Does the Law of One Price Hold in a High-Inflation Environment? A Tale of Two Cities in Turkey

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Does the law of one price hold in a high-inflationenvironment? A tale of two cities in TurkeySule Akkoyunlua & Boriss Siliverstovsa

a KOF Swiss Economic Institute, ETH Zurich, Weinbergstr. 35, 8092 Zurich, SwitzerlandPublished online: 03 Jun 2014.

To cite this article: Sule Akkoyunlu & Boriss Siliverstovs (2014): Does the law of one price hold in a high-inflationenvironment? A tale of two cities in Turkey, Applied Economics, DOI: 10.1080/00036846.2014.925190

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Does the law of one price hold in a

high-inflation environment? A tale of

two cities in Turkey

Sule Akkoyunlu and Boriss Siliverstovs*

KOF Swiss Economic Institute, ETH Zurich, Weinbergstr. 35, 8092 Zurich,Switzerland

This study addresses the price convergence in two cities in Turkey (Istanbul andAnkara) using annual data over the three-quarters of the twentieth century (1922–1998), characterized by prevailing high inflation rates for most of the period. Incontrast to the rest of the literature addressing convergence in price levels with atypical result of extremely slow convergence rates at best, we argue that conver-gence is much easier detected in growth rates rather than levels of prices. Wesuggest using the bounds testing procedure of Pesaran et al. (2001) for thispurpose. We find a clear-cut evidence on the existence of a common drivingforce behind inflation dynamics in Istanbul and Ankara – a finding that is incontrast with the results typically reported in related literature.

Keywords: price convergence; structural breaks; bounds testing procedure

JEL Classification: C22; C32; C52; E31

I. Introduction

Purchasing power parity (PPP), conveying an intuitivelyappealing argument that national price levels once con-verted to a common currency should be the same, is a topicthat attracted a lot of attention in the economic literaturefor a long time. Frenkel (1978) provides a comprehensivereview of the origins of the PPP doctrine, widely acknowl-edging the contribution of the Swedish economist GustavCassel to popularization of the PPP hypothesis in the1920s (Cassel, 1921, 1922).

Since the introduction of unit-root (Dickey and Fuller,1979) and cointegration (Engle and Granger, 1987) con-cepts, much of the research on PPP applied unit-root andcointegration tests in order to determine whether realexchange rates are best characterized either as mean sta-tionary or as random-walk processes. Empirical evidencesupporting stationarity of real exchange rates implies that

the effects of shocks to real exchange rates diminish overtime. Hence, deviations from PPP of national price levelsare of transitory nature.

A thorough summary of the earlier literature on testingthe PPP hypothesis can be found in Froot and Rogoff(Froot and Rogoff, 1995) and Rogoff (1996).Summarizing their observations, Froot and Rogoff(Froot and Rogoff, 1995, p. 1648) conclude that: ‘[…]cointegration approaches have sometimes created as muchconfusion as clarity on the issue of PPP’. However, theyalso point out PPP is not a short-run phenomenon and longspans of data are necessary in order to find evidence infavour of it. Also Rogoff (1996) similarly suggests thatPPP finds at best only a limited support in empiricalliterature. This prompted Rogoff (1996) to announce thePPP puzzle in his seminal contribution.

In order to abstract from such issues like prevailingtrade barriers, exchange rate volatility, sticky nominal

*Corresponding author. E-mail: [email protected]

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wages and prices that can serve as a potential explanationfor reported difficulty in detection of PPP as well as anextremely slow convergence to PPP observed at the inter-national level, more recent literature investigated priceconvergence at the city/region level within a commoneconomic space involving a common currency and theabsence of trade barriers. For example, Chen andDevereux (2003) applies the augmented Dickey–Fuller(ADF) test for testing for unit root in relative city pricelevels or ‘city real exchange rates’ in 19 US cities over theperiod 1918 to 2000. The null hypothesis of unit root isrejected in six out of 19 cases at the 5% significance level.When using the 10% significance level, the rejection rateincreases to 11 out of 19 cases. Moreover, Chen andDevereux (2003) observe that the estimated convergencespeed in the intranational data is slower than that typicallyreported in international data, which becomes anotherpuzzling result added to the existing literature on PPP.

