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Purchasing Power Parity Bysectors From Selected EuropeanCountries: Cointegration andStructural BreaksProfessor Amalia Morales Zumaquero aa University of MálagaPublished online: 10 Jul 2007.

To cite this article: Professor Amalia Morales Zumaquero (2002) Purchasing Power ParityBy sectors From Selected European Countries: Cointegration and Structural Breaks,International Economic Journal, 16:4, 107-119

To link to this article: http://dx.doi.org/10.1080/10168730200000031

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INTERNATIONAL ECONOMIC JOURNAL Volume 16, Number 4, Winter 2002

PURCHASING POWER PARITY BY SECTORS FROM SELECTED

EUROPEAN COUNTRIES:

i COINTEGRATION AND STRUCTURAL BREAKS

AMALIA MORALES ZUMAQUERO*

University of Malaga

In this paper we study the long-run Purchasing Power Parity (PPP) hypothesis by traded and non-traded sectors using cointegration techniques in the presence of structural breaks, for a set of European countries during the period 1975: 1-1995: 12. This approach is complementary to many existing approaches to investigate the PPP hypothesis. We find evidence in favor of long-run PPP hypothesis when commodity prices are used in the presence of structural breaks. This result lends support to the integration process in the European Union. [C22, F30]

1 1. INTRODUCTION

Recently, research on the long-run Purchasing Power Parity (PPP) has progressed in three directions. First, univariate techniques have been applied to long-horizon real exchange rates spanning one to two centuries. Second, tests for unit root in panel data have been used to study the PPP hypothesis. Third, the issue on structural breaks has been applied in testing the PPP hypothesis. This paper focuses on the latter.

Several recent studies have tested the long-run PPP hypothesis in the presence of structural breaks. Some authors such as Canarella, et al. (1990) reexamine the PPP hypothesis using a time-varying parameter approach. In addition, Perron and Vogelsang (1992), using the so-called additive outlier and innovational outlier models, for two real exchange rates obtain empirical evidence in favor of the PPP hypothesis. Dropsy (1996), using sequential tests by Banergee, et al. (1992), obtains significant empirical evidence of breaks for seven real exchange rates out of ten. Moreover, Wu (1997) analyzes the PPP hypothesis for eleven OECD countries using Zivot and Andrews' (1992) test. His results provide evidence in support of long-run PPP for the majority of OECD countries. Finally, Agganval,

I *I would like to express my gratitude to Consuelo Gamez, Alfonso Novales, Teodosio Perez, the participants in the Workshop on Exchange Rates (Spain, 2001), particularly to Antonio Montafies, the Editor of this Journal and two anonymous referees for their valuable comments. Special thanks to Rodrigo Peruga for excellent research assistance.

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et al. (2000) find strong evidence in favor of the PPP hypothesis in the bilateral real exchange rate between the Japanese yen and the currencies of the most important southeast Asian economies. In sum, all these papers present evidence in favor of the PPP hypothesis using aggregate price levels.

However, this is not the case in Corbae and Ouliaris (1990), Flynn and Boucher (1993), Bahmani-Oskooee (1995), among others. Corbae and Ouliaris (1990), using Perron's (1989) test, do not provide evidence in favor of the PPP hypothesis. Flynn and Boucher (1993) examine the empirical evidence on PPP for Canada and Japan relative to United State, for the fixed and flexible exchange rate eras. They compare results from the Perron (1989) and Dickey-Fuller (1981) methodologies. Their results do not support the PPP hypothesis. In addition, Bahmani-Oskooee (1995), using Perron's (1989) statistic, for 19 OECD industrial countries and the real effective exchange rate concept, finds that only five countries yielded empirical support for the PPP hypothesis. Thus, these papers do not obtain evidence in favor the PPP using aggregate price levels.

In short, the results in previous empirical literature on PPP are mixed when structural breaks are taken into account and aggregate price levels are used.

This paper differs in several dimensions from previous research. In the first place, most previous studies have analyzed the behavior of real exchange rate for major economies relative to United States. However, this paper only concentrates on analyzing the PPP hypothesis for a set of European countries for several reasons. First, there are many previous papers that tend to reject the PPP more frequently when United States dollar is the referenced currency. Second, we study the PPP hypothesis for all possible bilateral relationships and so our analysis is not conditioned to one referenced country. Third, if we find evidence in favor of the PPP hypothesis it would be evidence of integration into the European Union (EU).

