purchasing power parity: error correction models and structural...

Open economies review 13: 5–26 (2002)c© 2002 Kluwer Academic Publishers. Printed in The Netherlands.

Purchasing Power Parity: Error CorrectionModels and Structural Breaks

AMALIA MORALES ZUMAQUERO [email protected] de Teorı́a Económica, Facultad de Ciencias Económicas y Empresariales, Campusde El Ejido, s/n, Universidad de Málaga 29013, Málaga, Spain

RODRIGO PERUGA URREADepartamento de Economı́a Cuantitativa, Universidad Complutense de Madrid, Spain

Rodrigo died October 1, 1999. He was Ph.D. from San Diego and he was professor at the De-partment of Fundamentos del Análisis Económico II in the Universidad Complutense de Madrid.His research areas were Macroeconomics (mostly, International Economics) and Econometrics.The co-author of this paper wants to give special thanks to Rodrigo Peruga for excellent researchassistance.

Key words: purchasing power parity, error correction models, multiple structural breaks

JEL Classification Numbers: C22, F30

Abstract

This paper examines purchasing power parity (PPP) behavior using error correction models (ECM)and allowing for structural breaks. We distinguish four different objectives: first, this paper exam-ines which variable or variables (the exchange rate and/or international relative prices) exhibit asignificant error correction mechanism. Second, this paper presents empirical evidence about theadjustment velocity to the long-run equilibrium. Third, it examines the evidence regarding cointe-gration and the adjustment coefficients parameter instability, and finally, it analyzes whether tradedand non-traded sectors exhibit different behavior. The most important results are: (1) the predomi-nant adjustment is in the exchange rate with a larger velocity adjustment than in relative prices; (2)the evidence suggests that when there are strong depreciations or appreciations in the exchangerate, the international relative prices adjust (i.e., there is evidence of pass-through); (3) the dynamicadjustment to equilibrium is, in general, stable.

This paper analyzes PPP behavior using the error correction model (ECM)methodology. It has four objectives: the first is to examine which variable or vari-ables exhibit a significant error correction mechanism. The second is to presentempirical evidence about the adjustment velocity to the long-run equilibrium.The third is to examine the evidence regarding cointegration and adjustmentcoefficients parameter instability and, finally, the fourth is to analyze whethertraded and non-traded sectors exhibit different behavior.

Although there is an extensive empirical literature on testing PPP using coin-tegration methodology,1 the cointegration analysis does not offer us relevant

6 ZUMAQUERO AND URREA

information. It allows us to analyze whether or not there is a long-run equilibriumrelationship between different variables which does not give us usefulinformation, except for the coefficients sign. However, from ECM we can studythe short- and long-run dynamics of variables simultaneously and obtain richerinformation. Thus, first, we can find which are the endogenous variables of thesystem in the long-run and, in addition, we can find the adjustment velocity.

The adjustment variable analysis is interesting, because if we know the ad-justed variable we know the endogenous variable and then we obtain a moreefficient analysis. In addition, from this analysis we can conclude that either novariables (neither the nominal exchange rate nor international relative prices)show an error correction mechanism (similar to no cointegration) or the oppo-site, the nominal exchange rate and/or international relative prices show thatmechanism (similar to cointegration).

At first, the PPP hypothesis does not exclude any of the possible ECM cases.For example, if we assume that there are identical real shocks in different eco-nomic sectors in each country, the exchange rate adjustment would correctthe deviations from the PPP hypothesis, and then this variable would show anerror correction mechanism. However, this hypothesis would be less likely ifthe internal relative prices were a stationary series.2 So, if PPP holds in morethan one economic sector, the internal relative prices would explain part of theadjustment.

On the other hand, the adjustment velocity analysis offers us informationabout the percentage of response of the variables to long-run equilibriumdeviations.3 Therefore, large values of the adjustment coefficients indicate thatthere is a large percentage of variable adjustment while small values indicatethat the variables adjust slowly. Thus, if we know the adjustment velocity we cantest whether it is faster in integrated markets than in nonintegrated markets.

In addition, this paper analyzes the evidence regarding multiple parameterinstability, not only in the cointegration coefficients but in the adjustment co-efficients associated with the error correction mechanism, too. The evidenceof multiple instability in the adjustment coefficients would indicate whether thebehavior of dynamic adjustment to long-run equilibrium changes in time ornot. For example, it is possible that prices adjustment depends on the dise-quilibrium magnitude. Then, for small changes in the exchange rate, the priceresponse can be insignificant due to its slow progress. However, when thereare significant devaluations, similar to those in the European Monetary System(EMS), the price response could be more significant. Then we would concludethat prices adjustment velocity can show evidence of instability throughout thesample.

To study how the parameter instability affects the PPP hypothesis, we use theeconometric methodology of Bai and Perron (1998). This consists of estimatingand testing linear models with multiple structural breaks at an unknown date.This methodology allows us not only to detect multiple structural breaks butto estimate the potential structural breaks points, too. In addition, how can we

PURCHASING POWER PARITY 7

use ECM information to analyze whether there is a different behavior betweentraded and non-traded sectors? If we assume that traded sectors are moreintegrated than non-traded sectors, we expect a large prices adjustment in thefirst one. Thus, if the PPP hypothesis holds more frequently in traded sectors,the error correction mechanism in these sectors must be in prices.

Finally, there are some previous works which use ECM to analyze the PPPhypothesis such as those of Taylor and McMahom (1988), Johnson (1990), Kim(1990), Kugler (1990), Fisher and Park (1991), Ngama and Sosvilla-Rivero (1991),and Taylor (1992), among others.