Empirical literature responded in several ways, attempt-ing to find a solution to this puzzling outcome. First,referring to a rather low power of the ADF test,Cecchetti et al. (2002) apply panel unit-root tests sug-gested in Levin and Lin (1993) and Im et al. (2003) inorder to test the null hypothesis of unit root in relative cityprice levels of 19 major US cities over the period 1918 to1995. As it is commonly argued that by pooling the data,one typically gains in power when statistically testing theunit-root hypothesis. Even though Cecchetti et al. (2002)are able to reject the null hypothesis of unit root in cityprice differentials, they similarly report a puzzling evi-dence that the pace of convergence among city prices inthe United States is much slower (about three times) thanthe convergence rate typically found in cross-nationalstudies. Culver and Papell (1999) also apply panel unit-root tests for PPP testing not only in the price level data forUnited States but also for Canada and several countries ofthe EU. They report a striking result that there is a muchstronger evidence of PPP in the EU data rather than in theUS and Canadian data sets.

Second, Sonora (2008) uses more powerful univariateunit-root and cointegration tests in order to test the PPPhypothesis and provide alternative estimates of the con-vergence speed in the city real exchange rates, usingpractically the same data set as in Cecchetti et al. (2002).As reported in Sonora (2008), although the unit-roothypothesis is rejected as before in Cecchetti et al.(2002), the estimated speed of convergence is onlyslightly faster than in Cecchetti et al. (2002).

The next generation of papers proposed that a typicalfinding of puzzlingly slow convergence – or even itsabsence – between price levels in different geographicalmarkets could be explained by an improper modelling ofthe underlying time series. Most of the applied researchinvestigating the law of one price typically fails to accountfor the presence of structural breaks, leading to spurious

finding of high persistence (nonstationarity) of relativeprices, which as implied by PPP should be stationary;see Perron (1989) for consequences of unmodelled struc-tural breaks on unit-root test outcomes. Sonora (2009)applies Zivot and Andrews (1992) and Clemente et al.(1998) unit-root tests that account for the existence ofpossible structural breaks in tested time series using alonger version of CPI data set for major US cities thanone used in Cecchetti et al. (2002). As a main result,Sonora (2009) argues that city relative prices can bedescribed as stationary but containing structural breaks.An additional important finding is that when accountingfor structural breaks, the estimated convergence rates areof a smaller magnitude reported when using panel unit-root tests. Similar conclusions are also reported in otherstudies which account for structural breaks when addres-sing relative price convergence among the US cities(Basher and Carrion-i-Silvestre, 2009, 2011; Hegwoodand Nath, 2013).

Rather than looking for innovative econometric techni-ques, one alternative is to look for empirical support ofPPP in countries experiencing radically different eco-nomic conditions, for example, from those prevailing inthe United States. Sonora (2005) applies both univariate(the ADF test) and panel (Levin and Lin, 1993; Im et al.,2003) unit-root tests for testing convergence in relativecity price levels in Mexico. The city CPI data for 34Mexican cities available over the period from 1982 until2000 are used in the analysis. During the period of inves-tigation, Mexico was a high-inflation country with a meanannual inflation of 33% over the whole period.Nevertheless, the results support convergence in relativeprice levels, which is much faster than that recorded in theUS cities in Cecchetti et al. (2002). Sonora (2005)explains this fact that in the high-inflation environment,menu costs for adjusting prices are quickly absorbed byrapidly rising prices, providing incentives for quick priceadjustments.

In this article, we suggest another alternative approachto testing PPP while dealing with several problematicissues highlighted above. There are several features ofour approach that are worth emphasizing. First, consistentwith the remark of Froot and Rogoff (1995) that PPP is nota short-run phenomenon, we use, as an illustration of ourapproach, long time-series data on prices collected at theannual frequency for two Turkish cities (Ankara andIstanbul) for the period covering 1922 till 1998. Theperiod in question spans about three-quarters of the twen-tieth century, allowing us to focus on a truly long-runrelationship between these two price indices. Several per-iods of very high inflation rates make our exercise moreinteresting as it allows us investigate whether the law ofone price held also in such high-inflation environment. Anadditional benefit of using the long time series is that ithelps us reconsider the conclusion reached in Özcicek

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(2007), where the intraregional price convergence among19 Turkish provinces is investigated for the period1994:01 to 2003:12. To the best of our knowledge,Özcicek (2007) is the only study that investigates intrana-tional PPP for Turkey. Özcicek (2007) finds no evidenceof price convergence on the basis of univariate and panelunit-root tests.

