Understanding European Real Exchange Rates
By MARIO J. CRUCINI, CHRIS I. TELMER, AND MARIOS ZACHARIADIS*
We study good-by-good deviations from the Law-of-One-Price (LOP) for over 1,800
retail goods and services between all European Union (EU) countries for the years
1975, 1980, 1985, and 1990. We find that for each of these years, after we control
for differences in income and value-added tax (VAT) rates, there are roughly as
many overpriced goods as there are underpriced goods between any two EU
countries. We also find that good-by-good measures of cross-sectional price dispersion are negatively related to the tradeability of the good, and positively related
to the share of non-traded inputs required to produce the good. We argue that theseobservations are consistent with a model in which retail goods are produced by
combining a traded input with a non-traded input.

The LOP states that identical goods in different countries should have identical prices, oncethe prices are expressed in common currency
units. Purchasing Power Parity (PPP) is the notion that this should hold on average; similarbaskets of goods should cost the same once
expressed in common units. Each of these propositions is essentially a statement about thecross-sectional distribution of international relative prices. Due to data limitations, however,most empirical work has examined the timeseries distribution of international relative
prices. That is, because most data take the formof index numbers, most of what we know about
LOP and PPP deviations involves the volatility
and persistence of changes in relative prices.
We know relatively little about the absolute
relative prices themselves. This is particularly
troublesome given that economic theory places
much starker restrictions on absolute LOP deviations than on their changes.

This paper uses a novel dataset on absolute
LOP deviations to bridge this gap. Our data arelocal-currency retail prices for a broad set ofgoods and services in all EU countries over
five-year intervals between 1975 and 1990. The
data are quite comprehensive, covering most
CPI categories, and are collected with the explicit goal of generating cross-country comparisons of individual goods and services that are
as similar as possible.
We focus on the cross-sectional distribution of the LOP deviations from this dataset.
For each good, the deviation is defined relative to that good’s intra-European average
price. We have two sets of results, the first
relating to the mean of the distribution andthe second relating to the variance. For themean, we compute the average LOP deviation
across goods for each country. We find that,after controlling for national income and
VAT differences, most of the means are close
to zero. In only four of 47 cases is a mean
greater than 10 percent in absolute value. Thisphenomenon is quite stable over the time period we study. In simple terms, if we consider
most pairs of EU countries with similar incomes and VATs, at any point in time between 1975 and 1990, there are roughly as
many overpriced goods as there are underpriced goods.
Our results about the mean go against thegrain of many previous studies, which haveemphasized large and persistent deviations from
PPP. Most of these studies, however, have involved the U.S. dollar and have involved timeseries variation over short (i.e., quarterly)* Crucini: Department of Economics, Vanderbilt University, Box 1819, Station B, 415 Calhoun Hall, Nashville, TN37235 (e-mail: mario.j.crucini@vanderbilt.edu); Telmer: Carnegie Mellon University Graduate School of Industrial Administration, 350 Posner Hall, Frew and Tech Streets, Pittsburgh,
PA 15213, and Universitat Pompeu Fabra (e-mail: chris.
telmer@cmu.edu); Zachariadis: Department of Economics,
University of Cyprus, P.O. Box 20537, 1678 Nicosia, Cyprus,and Department of Economics, Louisiana State University(e-mail: zachariadis@lsu.edu). In addition to participants atnumerous seminars and conferences, we thank Stephen Cosslett, Mick Devereux, Paul Evans, Burton Hollifield, John Rogers, Kjetil Storesletten, Stan Zin, and, in particular, Charles
Engel for helpful comments. We gratefully acknowledge thefinancial support of the National Science Foundation (SES0136979) and the Carnegie Bosch Institute.
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CRUCINI ET AL.: UNDERSTANDING EUROPEAN REAL EXCHANGE RATES

horizons. Our results, in contrast, apply only tointra-European prices and are characteristic ofabsolute price dispersion at four different points
in time (1975, 1980, 1985, and 1990). They arealso consistent with several independent data
sources (documented below). Our main point isthat one should be wary of extrapolating the“consensus” about real-exchange rate behavior.
“Large and persistent deviations from PPP” isnot a good description of Europe between 1975
and 1990.
While the mean is across goods for eachcountry, the variance is across countries foreach good. That is, we focus on good-by-gooddispersion in the absolute LOP deviations. We
find that much of this dispersion can be attributed to two classic characteristics of goods: how
tradeable they are, and how tradeable the inputs
required to produce them are. For example, theaverage amount of price dispersion in our datais 28 percent. The average is 25 percent versus
40 percent, however, for traded versus nontraded goods. Similarly, the average is 25 percent versus 32 percent for goods requiring a
below-average versus an above-average shareof non-traded inputs. Combining these effects ina regression framework, we find that if we consider a non-traded good with the maximum
share of non-traded inputs, the predicted pricedispersion is 43 percent. In contrast, the prediction for the most-traded good, requiring thelowest share of non-traded inputs, is just 12
percent. The difference of 31 percent is large,
relative to both the unconditional amount ofdispersion in the data, 28 percent, and the rangeof the good-specific dispersion measures, 2 percent to 82 percent. Interestingly, our estimatessuggest that the lion’s share of the price dispersion is attributable to the tradeability of inputs,
not tradeability of the final good.
Our results stand on their own as empiricalfacts. In order to provide a tighter link between
facts and theory, however, we begin our paper byoutlining a simple model of retail price determination. Retail goods are produced by combining a
traded input with a non-traded input. LOP deviations are a convex combination of input cost deviations. This simple theory provides a coherent
economic context for the motivation and interpretation of our regressions. It also provides functional form restrictions, which we test. We findthat, while the explanatory variables suggested by
the theory are supported by the data, the functional

