the behaviour of relative prices in the european union: a sectoral analysis

European Economic Review 48 (2004) 1257–1286www.elsevier.com/locate/econbase

The behaviour of relative prices in theEuropean Union: A sectoral analysis

Natalie Chena;b;c;∗aDepartment of Economics, London Business School, Regent’s Park, London NW1 4SA, UK

bECARES, Universit%e Libre de Bruxelles, 50 av. Roosevelt, 1050 Brussels, BelgiumcCEPR, 90-98 Goswell Road, London EC1V 7RR, UK

Accepted 25 April 2003

Abstract

Using multivariate unit root test methods, this paper investigates the Purchasing PowerParity (PPP) hypothesis at the sectoral level across six European countries over the last 17years. Evidence of mean reversion towards PPP is found for the relative prices of some sectorsand countries. Mean reversion in relative prices is explained by cross-country and cross-sectoralcharacteristics such as the distance between countries, nominal exchange rate volatility, di1er-ences in GDP per capita, non-tari1 barriers, research and development, advertising, industrialconcentration and tradeability of the products.c© 2003 Elsevier B.V. All rights reserved.

JEL classi3cation: C23; F31; F41

Keywords: PPP; LOOP; Multivariate unit root tests; Persistence; Mean reversion

1. Introduction

The comparison of prices across countries is one of several possible ways of in-vestigating the extent of market integration. The ;nding that prices of similar goods,expressed in a common currency, fail to equalize between locations, is generally con-sidered as an indication that the markets are not perfectly integrated.Various factors are usually identi;ed as preventing prices of similar products to

be equal across countries. Among these are the geographical separation of markets,

∗ Corresponding author. Department of Economics, London Business School, Regent’s Park, London NW14SA, UK. Tel.: +44-20-7262-5050x3395; fax: +44-20-7402-0718.

E-mail address: [email protected] (N. Chen).URL: http://www.london.edu/

0014-2921/$ - see front matter c© 2003 Elsevier B.V. All rights reserved.doi:10.1016/S0014-2921(03)00055-2

mailto:[email protected]

http://www.london.edu/

1258 N. Chen / European Economic Review 48 (2004) 1257–1286

and di1erences in consumer tastes or in product quality. Countries are more likely totrade with neighbours because transportation costs are lower, thus facilitating arbitrage,but crossing borders may become expensive due to the existence of tari1s and traderestrictions. However, arbitrage, which is expected to favour price convergence betweenlocations, is only possible if consumers are both willing and able to transfer theirdemand between suppliers of di1erent countries. Ability to engage in arbitrage is mainlya function of cost and the existence of regulatory barriers, whereas the willingness toengage in arbitrage depends upon the preferences of consumers and the perceivedquality of the products.As a consequence of these trading frictions, prices usually tend to be sticky in

local currencies. In that case, changes in nominal exchange rates play a role sincea highly volatile nominal exchange rate between two countries will produce highlyvolatile relative prices of similar goods across these countries. Also, the discriminatorypricing behaviour of ;rms with market power is another potential source of pricedispersion.The European Union (EU) is a case of particular interest since price di1erentials

are usually expected to be small between its member states due to two factors. Firstly,these countries are located close to each other and have succeeded in dismantling manyrestrictions on trade, allowing arbitrage to become more eHcient; the situation has beenfurther reinforced with the implementation of the Single Market Programme (SMP),launched in the mid-1980s.Secondly, since March 1979, several EU countries attempted to stabilize their ex-

change rates by participating in the Exchange Rate Mechanism (ERM) of the EuropeanMonetary System (EMS). Under this system, nominal exchange rates remained ;xedwithin a narrow band, but with potential for periodic adjustment or realignment. Therecent introduction of a common currency, the euro, is expected to increase price trans-parency, and should therefore further inJuence the behaviour of cross-country prices.The comparison of prices across borders should become easier, allowing for lowerprice dispersion between countries.On the whole, the SMP, through the removal of non-tari1 barriers, and the intro-

duction of the euro, should decrease the cost of cross-border trade within the EU andhence facilitate arbitrage activities.Focusing on six EU countries, our analysis is based on output price indices, disag-

gregated at the sectoral level, between January 1981 and December 1997. It addressesthree key questions: What is the extent of market integration among these Europeancountries? Are there any signi;cant di1erences in the behaviour of prices across sec-tors? What is the relative importance of various factors in explaining the behaviour ofprices across countries and sectors?The analysis is undertaken in two stages. Firstly, we investigate the behaviour of

price indices across sectors and countries. The failure of the Law Of One Price (LOOP)and Purchasing Power Parity (PPP) is usually recognized as evidence that markets arenot completely integrated. One way to test the empirical validity of these conceptsclosely relates to investigating the presence of unit roots in relative prices. If theunit root hypothesis is rejected, relative prices are mean reverting, and PPP is saidto hold in the long-run. Drawing on the recent literature on PPP, unit root tests are

N. Chen / European Economic Review 48 (2004) 1257–1286 1259

implemented using panel data, taking into account the presence of serial and cross-sectional correlations between relative price series. In addition, using disaggregateddata at the sectoral level and considering all possible country pairs in the sample, thepaper estimates di1erent speeds of mean reversion across sectors and countries.The second stage uses the results from the multivariate unit root estimations to in-

vestigate the relative importance of various factors which may explain di1erences inmean reversion across sectors and countries. The analysis includes country type vari-ables such as nominal exchange rate volatility, the geographical separation of marketsand di1erences in GDP per capita, as well as sectoral characteristics such as the ex-tent of vertical di1erentiation, the degree of industrial concentration, the existence ofnon-tari1 barriers and the tradeability of the products.The paper is organized as follows: Section 2 brieJy reviews the basic concepts

of the LOOP and PPP, and some of the empirical results obtained in this researcharea. Section 3 describes the data and provides summary statistics. The econometricmethodology implemented to test for unit roots in panel data is formalized in Section 4,which also reports the results. Section 5 examines the importance of various elementsin explaining mean reversion in relative prices across sectors and countries. Section 6concludes.

2. Framework

The main concept used in the literature to analyse the price behaviour of identicalgoods in di1erent markets is the LOOP. The absolute version of the LOOP states that, ifmarkets are perfectly integrated, identical goods should sell at the same price (expressedin common currency) in di1erent countries. This concept relies upon a simple arbitrageargument which suggests that, abstracting from tari1s and transportation costs, tradein goods should allow prices, expressed in a common currency, to equalize acrosscountries.Empirical studies of the LOOP, and of PPP which is a generalization of the LOOP

to national, aggregate price levels, 1 are however subject to a number of data prob-lems. Firstly, it is usually impossible to select identical goods across countries: manyitems produced in one country do not have near-perfect substitutes in other countries.Secondly, aggregate price indices, such as consumer or wholesale price indices, areconceptually similar across countries, but may nevertheless be calculated di1erently. Inaddition, when looking at time series there is the problem of introducing new goodsin the basket, which implies changing the relative weights of the components of thebasket. Finally, since the data generally available are in the form of price indices rel-ative to a base-year, 2 nothing can be inferred about the validity of the LOOP or ofthe PPP for that particular year.

1 For a recent survey of the literature, see Froot and Rogo1 (1995) and Rogo1 (1996).2 Crucini et al. (2000), Rogers (2001) and Haskel and Wolf (2001) are among the few papers which use

actual price levels of disaggregated consumer goods.


As a consequence, the bulk of the empirical literature focuses on testing the relative,rather than the absolute, version of the LOOP or PPP because it allows for a constantprice di1erential across countries. Denoting by pt and p∗

t the (logarithm of) domesticand foreign aggregate price level at time t and by et the (logarithm of) domestic priceof foreign currency (nominal exchange rate), relative PPP requires the rate of growth inthe exchange rate to compensate the di1erential between the rates of growth in prices:

Mpt =Mp∗t +Met ; (1)

where M is the di1erence operator.The starting point of most empirical studies is the real exchange rate, which is the

nominal exchange rate deJated by the ratio of national prices. The (logarithm of) realexchange rate, denoted qt , is:

qt = p∗t + et − pt (2)

and is a measure of the deviations from PPP. It is well-known that short-run deviationsfrom PPP are usually large and volatile. Therefore, recent studies investigate the validityof this concept in the long-run. One way to test for long-run – relative – PPP isto determine whether the hypothesis of a unit root in the real exchange rate qt canbe rejected. Univariate unit root methods rely on Dickey–Fuller tests, based on theregression:

Mqt = �+ �qt−1 + �t ; (3)

where � and � are parameters and �t is a disturbance term. The null hypothesis, �=0,implies that qt contains a unit root (the deviations from PPP are permanent), whereasthe alternative, �¡ 0, indicates that there is mean reversion in qt and hence that PPPholds in the long-run (the deviations from PPP are temporary, so there is a tendencyfor the real exchange rate to revert to its mean value). Under the alternative, � canbe interpreted as the rate of decay of deviations from PPP per time period, and allowsto calculate the corresponding half-life which represents the expected number of timeperiods for these deviations to decay by 50%. The closer � is to zero, the longer theestimated half-life of a shock. Consensus estimates put this half-life between three and;ve years among industrialized countries, implying a slow speed of reversion (a strongpersistence) of relative prices.A large body of the early literature was unable to ;nd evidence against the unit root

hypothesis. This is because unit root tests are characterized by low statistical power toreject the null hypothesis in small samples, making it diHcult to distinguish betweena unit root and a stationary series mean reverting very slowly. Recently, some studieshave tried to circumvent the problem by looking at very long horizon data sets, butthis approach is often criticized because it neglects the e1ects of a possible structuralchange in real exchange rates between ;xed (before the Bretton Woods collapse) andJoating rate periods. Engel (2000) also argues that when a random variable evolvesaccording to the sum of two processes (a stationary but persistent component and anon-stationary component), unit root tests are incorrectly sized if implemented over along horizon.


