NBER WORKING PAPER SERIESMICROECONOMIC SOURCES OF REAL EXCHANGE RATE VARIABILITY
Mario J. Crucini
Christopher I. Telmer
Working Paper 17978
http://www.nber.org/papers/w17978
NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
April 2012

Financial support of the National Science Foundation, SES #1030164 and SES # 0524868 is gratefully
acknowledged. The views expressed herein are those of the authors and do not necessarily reflect theviews of the National Bureau of Economic Research.
NBER working papers are circulated for discussion and comment purposes. They have not been peerreviewed or been subject to the review by the NBER Board of Directors that accompanies official
NBER publications.
© 2012 by Mario J. Crucini and Christopher I. Telmer. All rights reserved. Short sections of text, notto exceed two paragraphs, may be quoted without explicit permission provided that full credit, including© notice, is given to the source.

Microeconomic Sources of Real Exchange Rate Variability
Mario J. Crucini and Christopher I. Telmer
NBER Working Paper No. 17978
April 2012
JEL No. E3,F31,F4
ABSTRACT
We provide three sets of variance decompositions on microeconomic international relative price data.
The first shows that the overall distribution of absolute deviations from the Law of One Price (LOP)
is dominated by cross-sectional variation in long-term averages, not by time-series variation aroundthe long-term averages. The second shows that time-series variation in changes in LOP deviations
is dominated by idiosyncratic, goods-specific variation, not by aggregate variation such as that arisingfrom nominal exchange rates. The third shows that time-series and cross-sectional variance are connectedacross goods. Goods that exhibit high cross-sectional variance also exhibit high time-series variance.
Moreover, when this connection is made conditional on the tradeability of a goods, a two-factor structure
for the goods-specific cross-section is revealed. We argue that this factor structure, in addition to ourother variance decompositions, is informative for the construction of models that can synthesize themicro and macroeconomic behavior of relative prices.
Mario J. Crucini
Department of Economics
Vanderbilt University
Box 1819 Station B
Nashville, TN 37235-1819
and NBER
mario.j.crucini@vanderbilt.edu
Christopher I. Telmer
Tepper School of Business
Frew and Tech Streets
Carnegie-Mellon University
Pittsburgh, PA 15213
chris.telmer@cmu.edu

1Introduction

This paper provides some variance decompositions on microeconomic international
relative price data that are meant to inform the burgeoning literature bringing
together international macroeconomics and trade. International macro typicallyfocuses on the intertemporal dimension of prices. Trade places more weight on thespatial dimension. The intersection between the two (e.g., Burstein and Atkeson(2008), Ghironi and Melitz (2005)) emphasizes both time and space. Our variancedecompositions are explicitly designed with this in mind. We parse the total
variation in Law-of-One-Price (LOP) deviations into cross-sectional and time series
components. The former is the variance in LOP deviations across locations andgoods, after averaging away the time series variation. We associate it with thetrade literature, which emphasizes imperfect competition and barriers to trade.
The latter is the variation around these cross-sectional, long-run averages. We
associate it with DGSE models, which emphasize productivity and policy shocks
and how they interact with nominal rigidities. Our goal is to better understandeach of these dimensions of the data and, in particular, any interactions between
them.
Our results boil down to three sets of variance decompositions. What theyshow is as follows. First, cross-sectional variance in long-term absolute deviations
from the Law of One Price (LOP) is large relative to time-series variance. Second,
time-series variance in changes in LOP deviations is dominated by good-specificvariation, not country-specific variation such as arises from nominal exchange rates.
Third, cross-sectional and time-series variation are connected when we look acrossgoods. This connection has several facets. The simplest is unconditional: goods
that exhibit high cross-sectional variance in long-term, mean LOP deviations also2

exhibit high time-series variation around these long-term means. A richer pattern arises when we condition on the tradeability of goods. Non-traded goods
exhibit relatively high cross-sectional variation, but relatively low time-series variation. We show that this implies the existence of a second source of cross-sectional(across goods) variation, above and beyond tradeability. This second ‘factor’ generates a positive association between cross-sectional and time-series variation, and
it is large in the sense that it clouds the negative relationship associated withtradeability. We argue that these variance decompositions provide valuable information for the construction of models aimed at synthesizing the microeconomic
and macroeconomic behavior of international relative prices.
We now elaborate on each set of results in turn. To better understand thefirst set, consider a specific good: an apple. We first compute the absolute LOP
deviation for apples between 123 major cities in the world, for each year between
1990 and 2005. We then compute the time-averaged, long-term LOP deviation —the ‘fixed effect’ — for each pair of cities. We find that cross-sectional variationin these fixed effects is large relative to time-series variation around them. Thatis, apples simply tend to be expensive in some cities and cheap in others, thiscity-specific tendency is stable over time, and the time-variation that does exist is
relatively small. Our data include the prices of many other goods and services, notjust apples. This relative price behavior is broadly representative of most goods
and services in the typical urban consumption basket.
What does this tell us about economic models? Consider sticky-price models,for example. They emphasize frictions in the mechanism through which prices
change. They often ignore frictions which cause long-term LOP deviations. Our
results suggest that what they are ignoring is large. The overall distribution of LOP
deviations is dominated by something that sticky-price models ignore, basically by3

construction. Is this likely to matter? We think so. It seems likely that whatever
are the frictions underlying long-term LOP deviations, these frictions also playa role in governing how the deviations change over time. Much of our paper isdedicated to substantiating this. For now, we simply emphasize an interpretative
point. Suppose that one is ultimately interested in the transmission of shocks.
We don’t deny that at a sufficiently short horizon, goods prices — in particularinternational goods prices — are sticky, and that understanding the frictions thatdrive this is important. But nevertheless, a friction that generates a 5 or 10%
change in a relative price seems less striking in a world where long-term LOP
deviations average 50% than in a world where they average zero.
Our second set of results address real and nominal exchange rate variability
more directly. To motivate them, consider the Canada-U.S. real exchange rate,
depicted in Figure 1. This graph is representative of the common wisdom — often
attributed to Mussa (1986) — that real and nominal exchange rates are basicallythe same thing. This evidence has motivated much economic discussion and modelbuilding. It is at the root of the notion that nominal exchange rate variability
creates allocative distortions in international consumption and investment decision
making. It plays a central role in Rogoff’s (1996) ‘PPP Puzzle:’ the statement that
PPP deviations are too large and persistent to be reconciled by some combinationof nominal rigidities and real shocks. Finally, it is often used to motivate stickyprice models. A caricature of Figure 1’s interpretation in this context is that theworld is described by fixed prices in domestic and foreign currency units and that
nominal exchange rate variability simply ‘shifts around’ the entire distribution ofindividual goods prices.

4Figure 1
Canada-U.S. Real and Nominal Exchange Rates(Annual Data: Indexed 1971=1)

We ask if these types of interpretations are consistent with the behavior ofchanges in microeconomic LOP deviations. Following the above example, wefirst compute the city-specific relative price of apples, 1990-2005. We do so on
a bilateral-pair basis (e.g., the relative price of apples between Pittsburgh andToronto, 1990-2005). We then compute changes in these relative prices, 19912005, and do the same thing for bananas, toaster ovens, haircuts and many othergoods and services. Finally, for each bilateral city-pair we decompose the varianceof the changes into two orthogonal components: a city-pair-specific component
and a good-specific component.
What we find is that the magnitude of the city-specific component is small relative to the good-specific component. This is true for city-pairs which are withina country. It is only slightly less true for for city-pairs that are not. For example,
5among intra-U.S. city-pairs the average amount of total variation attributable tothe city-specific component is 1.8%. The analogous number for U.S.-Canadiancity-pairs is 6.9%. One’s natural inclination is to attribute the difference to nominal exchange rates. This inclination is correct; the correlation between the U.S.Canadian city-specific component and changes in the nominal exchange rate is
0.93. The main point, however, is that roughly 93% of the variation in changes in
U.S.-Canada LOP deviations has nothing to do with nominal exchange rates. It
is specific to the goods themselves.
What does this tell us about economic models? That they place heavy weighton country-specific price shocks (like the nominal exchange rate) at their peril.
What about the empirical evidence on aggregate real exchange rates discussed
above? Our results do not contradict them. When we aggregate across the microeconomic prices our real exchange rate picture is very similar to Figure 1. What
our results do contradict, however, are some of the popular interpretations of Figure 1. If you think that real exchange rate variability is driven by nominal exchange
rates moving around a distribution of microeconomic sticky prices, you are wrong.
There is a great deal of movement within the distribution. Microeconomic prices
in local currency units move around a lot more than the nominal exchange rate
does.
At this point, one might argue that our results are not surprising. Qualitatively,
we agree. It is not surprising that long-term deviations from LOP exist between
two cities. Retail goods are bundles of traded and non-traded goods and this isexactly what we should expect. Neither is it surprising that changes in goodlevel relative prices are more variable than changes in aggregate prices. Thisis an obvious implication of averaging. The importance of our point, then, isquantitative, not qualitative. It is important to know that 2/3 of the total variation
6