725

form restrictions are not. We discuss reasons forthe latter and what it suggests about future research directions.
Our work is most closely related to a large
body of empirical work on the international
comparison of microeconomic prices. Most data
either take the form of index numbers acrossrelatively broad sets of goods, or absolute prices
across a very narrow sets of goods. Examples ofthe former are Charles Engel (1993), Engel andJohn H. Rogers (1996), Alberto Giovannini(1988), Peter Isard (1977), Rogers and Michael
Jenkins (1995), and J. David Richardson(1978). Examples of the latter are Robert E.
Cumby (1996), Harry Flam (1992), Kenneth
Rogoff et al. (1995), Atish R. Ghosh and Holger
C. Wolf (1994), Jonathan Haskel and Wolf
(2000), Michael M. Knetter (1989, 1993), Matthias Lutz (2004), and David C. Parsley andShang-Jin Wei (2000). Our data, in contrast, aredistinguished by absolute prices across a verybroad set of goods. This allows us to say something akin to absolute PPP and also to relate
absolute price dispersion to the characteristics
of goods in the cross section.1
The remainder of the paper is organized asfollows. We begin in Section I by outlining a
conceptual framework, both in terms of data
objects and economic theory. Section II describes our data. Our analysis is organizedaround understanding the mean and the variance of the cross-sectional distribution of the
LOP deviations from this data. Section III examines the mean and Section IV examines thevariance. Section V concludes.
I. Conceptual Framework

Before describing our data, it is useful todevelop a conceptual framework with which to1
Some recent work that has used a broad cross-sectional
dataset on absolute prices from the Economist Intelligence
Unit includes Crucini and Mototsugu Shintani (2004), Engel and Rogers (2004), Parsley and Wei (2003), and Rogers(2001). These data are quite broad in terms of countries, butlack the detail and, to some extent, the comparability, of thegoods in our Eurostat (the Statistical Agency of the European Community) source. It also covers a more recent time
period, 1990 –present. In addition Collin Crownover et al.
(1996) use data on price levels from Internationaler Vergleich der Preise fur die Lebenshaltung, published by theGerman Statistical Office. The data are annual from 1927 to1992 and cover six major industrialized countries.

726

THE AMERICAN ECONOMIC REVIEW

organize it. The price data we seek to understand are denoted Pij: the price of good i incountry j, expressed in units of some numeraire
currency. None of our analysis will depend on
what this numeraire currency is. We transformthe price data into log deviations from thegeometric-average European price, which wedenote qij:冘 log P /MM

(1)

q ij ⬅ log Pij ⫺

ij

j⫽1

where M is the number of countries. Note thatqij is independent of the numeraire.
Most of our paper attempts to relate dispersion in qij , across countries j, to economicallymeaningful characteristics of the goods i. Following Bela Balassa (1964), William J. Baumoland William G. Bowen (1966), Paul A. Samuelson (1964), Wilfred Ethier (1979), Irving B.
Kravis and Robert E. Lipsey (1983), and Alan
C. Stockman and Linda L. Tesar (1995), we
focus on two characteristics: the international
tradeability of the good and the amount of nontraded inputs required to produce the good. To
be concrete, consider a typical non-traded good,a taxi ride. As is often asserted, all retail goods
involve significant amounts of non-traded inputs, such as labor. A taxi ride is no exception.
Less well appreciated, however, is the fact that
all non-traded goods involve traded inputs, inthis case the automobile and gasoline. We use
the following simple framework to organize thisview of what distinguishes goods in different
locations.
We view retail goods as being produced by
combining a non-traded input with a traded
input. With perfect competition, Cobb-Douglas
technology and constant returns to scale, we
have
(2)

⫺ ␣i 兲
P ij ⫽ W ␣j iT 共1
ij

where Wj is the cost of the non-traded input incountry j (e.g., the wage rate), ␣i is the share of
the non-traded good required to produce good i,
and Tij is the cost of the traded input for good iin country j. Inherent in the notation are twostandard assumptions. The first is that factor
mobility is much higher across sectors within acountry than across countries; Wj is countryspecific, not good-specific. The second is that

JUNE 2005

retailers in all countries produce good i using
the same production technology; ␣i is goodspecific, not country-specific.
Taking logs of equation (2) and subtracting
the geometric average (across j) gives(3)

q ij ⫽ ␣ i w j ⫹ 共1 ⫺ ␣ i 兲t ij

where, following equation (1), wj and tij denotelog differences from the cross-country geometric average. Equation (3) says that deviations
from LOP should be related to cross-country
differences in non-traded and traded factor input
costs, as well as differences in the production
share attributable to each. Differences in nontraded input costs are the crux of the classic
Balassa-Samuelson hypothesis, with wj being
positive for countries with higher productivity
in the traded sector relative to the non-tradedsector. Differences in traded costs are often
thought of as deriving from transport costs, withtij being positive for an importer of good i andnegative for an exporter.
Our empirical work is organized aroundequation (3). In Section III we begin by examining the country-specific cross-sectional
means, which we denote E(q ij 兩j). These variables are close cousins of real exchange rates.
We find that w j is important in the sense thatthe mean is negative for relatively poor countries. We also find that, having controlled forincome differences, E(q ij 兩j), is often quite
close to zero for most European countries.
The interpretation offered by equation (3) isthat t ij changes sign a lot across goods. In
other words, countries import some goods,
export others, and on average the effects on
LOP deviations cancel out.
In Section IV we examine the cross-sectionalvariances, denoted Var(qij兩i). That is, we examine how cross-country dispersion in LOP deviations varies across goods. According to equation (3),(4)

Var共q ij 兩i兲 ⫽ ␣ 2i Var共w j 兲⫹ 共1 ⫺ ␣i 兲2Var共tij兩i兲
⫹ 2␣i 共1 ⫺ ␣i 兲Cov共wj , tij兩i兲.