Another way to increase the power of unit root tests is to introduce cross-sectionvariation in the data, involving the use of panel samples in which the real exchangerates of various countries are all computed with respect to a benchmark country. SinceLevin and Lin (1992) ;rst introduced unit root tests applicable to panel data under theassumption of i.i.d. disturbances, there has been an increasing interest in testing forlong-run PPP using panel data methods. 3 Drawing on the work of Abuaf and Jorion(1990), O’Connell (1998) however shows that the limiting distributions derived byLevin and Lin (1992) are not appropriate because they ignore the additional informationwhich is contained in the contemporaneous correlations between real exchange rates.Indeed, in panel samples, real exchange rates are correlated by construction becausethey share two common components: the nominal exchange rate and the price indexof the benchmark country. Generalizing the Levin and Lin (1992) model to controlfor contemporaneous correlations in the panel, O’Connell (1998) shows that it is stillpossible to implement powerful panel unit root tests. Flores et al. (1999) lend supportto the utility of exploiting cross-correlations in multivariate tests, and also demonstratethat power can be further increased by allowing the mean reversion coeHcient to di1eracross countries in the panel. Papell (1997) argues that ignoring serial correlation inreal exchange rates may also distort the results.Another strand of the literature seeks to explain deviations from the LOOP. Using

the price indices of disaggregated consumer goods in various countries and cities, Engeland Rogers (1996, 1998, 2000, 2001) show that nominal exchange rate volatility has agreat deal of power in explaining the failures of the LOOP, reJecting the importance ofnominal price stickiness. Distance (which is a proxy for the cost of arbitrage activities)also contributes to price dispersion. One of their main ;ndings is the role of the borderas an additional contributor to cross-country price dispersion: maintaining both distanceand the nominal exchange rate constant, price di1erentials appear to be stronger betweentwo cities when they are separated by a national border (Parsley and Wei, 1995, 1996,2000; Crucini et al., 2000; Papell and Theodoridis, 2001).Other researchers have contributed to a better understanding of the sources of per-

sistence in the deviations from PPP. Convergence towards PPP is shown to be fasterbetween locations that are closer to each other (Campa and Wolf, 1997; Cecchettiet al., 2000). Campa and Wolf (1997) also show that a larger market size acceleratesthe rate of PPP reversion, but surprisingly, they also ;nd that greater bilateral tradeleads to slower reversion, contradicting the goods-arbitrage based view of long-run PPP.This result is however not isolated since Cheung et al. (2001) report that the more openan economy is to international trade, the more persistent is its real exchange rate. Theseauthors also highlight that nominal exchange rate volatility, as well as an imperfectly

3 Among others, Abuaf and Jorion (1990), Parsley and Wei (1995), Frankel and Rose (1996), Oh (1996),Jorion and Sweeney (1996), Cumby (1996), Papell (1997), Taylor and Sarno (1998), Wu and Wu (1998),Canzoneri et al. (1999), Flores et al. (1999), Cecchetti et al. (2000), Fleissig and Strauss (2000), Papelland Theodoridis (2001) and Cheung et al. (2001) ;nd evidence of PPP whereas Engel et al. (1997) andO’Connell (1998) do not.


competitive market structure, play a signi;cant role in explaining the persistence ofsectoral PPP deviations. See also Cheung and Lai (2000).

3. Data and descriptive statistics

Researchers are faced with a dilemma concerning the price index used in their em-pirical work. Consumer price indices usually contain a non-traded goods componentbecause of retailing services (shipping costs, insurance during the transport, taxes, dis-tribution, etc). Some researchers argue that consumer indices are appropriate becausethey include the prices of goods which are relevant to the typical consumer. However,it is also thought that the existence of a non-traded component may explain the frequentrejection of the PPP hypothesis, so other researchers prefer to use output or wholesaleprice indices, which cover a higher proportion of tradeable goods.The data used in this study were obtained from Eurostat, the Statistical OHce of

the European Commission. In order to minimize the role of non-traded components,and hence to abstract from the Balassa–Samuelson e1ect, domestic output price indices(for manufacturing industries), in ecus, are chosen for the analysis. Price indices aredisaggregated at the 3-digit Nace rev.1 level 4 for most European countries betweenJanuary 1981 and December 1997, giving 204 monthly observations. All price indicesare equal to 100 in June 1995. Monthly bilateral exchange rates are end of periodvalues.We exclude from the analysis countries with an insuHcient number of observations.

The data for six remaining countries, Germany, Belgium, France, Italy, Spain and theNetherlands, allow to construct a balanced panel sample for 17 sectors.For a given month t and a given sector k, relative prices, denoted qij;k; t , are computed

as the (logarithm of) ratio of the price index pi;k; t of country i to the price index pj;k; t

of country j (i �= j). That is, qij;k; t = ln(pi;k; t) − ln(pj;k; t), where pi;k; t and pj;k; t areboth expressed in ecus.Table 1 contains summary statistics. We measure volatility by the standard deviation

of one-month changes of a series between February 1981 and December 1997. Thetop line of the table reports, for all country pairs (with six countries, there are 15di1erent country pairs), the volatility of nominal exchange rates, volij = std(Mlneij; t)where eij; t is the bilateral exchange rate between countries i and j. On the whole,nominal exchange rates do not appear to be strongly volatile. The lowest volatilitiesover the period are obtained between Germany, the Netherlands, France and Belgium,with Germany and the Netherlands displaying the lowest one (equal to 0.296%). Thestandard deviations of the nominal exchange rates for Spain, and then for Italy (withrespect to other countries), are somewhat higher, with the highest one being obtainedbetween Spain and Italy (equal to 1.97%). However, in contrast to Germany, France,Belgium and the Netherlands, which participated in the ERM during the whole periodunder consideration, Spain only joined the ERM in June 1989 and Italy’s participationwas suspended in September 1992.

4 Nace rev.1 is the General Industrial Classi;cation of Economic Activities within the EU.

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Table 1Volatility (%) of nominal exchange rates and of relative prices across sectors and countries and distance between locations

Country pair

Sector FR–GER BE–GER IT–GER SP–GER NL–GER BE–FR IT–FR SP–FR NL–FR IT–BE SP–BE NL–BE SP–IT NL–IT SP–NL

Nominal exchange rate 0.896 0.730 1.840 1.804 0.296 0.921 1.814 1.810 0.879 1.892 1.797 0.721 1.970 1.858 1.763Whole manufacturing 0.812 0.787 1.618 1.413 0.666 0.885 1.508 1.379 0.929 1.617 1.426 0.854 1.582 1.663 1.445Textiles (17.4) 1.09 1.31 1.83 1.61 0.56 1.47 1.88 1.71 1.14 2.19 1.89 1.43 1.82 1.93 1.65Footwear (19.3) 1.38 1.52 1.81 1.56 0.69 1.90 2.18 1.78 1.52 2.18 1.90 1.66 1.88 1.88 1.60Carpentry (20.3) 1.04 1.05 1.80 1.79 0.63 1.14 1.80 1.80 1.08 1.99 1.94 1.15 1.94 1.75 1.80Wooden containers (20.4) 1.24 1.69 1.80 1.78 0.82 1.89 1.71 1.74 1.31 2.34 2.24 1.70 1.94 1.85 1.80Paper (21.1) 0.96 1.31 1.95 2.16 0.97 1.44 1.78 2.05 1.20 2.15 2.47 1.53 2.38 2.06 2.22Articles of paper (21.2) 1.01 1.17 1.72 1.67 0.56 1.34 1.79 1.72 1.10 1.89 1.89 1.23 1.89 1.76 1.64Chemicals (24.1) 1.31 1.03 1.96 1.65 1.32 1.37 2.07 1.85 1.59 2.22 1.76 1.48 2.04 2.28 1.88Paints (24.3) 1.40 2.30 1.91 2.03 1.13 2.19 1.79 1.88 1.18 2.70 2.55 2.17 1.93 1.88 1.80Detergents (24.5) 1.15 1.10 1.77 1.67 0.71 1.31 1.76 1.65 1.07 1.83 1.65 1.00 1.76 1.76 1.52Rubber (25.1) 1.29 1.79 1.99 2.01 1.14 1.64 1.76 1.78 1.07 1.96 2.18 1.41 1.90 1.74 1.79Plastic (25.2) 1.13 1.10 1.81 1.78 0.96 1.14 1.66 1.66 1.09 1.67 1.59 0.90 1.73 1.75 1.65Glass (26.1) 1.19 0.97 1.99 1.69 0.92 1.21 1.94 1.73 1.37 1.96 1.82 1.15 2.03 2.09 1.91Bricks (26.4) 1.10 1.74 1.89 1.75 1.30 1.82 1.88 1.79 1.55 2.37 2.16 1.93 2.00 2.27 2.05Cement (26.5) 1.20 1.58 2.16 2.04 0.91 1.78 2.29 2.20 1.29 2.34 2.33 1.50 2.43 2.14 1.98Articles of cement (26.6) 1.03 0.95 1.85 1.65 0.63 1.24 1.83 1.66 1.00 1.95 1.69 1.07 1.80 1.86 1.67Metals (27.4) 1.40 4.00 2.23 2.36 2.02 4.07 2.07 2.21 1.89 4.50 4.47 4.22 2.82 2.11 2.56Computers (30.0) 3.64 1.14 2.33 2.28 1.56 3.68 3.93 4.06 3.77 2.56 2.16 1.77 2.94 2.83 2.51

Distance (km) 480 319 959 1448 362 262 1108 1054 428 1173 1316 174 1365 1294 1482

Notes: Volatility is computed as the standard deviation of one-month changes of a series between February 1981 and December 1997. The top row of the tablegives the volatility of nominal exchange rates, that is std(Mln eij; t) where eij; t is the bilateral exchange rate between countries i and j. Other column entries give,for each country pair ij, the volatility of relative prices for each sector k, std(Mqij;k; t). The last row reports, for each country pair, the distance (in kilometres)between the economic centres of each country (Germany (GER), Frankfurt; France (FR), Paris; Belgium (BE), Brussels; Netherlands (NL), Amsterdam; Italy(IT), Rome; Spain (SP), Madrid).