Second, instead of looking for convergence amongprice indices, we opt for testing whether the law of oneprice holds for growth rates of prices or inflation. Thus,our approach of testing for price convergence is consistentwith the relative PPP hypothesis described in Frenkel(1978, 1981), where in the international context changesin exchange rate are related to changes in inflation differ-ential. In the intranational context with a common cur-rency, the version of relative PPP reduces to testingwhether there exists a long-run relationship in the formof inflation differential. Existence of such a long-run rela-tionship would imply that inflation dynamics is governedby a common factor whose presence rules out persistentdeviations in inflation in the long run, implying that mar-kets are integrated and PPP holds in a relative form.

Third, our focus on inflation rather than on price levelsgreatly facilitates treatment of structural breaks in timeseries under scrutiny.1 These structural breaks are verylikely to occur in our data set as it covers more thanthree-quarters of the twentieth century.2 We accommodatethese structural breaks by means of impulse dummies.Observe that what appears as a spike in inflation translatesitself to a stepwise shift in the associated price level data,i.e. outliers of a different magnitude observed in inflationrates result in persistent deviations of price levels, whichare much more difficult to account for and that are likely toexplain the puzzling result of extremely slow (if any)convergence between price levels that is typically reportedin the relevant literature.

Last but not least, we propose to address the existenceof the law of one price in two distant markets by testing forthe existence of a long-run relationship between inflationrates by employing the bounds testing procedure ofPesaran et al. (2001). The advantage of using this proce-dure is that it can be applied in cases when regressors canbe I(1), I(0) or mutually cointegrated. Furthermore, theprocedure is based on an unrestricted error-correctionmodel, which permits joint estimation of long- as well asshort-run effects. As pointed out in Banerjee et al. (1998),joint estimation has better statistical properties than the

two-step Engle–Granger procedure that pushes the short-run dynamics into the error term.

The use of the procedure of Pesaran et al. (2001) in thecurrent context also can be supported by the fact that so farthere is no uniform agreement in the literature on whether(logs of) prices should be modelled as an I(2) or I(1)process. This naturally has implications for the order ofintegration of growth rates of prices or inflation. In theformer case, inflation is also a unit-root process, whereasin the latter case, inflation, correspondingly, should bemodelled as an I(0) process. On the one hand, a commonobservation of a rather high persistence in inflation ratessupports the former view reflected in Banerjee et al. (2001)and Juselius (1995), for example, where prices were expli-citly assumed to be I(2) variables. However, treating infla-tion as a unit-root variable is at odds with economic modelssuch as the sticky price model of Taylor (1979) or thePhillips curve model proposed in Calvo (1983), forinstance. On the other hand, Hendry (2001) views theprice level data as integrated of order one (I(1)) with super-imposed major breaks such that they mimic behaviour ofI(2) processes. As a consequence, inflation is modelled asan I(0) process with breaks. Romero-Ávila and Usabiaga(2009) report evidence based on unit-root tests carried outin a panel data setting, jointly accounting for cross-sectionaldependence and for the presence of unknown number ofbreaks that inflation in selected 13 OECD countries can beconsidered as an I(0) process with structural breaks. Thisfinding supports regime-wise stationarity of inflation.

Our main finding is that we provide a clear-cut evidenceconcerning the existence of a long-run relationship betweeninflation rates in Ankara and Istanbul, supporting an intui-tively appealing notion of a common driving force behindprice dynamics in these two distant markets in Turkey. Ourfinding is in sharp contrast to that reported in Özcicek(2007). The discrepancy between our findings and thoseof Özcicek (2007) can be explained by several factors.Özcicek (2007) addresses convergence in price levelsusing a much shorter sample of data collected at themonthly rather than annual frequency. In addition, inÖzcicek (2007), no proper accounting for the presence ofstructural breaks is made, which is likely to negativelyinfluence the power of unit-root tests, as discussed above.

