Price Dispersion: The Role of Borders, Distance and Location

Price Dispersion: The Role of Borders, Distance
and Location
Mario J. Crucini¤, Chris I. Telmeryand Marios Zachariadisz
December 2003
Abstract
1. Introduction
We study deviations from the Law-of-One-Price using microeconomic data on the
retail prices of approximately 220 individual goods and services across 122 cities
located in 79 countries over the period from 1990 to 2000. This paper builds on
our earlier work (Crucini, Telmer and Zachariadis (2001)) which focused on how
price dispersion within a …xed geography (the European Union) varied by type
of good or service. For example, in moving from the least traded good with the
largest share of non-traded inputs into retail production (a haircut) to the most
traded goods with the lowest share of non-traded inputs into retail production
(a desk-top PC), the standard deviation of price across locations dropped from
about 32% to 16%. Moreover, the median (and majority) of goods and services
fell between these two extremes.
In this companion essay we are interested in the interaction of the character-
istics of goods and economic geography in determining relative prices. This boils
down to addressing two related questions. At the level of an individual good we
¤Department of Economics, Vanderbilt University; mario.j.crucini@vanderbilt.edu.
yGraduate
School
of
Industrial
Management,
Carnegie
Mellon
University;
chris.telmer@cmu.edu.
zDepartment of Economics, Louisana State University; zachariadis@lsu.edu.

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ask: How does price dispersion change as we alter the set of locations included in
the analysis? We expect the answer to this question to depend whether a border
is crossed and the physical distance between the locations. The second question
is how these properties di¤er across goods.
We begin in section 2 with a description of the data and a summary of our
main …ndings with the details for each …nding considered in subsequent sections.
Section 3 develops a retail price model in which the Law-of-One-Price deviation is
a weighted average of a location speci…c relative price for non-traded inputs (which
we associate with relative wages) and a location- and good-speci…c relative price
for traded inputs (which we associate with transport costs). The role of non-traded
inputs is to raise prices of all goods in rich countries relative to poor countries,
with e¤ect rising with the share of non-traded costs in production. The role of
traded inputs is to create a dependence of relative prices on distance (trade costs
are assumed to be log-linear in distance), with e¤ect falling with the share of
non-traded costs in production.
Section 4 examines the properties of the average (across goods) deviation from
the Law-of-One-price, a basic building block of Purchasing Power Parity. We
…nd evidence of a border in the sense that there is greater dispersion in price
levels internationally than intranationally. Some, but not all, of this di¤erence
is attributed to greater income di¤erences internationally (the Balassa-Samuelson
theory). We …nd no evidence of distance e¤ects in the mean either within or
across countries provided we control for income di¤erences internationally. We
interpret the absence of distance e¤ects in the means as re‡ecting an ‘averaging-
out property’ of trade costs in our retail model.
Section 5 studies the variance of Law-of-One-Price deviations across goods for
each bilateral pair of cities. We …nd as we did with the means that borders and
income matter. However, we also …nd that distance matters which we interpret
as evidence that the averaging out property of trade costs does not occur in the
variances. The distance coe¢cients for intranational and international bilateral
panels are not too di¤erent suggesting some robustness to the role of distance in
accounting for price dispersion. Taken together, these …ndings suggest that the
border e¤ect is once again relegated to the constant term.
Section 6 moves from cross-section variation to time series variation. Here the
unit of observation is the variance of a bilateral relative price over time. This
metric is similar to the one used by Engel and Rogers (1996) except that we
use the level and they use the di¤erence. Since the level and the di¤erence have
similar variability in the micro-data, the transformation used before computing
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variability turns out not have a much of an e¤ect on the results. The pattern that
emerges here is similar to that found in Section 4 (analysis of means). Distance
matters internationally, but not intranationally. Moreover, there is a border in the
sense that conditional on distance, international prices are more volatile. While
it is trivial to attribute some of this e¤ect to nominal exchange rate variability
given the identity linking real and nominal exchange rates, it is far from obvious
how to interpret the correlation. On the one hand, domestic nominal prices are
not fully responding to nominal exchange rate variation, but on the other hand
it is unclear why they should if the absolute deviations are large and re‡ect real
factors that segment markets.