The second line reports, for all location pairs, the volatility of relative prices forthe whole manufacturing sector. There appears to be a strong correlation between thestandard deviation of nominal exchange rates and the standard deviation of this realexchange rate (the sample correlation is equal to 0.98), a ;nding clearly consistentwith stickiness in nominal prices.The next rows contain the volatility, over the same period, of relative prices qij;k; t for

all sectors and country pairs, that is std(Mqij;k; t). Despite the large di1erences in thedegree of volatility of relative prices across sectors, nominal exchange rate volatilityagain appears to account for some of the behaviour of relative prices across countries.For instance, whatever the sector considered, relative prices are systematically morevolatile between Spain and the Netherlands than between the Netherlands and Germany.Besides, the relative prices for some particular sectors, whatever the country pair

considered, are systematically more volatile compared to other ones (compare for in-stance textiles (17.4) and computers (30.0)). This is an indication that not only arecountry type factors required to explain the behaviour of prices, but that the role ofsectoral characteristics is also important.Some of the change in nominal exchange rates over time is, in general, due to di1er-

ing inJation rates between countries. Accordingly, one may expect nominal exchangerate volatility to be higher than real exchange rate volatility (and higher than sectoralreal exchange rate volatilities as well). However, note that for some country pairs,the volatility reported for many sectors is often greater than the volatility of both thenominal exchange rate and of relative prices for the whole manufacturing sector (thisresult is however not isolated, see Engel and Rogers, 1998). One possible explanationcould be a measurement error that exaggerates the volatility of relative prices at thesectoral level (because the baskets of goods compared across countries are not exactlythe same, see Knetter, 1998). Another possibility could be that some individual volatil-ities at the sectoral level are greater than the volatility of the real exchange rate, butcompensate each other in the aggregate.The last row of the table reports, for each country pair, the distance (in kilome-

tres) between the economic centres of each country. 5 The country pairs that havethe lowest volatilities are in general closer. This indicates that distance, which proxiesfor unobservable transportation costs, probably contributes to price dispersion acrosscountries.Finally, from a dynamic perspective, Fig. 1 plots, for each country pair and all

sectors, the volatility of relative prices over three di1erent sub-periods: February 1981–January 1987, March 1987–August 1992 and October 1992–December 1997. The sub-periods roughly correspond to the di1erent phases of the EMS. The so-called Hard-EMSperiod, which witnessed no re-alignment of oHcial parities, began in 1987 after someturbulence in foreign exchange markets during the early 1980s. This calm in foreignexchange markets was however broken in September 1992 when Italy’s participationfrom the ERM was suspended.

5 Economic centres are Frankfurt (Germany), Paris (France), Brussels (Belgium), Amsterdam (theNetherlands), Rome (Italy) and Madrid (Spain).


In most cases, volatility has decreased between the two ;rst sub-periods, providingevidence that the markets have, on the whole, become more integrated during theHard-EMS period. During the third sub-period, volatility has generally increased as

0.0

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1.0

1.5

2.0

2.5

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4.0

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(a) Netherlands−Germany

(c) Netherlands−France

(e) Belgium−France (f) France−Germany

(b) Netherlands−Belgium

(d) Belgium−Germany

Fig. 1. Volatility of relative prices, for each country pair and all sectors, between February 1981–January1987, March 1987–August 1992 and October 1992–December 1997: (a) Netherlands–Germany; (b) Nether-lands–Belgium; (c) Netherlands–France; (d) Belgium–Germany; (e) Belgium–France; (f) France–Germany;(g) Spain–France; (h) Spain–Germany; (i) Spain–Netherlands; (j) Spain–Belgium; (k) Spain–Italy;(l) Italy–France; (m) Italy–Belgium; (n) Netherlands–Italy; (o) Italy–Germany.


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(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

2.6

2.8

3.0

(17.4

)

(19.3

)

(20.3

)

(20.4

)

(21.1

)

(21.2

)

(24.1

)

(24.3

)

(24.5

)

(25.1

)

(25.2

)

(26.1

)

(26.4

)

(26.5

)

(26.6

)

(27.4

)

(30.0

)

sectors

vola

tility

(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

1.0

1.5

2.0

2.5

3.0

3.5

(17.4

)

(19.3

)

(20.3

)

(20.4

)

(21.1

)

(21.2

)

(24.1

)

(24.3

)

(24.5

)

(25.1

)

(25.2

)

(26.1

)

(26.4

)

(26.5

)

(26.6

)

(27.4

)

(30.0

)

vola

tility

(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

(17.4

)

(19.3

)

(20.3

)

(20.4

)

(21.1

)

(21.2

)

(24.1

)

(24.3

)

(24.5

)

(25.1

)

(25.2

)

(26.1

)

(26.4

)

(26.5

)

(26.6

)

(27.4

)

(30.0

)

sectorssectors

vola

tility

(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

(17.4

)

(19.3

)

(20.3

)

(20.4

)

(21.1

)

(21.2

)

(24.1

)

(24.3

)

(24.5

)

(25.1

)

(25.2

)

(26.1

)

(26.4

)

(26.5

)

(26.6

)

(27.4

)

(30.0

)

sectors

vola

tility

(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

(17.4

)

(19.3

)

(20.3

)

(20.4

)

(21.1

)

(21.2

)

(24.1

)

(24.3

)

(24.5

)

(25.1

)

(25.2

)

(26.1

)

(26.4

)

(26.5

)

(26.6

)

(27.4

)

(30.0

)

sectors

vola

tility

(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

(g) Spain−France (h) Spain−Germany

(i) Spain−Netherlands (j) Spain−Belgium

(k) Spain−Italy (l) Italy−France

Fig. 1. (continued).


0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

5.5

6.0

(17.4

)

(19.3

)

(20.3

)

(20.4

)

(21.1

)

(21.2

)

(24.1

)

(24.3

)

(24.5

)

(25.1

)

(25.2

)

(26.1

)

(26.4

)

(26.5

)

(26.6

)

(27.4

)

(30.0

)

sectors

vola

tility

(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

(17.4

)

(19.3

)

(20.3

)

(20.4

)

(21.1

)

(21.2

)

(24.1

)

(24.3

)

(24.5

)

(25.1

)

(25.2

)

(26.1

)

(26.4

)

(26.5

)

(26.6

)

(27.4

)

(30.0

)

sectors

vola

tility

(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

(17.

4)

(19.

3)

(20.

3)

(20.

4)

(21.

1)

(21.

2)

(24.

1)

(24.

3)

(24.

5)

(25.

1)

(25.

2)

(26.

1)

(26.

4)

(26.

5)

(26.

6)

(27.

4)

(30.

0)

sectors

vola

tili

ty (

%)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

(m) Italy−Belgium

(o) Italy−Germany

(n) Netherlands−Italy

Fig. 1. (continued).

compared to the Hard-EMS period, but remains lower than during the ;rst sub-period(before 1987). In contrast, in the cases where Italy is involved, volatility is, in general,highest during the third sub-period (Figs. 1(k)–(o)). The suspension of the Italianlira from the ERM in September 1992 probably explains this increase in volatility.Fig. 2 again distinguishes Italy from the other countries by plotting, for each countrypair, the volatility of relative prices for the whole manufacturing sector over the threesub-periods.

4. Testing for unit roots

The ;rst part of this section describes the econometric methodology implemented totest for unit roots in panel samples of relative prices computed for various country pairsand sectors. In most studies, the joint null hypothesis states that all series considered inthe panel are unit root processes. Consequently, non rejection of the null does not tellanything about whether some of these series are in fact stationary. In this paper, thetests allow the speed of mean reversion to di1er across industries and country pairs,which permits us to determine whether the unit root hypothesis can be separately


0.3

0.5

0.8

1.0

1.3

1.5

1.8

2.0

2.3

2.5

2.8

NL-GER

NL-BE

NL-FR

BE-GER

BE-FR

FR-GER

SP-FR

SP-GER

SP-NL

SP-BE

SP-ITIT

-FR

IT-B

ENL-IT

IT-G

ER

country pairs

vola

tility

(%

)

1981:2-1987:1

1987:3-1992:8

1992:10-1997:12

Fig. 2. Volatility of relative prices, for the whole manufacturing sector and all country pairs, betweenFebruary 1981–January 1987, March 1987–August 1992 and October 1992–December 1997. Abbreviationsfor the countries are as follows: Germany, GER; France, FR; Belgium, BE; Netherlands, NL; Italy, IT;Spain, SP.

rejected for each of the series. These tests are thus not panel unit root tests in theconventional sense (where the speed of mean reversion is restricted to being the samefor all series in the panel), but are more akin to a Seemingly Unrelated Regressions(SUR) approach. The existence of both serial and contemporaneous correlations iscarefully taken into account by the procedure. The results are examined in the secondpart of this section.