in LOP deviations is cross-sectional. It is important to know that changes innominal exchange rates account for less than 10% of the variation in good-specific
LOP deviations. This being said, the final section of our paper goes further,drawing some informative connections — both qualitative and quantitative —between the long-term and the short-term, and between the tradeability of goods
and whatever else it is that drives price dispersion.
Our third set of variance decompositions articulates these connections. We
begin by showing that there exists an unmistakable positive relationship between
cross-sectional and time-series variance. That is, if apples are associated with relatively large long-term, mean LOP deviations, then the variation around thesemeans also tends to be relatively large. This is an unconditional statement (inthe goods dimension). One’s first reaction to it, motivated by years of theory andevidence, is to ask whether the tradedness of goods can shed any light. We doso, conditioning on tradeability in the cross-section. What we find, at first blush,
might seem to contradict the unconditional evidence. Consistent with the standard
Balassa-Samuelson (Balassa (1964), Samuelson (1964)) idea, non-traded goods exhibit more variance than traded goods, but this is only the case for cross-sectionalvariance. In the time-series dimension, traded goods exhibit larger deviations from
LOP. Where is the contradiction? If non-traded goods have high cross-sectionalvariation, and cross-sectional variation is positively associated with time-series
variation, then shouldn’t non-traded goods also have relatively high time-series
variation?
The answer is no. There is no contradiction. Instead, there is a second sourceof variation across goods, above-and-beyond tradeability. Moreover, this source ofvariation is not just noise. It must display a systematic pattern. It must (i) move
both cross-sectional and time-series dispersion in the same direction, and (ii) be
7large enough to cloud the negative relationship induced by tradeability. We neither
model nor measure (directly) this source of variation. Our objective is simply toprovide some broad variance decompositions that can inform structural models aswell as further empirical work.
It is worth noting that our results, as they relate to tradeability, evoke thoseof Engel (1999). Broadly speaking, he showed that, in contrast with the basic
Balassa-Samuelson idea, variability in traded goods prices seems to play an important, perhaps dominant role in accounting for real exchange behavior. His
conclusions were based on index-number data, thus emphasizing time-series variation. Our findings are complementary. We show, while the Balassa-Samuelson,
traded/non-traded dichotomy gets it right in the long-run, in the short-run we see
the opposite, with time-series variation being larger for traded goods. What is going on? We provide additional empirical evidence suggesting that the shocks that
affect traded goods prices are larger than those affecting non-traded goods prices.
Anecdotally, this just says that the shocks that affect the cost of petroleum products and electronic components are large relative to those affecting haircuts (but,nevertheless, the cross-sectional dispersion in haircut prices is relatively large).
Another anecdote is that the Headline CPI Index — which includes the highly
tradeable food and energy components — is more variable that the Core CPI Index. In Section 5 go beyond anecdotes and show that our microeconomic data
displays such behavior.
The remainder of our paper is organized as follows. Section 2 describes our data
and the basic definitions and transformations that we employ. Section 3 presents
results based on absolute LOP deviations and Section 4 turns to changes in LOP
deviations. Section 5 provides some interpretation of our basic results and thendelves further into the linkages between sources of cross-sectional and time-series
8variation that we discuss above. Section 6 concludes.

2

Data

We use panel data on individual goods prices that vary across both geographic
locations and time. This allows us to study both absolute and differenced LOP
deviations. The body of work that exploits such data is by now large and growing.
Examples include Alessandria and Kaboski (2011), Bergin and Glick (2007), Broda
and Weinstein (2008), Campbell and Lapham (2004), Fischer (2012), Fitzgeraldand Haller (2008), Gagnon (2010), Gopinath and Rigobon (2008), Gopinath, Gourinchas, Hsieh, and Li (2011), Gorodnichenko and Tesar (2009), Hellerstein (2008),
Hummels (2007), Imbs, Mumtaz, Ravn, and Rey (2005) and Simonovska (2010),
as well as a previous paper of our own, Crucini, Telmer, and Zachariadis (2005).
The specific data that we use is as follows. We obtain local-currency retailprices from the Worldwide Cost of Living Survey coordinated and compiled by
the Economist Intelligence Unit (EIU). The target market for this data source arecorporations seeking to determine compensation levels for employees residing indifferent cities around the world. While the goods and services reflect this objective
to some extent, the sample is broadly representative of what would appear in the
consumption basket of an urban consumer.1 What makes the data attractive forresearch purposes is the fact that the prices are in absolute currency units and thesurvey is conducted by a single agency in a consistent manner over time. It also
has a limited intra-national dimension, thus providing a useful contrast between
domestic and international price dispersion.
1
Rogers (2002) conducts an extensive comparison between the EIU data and data from national
statistical agencies. He finds that the EIU data are broadly representative of what the consumer
price index data tell us.

9More specifically, the EIU dataset consists of local-currency retail prices, inclusive of sales tax, on as many as 301 goods and services, sampled in 123 cities
from 78 different countries. The data are annual, 1990-2005. The country with themost intranational observations is the U.S., with 16, followed by Australia, China
and Germany with 5, Canada with 4, Saudi Arabia with 3, and Brazil, France,
Italy, Russia, Spain, Switzerland, UK, India, Japan, Vietnam, New Zealand with
2. A number of recent papers have used this data, including Crucini and Shintani(2008), Engel and Rogers (2004), Parsley and Wei (2000) and Rogers (2002).2 .
We denote Pijt as the local-currency price of good i in city j in year t andSjk,t as the date t nominal exchange rate between cities j and k, in units of cityk (Sjk,t = 1 if cities j and k share the same currency). We transform prices intobilateral log deviations from the law-of-one-price (LOP):3

qi,jk,t = log(

Pijt Sjk,t
),
Pikt

(1)

In words, these LOP deviations are the date t (log) prices of good i in city j inunits of good i in city k. Appendix A provides additional details, including how
we clean the data and deal with missing observations.
Figure 2 shows estimates of the density function for qi,jk,t for 1990, 1995, 2000
and 2005, for both international city-pairs and U.S. city-pairs (the graph is quite
similar for intranational pairs more broadly). The graph shows that dispersion in
good-by-good LOP deviations is large, and substantially larger once we include a2

See http://bertha.tepper.cmu.edu/telmerc/eurostat for a list of all goods-and-services
and all cities
3
A previous version of the paper employed an alternative
LOP measure, the log deviation fromP
the cross-city geometric average: log(Sjn,t Pijt )/ M
j=1 log(Sjn,t Pijt ) where M denotes the total
number of cities and n denotes the numeraire currency in units of which all prices are expressed(our measures of price dispersion are independent of the choice of the numeraire currency). While
this definition results in lower overall LOP variability (by construction), the main message of ourpaper remains unchanged.

10

wide array of international location-pairs.

3

Variance in Absolute LOP Deviations

We begin by decomposing the variation in qi,jk,t , good-by-good, into a crosssectional and a time-series component:Var jk,t (qi,jk,t | i) = Var jk Et (qi,jk,t | i, jk) + Ejk Var t (qi,jk,t | i, jk) (2)= Ti + Fi .

(3)