In the second place, we test the PPP hypothesis with a different testing methodology than previous papers: we allow for structural breaks not only in the original variables (nominal exchange rate and international relative prices) but also in the cointegration relationships. In the original variables, we use a set of sequential unit root statistics that allow for the possibility of structural breaks. We do this because structural breaks, which are caused by changes in demand and supply conditions, occur in the course of economic growth and tend to affect the internal relative price structure. In the cointegration relationships, we use two sequential statistics to detect structural breaks under the cointegration approach. We test cointegration without structural breaks and cointegration in the presence of a single break, analyzing the cointegration over subsamples when the breaks points are isolated, and then we compare results.

In the third place, we use disaggregate price level by commodities in contrast with previous literature. One of the problems of the PPP hypothesis is that it assumes the PPP holds for all kind of goods. However, it is of great interest to differentiate between traded and non-traded goods. It is probable that the PPP

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PPP BY SECTORS FROM SELECTED EUROPEAN COUNTRIES 109

hypothesis holds more frequently for traded than for non-traded goods due to the fact that the traded good prices are affected by international competition, while the non-traded good prices will be determined by internal demand and supply factors. Thus, if we assume that traded sectors are more integrated than non-traded sectors,

I we would expect the PPP to hold more frequently in the former. Thus, our approach is complementary to the previous literature, studying the

PPP hypothesis allowing for structural breaks and using price levels by commodities.

The rest of the paper is organized as follows. Section 2 describes the econometric methodology. Section 3 presents the data set. Section 4 summarizes the empirical results. Finally, Section 5 provides some concluding remarks.

2. ECONOMETRIC METHODOLOGY

1 A. Description of the Methodology

To analyze the stochastic behavior of our data set we consider the possibility of structural breaks. We only concentrate on sequential unit root tests. From the sequential version of the ADF test usually considered in the literature (Banerjee, et al. 1992; Zivot and Andrews, 1992; Perron and Vogelsang, 1992; and Montaiies, 1996a, 1996b), we use a set of three statistics (each with its potential break point estimate): the standard t-statistic for the unit root null hypothesis, the absolute value of the t-statistic for the null hypothesis of no structural breaks and the absolute value of the t-statistic for the null hypothesis of no structural breaks, under the unit root constraint. Banerjee, et al. (1992) suggest computing "the supremum" of them.

On the other hand, for testing the PPP hypothesis, we focus on the long-run analysis1 using the next two long-run models specifications in logarithm2:

where st is the nominal exchange rate, pi is the domestic price, is the foreign I price and E,, E,' are random error terms. These two specifications allow us to

i not impose the direction of causality. However, we have made two additional

I ' ~ n analysis of the dynamic adjustment process, for the same data set of this paper, can be

seen in Morales and Peruga (2002). 2 ~ n a cointegrating setting there are no endogenous and exogenous variables. Asymptotically,

the results should be the same whether one puts one or the other variable on the left-right-side.

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110 AMALIA MORALES ZUMAQUERO 1

assumptions: the existence of a constant term ( q and q ', respectively) and that the domestic and foreign prices exhibit the same coefficient value (symmetry restriction): p in equation (1) and unity in equation (2). For a correct specification of our models, we previously test them before imposing these. In addition, we test the homogeneity restriction, /3 (P ' ) = 1 (absolute PPP).

We use the single equation estimation technique by Engle and Granger (1987) to estimate (1) and (2) for all bilateral cointegration relationships between the countries that we analyze. We are aware that Engle and Granger's (1987) methodology has been criticized relative to other tests. However, for internal coherence between the different stages of our econometric analysis we use Engle and Granger's (1987) methodology.3 In particular, we use the ordinary least square (OLS) and the fully modified (FM) estimators (Phillips and Hansen, 1990). To make sure the estimates are reasonable, after estimating the model we apply a unit root test on the residuals of the OLS regressions. In addition, for testing linear restrictions and testing the significance of individual parameter, we propose the Wald modified statistic. Moreover, this statistic allows us to test the homogeneity hypothesis P ( P ' ) = 1.

