Purchasing power parity: Evidence from a transition economy

Journal of Policy Modeling 27 (2005) 665–672

Purchasing power parity: Evidence froma transition economy

James Paynea,1,2, Junsoo Leeb,∗, Richard Hoflerc,3

a Department of Economics, Illinois State University, Normal, IL 61790-4200, USAb Department of Economics, Finance & Legal Studies, The University of Alabama,

Tuscaloosa, AL 35487, USAc Department of Economics, University of Central Florida, Orlando, FL 32816, USA

Received 1 February 2004; received in revised form 1 November 2004; accepted 1 March 2005Available online 19 April 2005

Abstract

Whether the purchasing power parity (PPP) theory of exchange rate determination holds for tran-sition economies is an interesting question, given peculiar situations of transition economies. In thispaper, we examine the real exchange rate for Croatia, a transition economy that has had some suc-cess in moving towards a market economy. Using a battery of tests that allow for a maximum oftwo structural breaks whose locations are determined endogenously from the data, we failed to findevidence supporting the validity of PPP for the Croatian economy. Thus, the conjecture that transitioneconomies experiencing growth in productivity and real wages should experience real appreciation(thereby introducing doubt as to whether purchasing power parity holds) is substantiated by ourresults.© 2005 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.

Keywords: Purchasing power parity; Croatia; Transition; Productivity

∗ Corresponding author. Tel.: +1 205 348 7842; fax: +1 205 348 0590.E-mail address: [email protected] (J. Lee).

1 Professor Payne contributed to this article while a Visiting Associate Professor in the Department of Economicsat the University of Kentucky.

2 Tel.: +1 309 438 8625.3 Tel.: +1 407 823 2606.

0161-8938/$ – see front matter© 2005 Society for Policy Modeling. Published by Elsevier Inc. All rights reserved.doi:10.1016/j.jpolmod.2005.03.001

666 J. Payne et al. / Journal of Policy Modeling 27 (2005) 665–672

1. Introduction

The purchasing power parity (PPP) theory of exchange rate determination states thatexchange rates adjust to reflect domestic, and foreign price levels. Researchers typicallytest the validity of purchasing power parity by examining the stationarity of the real exchangerate. The real exchange rate,qt, measures the deviation from purchasing power parity in thefollowing equation:

qt = st + pft − pd

t (1)

wherest is the logarithm of the nominal exchange rate,pft the logarithm of the foreign price

level, andpdt is the logarithm of the domestic price level. A finding that the real exchange

rate follows a stationary process supports the purchasing power parity proposition. Theempirical evidence on the purchasing power parity proposition is mixed;Froot and Rogoff(1995)andRogoff (1996)provide in-depth survey of the literature.

Given the restrictive assumptions underlying purchasing power parity in conjunctionwith the transition process itself there is some doubt about whether purchasing powerparity will hold for transition economies (Brada, 1998). For example,Halpern and Wyplosz(1997)suggest that equilibrium exchange rates should exhibit an upward trend as transitioneconomies experience growth in productivity and real wages. They argue that, consequently,shocks to real exchange rates are largely permanent (stochastic) during the “catch-up” phaseof transition. Additionally,Desai (1998)argues that the currencies are undervalued for manytransition economies. In such cases, real appreciation of the currency is a likely responseas currencies move towards the long run equilibrium rate (i.e., PPP rate). Moreover,Brada(1998)andOrlowski (1998)state that liberalization of the capital accounts of transitioneconomies, thus inducing capital inflows, might appreciate the real exchange rate. Given theconcerns over the behavior of the real exchange rate in transition economies, the empiricalevidence is limited.1