Taylor and McMahom (1988) test the PPP hypothesis using cointegrationmethodology and find error correction mechanism results coherent with previ-ous cointegration results. They conclude that PPP holds in the long-run but it de-viates in the short-run. On the other hand, Johnson (1990) estimates the pricesand exchange rate short-run dynamic using ECM, for two subsamples withdifferent exchange rate systems. In fixed exchange rates systems the pricesadjust, while in flexible exchange rates systems not only do the prices ad-just but so do the exchange rates. These results show how the exchange ratesystems influence the adjustment mechanism according to PPP. Similarly, Kim(1990) finds that PPP holds (using producer price indexes, PPI, monthly data,1900–1987) and estimates the ECM. His results show that the exchange rateadjusts between 30% and 50% every year, in the short-run. Fisher and Park(1991) estimate a set of bilateral error correction models for a flexible exchangerates period. His results show that exchange rates adjust frequently to long-runequilibrium. Ngama and Sosvilla-Rivero (1991) obtain cointegration evidence forthe peseta/mark exchange rate, using PPI, and estimate an ECM. The resultswith monthly data (1977:1–1988:12) show that not only does the exchange rateadjust but the prices adjust, too. However, with quarterly data (1977:1–1988:4),they find that the prices adjust.

In short, the results in the previous literature are mixed, but there is muchevidence of exchange rate adjustment in the short-run with flexible exchangerate systems.

The rest of the paper is organized as follows. Section 1 describes the econo-metric methodology. Section 2 presents the data set. Section 3 tests same re-strictions and summarize the instability and short-run dynamic results. Finally,Section 4 provides some concluding remarks.

1. Econometric methodology

In this section we describe the econometric methodology we used to achieveour objectives. First, we present a novel econometric technique to detect mul-tiple structural breaks at unknown dates by Bai and Perron (1998). After this,we describe the way we have used this methodology for our empiricalanalysis.


1.1. Description of the methodology

Bai and Perron (1998) suggest a procedure of estimation and testing linear mod-els with multiple structural breaks at unknown dates. These authors consider apartial structural break model, where not all coefficients change. They estimatetheir model by ordinary least square (OLS) with unknown potential structuralbreaks that will be estimated.

Bai and Perron (1998) use the next lineal regression with m structural breaks(m + 1 regimes):

yt = x ′tγ + z′tδ j + u j t = Tj−1 + 1, . . . , Tj (1)

for j = 1, . . . , m + 1 and where T0 = 0 and Tm + 1 = T . In model (1), yt is the de-pendent variable, xt (p × 1) and zt (q × 1) are the regressors with γ and δ j ascoefficient vectors, and ut is a random variable. In (1) they estimate regres-sion coefficients together with unknown break points, with T observations for(yt , xt , zt ). Model (1) shows partial instability because γ does not change (if p = 0it would be a totally unstable model). In addition, Bai and Perron (1998) ana-lyze the convergence, consistence, and empirical distributions of break pointestimators.

These authors suggest a sequential and efficient algorithm that reduces thenumber of regressions. In the traditional sequential methodology one breakpoint implies estimating n regressions, two break points imply estimating n2

regressions, m break points imply estimating nm regressions, and so on. How-ever, Bai and Perron’s (1998) sequential algorithm only requires a general re-striction about the maximum number of break points. Bai and Perron’s (1998)methodology offers us break point estimators and confidence intervals forthem.

1.2. Application of the methodology

In the application of the methodology we distinguish two stages. In Stage 1 wespecify and estimate the long-run model. In Stage 2 we estimate the ECM.

1.2.1. Stage 1: Long-run model specification. In this stage we specify andestimate4 two long-run models:

st = ϕ + β(pt − p∗t ) + εt (2)

and

(pt − p∗t ) = ϕ′ + β ′st + ε′t (3)

where st is the nominal exchange rate, pt is the domestic price, p∗t is the for-eign price, and εt , ε′t are random error terms. In Equation (2), direct regression,


the nominal exchange rate is the endogenous variable. Similarly, we estimatethe cointegration regression (3), reciprocal regression, where the internationalrelative price, (pt − p∗t ), is the endogenous variable. These two specificationsallow us not to impose the direction of the causality. However, we have madetwo additional assumptions: the existence of a constant term (ϕ and ϕ′, respec-tively) and that the domestic and foreign prices exhibit the same coefficientvalue (symmetry restriction5: β in Equation (2) and unity in Equation (3)). In thissense, for a correct specification of the long-run model, we previously test thembefore imposing them. First, we test the significance of the constant terms. Inthe context of PPP theory, this has important implications: a significant constantterm would imply that it is the relative version of the PPP hypothesis that is ful-filled. In contrast, the absolute version is only verified if the parameter ϕ (or ϕ′)equals zero. To do this, we estimate Equations (2) and (3) by the Phillips andHansen (1990) fully modified estimation (that correct for the endogenous biasand correlation between regressors) and test the significance of the constantterms using the Wald modified test. Second, we test the symmetry restrictionusing the Wald modified test, too.

In addition, the use of OLS with non-stationary variables regressions offersus superconsistence estimators with nonstandard distributions. Therefore, Baiand Perron’s methodology would not apply to regressions (2) and (3) directly.However, the break point estimator is consistent, so we can apply this method-ology for this objective. We would like to clarify a point: in this stage we areinterested, overall, in analyzing the evidence of multiple instability of the long-run coefficients β and β ′. In addition, we have run a set of Monte Carlo experi-ments with non-stationary regressors and have obtained a correct break pointlocation.

From this stage we can obtain several different cases:

1. β and β ′ unstable coefficients. In this case, we introduce in Equations (2)and (3), respectively, a dummy variable for every interval between the breakpoints we have detected. The estimated residuals from this more generalmodel will be a deviations equilibrium measure.