Our notational conventions are slightly non-standard. The conditional mean andvariance operators, Ex (· | y) and Var x (· | y), denote the mean and variance calculated by integrating across the variable(s) x while conditioning on the variable(s)y. So, for instance, Et [qi,jk,t | i, jk] is the mean of the time series of relative prices
for good i between cities j and k and Var jk (Et [qi,jk,t | i, jk]) is the cross-sectionalvariance, across location-pairs, in these time-series means.
To more easily interpret Equation (2), consider its individual pieces. First,
Et [qi,jk,t | i, jk] is the mean (over time) of the relative cost of good i between cities
j and k. If, for example, j = New York and k = Toronto, and if this mean ispositive, then good i tends to be more expensive in New York than in Toronto ina long-run sense. The first term in the decomposition, Ti , is the cross-sectionalvariance — across location-pairs — of these long-run means. It asks “how muchof the total variation for good i is due to long-run, city-specific ‘fixed effects?’
The second term, Fi , captures time-series variation around the long-term means.
It is the average (across location-pairs) time-series variance in the absolute LOP
deviation for good i. It asks “how much of the total variation for good i is due to11shocks that die out over time?”
Figure 3 provides an (intentionally stark) illustration. It plots the time seriesof LOP deviations between North American city-pairs for a typical non-traded
good and a typical traded good: haircuts and apples, respectively. The haircut
graph is dominated by long-run means. Cross-sectional variance in these means
is measured by Ti from Equation (3). Time series variance around the long-run
means is relatively small and is measured by Fi . Numerically, Ti and Fi are,respectively (for haircuts) 86% and 14% of the total variance. Apples tell quite
a different story. Time-series variance plays a much larger role. The analogous
numbers are 48% and 52%.
Why is this decomposition an interesting one? Because economic models often
make stark assumptions about its components. The archetypical trade model
assumes that the differences between home and foreign prices reflect tariff andtrade barriers, which vary across goods and locations, Ti > 0, but not time, Fi = 0.
The archetypical business cycle model assumes that unexpected shocks generatetransitory fluctuations in international relative prices, Fi > 0, away from a steadystate in which the LOP holds, Ti = 0. Our notation is chosen with this in mind.
The letter T represents ‘trade costs and trade theory’ and the letter F represents‘frictions, finance, and fluctuations.’
Table 1 moves from the anecdotal examples of Figure 3 to a more systematic
examination. It reports the average estimate (averaged across goods i) of Ti and Fi
from Equation (3). City pairs separated by an international border are separated
from those that are not. Consider first the total variance, Var jk,t (qi,jk,t | i). Among
U.S. cities the estimate is 0.128. Interestingly, the estimate is essentially unchanged
for Canada-U.S. city pairs. Once we include all international OECD city-pairs, incontrast, the total variance increases to 0.221. Including all international city pairs12(i.e., including non-OECD cities) further increases the variance to 0.275.
What’s driving this? One’s natural inclination might be to attribute it to variation in nominal exchange rates. The incremental increase in variance going fromthe U.S. to the OECD to the world is 0.093 and 0.147, respectively. These values
are in the same ballpark as that of the variance of changes in nominal exchange
rates, averaged across countries, for OECD pairs and world pairs, respectively.4
So, are nominal exchange rates at the root of increasing LOP variability? The remainder of the table says no. The majority of the total variance in LOP deviations— roughly 60% on average — is associated with long-run, good-and-city-specific“fixed effects.” Almost by their very nature, these things are unrelated to nominal
exchange rate variability combined with sticky prices, the story that motivates thisentire line of reasoning.
To summarize, between 60 and 70 percent the total variation in absolute LOP
deviations attributable to long-run LOP deviations. The lion’s share of what determines the international micro price distribution falls under the realm of trade
theory. Relatively little seems (directly) related to ‘frictions, finance, and fluctuations’ as is discussed above.

3.1

Good versus City Specific Variation

The previous results average across goods. They tell us how important long-run
means are for the LOP deviations of the average good. A related question decomposes variation in these long-run means into that which is city-pair specific and
4
Implicit in this comparison is an assumption about the persistence of real exchange rates. In
related work we find that the variance of the absolute level of the micro LOP deviations is roughly
the same as the variance of the change in the absolute level. If micro real exchange rates follow an
AR(1), this means that the autocorrelation is 0.5. In addition it means that it is coherent to add
estimates of the variance of the change in nominal exchange rates to estimates of the variance ofthe level of the real exchange rate, as we’re doing here.

13that which is not. That is, denoting the long-runs means as µi,jk ≡ Et (qi,jk,t | i, jk)(i.e., the term in the first large parentheses of Equation (2)), we writeµi,jk = µjk + εi,jk=⇒ Var i,jk (µi,jk ) = Var jk (µjk ) + Var i,jk (εi,jk ) .

(4)This decomposition examines the relevance of statements like ‘goods are always
expensive in New York.’ The previous section showed us that the ‘goods are always
expensive’ part describes the majority of the overall variation in LOP deviations.
Here, we examine the ‘in New York’ part. We ask how much of the variation in
the long-run means is related to city-wide factors like rent and wages. What’s left
over is good-specific; ‘wine is always cheap in Barcelona, but lots of other goods
are not.’5
In Table 2 we see that city effects, µjk , account for 15 to 20 percent of the total
variation in the long-term means. The particular set of city-pairs — ranging fromall pairs of U.S. cities to all global pairs — is important for the total variation inµi.jk , but much less so for the fraction attributable to city effects. The relatively
small magnitude of this number seems important to us. It is suggestive of theimportance of either good-specific factors — e.g., pricing-to-market being moreprevalent for some goods than others — or of good-specific sensitivity to common,
city-specific factors. An example of the latter is non-traded input costs (e.g.,
wages, rent, distribution services) varying across cities, with different goods using
different shares of non-traded versus traded inputs. Section 5 elaborates on these
themes.
Table 3 conducts a similar decomposition as Equation (4), but with the time5
We do not include a good-specific term, µi , in the decomposition (4) because, by construction,
the long-term average LOP deviations, µi,jk , average to zero across jk: Ejk µi,kj = 0

142
series variances from Equation (2) instead of the time-series means. Denoting σi,jk≡ Var t (qi,jk,t | i, kj) (i.e., the term in the second large parentheses of Equation (2)),
we decompose the good-city-pair specific time-series variances into three pieces:

2
2
σi,jk
= σi2 + σjk+ εi,jk .

(5)

2
The interpretative questions are similar to those above. The city-pair effect, σjkasks ‘are there city pairs for which the (absolute) LOP deviations exhibit relatively
much (relatively little) time-series volatility?’ If, for example, nominal exchange
rate variability is important, this should show up as such a city-pair effect.6 Similarly, high transport costs for cities on the geographic periphery may translate
2 .
into wider no-arbitrage regions, more LOP variability, and a larger value for σjk

The second term, σi2 , captures good-specific variation. It answers questions like‘are LOP deviations for some goods more volatile than for others?’ A common
interpretation of this involves traded versus non-traded goods.
What we see in Table 3 is fairly striking. Good-specific effects are substantiallymore important than city-specific effects. The unconditional time-series varianceof (absolute) LOP deviations seems more affected by things like a good’s tradeability than things like nominal exchange rate variability and city-wide productivity
shocks. Specifically, for the OECD set of city pairs, the good-specific variation
is 17% of the total variation whereas city-specific variation accounts for only 9%.
For U.S. cities and Canada/U.S. cities the difference is even larger at 25 or 30%
6This exchange-rate interpretation depends critically on the extent to which our data has agood balance of intra versus international city pairs. This varies a lot across the different city-pairsets in Table 3. For ‘Canada-U.S.’ about 1/3 of all city pairs are separated by a border. This
reflects a large number of U.S. cities (16), versus just 4 Canadian cities. For ‘OECD’ and ‘World,’
in contrast, borders separate about 90% and 97% of city pairs, respectively. This reflects a large
number of countries — 16 out of 78 — for which we only have data on one city per country (seeSection 2 for additional details). The effect of nominal exchange rates in Table 3, then, is quite
blurred. We rectify this in Section 4 where, instead of decomposing the variance of the shocks asin Equation (5), we decompose the shocks themselves.

15

versus 2 or 3%. For all ‘World’ city pairs, in contrast, things go the other way at
12 versus 15%. In Section 4 we show that the main reason for the latter is nominal
exchange rate variability.

4

Variance in Changes in LOP Deviations

We now examine the behavior of changes in good-by-good LOP deviations.

∆qi,jk,t ≡ qi,jk,t − qi,jk,t−1 .

One advantage of working with first-differences is that our findings do not dependon the precision with which we estimate the long-term LOP means, µi,kj , thatpermeate much of the analysis in Section 3 (i.e., the first LHS term in Equation(2)). In addition, much of the existing body of empirical (e.g., Figure 1) work
is based on first-differences, something necessitated by using index-number data.
What we will see here is that our results are broadly consistent with the existing
evidence, while at the same time offering new insights that derive from having
absolute prices and a large cross-section.
We begin with a decomposition that is analogous to the time-series versus
cross-sectional decomposition from Equations (2) and (3). Conditioning on eachcity-pair, jk, this is
Var i,t (∆qi,jk,t | jk) = Var t Ei (∆qi,jk,t | jk, t) + Et Var i (∆qi,jk,t | jk, t)= Cjk + Ijk .

(6)This decomposition asks a simple question. Consider a city-pair, jk. At each point
in time there is distribution of good-by-good LOP deviations. Equation (6) asks
16

“how much of the change (over time) in the LOP deviations represents changes
in the mean of the distribution versus movement within the distribution, aroundthe (time-varying) mean?” More specifically, Equation (6) decomposes the total
variance (of the changes) into two pieces: common across all goods (C) and idiosyncratic to each good (I). The common piece, Cjk , is basically real exchange ratevariation. That is, Ei (∆qi,jk,t | jk, t) is the date-t cross-good-average for city-pair
jk, a close cousin to the change in the CPI-based real exchange rate.7 Time-series
variation in this average, Cjk , measures the contribution of movement in the meanof the distribution of LOP deviations. The idiosyncratic piece Ijk , in contrast,
measures the contribution of movement around the mean of the distribution. It
takes the cross-sectional distribution for jk at date t, asks how different the change
in good i’s LOP deviation is from good l’s, and then time-averages the resulting
sequence of cross-sectional variances.
A stark example clarifies what Equation (6) is trying to measure. Consider twocities that use different currencies. Suppose that all local-currency goods prices
are fixed, so that all of the variation in ∆qi,jk,t is due to changes in the nominal
exchange rate. Then the change in each good’s LOP deviation would be the sameat each date t, the cross-sectional variance, Var i (∆qi,jk,t | jk, t) would be zero, andso would its time-series average, Ijk . We would say that all of the LOP variationis ‘common,’ as reflected by Cjk . In the less stark case, local currency prices also
move. If this movement is idiosyncratic — if it represents cross-sectional variation
around variation in the real exchange rate — then Ijk will pick this up.
Table 4 reports estimates of the moments in Equation (6). The answer tothe questions posed above are quite clear. Very little of the variation is common
7
Crucini, Telmer, and Zachariadis (2005) show that, for European data, equally-weighted,
cross-good averages of LOP deviations behave similarly with respect to CPI-weighted averages.
Also, Figure 6 below shows that for each date t, Ei (∆qi,jk,t | jk, t) is highly correlated with a
NIPA-based measure of the real exchange rate.

