In this paper, we employ some front page panel unit root tests to examine the validity of the purchasing power parity hypothesis in Turkey. Using monthly observations panel data of nine major county’s currency dates January 2003 through April 2010, we find that panel unit root tests are not rejected the mean-reversion of real exchange rates. Thus, the empirical results indicate significant support for the purchasing power parity holds in TurkeyPurchasing Power Parity, Real Exchange Rates, Panel Unit Root Tests, Floating Exchange Rates

Gozgor, Giray

English

Research Papers in Economics

 
 
Panel Unit Root Tests of Purchasing Power Parity 
Hypothesis: Evidence from Turkey 
 
 
Giray Gozgor 
Department of International Trade and Business, Dogus University, Kadikoy, Istanbul, Turkey 
E-mail: ggozgor@dogus.edu.tr 
 
 
Abstract 
 
 In this paper, we employ some front page panel unit root tests to examine the validity of the 
purchasing power parity hypothesis in Turkey. Using monthly observations panel data of nine 
major county’s currency dates January 2003 through April 2010, we find that panel unit root 
tests are not rejected the mean-reversion of real exchange rates. Thus, the empirical results 
indicate significant support for the purchasing power parity holds in Turkey. 
 
Keywords: Purchasing Power Parity, Real Exchange Rates, Panel Unit Root Tests, Floating 
Exchange Rates. 
JEL classification codes: C23, F30, F31. 
 
1.  Introduction 
To determine the exchange rates under floating exchange rates important for policy makers and 
theoretical considerations. Floating exchange rates are based on the collapsing of Bretton Woods 
System in 1973 and became a risk factor as the result of the transition to floating exchange rate 
regime as a consequence of the financial crisis in Turkey in February 2001, despite the emergence 
of many developed and emerging market economies have been predicated in 1973. One of the main 
critical issues that determining exchange rate, whether they are mean-reverting in the long run and 
the purchasing power parity (PPP) holds.  
There is a widespread literature to examine relation between real exchange rates and PPP. 
Froot and Rogoff (1995), Rogoff (1996), Taylor and Sarno (1998), O’Conell (1998), Anker (1999), 
Sarno (2000), Taylor et al. (2001), Sarno and Taylor (2002), Killian and Taylor (2003), Taylor and 
Taylor (2004), Breitung and Candelon (2005), Taylor (2006), Kalyoncu and Kalyoncu (2008), Lau 
(2009), Cuestas (2009), Hung and Weng (2010) have showed theoretical background and empirical 
evidences  of  PPP-real  exchange  rates  relationship.  In  this  paper,  we  investigate  whether  real 
exchange rates in Turkey are mean-reverting or not. We apply contemporaneous panel unit root 
tests to nine exchange rates which are defined by Turkish Lira (TL). We suggest that such approach 
could also provide valuable insight for further investigation of this phenomenon in Turkey. 
The  outline  of  this  study  is  as  follows:  Second  section  explains  the  data  and  the 
methodology, the third section presents the empirical findings and final section concludes. 
 
 
2. Data and Methodology 
In this section, we define the real exchange rates as panel framework from nominal exchange rates 
of  Australian  Dollar  (AUD),  Canadian  Dollar  (CAD),  Swiss  Franc  (CHF),  Euro  (EUR),  Great 
Britain Pound (GBP), Japanese Yen (JPY), Norwegian Kroner (NOK), Swedish Kroner (SEK) and 
United States Dollar (USD) against Turkish Lira (TL). We use 87 observations from January 2003 
to April 2010 and the frequency of data is monthly. The data used for this study come from the   
 
International Financial Statistics from the International Money Fund. Nominal exchange rates are 
converted into real exchange rates by using the consumer prices indices. Real exchange rates are 
constructed defining relative prices as the ratio of each country's CPI to Turkey CPI, and employed 
the method as follows: 
 
* ( ) ( ) log( ) log( ) log RER log NER P P = + −  
 
Where RER is the real exchange rate, NER is the nominal exchange rate and P
* and P are 
the foreign and domestic prices, respectively. 
And  we  define  the  following  equation  which  shows  the  model  of  mean-reverting  real 
exchange rate, 
 