2. Data
The source of our price data is the annual Economist Intelligence Unit retail
outlet price survey. Our data begins in 1990 and ends in 2000, e¤ectively creating
(ignoring missing data) a balanced 11-year panel of absolute prices for 220 goods
and 84 services across 122 major cities across the globe. The total number of
countries is 79 countries, with di¤erences between the number of cities and number
of countries re‡ecting the fact that in 58 of the 79 countries the EIU surveys
multiple cities. The country with the most intranational observations is U.S.,
with 16; the next largest number of intranational observations is 5 (Australia,
China and Germany)1 The same basic data source has recently been used by
Crucini and Shintani (2002), Parsley and Wei (2002), Rogers (2001) and Engel
and Rogers (2003).
Our basic data unit is Pij;t, the price, in units of local currency, of good i in
location j at time t. For most of our analysis we transform this data into qijk;t,
log deviations from the law-of-one-price (LOP) for each bilateral location-pair:
P
q
ij;tejk;t
ijk;t = log(
) ;
Pik;t
where ejk;t is the nominal exchange rate between locations j and k, in units of
location k, and ejk;t = 1 if locations j and k are in the same country.
Figure 1 shows estimates of the density function for qijt for 1990, 1995, 2000;
both intranational and international city pairs. Here we normalize the the world
1 Speci…cally, the number of intranational cities are (ordered from the most available cities
to the least): United States (16), Germany, China and Australia (5), Canada (4), Saudi Arabia
(3) and France, Italy, Russia, Spain, Switzerland, UK, India, Japan, Vietnam, New Zealand (2).
3

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average price, rather than use bilateral pairings (i.e. qijk;t = log(Pij;tejk;t ), where
Pi;t
Pi;t is the average price of good i across locations). We see what is obvious to
anyone who has ever traveled between two locations: the LOP is not very useful
for describing the properties of qjk;t. Moreover, as one might expect, price disper-
sion is considerably higher across international locations. Much of the existing
literature has therefore proceeded by describing a number of interesting empirical
regularities inherent in the international relative price distribution. The di¢culty
with this lies in moving from empirical regularities to economic interpretation.
Our approach, therefore, will be to (i) brie‡y list a set of interesting empirical
regularities, and then (ii) ‡esh out their economic interpretation using a simple
production function which relates deviations from LOP in retail prices to devi-
ations from LOP in non-traded inputs (such as labor) and transport costs. At
each step we compare and contrast the properties that exist within countries and
across countries.
Our data on qijk;t display the following features. In each case, speci…c details
are deferred until the relevant section of the paper. For properties 1. to 5. we
work with qijk (i.e. qijk = PT q
t=1
ijk;t).
1. The Balassa-Samuelson E¤ect for the Mean. The cross-good average value of
qijk is strongly related to income and labor productivity di¤erences between
locations j and k. More precisely, the cross-sectional mean, Ei(qijkj jk)
(across goods for each date and location-pair), tends to increase if location
j has high income/productivity.
2. The Balassa-Samuelson E¤ect for the Variance. The cross-sectional vari-
ance V ari(qijkj jk) increases in the absolute income/productivity di¤erence
between locations j and k.
3. The Averaging-Out Property. Once we control for income/productivity dif-
ferences, E(qijkj jk) is close to zero. Based on our model, we interpret this to
imply that once we control for the impact of income/productivity di¤erences
on non-traded input costs we are left with the contribution of traded input
prices which, according to a standard trade-cost model, tend to average out
across goods. That is, for most bilateral location-pairs, there tends to be as
many overpriced goods (imports) as underpriced goods (exports).
4. Distance Does Not Matter for the Mean. Intranationally, E(qijkjjk) does
not depend on distance. Internationally it does, but not once we control
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for income/productivity di¤erences. We interpret this latter …nding as evi-
dence of a correlation between bilateral income/productivity di¤erences and
bilateral distance.
5. Distance Matters for Cross-Sectional Dispersion. De…ning V ari(qijk;t j jk)
as the cross-sectional variance — the variance across goods for each date
and location-pair — we …nd that V ari(qijkjjk) is increasing in the distance
between locations j and k. This relationship holds irrespective of whether
an international border separates the locations. Moreover, the magnitude
of the relationship is not a¤ected by the existence of a border.