17

across goods. Almost all of the variation is idiosyncratic, representing movement
within the distribution, not movement of the distribution itself. This is particularly
true for city-pairs not separated by an international border, where the common
variation represents only 1 or 2% of the total. For city pairs that are separated
by a border, common variation is larger, but the magnitude remains small. The
ratio of the common to total variation is 7.3%, 20.0%, and 22.4% for Canada-U.S.,
OECD and “World” city pairs, respectively.
Figures 4 and 5 add some color, structure and detail to Table 4. Whereas
Table 4 reports cross-city averages, the figures report the actual values of the ratio
Cjk /(Cjk + Ijk ) for each jk. Figure 4 does so for the Canada-U.S. case. Figure 5
does so for all OECD city pairs.8 We see, especially in Figure 4, that the bordereffect holds pointwise, not just on average. We also see some structure emerge when
we organize city-pairs by nominal exchange rate variability. This is apparent in
Figure 5, where it is clear that higher nominal exchange rate variability is strongly
associated with a higher ratio of common to total variability.
The basic point, then, is that common sources of variation — most obviously
nominal exchange rates — play a minor role in accounting for variation in changes
in international, microeconomic relative prices. It is interesting to contrast thiswith what we know about macroeconomic relative prices. The Mussa (1986) evidence is that real and nominal exchange rates are basically the same thing. Put
differently, nominal exchange rates play a major role in accounting for variation ininternational relative prices. Is there a contradiction here?
Figure 6 shows that there is not. It plots, for the Canada-U.S. case, the NIPAbased change in the real exchange rate and the analogous object from Equation (6),8Including all remaining the remaining city-pairs, beyond the OECD, changes neither the
picture nor the point.

18

a time series of the cross-good average Ei (∆qi,jk,t | jk, t), one line for each bilateralcity-pair, jk. The Mussa evidence is quite apparent. The average correlation
between the NIPA and micro-based lines is 0.89. The reasoning is quite obvious.
Most of the variation in good-by-good LOP changes is idiosyncratic. Once weaverage-away this variation, we are left with the Mussa facts. To a certain extent
this is true-by-construction; averages vary less than the things being averaged.
But our basic point is not a tautology. It is simply that the magnitude of what isbeing averaged away is large. At the good-specific level, there is much more goingon than movement in nominal exchange rates.

5

Discussion

It is not surprising that long-term deviations from LOP exist between two cities.
Retail goods are bundles of traded and non-traded goods and this is exactly what
we should expect. Neither is it surprising that changes in good-level relative prices
are more variable than changes in aggregate prices. This is an obvious implicationof averaging. Qualitatively, then, there is nothing surprising about the above
results. Their importance is strictly related to the magnitude of the effects.
We now report additional results that go beyond ‘magnitude’ and shed somelight on the the economic forces affecting LOP deviations. The basic idea is to(i) establish links between the time-series and cross-sectional evidence presented
above, and (ii) partition the data into the classic traded versus non-traded dichotomy. The combination of (i) and (ii), we think, provides valuable information
for the construction of economic models that can synthesize the micro and macro
economic behavior of exchange rates.99Some recent examples are as follows. Sposi (2012) incorporates asymmetric trade costs into

19

5.1

Cross-Sectional and Time Series Variation Are Related

Figure 7 reports scatter plots of Ti versus Fi — cross-sectional variance versus timeseries variance — from Equation (3) of Section 3. There is an unmistakable positive
relationship, in particular for the ‘North America’ and the ‘Within-Country’ subsets of the data. Univariate regressions of Fi on Ti yield a positive and strongly
significant slope coefficient for all but the ‘OECD Cross-Border Pairs’ subset (NEpanel), where the coefficient is not significantly different from zero. The slope
coefficients (standard errors) are 0.26 (0.09), −0.0129 (0.14), 0.35 (0.11) and 0.52
(0.11) for the NW, NE, SW and SE panels, respectively. The R2 is 5%, .08%, 6%
and 9%, respectively. These results become sharper — coefficients become morepositive, standard errors become relatively smaller, the R2 coefficient becomes aslarge as 25% (‘OECD Within-Country Pairs’) — if we break the data down bytraded versus non-traded goods (anticipating our next set of results).
The message of Figure 7 is simple. Whatever it is that is generating therelatively large long-run fixed effects that were the focal point of Section 3 —be it geographic distance, non-traded input costs, product differentiability, etc. —there seems to be a important link with whatever it is that is generating time-series
variation around these fixed effects. This link is more pronounced for withincountry city pairs, suggesting that nominal exchange rate variation is masking
the relationship between the time-series and cross-sectional variation in the data.
From the perspective of models, our results suggest a potentially informative classof restrictions. Models of the transmission of shocks — e.g., New Keynesian models
the Eaton and Kortum (2002) model and, using Penn World Table sectoral data, finds that trade
costs can account for roughly half of the cross-sectional price dispersion. See also Giri (2012).
Alessandria and Kaboski (2011) persuasively argue that retail search costs are important for
absolute price dispersion. Regarding time-series variation, Kehoe and Midrigan (2007) show thata time-dependent pricing model can generate volatility and persistence in LOP deviations that isqualitatively similar to what we find here.

20with nominal rigidities — can be informed by the cross-sectional variation in thedata. When attempting to identify the frictions that are important for the timeseries behavior of relative prices one should look to the frictions that generate
long-run LOP deviations for confirmation.

5.2

Tradeability

Our next set of results relate to the tradeability of individual goods. A useful reference point is Engel (1999) and many papers that have followed. Engel found that,in contrast to the seminal Balassa-Samuelson model (Balassa (1964), Samuelson(1964)), variability in traded goods prices seems to play an important, perhaps
dominant role in accounting for real exchange behavior. Engel’s results, however,are based on macroeconomic index-number data and can only speak to time-series
variation. Here, we ask if microeconomic absolute-price data tell a similar story
and/or offer any new insights.
Tables 5 and 6 report the same variance decomposition as Tables 1 and 4, butwith the goods categorized as being either tradeable or non-tradeable.10 The basic
pattern that emerges is quite sharp: (i) cross-sectional variation is larger for nontraded goods, (ii) time-series variation is larger for traded goods. The latter is more
pronounced than the former. This is particularly apparent in Figure 8, where weplot the individual data-points that comprise the averages reported in Table 6.11
10

Appendix A describes the procedure with which we categorize every good as being either
tradeable or non-tradeable.
11
Figure 8 reports data on time-series variation. We do not report the analogous graph forcross-sectional variation because the structure of the data makes it hard to interpret. The reason(admittedly complex) derives from how we choose which dimensions of the data to condition on.
Our measures of cross-sectional variation, Ti , condition on goods. There are, of course, sometraded goods with relatively high Ti and some traded goods with relatively low Ti . Table 5 showsthat, on average, Ti is relatively low for traded goods. A plot of Ti for traded versus non-traded
goods, analogous to Figure 8, would (weakly) demonstrate this average, but not much more. Thisis because we lack any organizational structure with which to compare individual traded goods toindividual non-traded goods. Figure 8, on the other hand, derives from our city-pair-conditioned

21

The figure shows that city-pair-specific time-series variance is almost pointwise
greater for traded than for non-traded goods, and that this pattern is almost
exclusively driven by the good-specific component of the time-series variance.
The traded versus non-traded dimension of our data, then, is both consistent
with Engel’s (1999) basic finding, and with the main idea of the Balassa-Samuelsonmodel. Non-traded goods are associated with large, long-run deviations from LOP.
The difference with respect to traded goods is not large (Table 5), but it is certainly not the case that traded-good LOP deviations dominate in the cross-section.
Traded goods, on the other hand, do dominate in the time-series dimension. As an
anecdote, it’s what one would expect if (differential) shocks to the cost of petroleum
products and electronic components were large relative to those of haircuts, but
the long-run cost of getting a haircut in one location is always a lot larger than in
another location. As we will see below, this anecdote is consistent with the overallbehavior observed in our data.

5.3

Implications

We summarize the above findings as three empirical facts. Define x as a continuous
measure of tradeability, and recall that T and F denote cross-sectional and timeseries variability, respectively (Equation (3), Section 3). The facts are that
1. Cov (T, F ) > 0
2. E(T | x) is decreasing in x.
3. E(F | x) is increasing in x.
data, Cjk and Ijk . The variability within traded and non-traded goods categories averages out,
revealing the striking pattern that we see in the figure.