The rest of the article is organized as follows. Section IIcontains the description of data and its sources. In SectionsIII and IV, we describe methodology applied and reportestimation results. Section V concludes.

1As discussed above, the importance of accounting for structural breaks when testing PPP was already acknowledged in recent literature(see results of Sonora, 2009; Basher and Carrion-i-Silvestre, 2009, 2011; Hegwood and Nath, 2013, for example). Therefore, it is alsocrucial for the approach to testing of the PPP hypothesis suggested in our article that the influence of structural breaks or outlyingobservations can be accounted for in a simple and transparent way.2 For additional evidence supporting the presence of structural breaks in inflation data in Turkey, we refer to Önder (2009). Önder (2009)estimates Phillips curve for Turkey using a three-regime Markov-switching model. Önder (2009) reports that during the third regimecapturing a high-inflation episode in 1988 as well as two economic crises in 1994 and 2001, similarly characterized by high inflation andnegative output gap, the relationship between inflation and output gap breaks down.

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II. Data

All the data on price indices come from a single sourcePamuk (2000) and represent a constructed CPI based on acomparable consumption basket containing both food andnonfood items compiled from the following sources: datafor the period from 1914 till 1937 are due to Pamuk (2000,p. 22–23 for Istanbul and p. 58–59 for Ankara), for theperiod from 1938 till 1987 – the Undersecretariat ofTurkish Treasury – and for the period since 1988 – theTurkish Statistical Institute. Due to the fact that there areno continuous data for Ankara during the period from1914 till 1922, we restrict our estimation sample to startfrom 1922. According to Pamuk (2000), the same baseyear 1914 was chosen for both price indices.

In sequel, we will denote the CPI for Ankara andIstanbul in levels as pA and pI and the correspondinglogarithmic transformation of these two price indices asln pA and ln pI. Furthermore, the inflation in Ankara andIstanbul is denoted as INFA = Δln pA and INFI = Δln pI,respectively. Both the price indices (in logs) and the cor-responding inflation rates are displayed in Fig. 1.

The overall impression from Fig. 1 is that there arecertain common features shared by the price indices inthese two cities: relatively stable prices during the 1920sthat even decrease during the pre-Second World Warperiod, a stepwise increase during the beginning of the1940s and then further stabilization in the late 1940s. Bothprice indices have a tendency to increase since the 1950s,and, more importantly, this tendency became more pro-nounced since the late 1970s. The similar dynamics is alsoreflected in the pair of inflation time series: a moderateinflation rate during 1920s followed by deflation in thepre-Second World War period; a spike in inflation ratesduring the beginning of the 1940s, reflected in a stepwiseshift in the corresponding price levels and a relatively

stable inflation in the post-war period, which started toincrease during the 1950s, and then falling back to thepost-war levels in the 1960s. Both inflation rates displayan upward trending behaviour since the early 1970s withoccasional outbursts, e.g. in the late 1970s and in the mid-1990s. For a comprehensive review of inflation experi-ence in Turkey, we direct an interested reader toKibritçioğlu (2002).

The difference of log-price levels between Istanbul andAnkara is displayed in Fig. 2; unsurprisingly, there arequite persistent deviations to be observed, implying thatthe tests for price convergence when applied to pricelevels directly are likely to find no evidence supportingit; see Özcicek (2007) for an example using the Turkishdata. On the contrary, the cross-plot of inflation rates inIstanbul and Ankara presented in the right-top panel sug-gests that there is a close relationship between inflationrates in these two cities. The two lower panels in the samefigure present changes in inflation which look quite similaraside from the fact that changes inflation in Ankara havebeen more volatile in the 1980s than in Istanbul.

All in all, visual inspection suggests that the inflationrates in Ankara and Istanbul tend to move together, sug-gesting that these two markets are integrated and reactsimilarly to common shocks. It remains to see whetherthis informal conclusion will be verified by application ofstatistical methods.