2. β and β ′ stable coefficients. In this case, we calculate the deviations fromthe estimated residuals of Equations (2) and (3), respectively.

3. β stable and β ′ unstable (and the opposite case).

In short, in all these cases we use the estimated residuals of the static long-run regressions for the estimation of the dynamic model in Stage 2.

1.2.2. Stage 2: Error correction models. In this stage we estimate the ECM.There are two techniques for estimating ECM. The first one is the single equa-tion estimation technique by Engle and Granger (1987) and the second, is themultivariate estimation technique (Johansen, 1988, 1992). We use the first one.

We are aware the Engel and Granger’s (1987) methodology has been criticizedrelative to other tests such as modified single-equation methods (see Phillips


and Hansen, 1990) and multivariate methods suggested by Johansen (1988),Stock and Watson (1988), and Phillips and Ouliaris (1990). However, Bai andPerron’s (1998) methodology is for single equations and then we need to useEngel and Granger’s methodology for estimating the ECM: due to the absenceof multiple instability tests in the context of cointegrated long-run relations weneed to introduce some restrictions to use Bai and Perron’s methodology. Inthis sense, the common factor restriction could appear in the specified model(see Kremers, Ericsson, and Dolado, 1992).

The ECM we estimate is:

A(L)�st = B(L)�(pt − p∗t ) − α[st−1 − ϕ̂ − β̂(pt−1 − p∗t−1)] + ut (4)

where the exchange rate is the endogenous variable. Equally, we estimate theECM when the international relative prices are the endogenous variable:

A′(L) � (pt − p∗t ) = B ′(L)�st − α′[(pt−1 − p∗t−1) − ϕ̂′ − β̂ ′st−1] + u′t (5)

with

A(L) = 1 − α1L − α2L2 − · · · − αp L pA′(L) = 1 − α′1L − α′2L2 − · · · − α′p L pB(L) = 1 − γ1L − γ2L2 − · · · − γq Lq

B ′(L) = 1 − γ ′1L − γ ′2L2 − · · · − γ ′q Lq .

The terms in brackets in (4) and (5) are the error correction mechanisms, andthe coefficients α and α′ are the adjustment parameters.6

On the other hand, we have used, ad hoc, three lags for the exchange rateECM estimation and twelve lags for the international relative prices ECM estima-tion. We consider that these numbers of lags are able to capture the dynamic ofthe variables. However, we have made a sensibility analysis for several numbersof lags and the results do not change.

In our empirical analysis, we only care about the possible instability of somecoefficients in the ECM. In particular, we analyze cointegration coefficients(β, β ′) and adjustment coefficients (α, α′) parameter instability. Thus, we assumeA(L), A′(L), B(L), B ′(L) to have constant coefficients. Therefore, we reduce thecomputational cost that Bai and Perron’s methodology implies for ECM with alarge number of regressors (for example, the relative international price ECMhas 26 regressors: 12 dependent variable lags, 12 independent variable lags, aconstant, and the error correction mechanism).

This simplified procedure is similar to Johansen’s (1988, 1992). It consistsof first filtering the dependent variable and the error correction mechanism,and regressing both on dependent and independent variables lags. Second,the filtered dependent variable is regressed on a constant and the filtered errorcorrection mechanism, so we reduce the number of coefficients substantially.


The second of these is the adjustment coefficient whose instability we want toanalyze.7

In short, we have three channels of information:

(a) Which variables show an error correction mechanism.(b) Which variable is the endogenous variable.(c) If there is instability in the adjustment dynamic, Bai and Perron’s (1998)

procedure detects when the break point occurs and offers the estimatedadjustment coefficient, before and after the structural break. If there is noevidence of instability we estimate the adjustment coefficient for the fullsample.

To summarize, in the application of the methodology we have introducedsome restrictions in order to use Bai and Perron’s methodology. There areother alternatives that do not need so many a priori assumptions, but theydo not allow us to test for multiple structural breaks. An application can beseen in Morales and Peruga (1999a). These authors—for the same data setof this paper—estimate regressions (2) and (3) by Phillips and Hansen’s (1990)fully modified estimator, testing for cointegration (based on the single equationresiduals), and for structural breaks in the cointegration relationships using theinstability test proposed by Gregory and Hansen (1996) (similar to Hansen’s,1992 and Hansen and Johansen’s, 1993, instability tests). The evidence showsthat the potential break point estimated is one of the multiple break points es-timate for β(β ′) in this paper.

2. The data

The data used in this paper are disaggregated price indexes for Germany (GER),Belgium (BEL), Spain (SPA), France (FRA), the Netherlands (NED), Italy (ITA),and the United Kingdom (UK), and are supplied by Eurostatistics (Eurostat).They are: food less drinks and meals (P1); clothes, footwear including repairs(P2); rent, fuel and power (P3); household goods and services (P4); transportand communications (P6); recreation and education (P7); and other goods andservices including drinks and meals (P8). Initially, we consider P1, P2, and P4as traded price indexes and P3, P6, P7, and P8, non-traded price indexes.8

The disaggregated price series for Spain, supplied by Eurostat, shows a def-inition change in 1992. We have taken them from the Instituto Nacional deEstadı́stica (INE). The definitions of the indexes are the same as the definitionin Eurostat.

The disaggregated price indexes cover the period 1975:1–1995:12 forBelgium, France, Italy, and the United Kingdom, in all indexes; the period 1975:1–1995:12 for the Netherlands in all indexes except for P8 (1980:3–1995:12); theperiod 1976:1–1995:12 for Spain, and the period 1976:1–1995:7 for Germany.

The exchange rate data, supplied by International Financial Statistics(International Monetary Fund), are final period data and they are defined as


dollar/foreign currency. With these series we elaborate all possible bilateralnominal exchange rates.