22

At first blush there might seem to be a contradiction here. If non-traded goods havehigh cross-sectional variation (Fact 2), and cross-sectional variation is positively
associated with time-series variation (Fact 1), then shouldn’t non-traded goods
also have relatively high time-series variation (thus contradicting Fact 3)?
The answer is no, not necessarily. This logic is flawed because is confuses
unconditional covariance with covariance in conditional means. It ignores the possibility that goods differ in a higher-dimensional way than just tradeability. In fact,
these three facts indicate that there must necessarily be another source of variation. To see this clearly, consider the following decomposition of the unconditional
covariance:
Cov (T, F ) ≡ Ex Cov T , F | x + Cov x E(T | x) , E(F | x) ,where, as above, the subscript denotes the variable that the moment is integratingover (‘unconditional covariance equals average conditional covariance plus covariance of conditional means’). Fact 1 says that the LHS is positive and Facts 2 and 3
say that the second RHS term is negative. So Ex Cov T , F | x must be positive;
conditional on a level of tradeability, high T is associated with high F . This must
be strong enough to counter the negative term. This means that there must bea second source of variation because, if not, then Cov T , F | x = 0, making
Cov (T, F ) > 0 impossible.
So, there must be a second source of variation. Call it y.

Cov (T, F ) ≡ Ey Cov T , F | y + Cov y E(T | y) , E(F | y)(7)

Things aren’t as clear now because we don’t know what y is. However, it’s easy
to show that, if T and F are linearly related to x and y, then Facts 1-3 imply that23
Ey Cov T , F | y < 0. This is just the standard ‘omitted variable’ story. Thinkof a scatter-plot of Ti against Fi with two groups of points, one close to the origin
and one far away. The variable y is associated with distance from the origin. The
variable x, tradeability, is associated with a negative relationship between T and F
in each group of points (i.e., conditional on y). This tells us that the second termon the right must be positive and must be relatively large, something we returnto when summing-up.
To better articulate what we think is going on, we label y as differentiability andwrite (x, y) as the pair of characteristics that define each good, i. LOP deviations
can therefore be written qjk,t (x, y). Next, for every city pair jk with a positive
long-run LOP deviation, (i.e., Et (qjk,t (x, y) | jk, (x, y)) > 0), the symmetric counterpart, kj, must have a negative long-run mean. Without loss of generality, we
ignore all of the latter and write

qt (x, y) = α(x, y) + σ(x, y) εt ,(8)where α, σ > 0, εt is a shock that could have some dynamics, and the unnecessary
notation jk has been suppressed. Equation (8) says that each LOP deviation
depends on a good-specific, long-run ‘fixed effect,’ α(x, y), and good-specific timeseries variance, σ 2 (x, y).12 This equation isn’t implementable for us because welack data on y. It is simply a labeling device that helps us exposit some intuition
for what Facts 1-3 are saying.
12

There is good reason to believe that α and σ might also depend on the particular location
pair, jk. For example the long-run LOP deviation α, might depend on the geographical distance
between cities j and k. We ignore this because our analysis is focused on variation in the goodsdimension, thus averaging-away these sorts of things. That is, Fi asks, for good i, what is theaverage long-term LOP deviation across all city pairs. Similarly, Ti measures the cross-location,
average time-series variance.

24Fact 1 says that both α(x, y) and σ(x, y) are increasing in y. The former isnatural. It says that high differentiability permits producers to sustain relatively
large long-run markups and LOP deviations. It’s also consistent with differentiable goods being more susceptible to persistent measurement error such as an
inadequate accounting for quality. The latter — σ(x, y) increasing in y — might
be less natural, but it’s certainly plausible. If, for instance, time-variation in LOP
deviations is bounded by goods-market arbitrage, then this says that the arbitrage
bands are wider for more differentiable goods. ‘A larger LOP deviation is needed
to initiate arbitrage in the market for cars than in the market for wheat.’ Alternatively, one can just as easily imagine that differentiable goods are produced using
a less-diversified production structure and/or are subject to larger demand shocks.
Facts 2 and 3 say that α(x, y) is decreasing in x, but σ(x, y) is increasing in x.
Again, the former is quite natural; non-traded goods exhibit higher long-run LOP
deviations. This is one of the pillars of trade theory. The latter, in contrast, ishard to call natural. Taken at face value, it says that traded goods have ‘bigger’
LOP deviations than non-traded goods! Indeed, this is what made Engel’s (1999)
findings so provocative. Equation (8) shines some light. It says that, while theclassical traded/non-traded dichotomy gets it right in the long-run, in the shortrun traded goods are affected by shocks that are more volatile than those affecting
non-traded goods. This seems plausible to us. It seems plausible that shocks to
the relative cost of haircuts are less volatile than shocks to the relative cost of
food.
We offer two observations in support of all this ‘plausbility.’ The first is obvious. ‘Core CPI’ is widely-viewed as being more reliable than ‘Headline CPI.’ The
difference between the two is that (i) the former is less volatile than the latter,and (ii) the former excludes food and energy, two of the more tradeable goods out
25there. We are saying the same thing.
Our second observation is that the qualitative behavior of these CPI indeces
shows up in our micro data. Recalling that Pijt is the local-currency price of goodi in city j at date t, we define the price change, net of the city-specific overall
inflation rate, asvijt ≡ ∆pijt − Ei ∆pijt | j, t,where p is the logarithm of P and ∆ denotes the change from t − 1 to t. We thencompute the good-specific, average price volatility as

vi = Ej Stdev (vijt )



.

(9)

Figure 9 plots the estimated cross-sectional density for vi , where i is dichotomized
by traded/non-traded goods. What we see is consistent with our supposition. This
simple measure of the volatility of traded goods prices is 0.14, substantially higher
than that for non-traded goods prices, 0.10.
To summarize, consider again the scatter plots in Figure 7. The most basicmodel of how tradeability affects price dispersion — the Balassa-Samuelson — predicts that points associated with goods that are more tradeable should lie closer tothe origin (taken literally, it suggests that the traded-goods points should lie on theorigin). What we’ve found elaborates on their basic intuition. In the vertical dimension of the graphs, we do see the Balassa-Samuelson idea at work. In the longrun, traded goods exhibit less cross-sectional price dispersion. In the horizontal
dimension, in contrast, the opposite is true. Traded goods exhibit more time-series
variation, something we’ve attributed to higher-volatility in local-currency prices.
Finally, looking back at Equation (7), we’ve found evidence of a second source of26

(cross-good) variation, above-and-beyond tradeability. This second source, y, mustmove both cross-sectional and time-series dispersion in the same direction and its
effect must be large enough to cloud the negative relationship between T and F
that is induced by tradeability (i.e., Cov y (E(T | y) , E(F | y)) is large and positive). We’ve labeled this source of variation ‘differentiability,’ but this was only for
expository purposes. Theory is rife with other candidates, such as those related tothe distribution of final goods. It could also just be i.i.d. measurement error. We
leave the modeling and measurement of y for future work and hope that our simple
variance decompositions can help discriminate between alternative candidates.

6

Conclusions

This paper’s objective is to document some facts about microeconomic international relative prices that are informative for economic models and for the interpretation of aggregate data. We find that long-term LOP deviations — good-andcity-specific “fixed effects” — dominate the distribution of international relative
prices. Nominal exchange rates play a relatively minor role in determining therelative cost of goods and services between, say, Tokyo and Los Angeles. Somegoods are just always expensive in Tokyo and others are just always expensive inLA.
This is a statement about absolute deviations from LOP. Much of the existing literature on the behavior of real exchange rates — both aggregate and lessaggregate data — has focused on changes. Our second set of findings speaks tothis evidence. We find that changes in nominal exchange rates play a relatively minor role in whatever it is that moves microeconomic relative prices across national
borders. Other shocks (and probably a good dose of time-varying measurement27

error) are far more important.
When we consider the long-run dispersion and the short-run dispersion together, we find that there are some connections that are informative for what
distinghishes goods from one another. The traditional characteristic, tradeability,
does have some explanatory power in the cross-section. But there’s much moregoing on. A second source of cross-sectional variation is more important thantradeability, accounting for what is essentially a ‘level effect.’ It moves both thecross-sectional and the time-series variance in the same direction. It also shows
us that the effect of tradeability is more complex than the classical model suggests. While more tradeability is associated with less long-term, cross-sectional
dispersion, it is also associated with more time-series dispersion.
These results raise a number of interesting questions for further research. First,
what is the second source of cross-good dispersion in LOP deviations? In Section 5
we labeled it “differentiability,” and we provided some discussion that is consistent
with this label, but due to data limitations we cannot really say much more than‘there’s a second source of variation and here’s what it looks like.’ Second, why
do traded goods display more time-series variance than non-traded goods? Weprovided evidence — both anecdotal and statistical — suggesting a very simple
answer; ‘the shocks are bigger.’ But a richer explanation obviously needs to go
deeper. The set of goods that are traded is certainly an endogenous outcome.
Perhaps what we are finding here actually motivates trade? If supply and demand
shocks to the traded goods sectors of the economy are inherently larger, thenperhaps a role played by trade is to facilitate the smoothing of such shocks, sothat a region hit by a bad apple harvest doesn’t have to dramatically switch tothe consumption of pears? Our hope is that our simple variance decompositions
may be informative for the quantitative study of questions like this one.
28