We estimate a cross-sectional regression (acrossi) corresponding to this equation. We use
industry-level data on the share of non-tradedVOL. 95 NO. 3

CRUCINI ET AL.: UNDERSTANDING EUROPEAN REAL EXCHANGE RATES

inputs required for production as a proxy for ␣i.
We use industry-level data on the tradeability of
the final good—as measured by international
trade flows divided by total output—to proxy
for Var(tij兩i). We find that an economically important portion of the price dispersion acrossgoods can be accounted for by tradeability andnon-traded input cost shares.
Having laid out our data requirements, we
now describe our data.
II. The Data

Corresponding to equation (1), we begin bydescribing our data on local currency prices, Pij ,of goods i in countries j.
Our price data are from a series of publications of Eurostat (1975–1990).2 The publications contain the results of four surveys of retailprices in the capital cities of EU countries foreach of the years 1975, 1980, 1985, and 1990.3
For our purposes it is sufficient to treat thesurveys as four separate cross sections. It is
important to note, however, that the goods ineach cross section maintain a high degree ofcomparability, across both locations and time.
Table 1 presents basic information about whatthese cross sections entail. The 1975 survey
covers nine EU countries. Greece, Portugal, andSpain were added in 1980. Austria was added in
1985. The number of goods also grows overtime, from 658 items in 1975 to 1,896 items in
1990. Finally, a substantial fraction of goods arelabeled as “branded goods.” The importance,for our purposes, is in terms of comparability ofgoods. In many cases we are literally talking
about the same automobile, portable radio, ortype of cheese.4
As Table 1 indicates, there are a great numberof missing observations in the price surveys: 13
percent in 1975, an abrupt increase in 1980 to
36 percent, and a similar level in 1985 and1990. This increase does not reflect a discrete
2
The data were not made available to us by Eurostat. We
obtained hard-copies of the publications from various libraries and had the data entered into an electronic format by aprofessional data-entry firm.
3
Exceptions are the survey data for Germany and theNetherlands in 1980, 1985, and 1990, where the prices areaverages across cities within each country.
4
A comprehensive list of the goods is available at http://
www.e-aer.org/data/june05_app_crucini.pdf. The raw data
will also be made available at this location in the future.

727

TABLE 1—SCOPE OF THE PRICE SURVEYS
1975

1980

1985

1990

13
1805
38%
25%
53%
48%

13
1896
44%
32%
55%
54%

Panel A: Raw survey data
Number of countries
Number of goods
Proportion missing
Least missinga
Most missinga
Proportion of branded goods

9
658
13%
9%
27%
31%

12
1090
36%
23%
47%
42%

Panel B: After eliminating goods with insufficient dataand outliers
Number of countries
Number of goods
Proportion missing
Least missinga
Most missinga
Proportion of branded goods

9
594
10%
4%
22%
31%

12
686
17%
3%
28%
28%

13
1164
19%
7%
37%
33%

13
1101
23%
9%
34%
38%

Notes: The countries are Belgium, Denmark, France, Germany, Ireland, Italy, Luxembourg, the Netherlands, andUnited Kingdom (all years), Greece, Portugal, Spain (added
in 1980), and Austria (added in 1985). In panel B, weeliminate any observation that has a relative price more thanor less than five times that of the EU median. Then we
eliminate goods for which there are more than four missing
observations in 1975, five in 1980, and six in 1985 and 1990
(this ensures that, for each good, we have data for at least
half of the countries). The category “Proportion of branded
goods” refers to the proportion of goods for which two or
more brands exist in the price survey. Explicit descriptionsof the goods are available at http://www.e-aer.org/data/
june05_app_crucini.pdf.
aBelgium is the country with the least number of missing observations in every year, and Ireland is the country
with the greatest number of missing observations in eachyear, except for 1990, in which case the United Kingdom
has the most missing.

change in the data collection procedure, butinstead (we hypothesize) the inclusion of lowerincome countries which tend to consume fewer
items of the survey’s basket of goods. The number of missing observations also differs systematically across countries from a low of about 9
percent to a high of about 55 percent. Belgium
is consistently the country with the fewest missing observations, while Ireland is consistently
the country with the most missing observations.
Since our main focus is on explaining pricedispersion across countries, we eliminate any
good that has an insufficient number of crosscountry observations, which we define as fourin 1975, five in 1980, and six in 1985 and 1990.
The increments reflect the fact that the numberof countries in the sample increases over time.

728

THE AMERICAN ECONOMIC REVIEWJUNE 2005

TABLE 2—SAMPLE RECORDS FROM PRICE SURVEY
CodeGood description

Units

AUS

BLG

DEN

FRF

GER

GRC

IRL

ITL

LUX

NET

11111
11251
11421
11621
11911
13112
21112
22121
41112
42111
43121
43161
45111
52211
61113
61212
63111
71131
71311
72221

Long grn rice, carton
Chicken-fresh, 70% presCond. milk 9–10% b.f.
Dried almonds
Ground blended coffee
Liqueur—s.b.
Man’s k-way jacket
Ladies boots, box caf
Chest of drawers
Spring mattress: s.b.
Dishwasher: s.b.
Iron: steam, s.b.
Washing powder: s.b.
Hearing aid: s.b.
Car: 1200–1700 cc, s.b.
Bicycle: racing, s.b.
Bus fare, 6 km, no transf
Record player, s.b.
Cassette for game: s.b.
Rental of television

500 g
1.2 kg
410 g
100 g
1 kg
0.7 L
1 nb
1 pr
1 nb
1 nb
1 nb
1 nb
700 g
1 nb
1 nb
1 nb
1 tik
1 nb
1 nb
1 mo