1 ( ) ( ) t t t log RER log RER α β ε − = + +  
 
α andε are constant and error term respectively. PPP suggest that real exchange rate series 
should be stationary. If there is a unit-root in the real exchange rate this implies that shocks to the 
real exchange rate are permanent and PPP does not exist between two countries. 
The classical unit root tests of the real exchange rates such as Dickey and Fuller (1979) are 
subject to some criticism that is occurred from the low power of these tests in small samples in 
order to define PPP relationship. Consequently, panel unit root tests began to be widely used in 
literature. In this study, we employ panel unit root tests can be arranged in groups by cross section 
dependence  or  independence,  heterogeneous  or  homogenous  unit  roots  which  are  defined  by 
Maddala and Wu (1999), Breitung (2000), Hadri (2000), Choi (2001), Levin et al. (2002), Im et al. 
(2003). 
To define these test’s approach, we consider a following AR(1) process for panel data: 
 
it i it-1 it i it y  =  y + X  +  ρ δ ε
 
 
Where  1,2,...... i N =  cross-section units or series that are observed over periods  1,2,....... t Ti =  
Xit represent the exogenous variables in the model, including any fixed effects or individual trends, 
i ρ  are the autoregressive coefficients, and the errors  it ε  are assumed to be mutually independent 
idiosyncratic disturbance. If 1 i ρ < ,  i y said to be weakly (trend) stationary. On the other hand, if 
1 i ρ =  then  i y contains a unit root. 
For purposes of testing, there are two natural assumptions that we can make about the i ρ .  
First, one can assume that the persistence parameters are common across cross-sections so that 
i ρ ρ =   for  all  i   Levin  at  al.  (2002),  Breitung  (2000),  and  Hadri  (2000)  tests  all  employ  this 
assumption. Alternatively, one can  allow i ρ   varying  freely  across cross sections. The Im et al. 
(2003), and Fisher-ADF and Fisher-PP tests define by Maddala and Wu (1999) and Choi (2001) are 
of this form. 
Levin  at  al.  (2002),  Breitung  (2000),  and  Hadri  (2000)  tests  all  assume  that  there  is  a 
common unit root process so that  i ρ is identical across cross-sections. The first two tests employ a 
null hypothesis of a unit root while the Hadri (2000) test uses a null of no unit root. Levin at al. 
(2002) and Breitung (2000) both consider the following basic ADF specification: 
 
1 1
pi
X ij it it it j it it j
y y y α β δ ε ′ ∑ = + + + − − −
∆ ∆  
  
 
Where we assume a common  1 α ρ = −  but allow the lag order for the difference terms, 
i ρ to vary across cross-sections. The null and alternative hypotheses for the tests may be written 
as H0:  0 α =  H1:  0 α <  so under the null hypothesis, there is a unit root, while under the alternative, 
there is no unit root. 
The  Im  et  al.  (2003),  the  Fisher-ADF  and  PP  tests  all  allow  for  individual  unit  root 
processes  so  that  may  i ρ   vary  across  cross-sections.  The  tests  are  all  characterized  by  the 
combining of individual unit root tests to derive a panel-specific result. Im et al. (2003) begin by 
specifying a separate ADF regression for each cross section: 
 
1 1
pi
X ij it it it j it it j
y y y α β δ ε ′ ∑ = + + + − − −
∆ ∆  
H0: 0 α =  for all i while the alternative hypothesis is given by 1
0 1,2, 1
0 1, 2,....
for i N i
for i N N N i
H
α
α
= =
< = + +
 

 
K
K
 
 
(Where they may be reordered as necessary) which  i may be interpreted as a non-zero fraction of 
the individual processes is stationary. 
An alternative approach to panel unit root tests uses Fisher’s (1932) results to derive tests 
that combine the p-values from individual unit root tests. This idea has been proposed by Maddala 
and Wu (1999) and by Choi (2001). 
 
3.  Empirical Results 
We apply panel unit root tests which are defined by Maddala and Wu (1999), Breitung (2000), 
Hadri (2000), Choi (2001), Levin et al. (2002), Im et al. (2003) to mentioned real exchange rates. 
Following Kalyoncu and Kalyoncu (2008), we employ the panel unit root tests are performed on 
the level of variable. The model trend is adopted in the empirical analysis, because recent studies a 
time trend is included in the unit root test. According to Marcela et al. (2003), allowing for a trend 
in the data is equivalent to accepting the existence of factors with a systematic influence on the real 
exchange rate due to Balassa–Samuelson effect and a demand-side bias in favor of non-traded 
goods. Another argument for inclusion of time trend is motivated by the non-stationary of real 
exchange rates for traded goods because of menu costs or pricing-to-market strategies. Therefore 
we apply the panel unit root tests including constant and trend, results are shown in table 1 as 
follows: 
 