Finally, the broad economic implications of our results — even the simpler ones
— seem interesting to us. For example, there is a popular notion that nominal
exchange rate ‘noise’ distorts the international flow of goods and capital. Thisnow seems less convincing. Yes, as Mussa (1986) so provocatively pointed out 20
years ago, nominal exchange rates and aggregate, CPI-based real exchange rates
are essentially the same thing. This is true in our data just as it was in Mussa’s.
Yes, nominal exchange rates seem disconnected in many ways from macroeconomic
fundamentals. But does this mean that nominal exchange rates are distorting theallocative role of the international price system? Our results indicate that there’s
a lot going on within the distribution of international prices which is not apparent
in the behavior of the mean of the distribution. Exchange rates govern the mean,
not variation around the mean. Whatever it is that is driving the variation, it is
this that probably plays the dominant role in determining allocations. Firms don’texport and import the CPI basket. They import and export goods and services.
The consumer price signals which inform these goods flows are subject to many
shocks of which the nominal exchange rate is but a relatively small one.

29

References
Alessandria, George A., and Joseph P. Kaboski, 2011, Pricing to market and thefailure absolute ppp, American Economic Journal: Macroeconomics 3, 91–127.
Andrade, Phillipe, and Marios Zachariadis, 2012, Global versus local shocks inmicro price dynamics, Unpublished manuscript, University of Cyprus.
Balassa, Bela, 1964, The purchasing power parity doctrine: A reappraisal, Journalof Political Economy 72, 584–596.
Bergin, Paul, and Reuven Glick, 2007, Global price dispersion: Are prices converging or diverging, Journal of International Money and Finance 26, 703–729.
Broda, C., and David Weinstein, 2008, Understanding international price differences using barcode data, NBER Working Paper 14017.
Burstein, Ariel, and Andrew Atkeson, 2008, Pricing to market, trade costs, andinternational relative prices, American Economic Review 98, 1998–2031.
Campbell, Jeffrey R., and Beverly Lapham, 2004, Real exchange rate fluctuations
and the dynamics of retail trade industries on the u.s.-canada border, American
Economic Review 94, 1194–1206.
Crucini, Mario J., and Mototsugu Shintani, 2008, Persistence in law-of-one-pricedeviations: evidence from micro-price data, Journal of Monetary Economics 55,
629–644.
Crucini, Mario J., Christopher I. Telmer, and Marios Zachariadis, 2005, Understanding european real exchange rates, American Economic Review 95, 724–738.
Eaton, Jonathan, and Samuel Kortum, 2002, Technology, geography and trade,
Econometrica 70, 1741–1779.
30

Engel, Charles, and John H. Rogers, 2004, European product market integration
after the euro, Economic Policy 19, 347–384.
Engel, Charles M., 1999, Accounting for u.s. real exchange rate changes, Journalof Political Economy 107, 507–538.
Fischer, Christoph, 2012, Price convergence in the emu? evidence from micro data,
Forthcoming, European Economic Review.
Fitzgerald, Doireann, and Stephanie Haller, 2008, Exchange rates and producer
prices: Evidence from micro-data, Unpublished manuscript, Stanford University.
Gagnon, Etiene, 2010, Price setting during low and high inflation: Evidence frommexico, Quarterly Journal of Economics 124, 1221–63.
Ghironi, Fabio, and Marc J. Melitz, 2005, International trade and macroeconomic
dynamics with heterogeneous firms, Quarterly Journal of Economics 120, 865–
915.
Giri, Rahul, 2012, Local costs of distribution, international trade costs and microevidence on the law of one price, Journal of International Economics 86, 82–100.
Gopinath, Gita, Pierre-Olivier Gourinchas, Chang-Tai Hsieh, and Nicholas Li,
2011, International prices, costs and markup differences, American Economic
Review 101, 2450–2485.
Gopinath, Gita, and Roberto Rigobon, 2008, Sticky borders, Quarterly Journal of
Economics 123, 531–75.
Gorodnichenko, Yuriy, and Linda L. Tesar, 2009, Border effect or country effect?
seattle may not be so far from vancouver after all, American Economic Journal:
Macroeconomics 1, 219–241.
31

Hellerstein, Rebecca, 2008, Who bears the cost of a change in the exchange rate?
pass-through accounting for the case of beer, Journal of International Economics
76.
Hummels, David, 2007, Transportation costs and international trade in the second
era of globalization, Journal of Economic Perspectives 21, 131–154.
Imbs, Jean, Haroon Mumtaz, Morten Ravn, and Helene Rey, 2005, Ppp strikes
back: Aggregation and the real exchange rate, Quarterly Journal of Economics
120, 1–43.
Kehoe, Patrick, and Virgiliu Midrigan, 2007, Sticky prices and real exchange rates
in the cross-section, Unpublished manuscript, New York University.
Mussa, Michael, 1986, Nominal exchange rate regimes and the behavior of realexchage rates: Evidence and implications, Carnegie-Rochester Series on Public
Policy 25 (Autumn): 117-214.
Parsley, David, and Shang-Jin Wei, 2000, Explaining the border effect: the role ofexchange rate variability, shipping costs, and geography, NBER Working Paper
No. 7836, August, forthcoming Journal of International Economics.
Rogers, John H., 2002, Monetary union, price level convergence, and inflation:
How close is europe to the united states?, Federal Reserve Board International
Finance Discussion Paper No. 740.
Rogoff, Kenneth, 1996, The purchasing power parity puzzle, Journal of Economic
Literature 34 (2), 647–668.
Samuelson, Paul A., 1964, Theoretical notes on trade problems, Review of Economics and Statistics 46, 145–154.

32

Simonovska, Ina, 2010, Income differences and prices of tradables, NBER Working
Paper 16233.
Sposi, Michael, 2012, Trade barriers and the relative price tradables, Working
Paper, University of Iowa.

33

Appendix A
Data Description

The EIU dataset consists of local-currency retail prices, inclusive of sales tax,
on as many as 301 goods and services, sampled in 123 cities from 78 different
countries. A list of all goods-and-services and all cities is available at http://
bertha.tepper.cmu.edu/telmerc/eurostat. The data are annual, 1990-2005.
The country with the most intranational observations is the U.S., with 16, followedby Australia, China and Germany with 5, Canada with 4, Saudi Arabia with 3, andBrazil, France, Italy, Russia, Spain, Switzerland, UK, India, Japan, Vietnam, New
Zealand with 2. Average nominal exchange rates for each calendar year are also
provided by the EIU. We performed an extensive set of reliability checks using ourown nominal exchange rate data. Aside from the Turkish lira, which we replacedwith data from Datastream and IFS, the EIU data proved to be of high quality.
We transform the data as follows. We denote Pijt as the local-currency price ofgood i in city j in year t and Sjk,t as the date t nominal exchange rate between cities
j and k, in units of city k (Sjk,t = 1 if cities j and k share the same currency). We
transform prices into bilateral log deviations from the law-of-one-price (LOP):13

qi,jk,t = log(

Pijt Sjk,t
),
Pikt

(A1)

The data contain many missing observations. We clean the data using the following
algorithm. First we choose a set of cities (e.g., OECD, North America, etc.).
13

A previous version of the paper employed an alternative
LOP measure, the log deviation fromP
the cross-city geometric average: log(Sjn,t Pijt )/ M
j=1 log(Sjn,t Pijt ) where M denotes the total
number of cities and n denotes the numeraire currency in units of which all prices are expressed(our measures of price dispersion are independent of the choice of the numeraire currency). While
this definition results in lower overall LOP variability (by construction), the main message of ourpaper remains unchanged.

34

Second, for each year, we eliminate any good that has data for less than 50% of
the cities. Third, we remove outliers, defined as a relative price greater than 3 orless than 1/3. Fourth, we repeat step 2. This defines our basic data-structure,having done a first-pass removal of outliers and goods with too little cross-location
data. Our panel is unbalanced, having (for example) eliminated some goods forearlier years but not later years. Subsequent calculations involve further cleaning.
Whenever we compute a time-series moment, we insist that each good-city pair
have a complete set of time-series observations. For cross-sectional moments weinsist that a given good (or city) have 75% or more of the cities (goods) represented.
Finally, we have extensively experimented with different cleaning algorithms (e.g.,
eliminating goods with less than 75% of observations, using totally balanced panels,
etc..) and our results do not change in qualitatively-important ways. Our view isthat for the broad variance decompositions that are the focal point of this paper,an unbalanced panel is unlikely to be a problem.
Our traded versus non-traded classification is based on country-specific ratiosof imports to GDP, based on the 6-digit Harmonized System concordance between
import values available through the TRAINS dataset and the individual goods
from the EIU prices database. This measure is averaged across locations for eachgood to obtain good-specific measure of tradeability. This leaves us with, typically(across the different subsets of cities that we examine) about 50 non-traded goods
and 200 traded goods. The fact that traded goods are over-represented in the
EIU data is unavoidable. For a more detailed discussion of this, and many morepros and cons of the EIU data, see Andrade and Zachariadis (2012) who provide
a very thorough and careful analysis, including tables that list the traded versus
non-traded goods that are very similar to our study.
Matlab code is available upon request from the authors. The code will read in35

the generic form that the EIU distributes the data in (in Excel spreadsheets). The
data is, by now, widely available, at many academic libraries for example.