26
107

50
204
48
54
439
579
544
4027
6988

48
207

52
203

52

51
159

35
163

52

36

43

599
824
3692
4889
2674

589
1373
2645
2904

980
1331
2362
5078

35
586
414
872

54

425
1294
1596
4095
2192
3923

61
350
542
1022
3733
11400
3253

42
115
31
28

2089
316
25976

3018

28
234
1584
3720
2834
4070

56
34

23480
2436
414

2201
299

357298527091
873

524411
30
5190
850
2296

50

1340

1925
337
29528
341213
15147
58
5158
1299
1631

7186
23548
1916

310

19314
43
4172

9
10955

1191

2962

41
948
1382

12
4719
1072
1285

502
996
4422
3990

1745
313

18000
25
4848
1066
3136

54
49
355
599
1196
2615
7742
3803
1810
23343
346786
17788
39
4861
400
1490

POR

ESP

UK

39

32
148
42
50
446
910

88
56
37
451
1152
904
2745
3529

42
49
437
491
713
2951
4630

22705
2495

22823
2450

1485

17734
356516

19134

26054

17
4194

16
7828

1670

1795

3176
4065

15238
33
764
1487

Notes: Sample of 20 records from the original 1,805 records of the 1985 survey. Currency units are Belgian francs. Countries are Austria (AUS), Belgium (BLG),
Denmark (DEN), France (FRF), Germany (GER), Greece (GRC), Ireland (IRL), Italy (ITL), Luxembourg (LUX), the Netherlands (NET), Portugal (POR), Spain (ESP),and the United Kingdom (UK). Branded goods are denoted ‘s.b.’ (selected brand). Prices are rounded to the nearest franc, although the raw data (and our analysis)
are in units of francs and centimes. Blank entries denote missing data.

We also control for gross measurement error
by eliminating goods for which the commoncurrency price differs from the good-specificmedian by a factor of five or more. These filters
reduce our sample of goods from a total of
5,449 to 3,545, with the details for individualyears provided in panel B of Table 1. Of theremaining data, the proportion of missing observations never exceeds 25 percent. Our survey
data also contain a large number of brand-namegoods, typically accounting for about one-thirdof the goods that we utilize.
Table 2 reports a number of individual
records from the 1985 survey with the goods
chosen to represent the various categories ofgoods and services contained in our dataset. All
the surveys have a similar structure involving aEurostat code, a detailed description of the particular good, the units of measure, and columns
of price data. The retail prices are cash prices
paid by final consumers and therefore include
such taxes as VAT (we control for VAT below).
The prices are averages of the surveyed prices
across different city-wide sales points.5
As is evident from the sample of goods re5
The procedure for selecting sales points follows thepractice used to construct national consumer price indices.
Sales points are selected by the national statistical offices sothat the sample is representative of the distribution of prices
in the city with more observations collected for goods
having greater price dispersion within the city.

ported in Table 2, the surveys are as comprehensive as those used to construct national
consumer price indices. We see food items,
clothing, major appliances, automobiles, services, and so on. Although Eurostat reports theprices in local currency units, Table 2 presents
prices in Belgian francs to facilitate comparisons. The deviations we see from the LOP aresuggestive of what is to come. The rental cost ofa television, for example, varies widely acrosscountries, whereas the dispersion in the cost of
rice is considerably smaller.
The goods-descriptions published by Eurostat are abbreviated versions of those used by
the statistical agency to compile the data. The
level of detail in the published version also
varies across goods. In particular, goods can beplaced into two categories: those indicated as
selected brands (s.b. in Table 2) and those without such a designation. The reason provided byEurostat for the selected brand designation is
the need for confidentiality. While we might
like to know which automobiles are Mercedes
and which are Volvos, the record does not provide us with the necessary details. It is important to note, however, that the survey is
explicitly designed to assure comparability ofgoods across locations.
One last issue is the exact timing of thesurveys. While we find it convenient to refer toour cross sections by year, in reality the pricedata for each cross section are collected in aVOL. 95 NO. 3

CRUCINI ET AL.: UNDERSTANDING EUROPEAN REAL EXCHANGE RATES

sequence of surveys. In what we call “1985,”
for example, the prices of most services werecollected in September and October 1985, while
prices of most clothing items were collected in
December 1984. The nominal exchange ratedata, with which we convert prices into a common currency, take explicit account of this timing, taking the form of averages of daily dataover the relevant time intervals.
A. Supplemental Data
Following the discussion in Section I, we
supplement our retail price data with data on
tradedness and production structure. Because
these variables are unavailable at the level of theindividual good, we assign each good to anindustry and use the industry-level measure inplace of the good-specific measure.
The variable ␣i in equation (4) is the nontraded input share for good i. We measure thisas the ratio of non-traded input costs to total
cost where both numbers are computed from the1988 input-output tables of the United Kingdom.6 Table A1 of the Data Appendix (available at http://www.e-aer.org/data/june05_app_
crucini.pdf) contains the cost shares of non-tradedintermediate inputs by industry. The values range
from a low of 4.6 percent for tobacco to a high of
31.8 percent for forestry and fisheries.
The other variable in equation (4), Var(tij兩i),
is the cross-sectional variance (across locations j for each good i) in the traded input
cost. We proxy this with the tradeability of
the final good, measured as the ratio of thetotal trade among the countries in our sample,
in a particular industry, divided by total output of that industry across the same countries.7 The (admittedly coarse) idea is that, at
the retail level, the intermediate input is often
6

Non-traded inputs are assumed to include: utilities,
construction, distribution, hotels, catering, railways, roadtransport, sea transport, air transport, transport services,
telecommunications, banking, finance, insurance, businessservices, education, health, and other services.
7
We use the actual trade share whenever trade data
are available and assign an index of zero otherwise. The
industries assigned zero trade shares are: restaurants andhotels, transport, storage and communication, inlandtransport, maritime transport, communication, financing,insurance, real estate, and community, social, and personal services.