4.1. Methodology

Most multivariate PPP studies compute relative prices with respect to a benchmarkcountry (exceptions are Engel et al. 1997; O’Connell, 1998). Extending the sample toall possible country pairs allows a much larger country dimension. 6 But, as shown byEngel et al. (1997), when including all country pairs and estimating di1erent speeds

6 Many studies ;nd that PPP holds better when the German mark (or more generally, European currencies),rather than the US dollar, is used as the benchmark (e.g. Parsley and Wei, 1995; Jorion and Sweeney, 1996;Papell, 1997; Canzoneri et al. 1999; Papell and Theodoridis, 2001; Wu and Wu, 1998). This problem isavoided here since all possible country pairs are considered.


of reversion, there is no simple univariate representation for each of the relative priceseries. In particular, it can be shown that the right way to model the vector of rel-ative prices is not to model each element as a function of lags only of itself, butto write each variable as a function of its own lags and the lags of the other vari-ables. However, in this case, the notions of unit roots and speed of convergence areambiguous.Since we do not constrain the mean reversion coeHcients to be the same across

series, the only cross-equation restriction used here is the contemporaneous cross-correlation of the residuals. The cost of such joint estimation is that a huge variance-covariance matrix has to be estimated. With 15 country pairs and 17 sectors, therewould be 255 equations and 255( (255−1)

2 ) = 32385 o1-diagonal elements to estimate.The diHculty of getting precise estimates of these many terms clearly outweighs thepotential gain in power to be obtained from pooling.In this paper, the tests are therefore implemented over country pair speci;c samples,

in which sectors are all pooled together. Each sample only has 17 series (17 sectors),and the cross-correlations for a given country pair are higher.The following econometric procedure is applied to each of the 15 country pair

samples, each including 17 sectors. A multivariate unit root test, which allows fordi1erent speeds of mean reversion for each of the relative price series, isspeci;ed as

Mqk; t = �k + �kqk; t−1 + �k; t (4)

where, for each of the 15 country pair samples, qk; t is the relative price of sector k,k = 1; : : : ; K , t = 1; : : : ; T where K and T , respectively, denote the total number ofsectors (17) and time periods (203), and �k; t is a disturbance term. For simplicity, thecountry pair indices ij are now omitted. The sector speci;c constants �k are includedin the regression because price indices, rather than absolute price levels, are used tocarry out the test. For k = 1; : : : ; K and t = 1; : : : ; T , the null (the relative price seriesqk; t is a unit root process) and alternative hypotheses are formalized as:

H0:Mqk; t = �k; t : (5)

H1:Mqk; t = �k + �kqk; t−1 + �k; t : (6)

In (6), �k is the mean reversion coeHcient for sector k and �k ¡ 0.As already mentioned, it is important to control for the existence of contemporaneous

correlation within each panel. The exploitation of the information contained in thesecorrelations (together with the estimation of di1erent speeds of mean reversion) shouldtherefore allow to increase the power of the test. Consequently, SUR are implementedfor estimation.In order to control for serial correlation in the disturbance terms under the null, each

of the �k; t in the panel are ;rst ;tted by autoregressive AR(p) models, where p, theoptimal number of lags, is selected using the Schwartz criterion. That is:

�k; t = �1; k �k; t−1 + · · ·+ �p;k�k; t−p + �k; t (7)


Table 2Multivariate unit root tests. Mean reversion coeHcients and p-values in parentheses

Country pair

Sector FR–GER BE–GER IT–GER SP–GER NL–GER BE–FR IT–FR

Textiles (17.4) −0:028 −0:017 −0:026 −0:009 −0:046 −0:053 −0:082(0:042) (0:679) (0:410) (0:778) (0:114) (0:073) (0:031)

Footwear (19.3) −0:006 −0:014 −0:005 −0:054 −0:064 −0:005 −0:017(0:742) (0:737) (0:900) (0:151) (0:055) (0:848) (0:495)

Carpentry (20.3) −0:065 −0:022 −0:012 −0:003 −0:024 −0:085 −0:025(0:045) (0:261) (0:733) (0:913) (0:333) (0:018) (0:507)

Wooden containers (20.4) −0:009 −0:036 −0:013 −0:008 −0:047 −0:083 −0:067(0:836) (0:315) (0:743) (0:830) (0:209) (0:038) (0:090)

Paper (21.1) −0:017 −0:034 −0:034 −0:040 −0:001 −0:084 −0:054(0:708) (0:472) (0:449) (0:286) (0:949) (0:042) (0:153)

Articles of paper (21.2) −0:019 −0:049 −0:008 −0:008 −0:012 −0:076 −0:072(0:706) (0:235) (0:859) (0:753) (0:758) (0:049) (0:062)

Chemicals (24.1) −0:025 −0:026 −0:013 −0:020 −0:117c −0:078 −0:121(0:578) (0:414) (0:819) (0:625) (0:005) (0:033) (0:011)

Paints (24.3) −0:079c −0:025 −0:098 −0:063 −0:014 −0:021 −0:088(0:005) (0:585) (0:036) (0:102) (0:745) (0:632) (0:033)

Detergents (24.5) −0:015 −0:068 −0:056 −0:013 −0:031 −0:042 0:001(0:685) (0:094) (0:037) (0:737) (0:384) (0:246) (0:960)

Rubber (25.1) −0:051 −0:056b 0:000 −0:013 −0:094c −0:104b 0:005(0:215) (0:001) (0:957) (0:764) (0:005) (0:002) (0:988)

Plastic (25.2) −0:014 −0:029 −0:027 −0:007 −0:080 −0:057 −0:039(0:703) (0:501) (0:504) (0:847) (0:016) (0:124) (0:248)

Glass (26.1) −0:067 −0:067 −0:047 0:000 −0:007 −0:092b −0:057(0:115) (0:164) (0:320) (0:958) (0:845) (0:002) (0:125)

Bricks (26.4) −0:012 −0:046 −0:013 0:000 0:006 −0:026 0:000(0:813) (0:071) (0:610) (0:957) (0:992) (0:244) (0:951)

Cement (26.5) −0:013 −0:050 −0:049 −0:091 −0:046 −0:031 −0:018(0:738) (0:168) (0:134) (0:024) (0:211) (0:447) (0:632)

Articles of cement (26.6) −0:009 −0:081b −0:032 −0:068 −0:045 −0:015 −0:035(0:789) (0:001) (0:399) (0:077) (0:139) (0:721) (0:342)

Metals (27.4) −0:025 −0:060 −0:073 −0:064 −0:021 −0:084 −0:086(0:383) (0:114) (0:074) (0:100) (0:451) (0:032) (0:032)

Computers (30.0) 0:004 0:004 −0:014 −0:013 −0:062 0:003 0:008(0:970) (0:999) (0:534) (0:626) (0:117) (0:959) (0:995)

Notes: For each country pair speci;c sample, mean reversion coeHcients are obtained from a multivariateunit root estimation of Eq. (4) in the text. The tests control for serial and contemporaneous correlations.p-values are obtained by parametric bootstrap. a, b, c denote signi;cance at the 1%, 5% and 10% levels,respectively, after the use of Bonferroni bounds. Abbreviations for the countries are as follows: Germany,GER; France, FR; Belgium, BE; Netherlands, NL; Italy, IT; Spain, SP.

for each k = 1; : : : ; K , t = 1; : : : ; T and where the {�n;k}pn=1 are the estimated lag coef-;cients. 7 Eq. (7) can similarly be written as �k(L)�k; t = �k; t . The variance-covariance

7 The comparison of the various AR(p) processes is done for values of p running from 0 to 36, cor-responding to a period of three years with monthly data. The estimated lag lengths and coeHcients (notreported) vary between one and nine months.