36

Table 1
Variance in Absolute LOP Deviations

Total

Cross
Sectional

Time
Series

Cross Sectional
Total

U.S.

0.128

0.071

0.061

0.559

Canada-U.S.
Combined
International
Intranational

0.138
0.124
0.127

0.078
0.057
0.071

0.065
0.073
0.061

0.564
0.462
0.554

OECD
Combined
International
Intranational

0.215
0.221
0.123

0.143
0.147
0.069

0.077
0.079
0.058

0.666
0.667
0.561

World
Combined
International
Intranational

0.270
0.275
0.118

0.186
0.190
0.065

0.089
0.091
0.057

0.690
0.691
0.551

The table reports cross-good averages of the variables Ti and Fi from Equations(2-3), reproduced here:
Var jk,t (qi,jk,t | i) = Var jk (Et [qi,jk,t | i, jk]) + Ejk [Var t (qi,jk,t | i, jk)]
= Ti + Fi .
Section 3P
provides definitions and a detailed discussion. The first column of numbers are i (Ti + Fi )/M , where M is the number of goods. The second and thirdcolumns report the analogous averages of Ti and Fi , respectively. The last column is simply the ratio of the second to the first. The extent to which the sumof columns 2 and 3 is inconsistent with column 1 is due to missing observations.
Figure 7 provides information on the cross-good dispersion in Ti and Fi .

37

Table 2City-Specific Variation in Long-Run Average LOP Deviations

U.S.

Canada-U.S.

OECD

World

Total
City-Pair
Residual

0.07810.01300.06520.08380.01090.07310.15280.02310.13080.18210.03620.1491City-Pair/Total

0.16600.12970.15090.1989The table reports a variance decomposition of the variation in long-run average
LOP deviations into a city-specific component and a residual. Specifically, thetime-average of the LOP deviation for good i between city-pair jk is denotedµi,jk ≡ Et (qi,jk,t | i, jk). This is then writtenµi,jk = µjk + εi,jk=⇒ Var i,jk (µi,jk ) = Var jk (µjk ) + Var i,jk (εi,jk ) .
Rows 1, 2 and 3 report estimates of the total variance, Var i,jk (µi,jk ), the city-pairspecific variance, Var jk (µjk ) and the residual variance, Var i,jk (εi,jk ) for U.S. city
pairs, Canada-U.S. city pairs, all OECD pairs and all global pairs, respectively.
The last row reports the fraction of the total variance attributable to city-effects.
This decomposition is the same as “city-pair-specific dummy variables,” or “1factor ANOVA.” Additional details and discussion are provided in Section 3.1.

38

Table 3City-Specific and Good-Specific Variation in Time-Series Variancesof Absolute LOP Deviations

U.S.

Canada-U.S.

OECD

World

Total
Good
City-Pair
Residual

0.003460.00105
0.000070.002360.003640.000900.00009
0.00268

0.00432
0.000730.000400.003270.005850.000690.000900.00438

Good/Total
City-Pair/Total

0.30491
0.02157

0.24833
0.025900.169200.092290.117170.15385

The table reports a variance decomposition of the total cross-sectional variance ofthe time-series variances of absolute LOP deviations into city and good-specificsources of variation, and a residual. More specifically, we denote the time-series
2≡variance of the absolute LOP deviation for good i between city-pair jk as σi,jk
Var t (qi,jk,t | i, jk). We write22+ εi,jk= σi2 + σjk
σi,jk
2
2
) + Var i,jk (εi,jk ) .
) = Var i (σi2 ) + Var jk (σjk=⇒ Var i,jk (σi,jk2 ), theRows 1, 2, 3 and 4 report estimates of the total variance, Var i,jk (σi,jk
2 ) andgood-specific variance, Var i (σi2 ), the city-pair-specific variance, Var jk (σjkthe residual variance, Var i,jk (εi,jk ) for U.S. city pairs, Canada-U.S. city pairs,
all OECD pairs and all global pairs, respectively. The last two rows report thefractions of the total variance attributable to good and city-pair effects. This
decomposition is the same as “city-pair and good-specific dummy variables,” or“2-factor ANOVA.” Additional details and discussion are provided in Section 3.1.

39

Table 4
Variance of Changes in LOP Deviations

Total

Common(across goods)

Idiosyncratic(good-specific)

Common
Total

U.S.

0.042

0.001

0.041

0.017

Canada-U.S.
Combined
International
Intranational

0.045
0.048
0.043

0.002
0.004
0.001

0.043
0.045
0.042

0.041
0.073
0.018

OECD
Combined
International
Intranational

0.050
0.051
0.041

0.009
0.010
0.001

0.041
0.041
0.040

0.185
0.200
0.017

World
Combined
International
Intranational

0.060
0.061
0.041

0.013
0.014
0.001

0.047
0.047
0.040

0.218
0.224
0.018

The table reports a decomposition of the variance of changes in LOP deviations into common
and idiosyncratic components. “Common” means “time-variation, common to all goods for eachlocation-pair,” and “idiosyncratic” means “time-variation that is good-specific, for each location
pair.” More specifically, the table reports cross-location averages of the variables Cjk and Ijk
from Equation (6), Section (4), reproduced here:
Var i,t (∆qi,jk,t | jk) = Var t Ei (∆qi,jk,t | jk, t) + Et Var i (∆qi,jk,t | jk, t)=

Cjk + Ijk .

Cjk measures, for a given city pair jk, variation in LOP changes that are common across goods.
Ijk measures variation (in changes) that is specific to each good. PSection 4 provides a moredetailed discussion. The first column of numbers (‘Total’) contains jk (Cjk + Ijk )/N , where N
is the number of city-pairs. The second and third columns report the analogous averages of Cjk
and Ijk , respectively. The last column is simply the ratio of the second to the first. The extent towhich the sum of columns 2 and 3 is inconsistent with column 1 is due to missing observations.
Figure 8 provides information on the cross-location dispersion in Cjk and Ijk .

40

Table 5
Variance in Absolute LOP Deviations: The Effect of Tradeability

Cross Sectional
TradedNon-Traded

Time Series
TradedNon-Traded

U.S.

0.063

0.113

0.064

0.048

Canada-U.S.
Combined
International
Intranational

0.070
0.051
0.063

0.138
0.099
0.142

0.068
0.076
0.064

0.054
0.057
0.051

OECD
Combined
International
Intranational

0.135
0.140
0.060

0.181
0.182
0.113

0.079
0.081
0.061

0.067
0.069
0.048

World
Combined
International
Intranational

0.184
0.188
0.057

0.198
0.200
0.106

0.088
0.089
0.059

0.098
0.100
0.045

The table reports cross-good averages of the variables Ti and Fi , broken-downby the tradeability of the goods. These variables are defined by Equations (2-3),
which we reproduce here:
Var jk,t (qi,jk,t | i) = Var jk (Et [qi,jk,t | i, jk]) + Ejk [Var t (qi,jk,t | i, jk)]
= Ti + Fi .
Section 3 provides further definitions and a detailed discussion. This table isidentical to Table 1, except for the traded, non-traded distinction.

41

Table 6
Variance in Changes in LOP Deviations: The Effect of Tradeability

Cross Sectional
TradedNon-Traded

Time Series
TradedNon-Traded

U.S.

0.001

0.002

0.045

0.023

Canada-U.S.
Combined
International
Intranational

0.002
0.004
0.001

0.003
0.005
0.002

0.047
0.049
0.046

0.023
0.024
0.023

OECD
Combined
International
Intranational

0.010
0.010
0.001

0.010
0.010
0.001

0.044
0.044
0.043

0.023
0.023
0.022

World
Combined
International
Intranational

0.013
0.014
0.001

0.015
0.016
0.002

0.050
0.050
0.043

0.030
0.031
0.023

The table reports cross-city-pair averages of the variables Cjk and Ijk , where thegoods used in the calculations are categorized as either traded or non-traded. The
variables Cjk and Ijk represent “common time-series variation” and “good-specifictime-series variation.” They are defined by Equation (6), Section 4, which is
reproduced here:
Var i,t (∆qi,jk,t | jk) = Var t Ei (∆qi,jk,t | jk, t) + Et Var i (∆qi,jk,t | jk, t)= Cjk + Ijk .
Section 4 provides further definitions and a detailed discussion. Figure 8 plots thecity-pair specific estimates of Cjk and Ijk that are the data used in to computethe averages in this table.