III. Methodology

In this section, we describe the methodology used fortesting the PPP hypothesis in absolute and relativeforms. The PPP hypothesis in the absolute form(Frenkel, 1978, p. 177) implies that deviations of the

1920 1940 1960 1980 2000

5

10

15ln PI

1920 1940 1960 1980 2000

5

10

15ln PA

1920 1940 1960 1980 2000

0.00

0.25

0.50

0.75 INFI

1920 1940 1960 1980 2000

0.00

0.25

0.50

0.75 INFA

Fig. 1. Actual data: price level (in logs) and inflation in Istanbul and Ankara

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price level in one location from that in another locationshould be short-lived, i.e. the log-price differential

qt ¼ lnðpItÞ � lnðpAt Þ (1)

should be a stationary variable. Then, the stationarity ofthe inter-city log-price differential is tested using the ADFunit-root test in the following form:

�qt ¼ μþ ρqt�1 þXn

i¼1

�qt�i þ εt (2)

The failure to reject the null hypothesis that the variableqt is an I(1) variable, i.e. H0: ρ = 0, provides no evidencefor supporting the PPP hypothesis. The results of the ADFtest serve as a benchmark in testing whether the PPPhypothesis holds for these two cities in Turkey.

Next, we describe the bounds testing procedure ofPesaran et al. (2001) that we apply for testing whetherthere exists a long-run relationship between inflation inAnkara and Istanbul. The bounds testing approach hasbroad applicability since the regressors can be I(1), I(0)or mutually cointegrated. This feature is of a particularimportance in our case, given inconclusive resultsreported in the literature on the order of integration ofinflation. Moreover, as discussed above, the structuralbreaks are much easier accommodated into the modelestimated for inflation rather than for price levels.

As a starting point for implementing the bounds testingprocedure, we assume that inflation in Istanbul INFI andinflation in Ankara INFA are related according to a VARmodel of order p that is further reduced to the followingconditional ECM,

�INF It ¼ αþ θ0INF

It�1 þ θ1INF

At�1

þXp�1

i¼1

λi�INF It�i þ

Xp�1

i¼0

βi�INFAt�i

þ ω0Dt þ υt

(3)

The lagged values of INFI and INFA form a long-runrelationship. The deterministic terms such as a constant anddummy variables are denoted by α andDt, respectively. Theshort-run dynamics is captured by means of lagged valuesof �INF I

t and current and lagged values of �INFAt . The

long-run relationship between inflation in Istanbul and inAnkara is given by the following vector ð1;�θ1=θ0Þ0(Banerjee et al., 1998). Observe that if inflation in thesetwo cities react homogenously to shocks, then the vector ofinterest reduces to 1;�1ð Þ0. The bounds testing procedureuses the conventional F-test for testing the null hypothesisH0: θ0 = θ1 = 0. Note that this statistic has a nonstandarddistributionwhich depends upon: (i) the order of integrationof the regressors, (ii) the number of regressors, (iii) the setof deterministic terms included in themodel and (iv) samplesize. Pesaran et al. (2001) provide the set of asymptoticcritical values. We, however, in the hypothesis testing relyon the critical values simulated in Narayan (2005) for asample size comparable to ours.

There are two sets of critical values. The first set givesthe lower bound, applicable when all regressors are I(0).The second gives the upper bound, applicable when allregressors are I(1). If the calculated F-statistic falls belowthe lower bound, the null hypothesis of no relationshipbetween inflation in both cities cannot be rejected.Conversely, if the F-statistic exceeds the upper bound,the null hypothesis of no long-run relationship is rejected.As noted above, these critical bounds can be appliedirrespective of the order of integration of the regressors.

1920 1940 1960 1980 2000

−0.2

0.0

0.2

ln P I − ln P A

0.0 0.2 0.4 0.6 0.8

0.00

0.25

0.50

0.75

1927

INF I × INF A

1920 1940 1960 1980 2000

−0.25

0.00

0.25

Δ INF I

1920 1940 1960 1980 2000

−0.25

0.00

0.25

Δ INF A

Fig. 2. Actual data: log-price differential (ln pI – ln pA); cross-plot of inflation in Istanbul and Ankara (INFI and INFA); changesin inflation (ΔINFI and ΔINFA) in Istanbul and Ankara

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Finally, if the F-statistic falls within the critical bounds,the order of integration of the variables must be estab-lished in order to obtain conclusive inference. In addition,as argued in Pesaran et al. (2001, footnote 17, p. 307), theasymptotic theory and the associated critical values mustnot be modified provided that fraction of observations forwhich one uses dummy variables tends to zero as the totalsample increases.

