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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
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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
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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.
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8 ZUMAQUERO AND URREA
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,
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PURCHASING POWER PARITY 9
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
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10 ZUMAQUERO AND URREA
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.
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PURCHASING POWER PARITY 11
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
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12 ZUMAQUERO AND URREA
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
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PURCHASING POWER PARITY 13
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.
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14 ZUMAQUERO AND URREA
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
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PURCHASING POWER PARITY 15
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.
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16 ZUMAQUERO AND URREA
Table 4. Adjustment variable, multiple instability in
adjustmentcoefficients and estimated values.
P3 AVa Ia α̂1 α̂2
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* –
P4 AVa Ia α̂1 α̂2
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.
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PURCHASING POWER PARITY 17
Table 5. Adjustment variable, instability in adjustment
coefficients and estimated values.
P6 AVa Ia α̂1 α̂2
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
P7 AVa Ia α̂1 α̂2
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.
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18 ZUMAQUERO AND URREA
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.
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PURCHASING POWER PARITY 19
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
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20 ZUMAQUERO AND URREA
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
-
PURCHASING POWER PARITY 21
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.
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22 ZUMAQUERO AND URREA
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.
-
PURCHASING POWER PARITY 23
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
-
24 ZUMAQUERO AND URREA
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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