729

very similar to the final good itself. A seller ofcomputers combines labor with computersand sells computers. The same applies to theseller of furniture. Since computers are moretradeable than furniture, however, the crosssectional dispersion in the “intermediate input
cost” for computers should be lower than thatfor furniture. Table A2 of the Data Appendix
reports the trade shares. Among traded goods,
average shares for the period 1974 to 1990
range from a low of 13 percent for tobacco
products and 15 percent for printing, publishing, and allied industries, to highs of 122
percent for professional goods and 121 percent for office and computing machinery. The
average trade share across goods for this period is a substantial 53 percent.
Comparing some of the numbers in Tables A1
and A2 suggests that the distinction between
tradeability and trade in “middle products” is important. Leather products, for instance, are highly
tradeable in the sense that their trade share is highand their non-traded input share is low. The exact
opposite is true of most service-related goods.
Forestry products (telecommunications), in contrast, are quite tradeable (non-tradeable), yet theyrequire a large (small) amount of non-traded inputs. From an economic standpoint it is unclear
whether a non-traded good with substantial traded
inputs will exhibit more or less price dispersion
than a traded good with substantial non-traded
inputs. Our empirical analysis is designed to identify these two economic effects separately.
The remaining supplemental data we use aredata on European nominal exchange rates, national income, and VAT rates. Details are provided in the Data Appendix.
III. LOP Deviations: The Mean of theDistribution

Figure 1 summarizes the empirical distribution of deviations from the LOP, qij defined inequation (1). The figure contains one chart foreach country. Each chart reports one kernel
estimate of the density of qij for each available
year. We see four striking features. First, andmost obviously, LOP deviations can be large,
with the support of most of the densities being
on the order of ⫾100 percent. Second, there isa clear income effect. The densities of the relatively poor countries—Greece, Portugal, and730

THE AMERICAN ECONOMIC REVIEWJUNE 2005

FIGURE 1. EMPIRICAL DISTRIBUTIONS OF LOP DEVIATIONS
Notes: Each line represents an estimate of the density of good-by-good deviations from the
LOP, relative to the European average price, for each of the years 1975, 1980, 1985, and 1990.
The exceptions are Austria, where we do not have data for 1975 and 1980, and Greece, Spain,
and Portugal, where 1975 is missing.

Spain in particular—seem to be located farther
to the left. Third, for the other (relatively wealthy)
countries, most of the densities seem to be locatednear zero. That is, there seem to be roughly as

many overpriced goods as underpriced goods. Finally, this latter phenomenon seems quite stable
over time. In spite of many relatively large nominal exchange rate movements, the location andVOL. 95 NO. 3

CRUCINI ET AL.: UNDERSTANDING EUROPEAN REAL EXCHANGE RATES

731

TABLE 3—AVERAGE (ACROSS GOODS) LOP DEVIATION
Panel A: Without VAT adjustment
Without income adjustment
Country
Luxembourg
Denmark
Netherlands
FranceBelgium
Germany
Austria
Italy
U.K.
Spain
GreeceIreland
PortugalStd. Dev.

With income adjustment

zj

1975

1980

1985

1990

1975

1980

1985

1990

0.299
0.260
0.126
0.126
0.122
0.105
0.096
0.061
0.035
⫺0.192⫺0.257⫺0.323⫺0.4570.232⫺0.009
0.177
0.023
0.119
0.042
0.066

0.030
0.215
0.018
0.112
0.044
0.089

⫺0.0450.132⫺0.022
0.072
0.002
0.055

⫺0.0870.050⫺0.100⫺0.170⫺0.029⫺0.2130.123⫺0.0270.219⫺0.007
0.072
0.053
0.053
0.078
0.034
⫺0.037⫺0.067⫺0.1730.012⫺0.2540.118⫺0.0970.081⫺0.031
0.084
0.006
0.046

⫺0.055⫺0.200⫺0.0430.222⫺0.055
0.075
0.067
0.013
0.096
⫺0.007⫺0.001⫺0.082⫺0.1700.048⫺0.1740.109⫺0.050⫺0.213⫺0.1050.054⫺0.018⫺0.0980.104⫺0.0460.077⫺0.1370.125⫺0.0880.034
0.032⫺0.0280.065⫺0.030⫺0.011
0.013⫺0.067
0.170
0.008
0.083

⫺0.1650.155⫺0.030
0.039
0.023
0.028
0.049
0.014
⫺0.0380.015⫺0.0230.102⫺0.1140.083⫺0.1950.129⫺0.052
0.094

Panel B: With VAT adjustment
Without income adjustment
Country
Luxembourg
Denmark
Netherlands
FranceBelgium
Germany
Austria
Italy
U.K.
Spain
GreeceIreland
PortugalStd. Dev.

With income adjustment

zj

1975

1980

1985

1990

1975

1980

1985

1990

0.299
0.260
0.126
0.126
0.122
0.105
0.096
0.061
0.035
⫺0.192⫺0.257⫺0.323⫺0.457
0.232

0.029
0.143
0.024
0.074
0.016
0.078

0.056
0.108
⫺0.001
0.065
0.015
0.077

0.002
0.048
⫺0.0310.036⫺0.0160.053⫺0.0970.056⫺0.018⫺0.088⫺0.060⫺0.134
0.078

0.018
0.144
⫺0.012
0.056
0.046
0.060
0.050
0.032
0.007
⫺0.048⫺0.1690.029⫺0.2510.103⫺0.0350.074⫺0.0150.049⫺0.011
0.063⫺0.042⫺0.152⫺0.0200.124⫺0.0730.041
0.036⫺0.0020.044⫺0.0280.016
0.003⫺0.0830.035⫺0.0870.060⫺0.039⫺0.161⫺0.1100.059
0.041⫺0.0360.037⫺0.0130.050⫺0.0890.053⫺0.0970.011
0.010⫺0.031
0.021⫺0.0450.009
0.072⫺0.009
0.123
0.044
0.062

⫺0.0820.098⫺0.029
0.032
0.024
0.042
0.028
0.017
0.005
0.012
⫺0.061
0.094⫺0.1500.069⫺0.2000.111⫺0.096
0.076

Notes: The variable zj denotes average log income differences, 1975–1990, relative to the EU average. The remaining data
are equally weighted averages of LOP deviations, across goods i, for each country j: E(qij兩j). Standard errors were reported
in the previous version of the paper (available at http://www.e-aer.org/data/june05_app_crucini.pdf) but are omitted here forspace considerations. All standard errors are between 0.01 and 0.02 with the exception of those from Greece, Portugal, andSpain which are between 0.015 and 0.025. Income and VAT adjustment are described in the text and the Data Appendix. For
these calculations we eliminate multiple brands of the same good.