SP–FR NL–FR IT–BE SP–BE NL–BE SP–IT NL–IT SP–NL

−0:010 −0:018 −0:095 −0:007 −0:012 −0:004 −0:035 −0:016(0:589) (0:516) (0:029) (0:825) (0:770) (0:866) (0:341) (0:657)

−0:005 −0:008 −0:004 −0:015 −0:059 −0:016 −0:008 −0:101(0:833) (0:613) (0:908) (0:733) (0:147) (0:653) (0:836) (0:018)

−0:004 −0:031 −0:031 −0:077 −0:085 −0:018 −0:013 −0:020(0:895) (0:372) (0:201) (0:013) (0:011) (0:609) (0:737) (0:619)

−0:108 −0:005 −0:064 −0:055 −0:045 −0:030 −0:062 −0:030(0:015) (0:893) (0:098) (0:154) (0:204) (0:416) (0:171) (0:464)

−0:032 −0:016 −0:043 −0:060 −0:026 −0:045 −0:041 −0:027(0:414) (0:608) (0:283) (0:113) (0:410) (0:209) (0:112) (0:406)

−0:012 −0:077 −0:041 −0:013 −0:080 −0:025 −0:018 −0:009(0:578) (0:040) (0:304) (0:616) (0:048) (0:359) (0:663) (0:715)

−0:059 −0:120c −0:064 −0:030 −0:048 −0:094 −0:131c −0:041(0:087) (0:005) (0:075) (0:300) (0:203) (0:023) (0:006) (0:235)

−0:072 −0:013 −0:033 −0:011 −0:032 −0:045 −0:035 −0:022(0:071) (0:800) (0:383) (0:796) (0:436) (0:301) (0:335) (0:604)

−0:005 −0:010 −0:045 −0:011 −0:007 −0:014 −0:032 −0:018(0:861) (0:784) (0:139) (0:786) (0:871) (0:572) (0:329) (0:588)

−0:008 −0:057 −0:016 −0:029 −0:083b −0:055 0:002 −0:011(0:844) (0:149) (0:419) (0:258) (0:002) (0:170) (0:981) (0:786)

−0:030 −0:050 −0:008 −0:177b −0:046 −0:003 −0:048 −0:031(0:541) (0:202) (0:841) (0:001) (0:261) (0:878) (0:167) (0:316)

−0:015 −0:001 −0:056 −0:028 −0:002 −0:025 −0:021 −0:003(0:697) (0:950) (0:145) (0:409) (0:944) (0:550) (0:757) (0:920)0:003 −0:020 −0:038c −0:015 −0:015 −0:008 −0:002 0:002(0:985) (0:510) (0:005) (0:402) (0:676) (0:783) (0:925) (0:977)

−0:020 −0:028 −0:085 −0:079 −0:025 −0:039 −0:031 −0:135b(0:646) (0:550) (0:033) (0:024) (0:505) (0:276) (0:340) (0:002)

−0:053 −0:008 −0:032 −0:054 −0:095 −0:088b −0:029 −0:081(0:151) (0:801) (0:396) (0:120) (0:013) (0:001) (0:444) (0:059)

−0:051 −0:026 −0:081 −0:091 −0:066 −0:099 −0:015 −0:045(0:174) (0:316) (0:047) (0:030) (0:079) (0:022) (0:569) (0:160)0:009 0:002 −0:002 0:005 0:000 −0:012 −0:019 −0:013(0:999) (0:948) (0:901) (0:994) (0:958) (0:431) (0:469) (0:699)

matrix � is then computed from the K series of residuals �k; t , that is � = E(�k; t�′k; t)

and is of dimension [K × K]. Note that O’Connell (1998) considers the disturbanceterms to be generated, under the null, by a restricted VAR(p) process where the serialcorrelation properties of all series in the panel are assumed to be identical. However,our ;nding of di1erent lag lengths (and estimated coeHcients) across the relative priceseries in each panel provides little support for such a restriction.Having estimated the serial and cross-sectional correlation properties of �k; t un-

der the null, the dependent and explanatory variables in Eq. (4), Mqk; t and qk; t−1,are each transformed by their corresponding lag polynomial �k(L) to produce some


Table 3Proportion of sectors converging towards relative PPP (%)

France Germany Belgium Netherlands Italy Spain

France — 18 (6) 53 (12) 12 (6) 35 (0) 18 (0)Germany — — 23 (12) 23 (12) 18 (0) 18 (0)Belgium — — — 29 (6) 35 (6) 23 (6)Netherlands — — — — 6 (6) 18 (6)Italy — — — — — 18 (6)Spain — — — — — —

Notes: For each country pair, the table reports the share of sectors for which the unit root hypothesis canbe rejected at the 10% level, before and after (in parentheses) the use of Bonferroni bounds.

new series denoted Mq∗k; t and q∗

k; t−1. These transformed variables Mq∗k; t and q∗

k; t−1are then simply replaced in Eq. (4) which, together with the variance-covariance matrix�, is estimated by SUR to yield the mean reversion coeHcients �k and their corre-sponding test-statistics t�k = �k=��k , where ��k is the standard error for the estimate of�k . For each panel sample, there are K (17) parameters �k to be estimated.Because the standard Dickey–Fuller tables do not apply in this multivariate con-

text, the critical values of the distribution of the test-statistics t�k , for each sector kin the panel, are tabulated by parametric bootstrap: for given values of K and T ,5000 panels of relative prices are generated under the null, all series indexed k be-ing constrained to have the same serial ({�n;k}pn=1) and cross-sectional (�) proper-ties as the ones previously estimated from the data. The p-values corresponding toeach of the estimated coeHcients are also calculated. See Appendix A for furtherdetails.

4.2. Results

The results from estimating Eq. (4) separately for each country pair are reported inTable 2. Since the estimated coeHcients are (mostly) negative, they should, Ta priori,be indicative of mean reversion.When looking at the various p-values indicating the signi;cance level at which the

unit root hypothesis can be rejected, the relative prices for some countries and sectorsappear as stationary processes over the period. However, in order to determine thenumber of mean reverting series in each panel, size-adjusted critical values, determinedby the so-called Bonferroni bounds, are used. Each test is conducted individually atthe �=N level (where N is the number of tests, N = 17, and � = 10%), so that theset of N tests have a joint size not greater than �. As discussed by Bowman (1999),ignoring size-adjusted critical values can lead to vastly mistaken inferences regardingthe “correct” number of unit roots in the panel sample. For each country pair, Table 3reports the share of sectors for which relative prices are mean reverting towards PPP,before and after the use of these size-adjusted critical values.Focusing on the results obtained with the Bonferroni bounds, Belgium and the

Netherlands both display some evidence of mean reversion towards all the other


countries considered. These two countries also exhibit the largest number of sectors forwhich the unit root hypothesis can be rejected. On the whole, the largest number ofcases in which relative prices revert towards their mean is obtained between Germany,France, Belgium and the Netherlands, four of the original six EU countries. 8

In contrast, for Italy and Spain there is relatively less evidence against the unit roothypothesis (even though the di1erence is small). This may be due to the fact that thevolatility of these countries’ nominal exchange rates is stronger than the ones observedbetween Belgium, France, Germany or the Netherlands. However, better results wereexpected for Italy than for Spain since the former joined the EU in 1958, whereas thelatter only joined in 1986.Relative prices also appear to behave di1erently across sectors. For instance, mean

reversion is never found in textiles (17.4), footwear (19.3), carpentry (20.3), woodencontainers (20.4), paper and articles of paper (21.1 and 21.2), detergents (24.5), metals(27.4) and oHce machinery and computers (30.0). On the contrary, the sectors forwhich the unit root hypothesis is rejected are chemicals (24.1), paints (24.3), rubber(25.1), plastic (25.2), glass (26.1), bricks (26.4), cement and articles of cement (26.5and 26.6).Recall that our methodology only gives two possible outcomes: either the series

contains a unit root, or it is stationary around a constant mean. Hegwood and Papell(1998) however argue that if a real exchange rate is stationary, but around a meanwhich is subject to occasional structural changes, the series will mimic the behaviour ofa unit root series if the structural changes are not properly taken into account. In otherwords, rejection of the relative PPP hypothesis may be caused by a convergence toabsolute PPP. From that perspective, the case of Spain is of particular interest since itonly joined the EU in 1986 and therefore has probably experienced a structural changesince then. Spain may have converged in absolute terms towards other countries suchas Germany and France, but here, this phenomenon would show up as a violation ofrelative PPP.This brings to an interesting point relating to the de;nitions used. If the long-lasting

changes in common currency relative prices are related to exchange rate changes, onemay infer that violations of relative PPP are violations of absolute PPP; if not, it maybe that convergence to absolute PPP (due, for instance, to a structural change) causesthe violation of relative PPP. Therefore, one should keep in mind that the economicinterpretation of the results obtained with our methodology crucially depends on thede;nitions used.Studies like ours, which use price indices instead of actual price levels, are however

unable to shed some light on the issue of price level convergence. Two recent papers,which exploit price level data in Europe, actually present some direct evidence on thisquestion. Using the prices of 168 goods and services in 26 cities in 18 countries in1990 and 1999, Rogers (2001) ;nds that prices have become less dispersed in the euroarea, especially for traded goods. But despite this ongoing process of convergence,he also shows that the deviations from the LOOP remain large. Similarly, Crucini

8 The six founding countries of the EU are Belgium, France, Germany, Italy, Luxembourg and theNetherlands.


Table 4Restricted multivariate unit root tests

Country pair FR–GER BE–GER IT–GER SP–GER NL–GER

� −0:015 −0:009 −0:018 −0:010 −0:017p-value 0.537 0.959 0.422 0.944 0.448

Country pair BE–FR IT–FR SP–FR NL–FR IT–BE� −0:026b −0:014 −0:007 −0:014 −0:018p-value 0.032 0.830 0.991 0.655 0.170

Country pair SP–BE NL–BE SP–IT NL–IT SP–NL� −0:018 −0:017 −0:016 −0:016 −0:016p-value 0.357 0.518 0.311 0.575 0.606

Notes: For each country pair speci;c sample, the mean reversion coeHcient � is obtained from a mul-tivariate unit root estimation of Eq. (4) where � is constrained to be identical across all sectors. The testscontrol for serial and contemporaneous correlations. p-values are obtained by parametric bootstrap. a ; b; c

denote signi;cance at the 1%, 5% and 10% levels, respectively. Abbreviations for the countries are asfollows: Germany, GER; France, FR; Belgium, BE; Netherlands, NL; Italy, IT; Spain, SP.