3. Empirical results

The previous empirical procedure is applied to all bilateral relationships be-tween countries9 for the seven disaggregated price indexes. We present theempirical results in three subsections: results of testing the significance of theconstant terms and the symmetry restriction; results of instability not only incointegration coefficients but in adjustment coefficients too; and results of theshort-run dynamics. Tables 1–6 exhibit the empirical results and this informationis summarized in Tables 7, 8.

3.1. Testing restrictions in the long-run model

In this section we test the existence of a constant term and the symmetry re-striction in the long-run model specification. A significant constant term impliesthat it is the relative version of the PPP hypothesis that is fulfilled. In the ab-solute version the constant term equals zero. If the symmetry restriction holds,then the domestic and foreign prices will exhibit the same coefficient value.In general, the results substantially support the significance of the constantterms, ϕ and ϕ′ in Equations (2) and (3), respectively. In particular, in the directregression, the constant term ϕ is significant in all bilateral relationships for allprice indexes, except for the bilateral relationship Germany–Italy for the priceindex P6. In addition, in the reciprocal regression, the constant ϕ′ is significantin 17/20 bilateral relationships for the price index P1, 15/20 for P2, 15/20 for P3,12/20 for P4, 18/20 for P6, 14/20 for P7, and 18/20 for P8.

The results of the fulfillment of the symmetry restriction show that, in thedirect regression, it holds in an important number of bilateral relationships.Particularly, it holds for P1 in 15/20 bilateral relationships, P2 in 12/20, P3 in13/20, P4 in 12/20, P6 in 15/20, P7 in 12/20, and P8 in 10/20. It highlights the priceindexes P1 and P6 where the evidence supports the fulfillment of the symmetryrestriction in 75% of the cases. In the reciprocal regression, the evidence infavor of the symmetry restriction is weaker than for the direct one (14/20 bilateralrelationships for P1, 12/20 for P2, 10/20 for P3, 9/29 for P4, 11/20 for P6, 12/20for P7, and 10/20 for P8).10

In short, there are several arguments that support the correct specificationof our bivariate model: (1) the empirical results show strong evidence for thesignificance of the constant terms (relative version of the PPP hypothesis holds);and (2) there is reasonable evidence in favor of the symmetry restriction.

3.2. Instability

Tables 1–2 exhibit the evidence of instability. This information is summarizedin Table 7 in four columns: the first one exhibits the disaggregate price index


Table 1. Evidence of multiple instability in cointegration coefficients β and β ′.

NXRT-RCPa RCP-NXRTa

GER–BELa 82:1 (P1), 82:1 (P7), 82:1/85:6 (P8) NO

GER–SPA NOb 79:3 (P6)

GER–FRA 76:1/82:5 (P2) 79:12 (P3)

GER–NED 80:6 (P1), 77:8/79:4/83:12 (P4), 89:1 (P1), 87:6/89:6 (P2), 91:3 (P6),78:7/79:8/80:10 (P6), 82:2 (P7) 77:4/86:1/91:6 (P7), 88:8 (P8)

GER–ITA 92:12 (P1), 92:11 (P2), 92:1 (P3), 92:11 (P4), NO92:9 (P6), 92:2 (P7), 92:11 (P8)

GER–UK 80:6 (P1), 85:4/92:6 (P2), 80:7/91:8 (P3), 79:5 (P1), 77:7 (P2), 79:5 (P4),80:6 (P6), 80:7 (P7) 79:6 (P6), 79:12 (P7), 79:12 (P8)

BEL–SPA NO 77:3/79:3 (P6), 78:3 (P8)

BEL–FRA 76:6/81:4/94:5 (P1), 76:8 (P3), 76:7 (P4), NO76:6 (P6), 76:7 (P7), 76:8 (P8)

BEL–NED 82:1 (P1), 80:7/82:1/89:12 (P2), 82:7/92:6 (P3), NO82:1 (P4), 82:1/90:2 (P7), 76:11/84:12 (P8)

BEL–ITA 76:2/92:12 (P1), 76:2/92:9 (P2), 82:11 (P3)76:2/77:1/82:1/92:12 (P3), 76:2/92:9 (P6),76:8/77:1//82:1/92:9 (P8)

BEL–UK 89:9 (P2), 92:8 (P3), 76:8/78:1/80:9 (P8) 80:1 (P1)

SPA–FRA 93:4 (P3), 93:4 (P4) NO

SPA–NED NO NO

SPA–UK 80:4/83:3 (P1), 80:5 (P3), 80:6 (P6), 80:5 (P7) NO

FRA–NED 76:7 (P4), 79:9 (P6), 76:7 (P7), 77:3 (P8) 88:12 (P1)

FRA–ITA 76:1/92:12 (P1), 76:1/92:12 (P2) 81:9 (P2), 82:5 (P4)76:1/78:4/92:9 (P3) 76:1/92:11 (P4),78:4/92:11 (P6), 76:2/78:4/92/12 (P7),76:1/78:4/82:7/92:8 (P8)

FRA–UK 92:8 (P1), 76:3/85:12/92:8/93:12 (P3), 79:6 (P7)80:7/92:8 (P4), 76:11 (P8)

NED–ITA 76:2/92:12 (P1), 76:2/92:11 (P4), 76:2/88:11/90:12 (P2),76:2/77:11/79:12/92:11 (P6), 76:2/87:12/89:12/91:2 (P7)76:3/92:12 (P7), 87:10 (P8)

NED–UK 80:4 (P1), 92:8 (P2), 92:8 (P3), 80:4 (P4), 79:5 (P1), 79:6 (P4), 79:6 (P6)76:8/78:2/80:4 (P6), 80:7 (P7)

ITA–UK 80:3 (P1), 80:3/93:7 (P2), 80:3 (P3), 82:12/84:1 (P6)78:9/80:3/93:7 (P4), 80:3 (P6), 80:3/93:7 (P7),80:3 (P8)

aNXRT-RCP: exchange rate as endogenous variable (long-run model Equation (2)). RCP-NXRT: in-ternational relative price as endogenous variable (long-run model, Equation (3)). For every bilateralrelationship this table presents the structural break dates (in brackets, the price index).bNO: no evidence of instability.