Table 1:   Panel Unit Root Tests Results 
 
Cross Section Independence  Cross Section Independence 
Homogenous Unit Roots  Trend and Constant 
Hadri (2000) HC Z-stat  1.649** (0.0495) 
Levin, Lin and Chu (2002) t-stat  -5.556* (0.0000) 
Breitung (2000) t-stat  -6.486* (0.0000) 
Heterogeneous Unit Root  Trend and Constant 
Im, Pesaran and Shin (2003) W-stat  -6.408 *(0.0000) 
Cross Section Dependence  Cross Section Dependence 
Heterogeneous Unit Root  Trend and Constant 
Maddala and Wu (1999) ADF-Fisher Chi Square  76.026* (0.0000) 
Choi (2001) ADF-Choi Z-stat  -6.148* (0.0000) 
Maddala and Wu (1999) PP-Fisher Chi Square  46.626* (0.0002) 
Choi (2001) PP-Choi Z-stat  -4.199* (0.0000)  
 
All panel unit root tests are null hypothesis tests of non-stationary real exchange rates, except that Hadri (2000) is 
stationary. 
All panel unit root tests are defined by Barlett kernel and Newey-West (1994) bandwidth, except that Hadri (2000) is 
defined by quadratic spectral kernel and Andrews (1991) bandwidth selection. 
Hadri (2000) assumes that the unit root test uses heteroskedasticity consistent. 
The optimal number of lags is chosen by Akaike Information Criterion (AIC). 
Probabilities  for  Fisher  tests  are  computed  using  an  asymptotic  chi-square  distribution.  All  other  tests  assume 
asymptotic normality. 
The  p-value  is  in  parentheses,  **  and  *  denote  the  rejection  of  the  null  hypothesis  at  5%  and  1%  significance, 
respectively. 
 
We find that the panel unit root tests result strongly support to stationary of real exchange 
rates  except  Hadri  (2000).  However,  Hadri's  panel  unit  root  test  experiences  significant  size 
distortion in the presence of autocorrelation when there is no unit root. According to Hlouskova and 
Wagner (2006), the Hadri test appears to over-reject the null of stationarity, and may yield results 
that directly contradict those obtained using alternative test statistics. 
 
 
4. Conclusion 
 
The evidence concludes that the Turkey show significant support for the PPP hypothesis existence 
of both cross-sectional dependence or independence in panel unit root tests except the rejection of 
the null hypothesis Hadri (2000) 5% significance. Empirical finding implies that the real exchange 
rates  of  Turkey  among  major  countries  can  be  described  as  stationary  and  support  long-run 
purchasing power parity. 
 
 
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A Comparative Study of Unit Root Tests with Panel Data and A New Simple Test”,

A More Powerful Panel Unit Root Test with An Application to PPP”,

Automatic Lag Selection in Covariance Matrix Estimation”,

Distribution of the Estimators for Autoregressive Time Series with A Unit Root”,

Nonlinear Mean-reversion in Real Exchange Rates: Towards a Solution to the Purchasing Power Parity Puzzles”,

Panel Unit Root Tests of Purchasing Power Parity for Central Asian Countries”,

Perspectives on PPP and Long-run Real Exchange Rates”,

Pitfalls in Panel Tests of Purchasing Power Parity”,

PPP and Structural Breaks: The Peseta Sterling Rate, 50 Years of Floating Regime”,

Purchasing Power Parity and the Real Exchange Rate”,

Purchasing Power Parity during Currency Crises: A Panel Unit Root Test under Structural Breaks”,

Purchasing Power Parity in Central and Eastern European Countries: An Analysis of Unit Roots and Nonlinearities”,

Purchasing Power Parity in OECD Countries: Evidence from Panel Unit Root”,

Real Exchange Rate Behavior in the Middle East: A Re-examination”,

Real Exchange Rates and Purchasing Power Parity: Mean-reversion in Economic Thought”,

Statistical Methods for Research Workers,

Testing for Stationarity in Heterogeneous Panel Data,

Testing for Unit Roots in Heterogeneous Panels”,

The Behavior of Real Exchange Rates during the PostBretton Woods Period”,

The Local Power of Some Unit Root Tests for Panel Data”, Advances in Econometrics, 15, Nonstationary Panels, Panel Cointegration, and Dynamic Panels,

The Overvaluation of Purchasing Power Parity”,

The Performance of Panel Unit Root and Stationarity Tests: Results from A Large Scale Simulation Study”,

The Purchasing Power Parity Debate”,

The Purchasing Power Parity Puzzle”,

Unit Root Tests for Panel Data”,

Unit Root Tests in Panel Data: Asymptotic and Finite-sample Properties”,

Why is it so Difficult to Beat the Random Walk Forecast of Exchange Rates?”

Panel unit root tests of purchasing power parity hypothesis: Evidence from Turkey

Panel unit root tests of purchasing power parity hypothesis: Evidence from Turkey

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