The purpose of this paper is to extend the literature on the time series behavior of the realexchange rate for transition economies in two directions. First, we examine the real exchangerate for Croatia, a transition economy that has had some success in moving towards a marketeconomy. Second, we employ a test that allows for a maximum of two structural breakswhose locations are determined endogenously from the data. Previous studies on the PPPof transition economies did not take into account of the effects of possible structural breaks.We use the minimum LM unit root tests ofLee and Strazicich (2003, 2004)—hereafterLS—to test for stationarity in the presence of possible structural breaks. The minimumLM tests may be fairly compared with the one-break minimum unit root test byZivot andAndrews (1992)or the two-break minimum test byLumsdaine and Papell (1997). Thesecomparable tests, while commonly used in the literature, typically assume no breaks underthe null. Although these minimum tests can be valid if the null hypothesis does not implyany break, their test statistics diverge when possible breaks exist under the null. This causessize distortions leading to frequent spurious rejections (seeLee & Strazicich, 2001; Nunes,Newbold & Kwan, 1997). In many applications using these tests, the unit root null is often

1 SeeThacker (1995)for the case of Poland.Kutan and Dibooglu (1998)examine the case of Hungary.

J. Payne et al. / Journal of Policy Modeling 27 (2005) 665–672 667

rejected and this result has been regarded as evidence supporting stationarity. Rejection ofthe null from these tests, however, does not necessarily imply rejection of a unit root perse, but may suggest rejection of a unit root without break. Conversely, the minimum LMtests of LS are free of such criticism as their tests allow for possible structural breaks in aconsistent manner under both null and alternative hypotheses.

2. Data and stationarity tests

We employ data on real effective exchange rates on a monthly basis from January 1992 toOctober 1999. They were obtained from the Ekonomski Institut, Zagreb. Two real effectiveexchange rates will be examined based on two price indices: the producer price index (IRET)and the retail price index (IRETM).Fig. 1displays the plot of the real effective exchangerates where a positive change in the real effective exchange rate indicates real depreciation.We can clearly observe structural shifts in the trend of the data.

Accordingly, it appears sensible to allow for structural breaks in testing for a unit root. Afew empirical issues still remain. Imposing pre-determined breaks might induce incorrectlyspecified break points. To examine the behavioral property of these data, we employ theminimum LM unit root tests of LS from which structural break points are endogenouslydetermined from the data. As previously noted, these tests are free of possible spuriousrejections even when breaks occur in the data and the null is true. To illustrate the underlyingmodel and testing procedure, we consider the following data generating process (DGP):

yt = δZt + ut, ut = βut−1 + εt, (2)

Fig. 1. Plot of the data.


whereZt is a vector of exogenous variables,A(L)εt = B(L)ut, andA(L) andB(L) are finiteorder polynomials withut ∼ iid (0, σ2). Perron (1989)initially showed the gain in powerfrom including a structural break and considered three types of models. Similarly, weconsider two models: the “crash” Model A that allows for a one-time change in leveland Model C that allows for a change in both level and trend. We defineZt = [1, t, D1t,D2t]′ in Model A, allowing for two changes in level, whereDjt = 1 for t ≥ TBj + 1, j = 1,2, and zero otherwise. Here,TBj denotes the time period when the break occurs. We alsodenoteBjt = 1 for t = TBj + 1, j = 1, 2, and zero otherwise. Note thatBjt =�Djt, where�is a lag operator. Model C includes two changes in level and trend, and is described byZt = [1, t,D1t , D2t , DT

∗1t , DT

∗2t ]

′, whereDT ∗jt = t for t ≥ TBj + 1, j = 1,2, and zero

otherwise.Test statistics for the LM unit root test are obtained from the following regression ac-

cording to the LM (score) principle:

�yt = δ′�Zt + φS̃t−1 + et, (3)

whereS̃t is a de-trended series such thatS̃t = yt − ψ̃x − Ztδ̃, t = 2, . . . , T (Schmidt &Phillips, 1992), δ̃ is a vector of coefficients in the regression of�yt on�Zt andψ̃x = y1 −Z1δ̃, whereZt is defined below;y1 andZ1 are the first observations ofyt andZt, respectively,and� is a difference operator. Corrections for autocorrelated errors are accomplished byadding augmented terms�S̃t−j, j = 1, . . . , k, in (3), as in the augmented Dickey Fullertest. Note that the LM testing regression(3) involves�Zt instead ofZt, where�Zt =[1, B1t , B2t , D1t , D2t ]′, for Model C, for instance. The unit root null hypothesis is describedby φ = 0, and the LM test statistics are given by:

τ̃ = t-statistic testing the null hypothesisφ = 0. (4)

The minimum LM test uses a grid search to determine the location of the two breaks(λj = TBj/T, j = 1, 2) as follows:

LM τ = Infλτ̃(λ) (5)

Note that critical values for Model A are invariant to the break locations,λ. This isan important property, as we do not need to simulate different critical values for dif-ferent locations of break points. In particular, the asymptotic distribution of the LMtest is free of the nuisance parameterλ, and the test does not exhibit spurious rejec-tions even when a finite number of breaks exist under the null. On the other hand,critical values of the LM test for Model C depend onλ. Fortunately, the LM testdoes not exhibit the spurious rejection problem even when breaks exist under the null.Therefore, for Model C, we use critical values corresponding to the estimated breakpoints.

3. Empirical results

For empirical implementation, we need to determine the number of augmentation terms�S̃t−i, i = 1, . . . , k that should be included in the testing Eq.(3). We first determine


the optimal value ofk for each combination of break points. We follow the ‘general tospecific’ procedure to determinek. Beginning with a maximum number of lagged termsmaxk = 8, we examine the last augmented term to see if it is significantly different fromzero at the 10% level (the asymptotically normal critical value is 1.645). We continue theprocedure until the maximum lagged term is found, ork = 0, at which point the proce-dure stops (see e.g.,Ng & Perron, 1995). Then, using the optimal number of augmen-tations for each combination of break points, we search for the optimal break locationsλ= (λ1,λ2)′ using the Eq.(5), over the time interval [0.05T, 0.95T], whereT is the samplesize.

We present empirical results from both the two-break and one-break minimum LM unitroot tests inTable 1, which also includes the estimated coefficients in the testing regression(3). Critical values are provided in the footnotes ofTable 1. These particular tests allow oneor two breaks to be determined endogenously from the data. As stated above, A is a crashmodel and C allows for shifts in both drift and a linear time trend. The null of a unit root isnot rejected for all cases, regardless of the type of model and the series.2

In most empirical studies, researchers demonstrate the increase in power from allow-ing structural changes in time paths. This common phenomenon does not occur in ourcase. As noted previously, the existence of breaks does not necessarily imply stationar-ity, since it is possible to have a break under the null, as the structural change modelsinitially suggested byPerron (1989)may indicate. Thus, rejection of the null using thetests assuming no break under the null may merely imply rejection of the null withoutbreaks, but not necessarily implying stationarity. As the minimum LM tests allow for afinite number of breaks under the null, the test results from these are free of such criti-cism of the tests not allowing for breaks under the null. Further, the minimum LM testshave decent power, compared to corresponding Dickey Fuller type extension tests (seeLS,2003, 2004). Our results confirm that the null of a unit root with possible breaks is notrejected.

The estimated break points usually lie in the last quarters in 1992 and 1993. This resultis consistent with our understanding of the events that occurred in Croatia. Those eventsbegin when, in the aftermath of establishing independence from the Former Yugoslaviain 1991, Croatia inherited a fixed exchange rate regime. In early 1992, the National Bankof Croatia established its own exchange rate and kept the rate constant until April 1992.After devaluation at the end of April 1992, the government allowed the exchange rate tobe determined by the foreign exchange market. However, in practice, the National Bankof Croatia attempted to maintain a constant real effective exchange rate. The inflationarypressures of the transition and the central bank’s maintenance of a constant real effectiveexchange rate translated into currency depreciation, both fueling inflation and resulting inreal appreciation. In October 1993, a stabilization program was announced in which theexchange rate was pegged to the deutsche mark. This pegging of the exchange rate lastedroughly 2 weeks, serving the purpose of reducing inflationary expectations. On October19, 1993, a new foreign exchange law was enacted in which banks were free to set theirexchange rates (Sonje & Skreb, 1995; Desai, 1998).