Table 2. Evidence of multiple instability in adjustment coefficients α and α′.

NXRT-RCPa RCP-NXRTa

GER–BELa 93:6 (P1), 81:5 (P3), 93:6 (P7), 93:6 (P8) NO

GER–SPA NOb NO

GER–FRA NO 85:3 (P3), 76:12 (P6)

GER–NED 76:12 (P1), 76:12 (P2) 84:12 (P1)

GER–ITA NO NO

GER–UK 86:1 (P1), 85:11 (P3), 86:1 (P6) 77:3 (P3), 78:6 (P4), 78:6 (P6)

BEL–SPA NO NO

BEL–FRA NO 76:9 (P2), 86:2 (P8)

BEL–NED 93:6 (P1), 81:5 (P2), 81:5 (P3), 76:12/86:12 (P8)81:12/93:6 (P4), 93:6 (P7)

BEL–ITA NO 89:9 (P1), 93:2 (P7)

BEL–UK NO 90:2 (P3)

SPA–FRA NO 76:12 (P6)

SPA–NED NO 78:3 (P4)

SPA–UK NO NO

FRA–NED NO 85:5 (P2)

FRA–ITA 80:12 (P3), 76:4 (P4), 79:12 (P7) 75:12 (P1), 76:4 (P2), 76:8 (P4)

FRA–UK NO 90:2/92:6 (P3)

NED–ITA NO NO

NED–UK NO 77:4 (P1), 78:11 (P6),

ITA–UK NO 92:6 (P2), 81:3 (P6)

aNXRT-RCP: exchange rate as endogenous variable (ECM, Equation (4)). RCP-NXRT: internationalrelative price as endogenous variable (ECM, Equation (5)). For every bilateral relationship this tablepresents the structural break dates (in brackets, the price index).bNO: no evidence of instability.

used; the second, the evidence of instability in the cointegration coefficients;the third, the evidence of instability in the adjustment coefficients; and the lastone, stable cases.

3.2.1. Cointegration coefficients instability. With regard to the instability inthe cointegration coefficient β (direct regression), we have obtained 80 cases ofinstability out of 140 possible cases. In addition, we observe that this evidenceshows little variation across indexes: it oscillates from 9 to 13 cases. Thus, theevidence of instability is not confined to a specific index. With regard to theevidence of instability in the cointegration coefficient β ′ (reciprocal regression),we have obtained 27 instability cases from 140 possible cases.

In sum, the evidence of instability is stronger for β than for β ′. This evidencecan be explained by the different stochastic behavior between the relative


Table 3. Adjustment variable, multiple instability in adjustmentcoefficients and estimated values.

P1 AVa Ia α̂1 α̂2

GER–BEL p/p* no −0.0486**b –GER–FRA s no −0.0837* –GER–ITA s no −0.1463* –GER–UK s yes −0.2153* −0.0248BEL–FRA s no −0.2122*BEL–NED p/p* no −0.1026*BEL–ITA s no −0.1224*

p/p* yes −0.0490* −0.0018BEL–UK p/p* no −0.0271* –SPA–UK s no −0.0936* –

p/p* no −0.0209* –FRA–NED s no −0.0610* –FRA–ITA s no −0.2208* –NED–ITA s no −0.1844* –NED–UK s yes −0.0683* –ITA–UK s no −0.0924* –

p/p* no −0.0179* –

P2 AVa MIa α̂1 α̂2

GER–BEL p/p* no −0.0078* –GER–FRA s no −0.0825* –GER–ITA s no −0.1580* –

p/p* no −0.0065** –GER–UK p/p* no −0.0432* –BEL–NED s yes 0.0200 −0.0777*BEL–ITA s no −0.1119* –BEL–UK s no −0.0662 –SPA–FRA s no −0.0505**FRA–ITA s no −0.2290* –NED–UK p/p* no −0.0348* –ITA–UK s no −0.1396* –

p/p* yes −0.0116* −0.0889*aAV: adjustment variable, I: evidence of instability (structuralbreak date in Table 3), α̂1: estimated adjustment coefficient be-fore structural break and α̂2: estimated adjustment coefficientafter structural break.b* and ** show statistical significance at 5% and 10% significancelevel, respectively.


Table 4. Adjustment variable, multiple instability in adjustmentcoefficients and estimated values.


GER–BEL s yes −0.0039 −0.0616*bGER–FRA s no −0.0653* –

p/p* yes 0.0161 −0.1082*GER–NED s no −0.1761* –

p/p* no −0.0717** –GER–ITA s no −0.1005* –GER–UK s yes −0.1747* −0.0087BEL–FRA s no −0.2991* –BEL–NED s yes 0.0069 −0.1115*BEL–ITA s no −0.1592* –BEL–UK p/p* yes 0.0033 −0.0442*SPA–UK s No −0.0385* –

p/p* no −0.0833* –FRA–NED p/p* yes 0.0047 −0.1396*FRA–ITA s yes −0.7295* −0.1639*FRA–UK s no −0.0874* –ITA–UK s no −0.1226* –

p/p* no −0.0426* –


GER–FRA s no −0.0665* –GER–ITA s no −0.1543* –

p/p* no −0.0076* –BEL–FRA s no −0.0580* –

p/p* no −0.0104* –BEL–UK p/p* no −0.0143* –SPA–FRA s no −0.0848* –SPA–UK p/p* no −0.0105** –FRA–NED s no −0.0865* –FRA–ITA s yes −0.0148* −0.2041*NED–ITA s no −0.2298* –NED–UK s no −0.0658* –ITA–UK s no −0.1472* –

p/p* no −0.0192* –aAV: adjustment variable, I: evidence of instability (structuralbreak date in Table 3), α̂1: estimated adjustment coefficient be-fore structural break and α̂2: estimated adjustment coefficientafter structural break.b* and ** show statistical significance at 5% and 10% signifi-cance level, respectively.