shape of the densities don’t seem to move aroundmuch.8To be more precise, Table 3 reports the
sample means, E(q ij 兩j), of the density esti8
There are several glaring exceptions but, interestingly,
they go against the notion that movements in the distribution are driven by movements in nominal exchange rates.
Between 1975 and 1980, for instance, average prices in
Ireland and the United Kingdom increased substantiallyrelative to Europe (see also Table 3), yet their currencies
actually devalued relative to Europe.

mates from Figure 1. The countries are organized from richest to poorest. The values in
the left-most columns of panel A confirm
what we see in Figure 1; many of the means forthe relatively rich countries are within the interval⫾10 percent. There are, however, some exceptions, most notably Denmark. With this in mind,
the remainder of the table makes the following
adjustments.
(a) First, we use industry/year-specific data
on VAT rates to reduce each price in our732

THE AMERICAN ECONOMIC REVIEWJUNE 2005

FIGURE 2. AVERAGE LOP DEVIATIONS(Raw data (circles) and income/VAT adjusted (filled circles))Notes: Each point is the average LOP deviation for a particular country/year. Vertical dashedlines delineate countries. Each point between these dashed lines is one particular year for thatcountry. Thus, the first four points represent Luxembourg for 1975, 1980, 1985, and 1990, thenext four represent Denmark for the same years, and so on. The countries are organized fromlowest to highest income, as in Table 3. Finally, open circles represent unadjusted data (i.e.,the means from Table 3 in the left-most columns of panel A), whereas filled circles representmeans which have been adjusted for income and VAT differences (i.e., from the right-mostcolumns of panel B in Table 3).

dataset to be a before-VAT rate. The VAT
data are described and documented in the
Data Appendix. Note that Denmark is by far
the highest VAT country. We then recompute the values qij and their cross-good averages. The results are reported in Table
3, in the left-most columns of panel B.
(b) Second, we adjust the means for relative
income differences via the regression
共5兲

E共q ij,t 兩j, t兲 ⫽ a ⫹ bz j,t ⫹ residuals

where z j,t denotes the (log) per-capita income difference between country j andthe EU average in date t, and (as above),and E(q ij,t 兩j) denotes the (cross goods i)average LOP deviation for country j rel-

ative to the EU average at date t. 9 The
results are reported in the rightmost columns of Table 3.
Net of these adjustments, the average deviations
from LOP are substantially reduced and arequite small in magnitude. Out of 47 average
LOP deviations, only four are outside the interval ⫾10 percent. The standard deviations of theaverages (across countries), shown in the final
row of each panel, are reduced by almost half.
Figure 2 provides emphasis by plotting the av-

9
The time subscript is included here to indicate that, in
our relative income adjustments, we incorporate the important changes that occurred during 1975–1990 (e.g., Ireland).

VOL. 95 NO. 3

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733

TABLE 4—AVERAGE (ACROSS GOODS) LOP DEVIATION BY TRADEDNESS
1975

Luxembourg
Denmark
Netherlands
FranceBelgium
Germany
Austria
Italy
U.K.
Spain
GreeceIreland
PortugalStd. Dev.

1980

1985

All

TradedNontradedAll

TradedNontraded⫺0.0350.074⫺0.0150.049⫺0.011
0.063

0.006
0.082
⫺0.0230.045⫺0.0120.049⫺0.273
0.020
0.016
0.063
⫺0.003
0.137

0.002
0.048
⫺0.0310.036⫺0.016
0.053

0.009
0.067
⫺0.0550.026⫺0.0340.040⫺0.031⫺0.064
0.109
0.098
0.094
0.128

⫺0.039⫺0.1610.000⫺0.151⫺0.247⫺0.222⫺0.096⫺0.115

0.017

0.076

0.076

0.151

⫺0.1100.059
0.041⫺0.0360.037⫺0.0130.050⫺0.0970.036
0.044⫺0.010⫺0.0020.026
0.047⫺0.1860.184
0.028⫺0.1600.261⫺0.222
0.153

1990

All

TradedNontradedAll

TradedNontraded⫺0.0890.053⫺0.0970.011
0.010⫺0.031
0.021⫺0.0450.009
0.072⫺0.009
0.123
0.044
0.062

⫺0.0640.063⫺0.1080.001
0.008⫺0.0460.010⫺0.026⫺0.026
0.079
0.007
0.085
0.076
0.059

⫺0.2390.001⫺0.027
0.068
0.026
0.051
0.083
⫺0.1650.217
0.017⫺0.1110.351⫺0.1330.158⫺0.0820.098⫺0.029
0.032
0.024
0.042
0.028
0.017
0.005
0.012
⫺0.061
0.094⫺0.1500.069⫺0.0430.101⫺0.049
0.038
0.018
0.022
0.015
0.039
⫺0.0560.015⫺0.0350.059⫺0.1170.058⫺0.3180.083
0.094⫺0.005
0.067
0.149
0.124
⫺0.1080.326⫺0.020⫺0.2780.298⫺0.301
0.211

Notes: See notes to Table 3. Data here are identical (income/VAT adjusted) except for the distinction between traded and non-traded goods.
A non-traded good is defined as having a trade share equal to zero according to Table A2 of the Data Appendix.

erage LOP deviations before and after income/VAT adjustment.10
What does the simple model of Section I haveto say about these results? First, the interpretation of the income adjustment is obvious; it
represents cross-country variation in wj in themanner of Balassa-Samuelson. Second, the factthat (net of VAT) the remaining average pricedifferences are small suggests that tij changes
sign a lot across goods. Countries import somegoods, export others, and on average the effects
on LOP deviations cancel out.
Further evidence is provided in Table 4,
where we distinguish the averages E(qij兩j) by thetradedness of the goods across which the average
is taken. We see that average prices for traded
goods tend to be much closer to zero than for
non-traded goods. While this is interesting in andof itself, our model suggests two possibilities.
First, cross-sectional variation in the ␣i’s for non10
In a previous version of the paper, available at http://
www.e-aer.org/data/june05_app_crucini.pdf, we show that
CPI expenditure share weighted averages tell very much thesame story as the equally weighted averages reported here.
In addition, we perform a number of consistency checks on
our data using different data sources. We show that (a)before income/VAT adjustment, our estimates of (absolute)
average LOP deviations are quite similar to the absolute
PPP data available from the OECD and from the Penn
World Tables (PWT); and (b) when we first-difference ourdata (necessarily over five-year intervals), the implications
for correlations between changes in real and nominal exchange rates (e.g., Michael Mussa, 1986) are consistent withthose from the PWT, the OECD, and the national CPI datacontained in the International Financial Statistics (IFS).