42

Figure 2
Distribution of LOP Deviations: log qi,jk,t

0.03

0.025

All Countries

0.02

0.015

0.01

0.005
U.S. Cities

0
−2.5

−2

−1.5

−1

−0.5
0
0.5
Log LOP Deviation

1

1.5

2

2.5

Density of log LOP deviations across (i) U.S. and Canadian location-pairs, and(ii) all location-pairs. The densities describe variation in qi,jk,t across goods i andlocation-pairs jk, where qi,jk,t is computed asqi,jk,t = log(

Pij,t Sjk,t
),
Pik,t

and P and S are local-currency prices and the nominal exchange rate. For each
set of cities there are four lines: t = 1990, 1995, 2000 and 2005.

43

Figure 3
Decomposing the Variance in Absolute LOP Deviations

LOP Deviation

Apples
1

1

0

0

−1

−1

Long−Run Mean

1990

1995

2000

2005

1990

1

1

0

0

−1

−1

1990
De−meaned LOP Dev

Haircuts

1995

2000

2005

1990

1

1

0

0

−1

−1

1990

1995

2000

2005

1990

1995

2000

2005

1995

2000

2005

1995

2000

2005

The intent of this figure is to help the reader visualize the variance decomposition in Equation (3) of Section 3. Start with the upper-left graph. Each line represents the time-seriesof log LOP deviations for a traded good, apples, between two particular North American
cities (e.g., Toronto/Pittsburgh). Our data represent 16 U.S. cities and 4 Canadian cities,
which makes for 190 bilateral pairs. The graph, therefore, could have as many as 190 lines
on it. To make it legible, we randomly select and plot just 20 of these pairs (the qualitative content of the graph is not changed as we increase the number of pairs and choosea different random sample). The upper-right graph does the same thing for a non-traded
good, haircuts. The middle-two graphs plot the time-series mean of each of the lines in theupper-two graphs. The cross-sectional variance of these time-series means is our variable
Ti , i=(apples, haircuts), from Equation (3). Finally, the lower-two graphs are simply thede-meaned versions of the upper-two graphs. Our variable Fi from Equation (3) is the
cross-sectional mean of the time-series variance of each of these lines. Further discussion
is provided in the text of Section 3.

44

Figure 4
Common Variation in Changes in Good-by-Good LOP Deviations
Canada-U.S. City-Pairs

0.12International, Mean = 7.3%

Fraction Due to Common Variation

0.1

0.08
Intranational, Mean = 1.8%
0.06

0.04

0.02

0
0

10

20

30

40

50

60

70

80

90

Canada−U.S. City Pairs
The horizontal axis represents Canada-U.S. bilateral city-pairs. The city-pairs are
sorted by geographic distance, from closest apart to farthest apart. There are 4
Canadian cities and 16 U.S. cities, which make for 190 bilateral pairs. Of these,
54 were eliminated due to insufficient data, leaving 84 intranational pairs and 52
international pairs. The upper (blue) graph represents the latter and the lower(red) line represents the former. The vertical axis represents the fraction of thevariance in the good-by-good changes in LOP deviations attributable to a sourceof variation which is common across all goods (for each city-pair). This fraction is,for each city-pair jk, Cjk /(Cjk + Ijk ) from Equation (6) in Section 4 of the text.

45

Figure 5
Common Variation in Changes in Good-by-Good LOP Deviations
OECD City-Pairs

OECD: All Goods
0.5

0.45

Fraction Due to Common Variation

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

0

200

400
600
800
1000
OECD City Pairs, From Lowest to Highest Nominal FOREX Vol

1200

The horizontal axis represents OECD bilateral city-pairs. The city-pairs are sortedby the volatility of the nominal FOREX depreciation rate between each pair ofcities, from lowest to highest. The vertical axis represents the fraction of thevariance in the good-by-good changes in LOP deviations attributable to a sourceof variation which is common across all goods (for each city-pair). This fraction is,for each city-pair jk, Cjk /(Cjk + Ijk ) from Equation (6) in Section 4 of the text.
The top (blue) line represents international city-pairs and the bottom (red) line
represents intranational city-pairs. The last bunch of international city-pairs all
include Istanbul. A list of the city-pairs and depreciation volatilities is availableat:
http://bertha.tepper.cmu.edu/eurostat/oecd1.txt

46

Figure 6
Common Component of Changes in LOP Deviations and Nominal
Depreciation Rate

0.2

0.15

CAD/USD Depreciation Rate

0.1

0.05

0

−0.05

−0.1

−0.15
1990

1995

2000

2005

This graph corresponds to the Canada-U.S. city pairs represented in Figure 4. The
dashed (blue) line is the annual depreciation rate in the U.S.-Canada nominal exchange rate (USD per CAD). It is computed using the annual, nominal exchange
rate data provided by the EIU, which corresponds to the times during the year during which the goods were sampled. However, the graph is not changed much if one
computes annual, nominal exchange rates as averages of daily exchanges rates overthe calendar year. The solid (red) lines are the ‘common factors,’ Ei (∆qi,jk,t | jk, t),
extracted from the changes in LOP deviations that are the basis of the variancedecomposition, Equation (6) in Section 4 of the text. There is one solid (red) line
per city-pair, jk. These lines are simply the time t, cross-good averages of changes
in LOP deviations. The average correlation between each of the solid (red) lines
and the dashed line is 0.89.

47

Figure 7
Variation in Absolute LOP Deviations: Time-Series Versus Cross-Sectional

Cross−Sectional Variance

Canada−U.S. Cross−Border Pairs

OECD Cross−Border Pairs

0.3

0.3

0.25

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05

0

0

0.05

0.1

0.15

0.2

0

0

Cross−Sectional Variance

Canada−U.S. Within−Country Pairs
0.3

0.25

0.25

0.2

0.2

0.15

0.15

0.1

0.1

0.05

0.05
0

0.05
0.1
0.15
Time Series Variance

0.1

0.15

0.2

OECD Within−Country Pairs

0.3

0

0.05

0.2

0

0

0.05
0.1
0.15
Time Series Variance

The figure reports scatter plots of time-series variance Ti (horizontal axes) versus
cross sectional variance Fi (vertical axes), defined by Equation (3) in Section 3,
reproduced here:
Var jk,t (qi,jk,t | i) = Var jk Et (qi,jk,t | i, jk) + Ejk Var t (qi,jk,t | i, jk)= Ti + Fi .
Regression slope coefficients, (standard errors) are 0.26 (0.09), −0.0129 (0.14), 0.35
(0.11) and 0.52 (0.11) for the NW, NE, SW and SE panels, respectively.

48

0.2

Figure 8
Time-Series Variance in LOP Changes: Common and Good-SpecificVariation Distinguished by Tradeability

Total

Blue = Traded Goods, Red = Non-Traded Goods
0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

Common

0

6

7

8

9

10

0

0.03

0.03

0.02

0.02

0.01

0.01

0

Good−Specific

5

5

6

7

8

9

10

0

0.08

0.08

0.06

0.06

0.04

0.04

0.02

0.02

0

5

6

7
8
Log Distance

9

10

0

0

0.05

0.1

0.15

0

0.05

0.1

0.15

0

0.05
0.1
FX Variability

0.15This graph shows that variation in changes in LOP deviations — “time-series variation”— is in general larger for traded goods than non-traded goods, and that this effect isalmost entirely a feature of good-specific time-series variation as opposed to location-pair
specific variation. Each point corresponds to a city-pair-specific object from Equation (6),Section 4, reproduced here:
Var i,t (∆qi,jk,t | jk) = Var t Ei (∆qi,jk,t | jk, t) + Et Var i (∆qi,jk,t | jk, t)= Cjk + Ijk .
The graph corresponds to all OECD city pairs. The middle two panels report Cjk , thecommon variation across all goods for city-pair jk. The bottom two panels report Ijk , thegood-specific variation, and the top two panels report the total variation, Cjk + Ijk . The
city pairs are organized by either distance from one-another (left-most column of panels),or by nominal exchange rate variability (right-most column of panels).

49

Figure 9Distribution of Good-Specific, Local Currency Price Volatility

Blue-Dashed = Traded Goods, Red = Non-Traded Goods
0.035

0.03

0.025

0.02

0.015

0.01

0.005

0
0

0.05
0.1
0.15
Standard Deviation of Log Price Change

0.2This graph plots kernel density estimates of the distribution of vi , parsed into traded andnon-traded goods, from Equation (9) from Section 5.3. The variables vi are, for eachgood i, the averages, across locations, of the time-series volatilities of log changes in localcurrency prices. The location-specific inflation rates are removed before computing thevolatilities. A high value for vi simply says that, for this good, the volatility of localcurrency price changes is large, on average, across cities. See Section 5.3 for an algebraic
derivation.

50