Table 5. Adjustment variable, instability in adjustment coefficients and estimated values.


GER–FRA s no −0.0423*b –GER–NED p/p* no −0.1000* –GER–ITA s no −0.1616* –GER–UK s yes −0.1790* −0.0208

p/p* yes 0.1157 −0.0418*BEL–FRA s no −0.0294* –

p/p* −0.0928* –BEL–ITA s no −0.1460* –BEL–UK p/p* no −0.0154* –SPA–FRA s no −0.0741* –SPA–UK s no −0.0741* –FRA–NED s no −0.0656* –FRA–ITA s no −0.1984* –NED–ITA s no −0.1815* –NED–UK s no −0.0549* –ITA–UK s no −0.0966* –

p/p* yes −0.2550* −0.0254


GER–BEL p/p* no −0.0386*b –GER–FRA s no −0.0541* –GER–NED s no −0.0626* –

p/p* no −0.1208* –GER–ITA s no −0.0984* –GER–UK s no −0.0830* –BEL–FRA s no −0.0481* –BEL–NED p/p* no −0.0421* –BEL–ITA p/p* yes −0.0132* 0.0105BEL–UK p/p* no −0.0116* –SPA–FRA s no −0.0755* –SPA–NED s no −0.0493** –SPA–UK s no −0.0759* –FRA–NED s no −0.0856* –

p/p* no −0.0252* –FRA–ITA s yes −0.1612* −0.1031*NED–UK s no −0.0750* –ITA–UK s no −0.1103* –

p/p* −0.0179* –aAV: adjustment variable, I: evidence of instability (structural break date in Table 3), α̂1:estimated adjustment coefficient before structural break and α̂2: estimated adjustmentcoefficient after structural break.b* and ** show statistical significance at 5% and 10% significance level, respectively.


Table 6. Adjustment variable, multiple instability in adjustment coefficientsand estimated values.

P8 AVa Ia α̂1 α̂2 α̂3

GER–ITA s no −0.0866 – –BEL–FRA s no −0.0496**b – –

p/p* yes −0.0184* −0.0774* –BEL–NED p/p* yes −0.0959* −0.0115 −0.1545*BEL–ITA s no −0.1966* – –

p/p* no −0.0122* – –SPA–FRA s no −0.0670 – –FRA–NED s no −0.1378* – –FRA–ITA s no −0.3172* – –

p/p* no −0.0190* – –FRA–UK s no −0.0451* – –NED–ITA s no −0.1327** – –ITA–UK s no −0.0921* – –

p/p* no −0.0430* – –aAV: adjustment variable, I: evidence of instability (structural break date inTable 3), α̂1: estimated adjustment coefficient before structural break and α̂2:estimated adjustment coefficient after structural break.b* and ** show statistical significance at 5% and 10% significance level,respectively.

Table 7. Summary of instability results.

Instabilitya Instabilitya Non instabilityb

β β ′ α α′ α, β α′, β ′

P1 13/20 3/20 4/20 4/20 7/20 15/20

P2 9/20 5/20 2/20 3/20 10/20 13/20

P3 12/20 2/20 4/20 5/20 7/20 14/20

P4 12/20 3/20 2/20 3/20 8/20 16/20

P6 11/20 6/20 1/20 5/20 9/20 12/20

P7 12/20 4/20 3/20 1/20 8/20 15/20

P8 11/20 4/20 1/20 2/20 9/20 14/20

Total 80/140 27/140 17/140 23/140 58/140 99/140

aNumber of instable cases out of total.bNumber of stable cases out of total.

international prices and the nominal exchange rates. The relative internationalprices are less volatile than the nominal exchange rates. So, how much volatileis the independent variable (exchange rate) it is more difficult to detect structuralbreaks, due to its large variance.


Table 8. Summary of adjustment variables results.

p/p*a sa s, p/p* No adjustment

P1 3/20b 8/20b 3/20b 6/20c

P2 3/20 6/20 2/20 9/20

P3 2/20 8/20 4/20 6/20

P4 2/20 6/20 3/20 9/20

P6 2/20 9/20 3/20 6/20

P7 4/20 9/20 3/20 4/20

P8 1/20 5/20 4/20 10/20

Total 17/140 51/140 22/140 50/140

ap/p*: international relative prices, s: nominal exchange rate.bNumber of adjustments out of total.cNumber of no adjustments out of total.

With regard to break point location, we observe that: (1) for the cointegrationcoefficients, β and β ′, the structural breaks are not exactly the same between bi-lateral relationships for a price index. However, we find several similar structuralbreaks: for cointegration coefficient β in the 1970s (mostly in 1976 and 1979),at the beginning of the 1980s, and in 1992, and for β ′ the structural breaks arelocated in the 1970s, mostly in 1976 and 1979; (2) the structural breaks usuallyare the same for a bilateral relationship through all price indexes; and (3) thebreak point location is not the same between direct and reciprocal regressions.