IV. Results

Application of the ADF test to the log-price differentialfrom Equation 1 yields the corresponding test statistic of−1.81, which is compared with the 5% critical value of−2.91. Thus, we cannot reject the null hypothesis that thelog-price differential between Istanbul and Ankara is anI(1) variable. This puzzling finding implies that prices inIstanbul can deviate by an arbitrary large magnitude fromprices in Ankara despite the fact that these two cities sharea common economic space, the same currency, language,historical and cultural ties.

In presenting the results of testing the PPP hypothesis inrelative form, we start from Table 1. In this table, the resultsof the lag order p selection procedure for Equation 3 aredisplayed. The information criteria (Akaike, AIC andSchwarz, SIC) as well as the Lagrange multiplier statistictesting for remaining autocorrelation up to the first andsecond orders in regression residuals are reported. Bothinformation criteria – AIC as well as SIC – select p = 1.For all considered values of p, there is no evidence ofremaining autocorrelation in the regression residuals.Given the results from the selection criteria and the evi-dence of no residual autocorrelation regardless of the valueof p, the model with p = 1 is preferred. Observe that in orderto account for the presence of outliers corresponding to theperiods of unusually large discrepancies between inflationrates in Istanbul and Ankara, the following impulse dum-mies (DYYt) have been included in the test regression:D27t,D29t and D44t each corresponding to the year 19YY.3

The corresponding F-test statistic for the joint nullhypothesis H0: θ0 = θ1 = 0 using the finite-sample criticalvalues simulated in Narayan (2005) for T = 75 correspond-ing to case III in Pesaran et al. (2001), i.e. with unrestrictedconstant and no linear deterministic trend, is reported inthe last column of Table 1. As seen, the null hypothesis ofno long-run relationship between inflation in Istanbul andAnkara can be decisively rejected for p = 1 and p = 2 at the

1% significance level. For p = 3, the test statistic fallsinside the bounds implying that without further pre-testingno definite conclusions on the existence of a long-runrelationship between inflation in these two cities can bereached. This indefinite results is, however, due to fact thatthe model with p = 3 is clearly overparametrized as indi-cated by the values of the information criteria.

Having established the existence of a long-run relation-ship between inflation in Istanbul and Ankara, we canestimate the coefficients of interest. Starting with theerror-correction model corresponding to p = 2 and afterdeleting the insignificant augmentation lags, we arrive atthe following parsimonious model4:

�INF It ¼ 0:012

ð0:007Þþ 0:808

ð0:053Þ�INFA

t � 0:252ð0:043Þ

D27t

þ 0:156ð0:043Þ

D27t � 0:156ð0:046Þ

D44t � 0:118ð0:049Þ

D81t

� 1:042ð0:092Þ

INF It�1 þ 1:040

ð0:093ÞINFA

t�1 þ υt

R2 ¼ 0:873;Fð7;67Þ ¼ 65:93½0:000�;T ¼ 75;FARð1�2Þ

ð2;65Þ ¼ 0:013½0:986�;FRESETð1;66Þ ¼ 0:070½0:792�;FARCHð1Þ

ð1;65Þ ¼ 0:037½0:981�;χNormð2Þ ¼ 0:073½0:964�;FHetero

ð9;58Þ ¼ 0:776½0:651�

where SEs are reported in parentheses and error probabil-ities – in brackets. The model above passes the standard

Table 1. Lag order selection, 1926–1998

P AIC SIC AR(1) AR(2) F IIIH0 :θ0¼θ1¼0

1 −6.256 −6.036 0.772 0.955 57.825***2 −6.206 −5.924 0.508 0.804 18.653***3 −6.213 −5.868 0.798 0.522 7.591+