To detect structural breaks in cointegration vectors we use two statistics: the InfADF statistics (Gregory and Hansen, 1996) -with its potential break point estimator- and the MeanADF statistic (Fernandez and Peruga, 1997). These two statistics are similar to Engle and Granger's (1987) cointegration statistic. Both of them test the null hypothesis of no cointegration against the alternative hypothesis of cointegration with structural breaks.

Gregory and Hansen (1996) consider the model:

where X, is the first-order integrated vector of regressors, E, is a stationary process, I(O), and 9, is a dummy variable:

where [v] indicates the integer part of ''T" and r E (0,l) is an unknown parameter. For each possible break point in the sample, indexed by z E [. 15,351, we calculate the ADF(z) statistic, that has a Dickey-Fuller distribution, under the null hypothesis. However, when there is a structural break at an unknown date,

3 ~ e have replicated our analysis using Johansen's (1988) technique and Hansen and Johansen's (1993) instability test and the results hardly differ from the results in this paper.

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PPP BY SECTORS FROM SELECTED EUROPEAN COUNTRIES 11 1

Gregory and Hansen (1996) consider the statistic InfADF = r t r min 15..851 ADF(t), the . .

minimum of all calculated values of the ADF statistic. These authors calculate the InfADF asymptotic distribution and obtain the potential break point estimator. On the other hand, Fernandez and Peruga (1997) consider the statistic MeanADF = C ADF(t), the mean of all calculated values

it[ 15 ,851

of the ADF statistic. The simulation results of these statistics4 show that the InfADF and MeanADF

statistics exhibit a good asymptotic power. This result prevent us discriminating between cointegrated and instable cointegrated models. However, in finite samples, the InfADF statistic shows good power too (even in short samples) but the MeanADF statistic presents, in general, less power than the InfADF except for contegration alternatives. Therefore, the MeanADF exhibits better power against non-structural breaks alternativks than against structural breaks ones. This result allow us to discriminate between cointegrated and instable cointegrated models. The power of both statistics worsens when there are two structural breaks.

B. Application of the Methodology

We apply the previous methodology following the next procedure: 1) We estimate equation (1) and (2) and calculate the cointegration statistics for

all possible bilateral relationships and price indexes. 2) If ADF, InfADF and MeanADF statistics reject the null hypothesis of no

cointegration simultaneously, we will conclude that there is no evidence in favor of cointegration in the full sample. This result, together with a significant and positive parameter would be strong support for the relative PPP hypothesis. In addition, if p(P 3 = 1 we will conclude that the absolute PPP hypothesis holds.

3) If the ADF, InfADF and MeanADF do not reject the null hypothesis simultaneously we will distinguish three cases: (a) only the InfADF statistic leads to rejection the null hypothesis and the structural break point is the same in equations (1) and (2). In this case we will take that break point to analyze subsamples cointegration; (b) only the InfADF statistic rejects the null hypothesis and the structural break point is different in equations (1) and (2). In this case we will take these two break points and analyze cointegration in subsamples; (c) if neither ADF, InfADF nor MeanADF reject the null hypothesis, we will take the different break points and analyze subsample cointegration.

The presence of different break points in cases (b) and (c) could be explained by the different stochastic behavior between the relative international prices and the nominal exchange rates (the more volatile the independent variable -the nominal exchange rate- the more difficult it is to detect structural breaks). The different break points can be also evidence of multiple instability in the cointegration

4 ~ e e Fernandez and Peruga (1997).

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112 AMALIA MORALES ZUMAQUERO

relationships. In addition, in cases (b) and (c), we check whether the break points hom the unit root analysis are similar to the break points from the cointegration analysis. If so, we report the subsample with stronger evidence of cointegration.

4) If the ADF, InfADF and MeanADF do not reject the null hypothesis we will conclude that there is no evidence of cointegration: the PPP hypothesis fails.