Finally, the instability of β is concentrated in the bilateral relationships GER–NED, GER–UK, HOL–FRA, BEL–NED, BEL–ITA, FRA–NED, FRA–ITA, FRA–UK,NED–ITA, NED–UK, and ITA–UK. The coefficient β ′ instability is concentrated inthe bilateral relations GER–NED and NED–UK. We observe from these resultsthat Spain is the country with less evidence of instability.

3.2.2. Adjustment coefficients instability. For the adjustment coefficientα (direct regression) we have only detected 17 cases of instability out of 140possible cases. Thus, there is little evidence in favor of instability. It varies be-tween 1 and 4 cases out of 20 possible cases. For the adjustment coefficient α′

(reciprocal regression) we have obtained 23 unstable cases from 140 possiblecases. It oscillates between 1 and 5 cases throughout the price indexes.

In general, the break point location is the same only in a few bilateral rela-tionships (for example in GER–BEL, GER–UK, BEL–NED for direct regression).Then, for the adjustment coefficients, the breaks points do not occur in similardates for a price index. We detect different break points across regressions.

On the other hand, the α instability is concentrated in the bilateral relationsGER–BEL, GER–UK, BEL–NED, and FRA–ITA. The α′ instability is concentratedin the bilateral relation GER–UK. In the rest of the bilateral relations there is littleevidence of instability. Finally, there are 15 simultaneous cases of instability in


the cointegration coefficient β and in the adjustment parameter α, for the directregression, and 9 cases for the reciprocal regression.

3.2.3. Noninstability results. For the direct regression there are 58 casesfrom 140 possible cases with noninstability evidence in the cointegration coef-ficient and the adjustment coefficient. This evidence oscillates between 7 and10 cases. For the reciprocal regression there are 99 stable cases out of 140possible cases.

3.3. Analysis of the short-run dynamics

From this analysis we obtain information concerning which is the adjustmentvariable and the adjustment velocity. Tables 3–6 present the empirical results.11

Every table has the following information: the price index used, the adjustmentvariable (exchange rate and/or relative prices), and the estimated values of theadjustment coefficients. These results are summarized in Table 8. It presentsthe price index used in the first column; in the second, the number of cases withrelative price adjustment (p/p∗); in the third, the number of cases with nominalexchange rate (s) adjustment; in the fourth, the number of cases with evidenceof adjustment in both variables; and in the fifth column, cases without evidenceof adjustment.

3.3.1. Adjustment variable. From Table 8 we observe 50 cases from 140possible cases (35% of cases) with evidence of non-adjustment and 90 cases(64% of cases) with evidence of adjustment. This adjustment can appear in asingle variable (exchange rate or relative prices) or in the two variables. Thereis one variable adjustment in 68 cases: the nominal exchange rate adjusts in51 cases and relative prices adjust in 17 cases. Two variables adjust in 22cases. Therefore, we conclude that there are 73 cases from 90 with exchangerate adjustment and 39 cases from 90 with relative price adjustment. Fromthese results we note that the majority of the countries participated during thesample period in the EMS, and so the results concerning exchange rates may bepartly conditioned by the functioning of the EMS. Although the EMS permittedshort-run deviations from the central parity, the bilateral exchange rates of theparticipating countries should be weakly exogenous.

Finally, by indexes, we would expect more adjustment in relative prices fortraded sectors. However, the price adjustment does not concentrate in thesesectors. By bilateral relations the price adjustment concentrates in GER–BEL,GER–NED, and BEL–UK, the exchange rate adjustment concentrates inGER–FRA, GER–ITA, SPA–FRA, FRA–NED, FRA–ITA, NED–ITA, and NED–UK,and the two variables adjustment in BEL–FRA and ITA–UK.

3.3.2. Adjustment velocity. In this subsection we summarize the adjustmentvelocity evidence for every price index. We want to know which variable has a


large adjustment velocity and whether the relative prices adjust faster than theexchange rate in traded sectors.

In general, the exchange rate adjustment velocity is larger than relative prices.For example, when we observe the bilateral relation GER–ITA, for every priceindex, we see that the exchange rate always adjusts. The adjustment magnitudeoscillates between 16.16% for P6 and 8.66% for P8. In addition, the exchangerate and the relative prices adjust too (but very slowly) for the price indexesP2 and P4. However, for example, in the bilateral relation BEL–UK, we observethat the relative prices adjust with a very short adjustment magnitude (between4.42% and 1.16%). Thus, from these two examples, we conclude that in theshort-run, the nominal exchange rate adjusts faster than relative prices.

On the other hand, when there are strong depreciations or appreciations inthe exchange rate, the international relative prices adjust. This evidence occurs,for example, in the bilateral relations GER–BEL for P1 and P7 and BEL–NED forP1, P7, and P8. We can consider the bilateral relationship ITA–UK for P6. Inthis relation the exchange rate adjustment magnitude is larger than in relativeprices, except for the price index P6. For this price the sequential proceduredetects a break point for α′ in 81:3. Up until this date the exchange rate suffersa strong depreciation and the relative prices adjust (25.50%).

In conclusion, the evidence shows that strong “jumps” in the exchange rateslead to relative price adjustments. For example, it occurs in the bilateral relationBEL–NED for P1 (Figure 1). The numerical results show that relative prices adjust

Figure 1. Nominal exchange rate between Belgium and the Netherlands, NXRT. International rel-ative price between Belgium and the Netherlands for P1, RCP1.


Figure 2. Nominal exchange rate between France and the Netherlands, NXRT. International relativeprice between France and the Netherlands for P3, RCP3.

10.26% every period (every month) in the short-run to achieve the long-runequilibrium. In this example the relative prices adjust for the strong exchangerate depreciation.