traded goods could bias our income adjustment,
which (in Table 4) is done based on the average
traded/non-traded LOP deviation. Second, it could
be the case that, among the set of non-traded
goods for a particular country, there is less “averaging out” associated with some traded inputs
being exported and others imported. Our supplementary data are not yet rich enough to distinguishbetween these possibilities.
IV. LOP Deviations: The Variance of theDistribution

We now examine good-by-good price dispersion which, as in equation (4), we measure as thevariance of qij across countries j: ␴2i ⬅ Var(qij兩i).
Figure 3 plots kernel estimates of the density of ␴ifor each year. We see that different goods canhave substantially different amounts of price dispersion, with the sample standard deviations ranging from 2 percent to 80 percent. While it mightseem that price dispersion increased after 1975, thisis instead an artifact of the sample of countries expanding in 1980 to include lower-income countries.
Table 5 reports means of the distributions from
Figure 3 broken down by year, tradeability, and thefraction of non-traded inputs required for production.
We see strong evidence that these variables are important determinants of good-by-good price dispersion. Average price dispersion across traded goods is
25 percent versus 40 percent for non-traded goods.
The average for goods with above-average share of
non-traded inputs is 32 percent versus 25 percent forgoods with a below-average share.

734

THE AMERICAN ECONOMIC REVIEWJUNE 2005

FIGURE 3. EMPIRICAL DISTRIBUTIONS OF Var(qij兩j)1/ 2
Note: Each line represents an estimate (for each year) of the density of Var(qij兩i)1/ 2, thestandard deviation of the LOP deviation for good i across countries j.

Next we consolidate this information in aregression framework.
A. Regressions
We begin by slightly rewriting our model ofprice dispersion, equation (4), as(6)

␴ 2i ⫽ ␣ 2i Var共w j 兲 ⫹ 共1 ⫺ ␣ i 兲 2 x i

where, for notational simplicity, we define
x i ⬅ Var(t ij 兩i). Recall that, as is discussed in
Section II A, we do not have direct data on t ij .
Instead, we proxy x i itself with a measure of
the tradeability of the final good. We also
assume that the conditional covariance fromequation (4) is zero.11 Based on this, Table 6

11

We do not have data that allow us to identify variationin Cov(wj , tij兩i) across goods i. Given this, the only alternative is to assume a constant instead of zero. The difference,
however, is minor, resulting in only a slightly more complex
quadratic function via the inclusion of the term ␣i(1 ⫺ ␣i).
Moreover, when we do this, we find that (a) the hypothesisthat the coefficient on the additional variable is zero cannot
be rejected; and (b) the economic implications of the re-reports estimates of the parameters of thefollowing regression:(7)

␴2i ⫽ a ⫹ b␣2i ⫹ c共1 ⫺ ␣i 兲2xi ⫹ residuals.

We see that the coefficients are all highly significant and that the regression function explains asignificant portion of the cross-sectional variationin our data on price dispersion. Moreover, thecoefficients are economically significant. For example, if we consider the good with the smallest
share of non-traded inputs ␣i , and the smallest xi(the latter meaning that the good is highly traded),
the predicted price dispersion (based on thepooled regression) is 0.12 (in standard deviation).
The opposite case—the good requiring the most
non-traded inputs with the highest xi (lowest tradeability)— gives a value of 0.43. The increase of
0.31 is substantial, both relative to the unconditional (average) dispersion in the data (standard
deviation of roughly 0.28), as well as the range of
␴i which is 0.02 to 0.82.
maining parameter estimates are almost identical to those ofequation (7).

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735

TABLE 5—AVERAGES OF GOOD-SPECIFIC MEASURES OF PRICE DISPERSION

All goods
Non-traded goods
Traded goods
Above avg. share of services
Below avg. share of services

1975

1980

1985

1990

Average

0.22900.31380.21640.26190.2116

0.29410.41460.27500.33720.27030.30240.42520.2846
0.34640.27790.28550.45370.2596
0.33780.25510.27770.40180.25890.32080.2537

Notes: Values are averages of good-specific measures of price dispersion. Each value is theaverage (across goods i) of Var(qij兩i)1/ 2, the good-by-good sample standard deviation, where
the standard deviation is across countries j.

What does theory add here? There are twomain differences between the regression (7) andthe (obvious) reduced-form regression of ␴2i on
␣i and xi. The first is the quadratic functional
form. This is a relatively uninteresting artifactof our choice of price-dispersion measure, thevariance. Empirically, it turns out to be of little
importance. The second difference relates toeconomics. The essence of the interaction term,(1 ⫺ ␣i)2xi , is that the explanatory power of the
tradeability variable, xi , should diminish forgoods requiring a high share of non-traded inputs, ␣i. If most of the cost of a taxi ride is labor,
then the relative price of gasoline shouldn’t
matter much.
We examined the importance of the interaction term in several ways. All of them indicated that this restriction is inconsistent
with our data. For example, if one writes out
equation (4) as a quadratic function of fivevariables, two of those will be ␣ i and x i . In nocase were we able to reject the hypothesis thatthe coefficients on the remaining variables
were equal to zero. Similarly, if we add theinteraction term to the simple linear specification involving ␣ i and x i , we cannot reject
the hypothesis that its coefficient is zero. Finally, we took a subsample of goods withrelatively high non-traded input shares andregressed the price dispersion measures fromthis subsample on our tradeability measure.
We found strong evidence that the opposite istrue. That is, the tradeability measure x i has
more explanatory power conditional on highnon-tradedness, not low non-tradedness.
Overall, the message is that ␣i and xi havestrong explanatory power for cross-sectional
price dispersion, but that the functional-form
restrictions from our theory are not an importantpart of this. This could represent a limitation of
the theory. It could also represent a limitation of

our data on the characteristics of individual
goods. One limitation is that we are forced touse industry-level data to try to explain goodspecific price dispersion. More important, in ourview, is our use of the trade share as a proxy for
trade costs. As is well known, the volume oftrade depends upon not only trade costs, butalso comparative advantage and the elasticity of
substitution between domestic and foreign
goods. Carolyn L. Evans (2003), for example,
shows how a traditional gravity model oftrade predicts that bilateral trade flows depend