et al. (2000), who exploit absolute retail price data covering about 1600 goods acrossEuropean capital cities in 1985, show that the deviations from the LOOP are large, butalso tend to average out across goods.We now turn to the analysis of the speed of convergence towards PPP which is based

on the �ij;k persistence parameters obtained for all country pairs ij and sectors k. Sincethose estimated coeHcients may be biased (Cecchetti et al., 2000), we bias-adjust theestimates of �ij;k using the formula suggested by Nickell (1981). 9 From these adjustedmean reversion coeHcients denoted �ij; k , we then compute the adjusted half-lives ofdivergences from PPP which are given by ln (0:5)=ln (1+�ij; k). Restricting our attentionto the cases for which the unit root hypothesis can be rejected at the 10% level(after the use of the Bonferroni bounds), the fastest mean reversion, correspondingto an adjusted half-life of four months, is obtained for the manufacture of plastic(25.2) between Belgium and Spain. In contrast, the slowest speed of mean reversionis obtained between Italy and Belgium for the manufacture of bricks (26.4) with anadjusted half-life of approximately 25 months (two years). These convergence ratestowards PPP are therefore faster (and the half-lives shorter) than those usually recordedin the literature. For instance, Parsley and Wei (1995) show that, in the case of theEMS countries, 51 months are necessary for the deviations from PPP to be reduced tohalf. Our ;ndings are more in line with those of Cumby (1996) who studies (across14 countries between 1986 and 1996) the prices of Big Mac hamburgers, and ;nds ahalf-life for the deviations from PPP of just under one year.Finally, the estimates of a constrained (single) mean reversion coeHcient for each of

the country pair samples are reported in Table 4. Only between Belgium and France is

9 Considering the ;rst-order autoregressive model yit = � + yit−1 + �it , i = 1; : : : ; N and t = 1; : : : ; T ,Nickell’s (1981) formula for the bias is plimN→∞( − ) = (ATBT )=CT where AT = −(1 + )=(T − 1),BT = 1 − (1=T )(1 − T )=(1 − ) and CT = 1 − (2 =[(1 − )(T − 1)])BT .


this coeHcient signi;cantly di1erent from zero (at the 5% level). This result contrastswith some other panel studies which also focus on European countries without distin-guishing between the countries which are converging towards PPP and those which arenot. For instance, the unit root hypothesis is strongly rejected by Jorion and Sweeney(1996) in a panel of seven European currencies (including Switzerland) between 1973and 1993, by Papell (1997) in a panel of European member states between 1973 and1994 and by Wu and Wu (1998) for both the EU and the EMS countries between 1973and 1997. One exception is Papell (1997) who is unable to reject the null hypothesisin the case of seven countries of the EMS. However, in contrast to the present paper,these empirical studies all rely upon aggregate price data and compute real exchangerates with respect to a benchmark country.To summarize, the use of disaggregated data at the sectoral level, the inclusion of

all possible country pairs in the sample and the estimation of heterogeneous speeds ofmean reversion prove informative. Mean reversion is more frequently reported for theNetherlands, Germany, Belgium and France, while relative prices for certain sectors,no matter which country pair is considered, appear to mean revert systematically moreoften than for other sectors.Finally, it is important to emphasize that one shortcoming of our empirical study

is the short time span of data available. Seventeen years of data may well be suf-;cient to detect di1erences in the behaviour of prices across sectors and countries,but may not be enough to ;nd additional statistical signi;cance against the unit roothypothesis.

5. Explaining mean reversion

The results analysed in the preceding section show that evidence of PPP is morefrequent for some countries and sectors than for others. In addition, the speeds ofreversion towards PPP, based on the estimated mean reversion parameters, appear tobe di1erent across country pairs and sectors. An important question is to determineempirically how this particular price behaviour may be related to the set of factorswhich are usually identi;ed as being responsible for the deviations from PPP and fortheir persistence.The theoretical model of Parsley and Wei (1995), which is in the same spirit as

Engel and Rogers (1996), serves as a guide to motivate our basic empiricalspeci;cations. In this model, price dispersion is positively related to the distance be-tween locations because shipping costs, which impede arbitrage activities, increase withdistance. Nominal exchange rate volatility contributes to price dispersion as well, re-Jecting that prices are relatively sticky in local currencies. Finally, the behaviour of rel-ative prices also depends on the physical properties and market structure of the productin question. However, these authors concentrate on the volatility of relative prices overa period, whereas here the objective is to explain persistence in relative prices.Particular attention is paid to the role of nominal exchange rate volatility, the geo-graphical separation of markets and of sectoral characteristics (Campa and Wolf, 1997;Cheung et al., 2001; Cecchetti et al., 2000).


To examine these questions, three alternative measures of relative prices’ persistenceare considered. Firstly, we aim to explain our (adjusted) persistence parameters, the�ij; k coeHcients obtained for all country pairs ij and sectors k. The closer �ij; k is tozero, the more persistent the relative price and the slower the speed of parity reversion.Secondly are examined the (adjusted) half-lives of divergences from PPP. Finally, thet-ratios associated with the persistence parameters are also investigated. 10

The next three sections are devoted to our analysis. The ;rst section motivates thechoice of country level factors in explaining persistence in relative prices. The secondfurther extends the analysis by considering the role of sectoral characteristics. Theresults are reported in the third section.

5.1. The country level

When comparing the behaviour of prices across countries, nominal exchange ratevolatility, which can be interpreted as a proxy for the exchange rate uncertainty thatprice setters face, needs to be considered. For instance, Delgado (1991) shows thatthis variability raises the level of uncertainty, and hence intensi;es price stickiness. Inother words, ;rms become less willing to adjust their prices since the exchange ratemay move back again later on. Parsley and Wei (1995, 2000) and Engel and Rogers(1996, 1998, 2000, 2001) also ;nd that nominal exchange rate volatility is signi;cantin explaining the failure of PPP across countries, while Cheung et al. (2001) show thatvolatility slows the speed of reversion. Accordingly, nominal exchange rate volatility,volij, is expected to slow the adjustment towards PPP.As noted by Engel and Rogers (1996, 1998, 2000, 2001) and Parsley and Wei

(1995, 2000), prices may not equalize between locations because of shipping costs.In addition, Campa and Wolf (1997) ;nd that a greater geographical distance, whichproxies for unobservable transportation costs, results in a slower PPP reversion. Thedistance (in kilometres), distij, between the economic centres of country i and countryj is therefore computed, and is expected to have a negative impact on the speed ofreversion towards PPP.A further way to capture other possible determinants of transportation costs is to

compute a dummy variable, adjij, which takes the value one when country i shares acommon border with country j and zero otherwise. This adjacency variable, which issimilar to the one considered by Parsley and Wei (1995), is expected to have a positiveimpact over the speed of reversion because arbitrage and trading activities should beeasier between countries close to each other, inducing ;rms to adjust their prices.It is worth pointing out that the interpretation of this “border” variable is not the same

as in Engel and Rogers (1996, 2000) and Parsley and Wei (2000), where prices arecompared within, and across, countries and where the border dummy variable reJectsthat price dispersion is higher between two cities when they are separated by a national

10 The results obtained when explaining a Bayesian transformation of the mean reversion coeHcients, aswell as a logistic transformation of the p-values corresponding to each of the mean reversion coeHcients,are not signi;cantly di1erent from the ones reported in this paper, and are hence omitted.


border. 11 Such a comparison between within-country and cross-border relative pricesis not possible in the present paper due to data unavailability.As noted previously, the rejection of (relative) PPP for Spain may be due to an

absolute convergence towards PPP. In terms of GDP per capita, Spain has e1ectivelyexperienced an upward (absolute) convergence towards the level of the other countries,probably implying an upward (absolute) convergence in prices (Crucini et al., 2000;Rogers, 2001). To capture such a phenomenon, the absolute change (between the twoyears 1981 and 1997) in the di1erence of the GDP per capita between countries, gdpij,is computed. A large value for gdpij, possibly capturing a structural change, shouldaccordingly be associated with more persistent relative prices.