In addition, there are some bilateral relationships which the relative pricesadjust but without strong “jumps” in the exchange rate. For example, in thebilateral relations GER–NED for P3, P6, and P7, GER–FRA for P3, GER–UK forP2 and P6, BEL–FRA for P8 and FRA–NED for P3. This price adjustment maybe due to the high volatility in prices. In the bilateral relation FRA–NED for P3(Figure 2) the relative price adjustment magnitude is 13.96% with high volatilityin prices.

Finally, in general, we do not obtain a large adjustment velocity in prices formore integrated sectors (as we would expect).

4. Concluding remarks

In this paper we have tested the PPP hypothesis using ECM methodology. Theempirical analysis yields the following conclusions:

1. The exchange rate adjustment appears in a large number of bilateral rela-tionships, showing that a change in the exchange rate affects all economicsectors, not only traded sectors but also non-traded sectors. Therefore, thepredominant adjustment is in the exchange rate. This result may be partiallyconditioned by the functioning of the EMS.


2. In general, the adjustment velocity is larger in the exchange rate than inrelative prices (we cannot forget the exchange rate overshooting withoutprices adjusting in the short-run). In addition, the evidence suggests thatwhen there are strong depreciations or appreciations in the exchange rate,the international relative prices adjust. In other words, there is evidence ofpass-through.

3. The evidence of instability of the cointegration coefficients is larger than inthe adjustment coefficients. Thus we conclude that the dynamic adjustmentto equilibrium is, in general, a stable adjustment because we have obtainedlittle evidence of instability.

4. With regard to the break points, we have localized three common dates witha clear economic interpretation: (a) break points in 1976 and 1979. Theycould be related to the oil crises; (b) break points at the beginning of the1980s (between 1980 and 1983). They are consistent with the three initialgeneral readjustments of EMS: the first one took place in 1981 (October), thesecond in 1982 (June) and the third in 1983 (March); (c) break points in 1992are consistent with a general EMS crisis: all currencies were appreciatedexcept the lira which was depreciated (this explains that Italy is present inthe bilateral relationships with evidence of instability in 1992).

5. The empirical results do not support the economic hypothesis that relativeprices adjust in international competitive markets, because there is evidenceof relative prices adjustment, although uniformly distributed between sec-tors. This result is consistent with the product differentiation hypothesis. Thetraded goods (mostly, manufactured products) are differentiated and this cancontribute to the fact of not finding more evidence of adjustment in thesesectors. In addition, it is possible that the disaggregation of the indexes isnot sufficient to capture the relative prices adjustment in traded sectors.

In conclusion, the evidence presented in this paper suggests that exchangerates adjust in all sectors, and so this variable would be affected by some vari-ables in addition to financial variables, for example, by the evolution of thegoods market. On the other hand, we have not found evidence of larger ad-justment prices in the traded sector than in non-traded sectors and this opensnew paths for future research, for example, to use more disaggregated priceindexes. Finally, the evidence shows that relative prices adjust when there arestrong depreciations or appreciations of the nominal exchange rate, so we ob-tain evidence of pass-through.

Acknowledgments

We would like to express our gratitude to Mariam Camarero, Consuelo Gámez,Teodosio Pérez, José Luis Torres, an anonymous referee, the participants inthe VI Jornadas de Economı́a Internacional, the participants in the 6◦ Encontrode Novos Investigadores de Análise Económica, and the participants in the


Southern Economic Association 70th Annual Conference for their valuablecomments.

Notes

1. See Edison and Klovland (1987), Taylor (1988), Enders (1988), Corbae and Ouliaris (1988, 1990),Canarella, Pollar, and Lai (1990), Mark (1990), Johnson (1990), Kim (1990), Ardeni and Lubian(1991), Fisher and Park (1991), Fraser, Taylor, and Webster (1991), Ngama and Sosvilla-Rivero(1991), Trozano (1992), Cheung and Lai (1993a, 1993b), Kugler and Lenz (1993), Chowdhuryand Sdogati (1993), Pérez Jurado and Vega (1993), Rogers and Jenkins (1995), Camarero andTamarit (1996), Gámez, Morales, and Torres (1996), Sosvilla, et al. (1997), and Dutton and Strauss(1997).

2. The results in Morales and Peruga (1999a) show a few cases of favorable evidence of stationaryinternal relative prices (for the same data set used in this paper).

3. The model is in logarithms.4. We thank Bai and Perron for providing us with the computer program to calculate our estima-

tions, written in GAUSS.5. Most researchers employ the bivariate specification (Equations (2) and (3)) where the sym-

metry restriction is imposed. See Frenkel (1981), Hakkio (1984), Taylor (1988), Kim (1990), andCanarella, Polard, and Lai (1990), among others.

6. Obviously, if we had directly estimated Equations (4) and (5), the model would be non-linear andthe Bai and Perron (1998) tests could not be applied.

7. We have carried out some simulations with the filtered model and with the non-filtered model.The results hardly differ between them.

8. We do not use the price index P5 (medicine and health care) because there are no homogenousseries for all countries.

9. Except to the bilateral relation SPA–ITA where the nominal exchange rate is I(0). The univariateseries analysis is not included in this paper, although it is available upon request.

10. The estimated numerical results of significance of the constant terms and symmetry restrictionfulfillment are available upon request.

11. An alternative way to obtain the direction of adjustment would be the weak exogeneity analysis.We have tested for weak exogeneity using the LR test statistic (see Johansen, 1988; Psaradakis,1994), and the results hardly differ from those in the second column of Tables 3–6. In these tableswe do not present all estimated adjustment coefficients from models (4) and (5) for all bilateralrelationships. We only present the estimated values for the bilateral relationships in which thereis evidence of adjustment.

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