6. Distance Does Not Matter For Intranational Time-Series Dispersion. We
de…ne V art(qijk;tj i;jk) as the time-series variance; the variance across time
for the relative price of good i between locations j and k. We …nd that, for
intranational location pairs, this variance does not depend on the distance
between locations j and k.
7. Distance Matters For International Time-Series Dispersion. If a border
separates locations j and k, the variance V art(qijk;t ji;jk) depends positively
on the distance between locations j and k.
We now demonstrate that each of these empirical regularities is consistent with
a retail-good production technology where deviations from LOP are sustained
through non-traded intermediate inputs and traded intermediate inputs which
are subject to transport costs.
3. Model
This section builds a simple partial equilibrium model retail price determination
at the level of individual goods sold in local markets. We assume that trade occurs
in intermediate inputs (goods) and retail …rms combine local inputs with traded
inputs for sale in the local market (allowing for trade in the …nal products involves
a trivial logical extension).
3.1. The Retailer’s Problem
In the notation that follows, we drop the time index to conserve notation and rein-
troduce it when we discuss time series properties. The retail production function
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is assumed to take the form:
Yij ´ (Nij)®i(Tij)1¡®i.
where Nij is a non-traded (i.e. local) input while Tij is an input which is either
exported from or imported into location j.
Two examples may help to …x ideas.
Suppose Yij is a men’s haircut in
Nashville. The traded input, Tij, might be shampoo. The local inputs are the
labor of the barber and the rental cost of the barber shop. If Yij was a PC sold
in Gateway country, the traded input would be the PC itself and the local inputs
would be sales personnel and the rental cost of the building housing the sales
operation. The value of ® is expected to be much closer to one for the haircut
than the computer.
The cost function is the solution to the following minimization problem at
each date:
min
C
N
T
fN
ij
= P N
j
ij + P T
ij
ij
(3.1)
ij ; Tij g
s.t. (Nij)®i (Tij)1¡®i ¸ Yij
(3.2)
where Cij is the cost of producing good i in location j; P N is the cost of a non-
j
traded input, common to all goods but di¤ering across locations; P T is the price
ij
of the traded input into production of retail good i in location j.
We have adopted two standard assumptions. The …rst is that factor mobility is
much higher across sectors within a location than across locations – P N is location-
j
speci…c, not good-speci…c. The second assumption is that retailers in all locations
produce good i using the same production technology – ®i is good-speci…c, not
location-speci…c.
3.2. Retail Price Determination
Under constant returns to scale, the cost function takes the form: Yij ¢ Ci(Pij;1)
where Yij is the output level, Pij = ³PN;PT
j
ij ´ and Ci(Pij;1) is the unit cost
function. Under the assumption of perfect competition, the unit cost is also the
retail price:
Pij = (P N )®i (P T )(1¡®i) .
(3.3)
j
ij
To compare this good and location speci…c price to the price of an identical good
sold in another location we work with the bilateral real exchange rate at the level
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of an individual good (ie. qijk = ln(EjkPij=Pik)):
qijk = ®iqN + (1
.
(3.4)
jk
¡ ®i)qTijk
As the equation makes clear, this price deviation is a linear combination of anal-
ogous deviations in the non-traded and traded input prices. The weights in the
linear combination are the shares of non-traded and traded inputs in production,
which add up to unity under our assumption of constant returns to scale.
The retailer solves the same problem in each period so it is valid to add time
subscripts to Equation (3.4) to re‡ect changes are input costs. When we use qijk
it should be understood that we have averaged the good-by-good real exchange
rate across time (i.e. qijk = T ¡1 Ptqijk;t) at the outset, thereby eliminating the
role of time series variation which is discussed separately.
3.3. The Balassa Samuelson E¤ect and Trade Costs
Equation (3.4) amounts to little more than an accounting device, relating input
prices to output prices. To push the model further in a structural direction we
make two assumptions about the properties of the relative prices on the right-
hand-side of equation (3.4).