3. THE DATA

The data used in this paper are disaggregated price indexes for Germany, Belgium, Spain, France, The Netherlands, Italy and the United Kingdom, all supplied by Eurostatistics (Eurostat). They are: food less dnnks and meals, P1; clothes, footwear including repairs, P2; rent, fuel and power, P3; household goods and service, P4; transport and communications, P6; recreation and education, P7; and other goods and services including drink and meals, P8. Initially, we consider PI, P2 and P4 traded price indexes and P3, P6, P7 and P8, non-traded price indexes.'

The disaggregate price series for Spain, supplied by Eurostat, show a definition change in 1992. We take them from the Instituto Nacional de Estadistica (INE). The definitions of the indexes are the same as the definition in Eurostat.

The series cover the period 1975: 1-1995: 12 for Belgium, 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); the period 1976: 1-1995: 12 for Spain; and 1976: 1 -1995:7 for ~ e r m a n ~ . The exchange rate series, supplied by International Financial Statistics (International Monetary Fund), are end month.

4. RESULTS

A. Testing Restrictions in the Long-Run Model

In this section we test the existence of a constant term and the symmetry restriction i11 the long-nm model specification. A significant constant term implies that it is the relative version of the PPP hypothesis that is fulfilled. In the absolute version the constant term equals zero. If the symmetry restriction holds, then the domestic and foreign prices will be exhibit the same coefficient value. In general, the results substantially support the significance of the constant terms, 9 and 9 ' in equation (1) and (2), respectively. In particular, in equation (I), the constant term 9 is significant in all bilateral relationships for all price indexes, except for the bilateral relationship Germany-Italy for the price index P6. In

'we do not use the price index P5 (medicine and health care) because there are no homogeneous series for all countries.

"or reasons of data availability, the sample size differs slightly from one country to other and ends in 1995.

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- Table 1. Cointegration Over Subsamples w

P

Pi

b,,, ADF INF MEAN SB ,L7fio,,, ADF INF M E W SB ,Be,, ADF INF MEAN SB

i Note: T h ~ s tablc exh~bits, for every b~lateral relationship, the estimated parameters W,,, and the statistics for regressions (I), upper rowr, and for (2). lower row and the break polnts (SB). F

m Critical values at 5% significance level are: for the ADF statist~c -2 920 (T=50), -2.890 (T=100), -2.880 (T=l50) and -2.873 (T=250): for the InfADF, -4.908; for the MeanADF, -3.783. Wl

Crltlcal values at 10% s~gnificance level are: for the ADb statistic 2 . 5 9 7 (T=50), -2.581 (T=100), -2.576 (T=150) and -2.572 (T=250): for the InfADF, -4.633; for the MeanADF. -3.517 2 * and * * show statistical s~gnificance at 5% and 10% significance level whlle the letter h shows that the homogene~ty hypothesis holds. The ital~c dates come from the unstable 5 cointegration analysis of the full sample. The bold dates show that we take the break point from the unit root analys~a of the or~ginal time series (from nominal exchange rate, S, or Q

international relative pnces, PIP*). s

Ger-Bel

xi 10-95.7

-2.755'

-2281

0.391'

1518'

I I I I I I I I I I I I I I I I I Ger-Spa 0.871''' -3.205' 4 . 5 ' ~ r -3.515' 81:12 Bel-Ita 0.443' -2.979' -5.442' -3.718" Ned-lta 0.688' -4.074' -4.675" -4.198' X7:X

I - 5 ( IN); ( -2 .907 ( 3 6 ( 3 . 0 5 ( _ I 0 ( 75 I d ( 0.725 1 -2.629 ( -3.825 ( -2.396 ( :::: ( W S W 7 ( 0.685' (-4.134 - 4 7 2 0 ( -3.977 1 8 1 7

0.770' -2.572" -6.686' -3.203 2.284' -3.271' -5.656' -3 055 -3.582' -4.402 -3 557" 93.1 z.2:: 1 0 6 1 -2707 1 5 . 0 5 8 1 -2.552 1 2 1 7 4 1 -3.830 1 4 . 8 8 3 1 -3.717 1 1 "":: 1 :I:: 1 -3.899 1 5.532* 1 - 3 . ~ 3 7 ~ 1 88:9

Ger-Uk 1.535' -2.635' -3.906 Spa-Ned 0.902"' -2.585" 4.613" Ita-Uk 1.956' -3.210' -5.054' -3.684- X0:6

79 8-95 7 1 6 3 2 1 - 3 . 2 1 4 . 8 :il; 1 1 7 I - I 1 0.87+84 1 4 . 4 1 :::A': 1 it': 1 7 9 1 2.243 1 3 0 1 - 4 . 4 3 1 3.198 1 81:.