2 We also calculate the test results from the no-break LM test (not reported), and obtain the same results.

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etal./JournalofPolicyM

odeling27

(2005)665–672

Table 1Test results from the minimum LM tests

Series No. ofbreaks

Model k̂ T̂B Teststatistics

Estimation results

IRET Two A 7 December 1992,September 1993

−0.969 �yt = − 0.025S̃t−1(−0.969)

− 0.360(−1.25)

− 3.58B1t(−2.51)

− 7.23B2t(−5.55)

+lags

C 8 September 1993,December 1997

−3.64 �yt = − 0.550S̃t−1(−3.64)

+ 0.817(1.13)

− 7.72B1t(−6.80)

− 0.254B2t(−0.265)

− 0.620D1t(−0.911)

+ .0459D2t(1.84)

+lags

One A 7 December 1992 −1.78 �yt = − 0.033S̃t−1(−1.78)

− 0.648(−2.47)

− 2.00B1t(−1.56)

+lags

C 5 November 1993 −2.74 �yt = − 0.211S̃t−1(−2.74)

− 0.235(−0.340)

+ 1.17B1t(0.863)

+ 0.019D1t(−0.024)

+lags

IRETM Two A 8 December 1992,September 1993

−1.51 �yt = − 0.054S̃t−1(−1.51)

− 0.422(−1.82)

− 3.32B1t(−1.87)

− 14.2B2t(−11.5)

+lags

C 7 February 1993,October 1993

−3.71 �yt = − 0.379S̃t−1(−3.71)

− 0.590(−0.538)

− 2.14B1t(−1.02)

− 3.52B2t(−1.40)

+ 0.883D1t(0.641)

− 0.678D2t(−0.636)

+lags

One A 0 December 1992 −1.96 �yt = − 0.079S̃t−1(−1.96)

− 0.956(−1.90)

− 5.32B1t(−1.49)

C 7 October 1993 −2.37 �yt = − 0.277S̃t−1(−2.37)

+ 1.49(0.919)

− 2.24B1t(−.748)

− 1.78D1t(−1.03)

+lags

Notes: t-statistics are reported in the parentheses. Estimated coefficients of the lagged augmented terms are omitted to conserve space. Critical values forModel A donot depend onλ, and they are given for samples of sizeT = 100 at the 1%, 5% and 10% levels as−4.55,−3.84 and−3.51 for the two-break LM test and they are−4.24,−3.57 and−3.21 for the one-break LM test. Critical values of the minimum LM test with linear trend (Model C) depend on the location of breaks (λ), but do not varymuch overλ. Critical values of Model C shown for the two-break LM tests as:−6.16,−5.59, and−5.28 forλ= (0.2, 0.4);−6.40,−5.74, and−5.32 forλ= (0.2, 0.6);−6.33,−5.71, and−5.33 forλ= (0.2, 0.8);−6.46,−5.67, and−5.31 forλ= (0.4, 0.6);−6.42,−5.4, and−5.43 forλ= (0.4, 0.8);−6.32,−5.73, and−5.32 forλ= (0.6,0.8). They are−5.12,−4.49 and−4.19 for the one-break LM test. Other critical values can be interpolated. Note that critical values are symmetric aroundλ1 andλ2.Note that the constant term corresponds to a linear trend inZt under the alternative.


4. Concluding remarks

In this paper, we investigated the purchasing power parity theory of exchange rate de-termination for the transition economy of Croatia by examining the stationarity of the realexchange rate. Using a battery of unit root tests with different numbers of endogenous struc-tural breaks, we failed to find evidence supporting the validity of purchasing power parityfor the Croatian economy. The conjecture that transition economies experiencing growth inproductivity and real wages should experience real appreciation (thereby introducing doubtas to whether purchasing power parity holds) is substantiated by our results.

Acknowledgement

We would like to thank Andrea Mervar of the Ekonomski Institut Zagreb for providingthe data and her insights. The authors will blame each other for any remaining errors.

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Purchasing power parity: Evidence from a transition economy