5.2. The sectoral level

The previous section has motivated the choice of country level variables in explainingpersistence in relative prices. In this section, the aim is to investigate the role of sectoralcharacteristics.It is conjectured that trade barriers act much like transportation costs in creating

wedges between the prices of traded goods in di1erent locations. This issue is examinedby considering a measure of non-tari1 barriers, ntbk , a qualitative variable taking thevalue one if sector k is subject to non-tari1 barriers and zero otherwise (Buigues et al.,1990). These barriers should have a negative impact on the speed of mean reversionsince they impede arbitrage activities.Engel and Rogers (1998) also point to the fact that monopoly power, reJecting

the ability of ;rms to price discriminate, should be considered in explaining pricedispersion across industries. In the same context, Cheung et al. (2001) empiricallytest whether di1erences in sectoral real exchange rate persistence systematically arisefrom di1erences in market structure. More speci;cally, they consider the hypothesisthat industries with a less competitive market structure have more persistent sectoralreal exchange rates. Using the price cost-margin across industries and countries toapproximate the pro;tability of an industry, Cheung et al. (2001) ;nd some evidencein favour of their hypothesis.In order to analyse the e1ect of market power on the persistence of sectoral PPP

deviations, the ;ve ;rm concentration ratio, conck , which represents the combinedproduction of the ;ve largest producers in the industry as a share of total EU-12 pro-duction, is considered (Davies and Lyons, 1996). In our context, the more concentratedan industry, the more likely its relative prices should be persistent.Another way to reJect the structure of an industry is to characterize the nature

of competition via the degree of product di1erentiation. For instance, an industry isbetter characterized as monopolistically competitive than perfectly competitive if ;rmssupply some di1erentiated products that are imperfect substitutes to each other. Cheunget al. (2001) use the GrXubel–Lloyd intra-industry trade index to reJect the extent of

11 Engel and Rogers (2001) further investigate the impact of crossing the border on price dispersion whilecontrolling for the e1ect of adjacency.


market power due to product di1erentiation. Consistent with prediction, sectors subjectto substantial intra-industry trade tend to have more persistent sectoral PPP deviations.If ;rms vertically di1erentiate their products, one can also expect them to invest in

R&D or advertising. Since these investments can create barriers to entry or can be usedby ;rms to vertically fragment the market (and hence limit competition), market poweris expected to be stronger in sectors where the nature of competition is mainly based onthe perceived quality of the products. Accordingly, to capture vertical di1erentiation ofthe products, we consider two variables: advk is equal to one when sector k is subjectto a high intensity in advertising and zero otherwise (Davies and Lyons, 1996), andrdk is the R&D intensity ratio (the share of R&D expenditure in production, averagedacross Germany, France, the Netherlands, Italy and Spain in 1993, Eurostat). Bothvariables are expected to adversely a1ect the speed of mean reversion towards PPP.Finally, since arbitrage activities should be easier for more tradeable products, we

may expect a negative relationship between tradeability and persistence. To check thisassumption, for each country pair and sector, a transportability measure, trij; k , is com-puted as the ratio of the weight (in kilos) of imports to the value of imports (averagedacross the three years 1988, 1989 and 1990; a low tradeability implies a high trij; k).Note that in contrast to the other variables, trij; k not only characterizes sectors but alsovaries across country pairs.

5.3. Results

Having explained the choice of various country and sectoral level variables, we nowanalyse the relationship between these variables and persistence in relative prices. Theregression speci;cation is given by:

persij; k = ci + �1lndistij + �2adjij + �3volij + �4lngdpij + �5ntbk

+�6lnconck + �7lnrdk + �8advk + �9lntrij; k + �ij; k ; (8)

where, for all country pairs ij and all sectors k, persij; k denotes the (adjusted) per-sistence parameters (the �ij; k coeHcients), the (logarithm of adjusted) half-lives andthe test-statistics corresponding to each of the mean reversion coeHcients. An increasein the mean reversion coeHcients (with �ij; k ¡ 0) indicates an increase in persistence;similarly, an increase in the test-statistics (where t�ij; k ¡ 0) is associated with morepersistence. The inclusion of separate dummies ci for each individual country i al-lows the speed of reversion to vary from country to country. In contrast, the inclusionof industry ;xed-e1ects is precluded because non-tari1 barriers, ntbk , and intensity inadvertising, advk , are captured by dummy variables.Three di1erent samples (corresponding to each dependent variable to be explained)

are derived from the results obtained in the previous section. Each of them, which ispurely cross-sectional, contains I((I − 1)=2)× K = 255 observations where, as before,I and K , respectively, denote the total number of countries (6) and sectors (17).When the mean reversion coeHcients are used as the dependent variable in (8), two

main issues arise from an econometric viewpoint. The ;rst refers to the fact that thisdependent variable is estimated rather than observed, implying that the error �ij; k is


heteroskedastic. Controlling for heteroskedasticity requires weighting less heavily thosemean reversion coeHcients which are relatively imprecisely estimated. To do so, andfollowing Slaughter (2001), Eq. (8) is ;rst estimated by OLS. Next, the squared resid-uals from this equation are used as a dependent variable and regressed on the estimatedvariances of the mean reversion coeHcients, along with these variances squared andcubed. The predicted values of this regression give the amount of the original squaredresiduals “explained” by the variance of the mean reversion coeHcients. The (inverseof the) predicted values are then used as weights for a weighted least squares (WLS)estimation of (8).The second directly relates to the choice of a two-stage approach for explaining

di1erences in mean reversion towards PPP. Such approach can be criticized on thegrounds that the explanatory factors used in the second stage (to explain persistence)could be viewed as omitted variables in the ;rst stage of the tests, which estimates thevarious speeds of mean reversion. Therefore, to check for the robustness of our results,we also applied an integrated approach which simultaneously estimates the degree ofmean reversion while controlling for the e1ects of the second stage explanatory factorson the mean reversion coeHcients. The implementation of this alternative methodol-ogy proved informative since the results appeared to be qualitatively similar to thosereported in the paper. Those robustness checks are not reported in order to save space(but are available from the author upon request). 12

Before getting to the results, which are reported in Tables 5–7 for the persistenceparameters, the half-lives and the test-statistics, respectively, the strong collinearity be-tween some country level variables has to be underlined. The correlations betweennominal exchange rate volatility, on the one hand, and the adjacency and distancevariables, on the other hand, are large (respectively equal to −0:52 and 0.75). A pri-ori, it seems obvious that countries closer together should display lower exchange ratevolatility, 13 but these correlations are stronger than those usually reported (Engel andRogers (1998) ;nd a 0.49 correlation between distance and the standard deviation ofmonthly exchange rates). As a result, the three explanatory variables are ;rst consideredseparately, and then in combination (Engel and Rogers (2001) include all three explana-tory variables together in a single regression). When considered simultaneously, notethat the individual signi;cance of each of the three variables is usually decreased,but in general, the di1erent speci;cations reported in each table qualitatively tellidentical stories.Is there any evidence that the adjustment in relative prices is impeded by distance?

From the ;rst and fourth columns in Table 5, the estimated slope coeHcient of distance,which is positive and signi;cant, indicates that convergence is indeed slower betweencountries of greater spatial separation, i.e. transport costs reduce arbitrage betweenlocations. From Tables 6 and 7, distance also appears to increase the half-lives of aPPP deviation but not the test-statistics. On the whole, these ;ndings are qualitatively

12 We thank an anonymous referee for this suggestion.13 The closer countries are to each other, the higher their trade share between them. This trade intensity

may therefore have a stabilizing impact over bilateral exchange rates in order to avoid large swings in tradeJows.


Table 5Persistence in relative prices (dependent variable: adjusted mean reversion coeHcients)

(1) (2) (3) (4)

ln distij 0:006b — — 0:006c

(2:06) (1:66)adjij — −0:008c — −0:012

(−1:83) (−1:04)volij — — 0:012c 0:012c

(1:85) (1:71)ln gdpij 0:015b 0:015b 0:012b 0:013b

(2:53) (2:57) (2:08) (2:21)ntbk 0:010b 0:010b 0:010b 0:010b

(2:27) (2:27) (2:31) (2:30)ln conck 0:001a 0:001a 0:001a 0:001a

(3:53) (3:53) (3:57) (3:56)ln rdk 0:007a 0:007a 0:007a 0:007a

(3:41) (3:41) (3:42) (3:41)advk 0:018a 0:018a 0:018a 0:018a

(2:82) (2:82) (2:80) (2:80)ln trij;k 0:001a 0:002a 0:002a 0:002a

(3:24) (3:25) (3:23) (3:32)

Adj − R2 0.135 0.134 0.134 0.132

Notes: Country dummies (not reported) are included, observations n = 255. The method of estimationis weighted least squares (see the text for details); t-statistics are reported in parentheses; a, b, c denotesigni;cance at the 1%, 5% and 10% levels, respectively.

consistent with Campa and Wolf (1997) and Cecchetti et al. (2000) but also with Engeland Rogers (1996, 1998, 2000, 2001), Parsley and Wei (1995, 2000) and Cruciniet al. (2000). Engel and Rogers (1996, 1998, 2000), however, argue that distance mayalso matter for reasons other than shipping costs. In particular, they point to the factthat places farther apart may have dissimilar cost structures and that the behaviour ofprices is closely inJuenced by wages. Indeed, wage disparities at the sectoral level(and perhaps between countries) could be considered to check whether labour marketpractices have an inJuence on the behaviour of relative prices. Finally, Cheung et al.(2001) ;nd that the estimated coeHcient of distance is not signi;cant in explainingpersistence and has the wrong sign.The results relating to adjacency are displayed in the second and fourth columns of

each table. When nominal exchange rate volatility and distance are excluded (sec-ond columns), the estimated coeHcients on adjacency are negative and signi;cantwhen explaining the mean reversion coeHcients (Table 5) and the adjusted half-lives(Table 6), suggesting that arbitrage accelerates the speed of reversion. However, thisresult disappears once the three country variables are included simultaneously (fourthcolumns). Note that in Parsley and Wei (1995), the estimated coeHcient of that dummyvariable is not signi;cantly di1erent from zero (and hence does not inJuence, in theircase, price dispersion).