Notes: p is the lag order of the underlying VAR model for theconditional ECM, see Equation 3. AIC and SIC are the Akaikeand Schwarz Information Criteria, respectively. AR(1) and AR(2) are the p-values of the Lagrange multiplier test statistics fortesting for residual autocorrelation of orders up to 1 and 2,respectively. Bold entries indicate the lag order for which therespective values of information criteria are minimized.F IIIH0:θ0¼θ1¼0 denotes the F-test statistic for the null hypothesis

H0: θ0 = θ1 = 0 using the finite-sample critical values reported inNarayan (2005) for T = 75 corresponding to case III in Pesaranet al. (2001), i.e. with unrestricted constant and no linear deter-ministic trend. ‘***’ indicates that the null hypothesis of inter-est can be rejected at the 1% significance level. ‘+’ indicates thatthe test statistic falls inside the bounds (see Narayan, 2005, p.1988) for T = 75.

3 The outliers have been identified as those residuals exceeding regression SE by a factor 2 in the estimated regression (3) with p = 1without intervention dummies. We also identified a recording mistake (see Pamuk, 2000, p. 59) for the price index in Ankara: the number13 010 appears both in 1984 and 1985. In private correspondence, S. Pamuk provided us with the correct data for 1984, 8652, which weuse in the current analysis.4Observe that in order to account for a moderate outlier in 1981, we inserted an additional impulse dummy for this year in our regression.

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specification tests such as tests of no residual autocorrela-tion, of no residual ARCH effects, of residual normalityand of no residual heteroscedasticity and the RESET testfor functional form misspecification. The overall impres-sion is that this parsimonious model delivers a satisfactoryfit to data, considering that the period under investigationthat stretches over three-quarters of the twentieth centuryis characterized by the Second World War, several domes-tic political and economic crises, two international oilcrises and major legislative and technological changes.

The estimated model allows us to compare the coeffi-cients belonging to the lagged inflation variables. Thesecoefficients are of a similar absolute magnitude with theimplied long-run vector of (1, –0.998)′ such that one cansafely impose a homogeneity restriction θ0 = –θ1, i.e. thelong-run relationship vector between inflation in Istanbuland Ankara is 1;�1ð Þ0. The restricted error-correctionmodel is reported below:

�INF It ¼ 0:011

ð0:005Þþ 0:808

ð0:053Þ�INFA

t � 0:251ð0:043Þ

D27t

þ 0:156ð0:042Þ

D27t � 0:156ð0:045Þ

D44t � 0:119ð0:047Þ

D81t

� 1:042ð0:091Þ

ðINFIt�1 � INFA

t�1Þ þ υt

R2 ¼ 0:873;Fð6;68Þ ¼ 78:06½0:000�;T ¼ 75;FARð1�2Þ

ð2;66Þ ¼ 0:013½0:987�;FRESETð1;67Þ ¼ 0:058½0:811�;FARCHð1Þ

ð1;66Þ ¼ 0:020½0:887�;χNormð2Þ ¼ 0:044½0:978�;FHetero

ð8;59Þ ¼ 0:810½0:597�

Imposing the homogeneity long-run restriction bringsno noticeable changes in the estimated coefficients. Asbefore, all retained coefficients including those belonging

to the impulse dummies are estimated with a high degreeof precision. These encouraging results are also supportedby the close match between the actual and the fitted valuesdisplayed in the left-top panel of Fig. 3; the correspondingcross-plot is displayed in the right-top panel. The esti-mated regression residuals and their autocorrelation func-tion up to the ninth order are reported in the same figure inthe left- and right-bottom panels, respectively. Finally, theresults of the Chow tests for recursive stability and therecursive estimates of the model parameters are shown inFigs 4 and 5, respectively. In Fig. 4, the values of the one-step, breakpoint and forecast Chow test statistics arescaled by their respective 1% critical values (Doornikand Hendry, 2001). None of the tests show any sign ofmodel instability.

V. Conclusion

We suggest a novel approach to testing whether the law ofone price holds in the long run between different geogra-phically distant markets. Inspired by the relative PPPhypothesis (see Frenkel, 1978, 1981) we suggest to con-duct testing for market integration using growth ratesrather than levels of prices.