TABLE 6—REGRESSION ESTIMATES

␴2i ⫽ a ⫹ b␣2i ⫹ c(1 ⫺ ␣i)2xi ⫹ residuals
Year

a

b

c

R2a

R2d

1975

0.083
(0.006)0.099(0.007)0.115(0.006)0.122(0.005)0.102(0.003)0.299(0.115)0.921(0.143)0.791(0.118)1.033(0.106)0.868(0.064)0.090(0.013)0.051(0.012)0.059(0.008)0.100(0.008)0.062(0.005)

0.433

0.120

0.291

0.107

0.319

0.106

0.537

0.291

0.417

0.129

1980
1985
1990
PooledNotes: Estimates of the parameters of the regression are
based on equation (7) in the text. ␴2i denotes our goodspecific measure of price dispersion: the sample variance ofqij from equation (1) in the text. ␣i denotes the non-traded
input share for good i and xi is (the negative of) the tradeshare of good i (see Section II A for details). Standard errors
are in parentheses. Because our explanatory variables areaveraged across different numbers of goods within industry
groups, the residuals will be heteroskedastic. We therefore
use a feasible GLS estimator (details are provided in the
Data Appendix). R2a denotes the regression R2 that results inaveraging the dependent variable in the same manner as the
explanatory variables. R2a denotes the regression R2 from the“raw regression” where, necessarily we are trying to accountfor variation in ␴2i using variables that have (potentially) had
some of their explanatory variation averaged away.

736

THE AMERICAN ECONOMIC REVIEW(negatively) upon the trade cost multiplied by
the elasticity of substitution. Thus, higher tradeshares could reflect lower elasticities of substitution, higher trade costs, or both. Future work
should concentrate on developing additional
microeconomic data on the characteristics ofindividual goods, including elasticities ofsubstitution.
V. Concluding Comments

A considerable body of empirical and theoretical work in international economics attempts
to answer two basic questions. The first question is: What determines whether a deviationfrom the LOP will be large or small? The second question is: What determines whether adeviation from the LOP will be enduring or
short-lived?
The empirical literature on the first questionis very limited due to a paucity of absolute pricedata on comparable goods across international
locations. The theoretical literature, in contrast,
is well-developed and offers a number of potential answers. The models of Bernard Dumas(1992) and Piet Sercu et al. (1995) emphasize
the magnitude of shipping costs in consumption
goods and physical capital, respectively. The
models of Paul R. Krugman (1987) emphasize
imperfect competition. The models of Balassa(1964) and Samuelson (1964) emphasize productivity differences across traded and nontraded goods. The models of Ethier (1979) andRonald W. Jones and Kalyan K. Sanyal (1982)
emphasize that much of international tradetakes place in intermediate inputs, not final
goods and services. In each case, the first-order
restrictions from theory are on absolute LOP
deviations. Our paper represents the development of better data to test these restrictions.
What we find is encouraging from the perspective of theory. An economically important partof the heterogeneity across goods in LOP deviations is related to the tradeability of the good
and the share of non-traded inputs required to
produce the good.
The empirical literature on the second question is vast, in part because persistence may bestudied using relative versions of the LOP and
PPP, thus eliminating the need for absoluteprice data. The consensus is that the half-livesof deviations from parity last between three and

JUNE 2005

five years.12 The theoretical literature, however,has focused almost exclusively on the adjustment (or lack of adjustment) of domesticcurrency prices to changes in the nominal exchange rate. In particular, the sticky-price models, which have followed Maurice Obstfeld andRogoff (1995), are distinguished by assumptions of when firms can change their prices and,
therefore, impose first-order restrictions onchanges in LOP deviations. Given the persistence of the deviations, most economists believethat sticky prices, in their various forms, cannot
account for the observed persistence in realexchange rates.
Is there an important link between these questions? We think so, in spite of the fact that thetwo bodies of literature addressing them have
evolved more or less independently. To understand this, consider the “PPP Puzzle” posed by
Rogoff (1996); the persistence and conditional
volatility in PPP and LOP deviations are toolarge to be consistent with sticky-price models
in conjunction with data on price-setting behavior. Models of goods-market arbitrage andnon-traded inputs, in contrast, restrict theunconditional volatility of PPP and LOP deviations. This is where the link lies. If the unconditional volatility restrictions are supported by
the data—as our study suggests—then we are
led to rethink our interpretation of the timeseries evidence. Rogoff (1996), for instance,interprets the evidence as suggesting, “International goods markets, though becoming more
integrated all the time, remain quite segmented,
with large trading frictions across a broad rangeof goods.” Our view is that this is too broad abrush. While it is certainly true for Big Macs,
the set of goods for which it is suspect goesbeyond gold bullion. Moreover, theory is informative for which goods are in the set and which
are not. A promising avenue for future work
involves further integration of arbitrage-basedmodels—which impose absolute bounds on
LOP deviations—with models which describe
behavior within the bounds, such as sticky-pricemodels and models where most trade is at thelevel of intermediate inputs, not final products.

12
See, for example, Jeffrey A. Frankel and Andrew K.
Rose (1996), Christian J. Murray and David H. Papell(2003), and Rogoff (1996).

VOL. 95 NO. 3

CRUCINI ET AL.: UNDERSTANDING EUROPEAN REAL EXCHANGE RATES737

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