, 75–102. 



Dorota Górecka, Dominik Śliwicki 

 

60

MacDonald, R., Ricci, L. (2001), PPP and Balassa-Samuelson Effect: The Role of the Distribu-
tion Sector, IMF Working Paper WP/01/38, International Monetary Fund, Washington. 

Rogoff, K. (1996), The Purchasing Power Parity Puzzle, Journal of Economic Literature, 34, 
647–668.  

Williamson, J. (1983), The Exchange Rate System, Institute for International Economics, Wash-
ington.  

Williamson, J. (1994), Estimates of FEERs, [in:] Williamson J. (ed.), Estimating Equilibrium 
Exchange Rates, Institute for International Economics, Washington. 

Zastosowanie modeli panelowych do modelowania kursów walutowych 
dla krajów skandynawskich i Europy Środkowo-Wschodniej  

Z a r y s  t r e ś c i. W artykule podjęto próbę empirycznej weryfikacji teorii parytetu siły nabyw-
czej w odniesieniu do sześciu krajów członkowskich OECD: Danii, Norwegii i Szwecji oraz 
Czech, Polski i Węgier. W związku z tym, że uzyskane wyniki nie potwierdziły prawdziwości 
weryfikowanej teorii, celem pracy stało się zidentyfikowanie czynników wpływających na po-
ziom kursów walutowych państw skandynawskich oraz państw Europy Środkowo-Wschodniej w 
latach 1999-2008 oraz wskazanie różnic między nimi.  

S ł o w a  k l u c z o w e: teoria parytetu siły nabywczej (Purchasing Power Parity, PPP), długo-
okresowy kurs równowagi, modele panelowe z ustalonymi efektami indywidualnymi.  