To this end, we propose using the bounds testing pro-cedure of Pesaran et al. (2001) which can be used insituations when there is no consensus in the literature onthe order of integration of the modelled variables. Inparticular, it can be used in situations when regressorscan be I(0), I(1) and/or mutually cointegrated. Anotheradvantage of our approach is that the presence of structuralbreaks can be much easier addressed when testing for the

1920 1940 1960 1980 2000

−0.25

0.00

0.25ΔINFI Fitted

−0.4 −0.3 −0.2 −0.1 0.0 0.1 0.2 0.3

−0.25

0.00

0.25 ΔINFI× Fitted

1920 1940 1960 1980 2000

−2

−1

0

1

2 r:ΔINFI (scaled)

0 5 10

−0.5

0.0

0.5

1.0ACF−r:ΔINFI

Fig. 3. Actual and fitted values; cross-plot of actual and fitted values; regression residuals (r:ΔINFI); autocorrelation functionof regression residuals (ACF-r:ΔINFI)

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presence of a long-run relationship between inflation ratesrather than price levels in different markets. Intuitively, anextraordinary large spike in inflation rate in one locationthat is unmatched in magnitude in inflation rate in anotherlocation results in an unusually large residual for a singleperiod when modelling the long-run relationship betweeninflation. In this case, its influence can be captured by animpulse dummy inserted in this particular period. On thecontrary, when testing for convergence in levels of prices,such a spike translates into a persistent deviation of oneprice level from another that has to be captured by astepwise shift or an intercept correction which is moredifficult to implement in practice. As the previous researchshows, failure to accommodate structural breaks whentesting for convergence between price levels typically

results in puzzling results of extremely slow (if any) con-vergence (see Özcicek, 2007, for an example testing forprice convergence in Turkey).

We illustrate our approach by testing whether the law ofone price holds between Istanbul and Ankara using theinflation time series covering three-quarters of the twentiethcentury, from 1922 until 1998. This period is characterizedby the Second World War, several domestic political andeconomic crises, two international oil crises and majorlegislative and technological changes. Needless to say, dur-ing most of the period under scrutiny very high inflationrates prevailed in Turkey. Despite all this, wefind a clear-cutevidence on the existence of a commondriving force behindinflation dynamics in Istanbul and Ankara – a finding that isintuitively appealing from the point of view of economic

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

0.5

1.0 1up CHOWs 1%

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

0.5

1.0 Ndn CHOWs 1%

1955 1960 1965 1970 1975 1980 1985 1990 1995 2000

0.5

1.0 Nup CHOWs 1%

Fig. 4. Recursive stability one-step, breakpoint and forecast Chow test statistics scaled by their respective 1% critical values

1960 1970 1980 1990 2000

0.00

0.02

0.04Constant× +/−2SE

1960 1970 1980 1990 2000

0.6

0.8

1.0 ΔINFA× +/−2SE

1960 1970 1980 1990 2000

−0.3

−0.2

−0.1 D1927 × +/−2SE

1960 1970 1980 1990 2000

0.1

0.2

0.3D1929× +/−2SE

1960 1970 1980 1990 2000

−0.2

−0.1

0.0D1944× +/−2SE

1960 1970 1980 1990 2000

−0.2

−0.1

0.0D1981× +/−2SE

1960 1970 1980 1990 2000

−1.2

−1.0

−0.8(INF

I−INFA)× +/−2SE

Fig. 5. Recursive estimates of model coefficients

8 S. Akkoyunlu and B. Siliverstovs

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theory. This finding signifies that the economies of thesetwo cities have been well integrated not only during normaltimes but also during periods of high inflation.

Acknowledgements

We are grateful to David Hendry as well as to the partici-pants at the KOF Brown Bag seminar (Zurich,Switzerland), the annual meeting of the Swiss Society ofEconomics and Statistics (Fribourg, Switzerland), theEECON Conference (Istanbul, Turkey), the seminar atthe Department of Economics, University of Neuchâtel(Switzerland), and the EcoMod conference in PontaDelgada (Portugal) for their constructive comments. Wealso would like to thank Prof. Sevket Pamuk for fruitfuldiscussions on construction of price indices.

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