-4.345

-5.144'

Bel-Spa

76 I - X Y 4

85:10

91.9

-3.625"

-3.177

-1.29 1'

-2.891'

0.749'

1.121'

Bel-Ned

SI 12-95 12

84 1-05 12

4.752"

4.729"

0.347'

0 463'

0.432'

0.760'

-3.789'

-3.170

79: 1

78:10

-3.637'

- 2 ~ "

-3.307'

-2.859"

4.137'

-3.033

4.038'

-3.338

4.803"

4.601"

-5.344'

4.486-

Fra-Ned

78 2-95 12

0.775'

0.760'

905

84.7

90:l

X9:10

-3.719'

-3.091'

Fra-lta

75 1-91 111

-3.775-

-3.939'

0 . 6 ~ 6 '

1.094'

-4.661''

-4.321

-3.667"

-3 949'

4.983'

4.740"

-4.056'

-3.200

82.4

X1:10

82:3

82:11

5 g

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a Table 2. Cointegration Over Subsamples: Summary of Results a -C

Ger-Spa

76.1-YO8

Gel.-lta Fra-Ncd

76:l-9/4 75:l-89 2

Bel-lta Fra-Ita

Ger-Fra

82:7-95:7

79:lO-95:7

Ccl--lta 1 Bel-Ita 1 Xi-d-lea

79:l-92:6 (S) 79:l-92:5(S) 79:l-92:6(S)

Spa-Uk

76: 1-85:s

Fra-Uk

75: 1-84.3

Bel-Fra

79:lO-95:12

Fra-Ita

75:l-91:ll

Bel-Spa

76: 1-89;!

Ger-Ita Fra-lta Ita-Uk

Fra-Ned

78:8-95: 12

83:l-95: 12

Ger-Bel

76:l-92.1

Ger-Ned

76:l-86:3(S)

Fra-Ned Ned-Uk

Ger-Uk

79.9-95:7

Bel-Ned

78:3-95: 12

82 I-92:h(PIP*) 76.1-86:8 79 8-95:12

Ger-lta Fra-Ned Ned-lta rn

-0 P8

l i e r - l k 1 Spa-Uk 1 Ned-1ta 1 79:9-95:7 76 1-86:3 79:l-92:6(S)

Ger-Bel Spa-Fra

76.1-90 7

Fra-Ned

85:f@Pb95.12

Note. These tables exhibit the bilateral relationships with c\,idence of cointegration over subsamples and the sample size of them. The ~ t a l ~ c dates come from the unstable

cointegration analysis of the full sample. The bold dates show that we take the break pomt from the unlt root analys~s of the original time series (from nominal exchange rate, S. or

lnternatlonal relative pnces, PIP*).

Spa-Uk Ned-lta

79:1(S)-92 10

Ned-Uk

78.9-95: 12

E Fra-Uk 2

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116 AMALIA MORALES ZUMAQUERO I

and for each price index. Table 3 presents the summarized results. 1 Table 3. Summary of Results

P1 P2 P3 P4 P6 P7 P8

C 2/20 0120 2120 1/20 1/20 0120 1/20

SC 14/20 7120 8120 7/20 12120 1 1120 9/20

NC 4/20 13/20 10120 12/20 7/20 9/20 10120

Note: This table presents the number of cointegrated relationships out of the total. C: cointegration in the full sample, SC: subsample cointegration, NC: no cointegration.

According to these results, we obtain that for the traded price index food less drinks and meals, P1, the ADF, InfADF, and MeanADF statistics simultaneously reject the null hypothesis of no cointegration only for 2 bilateral relationships in the full sample. However, when we test cointegration by subsamples, there are 14 cointegrated relationships. Thus, the evidence is much favorable to the PPP hypothesis when we consider the possibility of structural breaks.