Table 6Persistence in relative prices (dependent variable: the logarithm of adjusted half-lives)

(1) (2) (3) (4)

ln distij 0:436b — — 0:377c

(2:43) (1:65)adjij — −0:514b — −0:718

(−2:22) (−1:08)volij — — 0:889b 0:914c

(2:40) (1:69)ln gdpij 0:420 0:425 0:195 0:266

(1:30) (1:31) (0:78) (0:94)ntbk 0:208b 0:208b 0:213b 0:212b

(2:03) (2:04) (2:07) (2:08)ln conck 0:011 0:011 0:011 0:011

(1:51) (1:51) (1:56) (1:55)ln rdk 0:167b 0:167b 0:167b 0:168b

(2:14) (2:13) (2:11) (2:13)advk 0:680b 0:678b 0:671b 0:678b

(2:50) (2:49) (2:48) (2:47)ln trij;k 0:050c 0:048c 0:048c 0:049c

(1:65) (1:65) (1:67) (1:79)

Adj − R2 0.083 0.083 0.085 0.082

Notes: Country dummies (not reported) are included, observations n = 255. Standard errors are het-eroskedastic consistent (White); t-statistics are reported in parentheses; a, b, c denote signi;cance at the 1%,5% and 10% levels, respectively.

Campa and Wolf (1997) cast some doubt on the arbitrage explanation since theyshow that deviations from PPP and trade Jows are virtually uncorrelated in either di-rection (see also Cheung et al., 2001). Instead, they argue that mean reversion maybe induced by policy actions such as realignments in nominal exchange rates, whichimply an immediate reversion of relative prices towards their mean. This observationis important because during most of the period analysed, the six countries consideredin the present paper participated in the ERM, which implied limited nominal exchangerate Juctuations. However, the e1ects of the various nominal exchange rate realign-ments, which occurred in the ERM, cannot be investigated in the context of this modelsince our samples are purely cross-sectional and therefore do not contain any temporaldimension.When considering the e1ects of nominal exchange rate volatility (reported in the

third and fourth columns of each table), the coeHcients are positive and signi;cant inall cases (at the 10% level only), indicating that a higher volatility tends to slow thespeed of adjustment towards PPP. This result is consistent with that of Cheung et al.(2001) who also ;nd that an increased exchange rate volatility leads to a slower parityreversion.Finally, changes in GDP per capita di1erentials are signi;cant in explaining the per-

sistence parameters and their test-statistics, but not the half-lives. This ;nding suggests


Table 7Persistence in relative prices (dependent variable: test-statistics corresponding to the mean reversioncoeHcients)

(1) (2) (3) (4)

ln distij 0:162 — — 0:109(1:45) (1:34)

adjij — −0:155 — −0:173(−1:21) (−0:50)

volij — — 0:449c 0:474c

(1:88) (1:69)ln gdpij 0:558a 0:551a 0:461b 0:471b

(2:94) (2:94) (2:43) (2:45)ntbk 0:226 0:226 0:228 0:228

(1:45) (1:45) (1:49) (1:48)ln conck 0:018a 0:018a 0:018a 0:018a

(3:81) (3:80) (3:86) (3:85)ln rdk 0:188a 0:187a 0:188a 0:188a

(3:76) (3:76) (3:78) (3:77)advk 0:568a 0:566a 0:565a 0:566a

(2:97) (2:96) (2:97) (2:96)ln trij;k 0:042a 0:041a 0:042a 0:042a

(2:66) (2:63) (2:73) (2:73)

Adj − R2 0.156 0.154 0.160 0.155

Notes: Country dummies (not reported) are included, observations n = 255. Standard errors are het-eroskedastic consistent (White); t-statistics are reported in parentheses; a, b, c denote signi;cance at the 1%,5% and 10% levels, respectively.

that the violations of relative PPP reported for Spain may be caused by a convergencetowards absolute PPP. In contrast, since Italy experienced a high nominal exchangerate volatility during the period (rather than a convergence in its GDP per capita), itmay be that the violations of relative PPP found for that country are due to violationsof absolute PPP.As to the e1ects of non-tari1 barriers on the persistence parameters (Table 5), the

estimated coeHcients are positive and signi;cant at the 5% level. On the whole, the per-sistence parameters are higher for the sectors a1ected by non-tari1 barriers as comparedto other sectors, supporting the idea that these barriers tend to slow the adjustment to-wards PPP. This variable remains signi;cant in explaining the (adjusted) half-lives, butnot the test-statistics (Tables 6 and 7). For the sake of comparison, note that Engel andRogers (1998) ;nd that high barriers induce lower price dispersion. The two authors,however, remain skeptical about that puzzling result.In terms of the e1ects of industrial concentration, the estimated coeHcients of

conck are positive and signi;cant (except when explaining the half-lives). This ;nd-ing is consistent with the notion that the adjustment in relative prices is slowed bythe extent of market power. As expected, vertical di1erentiation of the products isalso associated with a slower speed of reversion towards PPP. The estimated coeH-cients of the R&D and advertising variables are positive and signi;cant in all cases.


These results are consistent with priors and with Cheung et al. (2001) and Cecchettiet al. (2000).Finally, less tradeable products have more persistent relative prices. This is again

consistent with the idea that arbitrage is impeded by a low tradeability of theproducts.On the whole, most ;ndings are in accordance with the other empirical results

obtained in this research area: when focusing on EU member states, nominal ex-change rate volatility, the geographical segmentation of markets, non-tari1 barriers,industrial concentration, vertical di1erentiation and the tradeability of the productsappear as signi;cant determinants of cross-country and cross-industry pricebehaviour.

6. Concluding remarks

The purpose of the paper was to investigate empirically the PPP hypothesis at thesectoral level, and to provide some explanations for the observed di1erences acrosssectors and countries.In a recent survey of international price behaviour, Rogo1 (1996, p. 665) concludes

that “international goods markets, though becoming more integrated all the time, remainquite segmented, with large trading frictions across a broad range of goods. These fric-tions may be due to transportation costs, threatened or actual tari1s, non-tari1 barriers,information costs, or lack of labour mobility. As a consequence of various adjustmentcosts, there is a large bu1er within which nominal exchange rates can move withoutproducing an immediate proportional response in relative domestic prices. Internationalgoods markets are highly integrated, but not yet nearly as integrated as domestic goodsmarkets”. On the whole, the present study ;nds support for this conclusion in theEuropean context.The recent introduction of the euro is expected to further inJuence the behaviour

of prices across countries and industries. The single currency should make marketsmore transparent, thereby a1ecting the behaviour of both consumers and producers.Consumers should be able to switch more easily to cheaper products sold in foreignmarkets, allowing to increase arbitrage between locations. Producers may be threatenedto decrease their discriminatory price setting practices on their home markets, andtherefore opt for a defensive strategy such as investing in product di1erentiation (which,in the context of this paper, is shown to slow the speed of reversion). This increasedtransparency may also encourage ;rms to enter other EU markets, thereby reducing theconcentration of industries at the national level (and hence allowing to speed reversionin relative prices). Finally, note that nominal exchange rate volatility (which, in thecontext of this paper, signi;cantly a1ects the behaviour of relative prices) is nowcompletely eliminated with the arrival of the euro.In sum, in the context of international price behaviour, the recent introduction of a

single currency in Europe opens the way to a new and potentially rewarding directionfor future research.


Acknowledgements

This paper is based on Chapter 1 of my Ph.D. dissertation at the UniversitZe Librede Bruxelles and is a revised version of CEPR Discussion Paper 3320. I especiallywish to thank AndrZe Sapir, my thesis supervisor, for very helpful discussions. I amgrateful to Micael Castanheira, Christophe Croux, Marjorie Gassner, Victor Ginsburgh,Jorge Rodrigues and seminar participants at the UniversitZe Libre de Bruxelles, theEEA99 Congress in Santiago de Compostela, the Enter Jamboree at University CollegeLondon, the 9Teme Ecole de Printemps in Aix-en-Provence, the NBER InternationalTrade and Investment Summer Institute 2000, the Directorate General for Economicand Financial A1airs of the European Commission in Brussels, the CEPR Conferenceof the Analysis of International Capital Markets in Trinity College Dublin and Birk-beck College in London. I would also like to thank the Editor, Jordi GalZ[, and twoanonymous referees for helpful comments and suggestions. Financial support from theresearch network on “The Analysis of International Capital Markets: UnderstandingEurope’s Role in the Global Economy”, funded by the European Commission underthe Research Training Network Programme (Contract No. HPRN-CT-1999-00067), isgratefully acknowledged.

Appendix A. Parametric bootstrap simulations

The parametric bootstrap simulations, which results are reported in Tables 2 and 4,are conducted as follows. For each country pair speci;c sample of dimension [T ×K],where T and K , respectively, denote the total number of time periods included inthe panel (203) and sectors (17), 5000 panels of real exchange rates qt of dimension[(T + 51) × K] are simulated under the null hypothesis, with q0 = 0. The inclusionof an extra 50 observations aims to control for initial-value bias. The moments ofthe real exchange rate innovations are chosen to match the estimates of {�n;k}pn=1and � obtained when estimating (7). As the objective is to control for cross-sectionalcorrelations, � is estimated unrestricted.The critical values and p-values are then derived from the simulated data: in

Table 2, where a di1erent speed of mean reversion is estimated for each industry k,i.e. �k , the corresponding signi;cance bounds are compiled for each of the �k coeH-cients; in contrast, in Table 4, where the speed of mean reversion is restricted to beingthe same across all industries in the panel, a single critical value is derived for eachpanel sample, allowing to determine the signi;cance level of the constrained meanreversion coeHcient �.

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