For the traded price index clothes, footwear including repairs, P2, there is no evidence in favor of cointegration in the full sample, but when we consider structural breaks there are 7 cointegrated bilateral relationships in the subsamples.

For the non-traded price index rent, fuel and power, P3, the cointegration tests show 2 cointegrated relationships in the full sample. When we analyze cointegration with structural breaks, there are 8 subsamples cointegrated relationships. In addition, for the traded price index household goods and services, P4, there are 7 cointegrated relationships and only 1 exhibits cointegration in the full sample.

For the non-traded price index transport and communications, P6, the cointegration statistics show only 1 cointegrated bilateral relationship in the full sample. When we jointly consider cointegration and structural breaks there are 12 relationships with evidence in favor of cointegration. Moreover, for the non- traded price index recreation and education, P7, the cointegration statistics do not show evidence in favor of cointegration in the full sample. However, there are 11 subsamples with evidence in support of PPP.

Finally, for the disaggregate index of other goods and services including drinks and meals, P8, we conclude that there is evidence of 1 cointegration relationship in I the full sample. However, when we take into account the structural breaks, there are 9 cointegrated bilateral relationships in the subsamples.

In general, the estimated parameters are positive and significant and the I

homogeneity hypothesis does not hold. Then, the evidence supports the relative

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PPP BY SECTORS FROM SELECTED EUROPEAN COUNTRIES 117

PPP hypothesis. In summary, these results suggest strong evidence in favor of the long-run PPP

I

I hypothesis when we use commodity prices and the presence of structural breaks is taken into account. Thus, these results clarify previous mixed evidence on the ' PPP hypothesis. In particular, these results differ drastically form previous results in which the PPP fails when an aggregate price level is used (Flynn and Boucher, 1993; Bahmani-Oskooee, 1995). In addition, we have obtained much stronger evidence in favor of the PPP hypothesis for the price index P 1, which can be considered as the most tradable consumer price index. However, the average number of cointegrated relationships for traded price indexes is 10 and for non- traded price indexes it is 11. Thus, in general the evidence in favor of the PPP hypothesis for traded sectors is no more favorable than for non-traded sectors. This results can be explained because many tradables contain non-tradable components in the form of retailing services, so that PPP may not hold for these tradable goods even in the long-run.

With regard to structural instability, this tends to be concentrated in 1979, in the 1980s, and early 1990s. These three dates have a clear economic interpretation. The first of these reflects the oil crises. The second date is related to the frequent currency reali nments at the onset of the European Monetary System (EMS) in 198 1-1987:' The third of these is consistent with the massive speculative attacks in 1992-1993 in the EMS: all currencies were appreciated except for the lira which was depreciated. In addition, Italy and UK left the Exchange Rate Mechanism in September 1993 and the subsequent widening of the permitted bands of exchange rate fluctuated to +15% for the remaining members.

Finally, the evidence in favor of cointegration is weak in the bilateral relationships with relative prices when these are I(2). If we exclude them, the results hardly differ from the previous ones.

5. CONCLUDING REMARKS

In this paper we have tested the long-run PPP hypothesis by sectors using cointegration techniques in the presence of structural breaks for a set of European countries, during the period 1975: 1 - 1995: 12. Our results have a central message: we find evidence in favor of the long-run PPP hypothesis when commodity prices are used. This result clarifies the previous mixed results on the PPP hypothesis. However, we are not able to find more evidence in favor of the PPP for traded sectors than for non-traded sectors. This could be explained because many goods thought of as being highly traded in fact contain significant non-traded components.

On the other hand, these favorable results for the PPP hypothesis lend support

I21n October 1981, February 1982, March 1983, April 1986, and January 1987.

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to the integration process for our set of European countries. This is because I European countries have experienced strong trade linkages and exchange rate stability among themselves. Factors such as relatively lower transport costs, the gradual abolition of trade barriers, and institutional agreements such as the EMS are thought to have facilitated commodity arbitrage among the European countries, creating a favorable environment for PPP.

1 I I

REFERENCES

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Mailing Address: Professor Amalia Morales Zumaquero , Department o f Economics, Campus de El Ejido s/n University of Malaga (Spain), Tel ,' 34-95- 2134146, Fax .' 34-95-2131299, E-mail: amalia@uma.es

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