The …rst assumption is that non-traded relative prices re‡ect productivity
di¤erences across locations. This assumption is based on the logic of the Balassa
Samuelson (1964) e¤ect. Because we lack reliable data on productivity we use
zjk ´ log(yj=yk) as a proxy for non-traded productivity di¤erence or qN.
jk
The second assumption is that traded intermediate inputs satisfy the Law-of-
One-Price up to a trade cost. Moreover, we assume that trade costs are related
to distance as follows: log(1+¿ i ) = log(D¯i) when the source is location k and
jk
jk
the destination is location j. Thus the log the deviation for the traded relative
price is qT =log{(1+¿
log(1 + ¿
¯i log D
is an
ijk
ijk)Iijk g = Iijk
ijk) = I i
jk
jk where I i
jk
indicator variable for the direction of the trade ‡ow (equal to 1 if goods travel
from k to j, and ¡1 if good go from j to k.
Combining these two assumptions we arrive at the observable implications of
a slightly more structured retail model:
qijk = ®izjk + (1 ¡ ®i)¯ Ii log D
i jk
jk .
(3.5)
where 0 < ®i < 1 and ¯ > 0:
i
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We see that for give given bilateral pair, the Balassa-Samuelson e¤ect has a
common sign, but the magnitude of the impact varies with the share parame-
ter. Greater distance between locations also increases price dispersion, but the
magnitude and the sign depend on speci…cs related to the good.
4. Properties of the Mean
We begin with an analysis of the cross-sectional mean Ei(qijkjjk), where it is
understood that we have averaged the good-by-good real exchange rate across
time (i.e. qijk = T ¡1 Ptqijk) at the outset.
Taking a simple average of both sides of the retail pricing equation, we arrive
at:
qjk = azjk + bjk log Djk.
(4.1)
where a = PN ®
(1
Ii .
i=1
i and bjk = N ¡1 PNi=1 ¡ ®i)¯i jk
4.1. Balassa Samuelson E¤ects
Ignoring the role of trade costs for the moment, the average deviation reduces to:
qjk = azjk. Since the parameter a is constant across bilateral pairs by virtue of the
common production function, the variance in the mean across jk is simply a scaled
version of the variance in income/productivity across locations. Consider a bilat-
eral pair countries with identical (vastly di¤erent) levels of income/productivity,
we would expect the average Law-of-One-Price deviation to be zero (very large).
Another way to visualize this e¤ect is to plot qjk = azjk against income. We
expect a strong positive correlation and as Figure 2 amply demonstrates we …nd
one.
4.2. Distance and Trade Costs
Consider, next the implications of the trade cost model and distance. The mul-
tiplier on distance is bjk = N¡1
due to the fact that despite the PN (1
Ii . The dependence on jk is
i=1
¡ ®i)¯i jk
assumption that the production and trade cost
parameters are independent of location, trade ‡ows obviously are not.
However, the jk subscripts represent little more than a nuisance because
we argue that the coe¢cient itself is expected to equal zero on a bilateral ba-
sis.
We refer to this notion as the ‘averaging out’ property of traded good
relative prices. The easiest way to see this is to suppose that the production
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and trade cost parameters are common across goods and an equal number of
goods are imported and exported. Then the expression is literally equal to zero:
(1 ¡ ®)¯N¡1 nPN=2(
1
i=1 ¡1) + PNi=(N=2)+1 o = 0. While some interesting asymme-
tries may give rise to positive or negative coe¢cient, we expect this property of
averaging out of the deviations to prevail for quite general production and trade
cost con…gurations.
4.3. Findings
Figure 3 plots the qjk against bilateral distance. It appears that distance matters
internationally, but not internationally. This visual impression is con…rmed by a
simple pair of regression estimates:
jqjkj = 0:244 + 0:0044 log Djk + "jk international
(4.2)
(0:0276)
(0:0031)
jqjkj = 0:130 ¡ 0:0044 log Djk + "jk intranational .
(4.3)
(0:0433)
(0:0059)
We use the absolute value of qjk so that the coe¢cient on distance has a consistent
sign across bilateral pairings.
Beginning with the international data we …nd evidence that distance matters as
it should based on the trade cost model. However, the magnitude of the coe¢cient
is small: going from cities that are neighbors to 100 miles apart adds 1% to the
price di¤erential, going and additional 2400 miles is needed to add another 0.5%!
Controlling for distance, though, the intercept is both highly economically and
statistically signi…cant. Thus even after conditioning on distance (a proxy for
trade costs), we resoundingly reject the Law-of-One-Price.
The intranational data tells a di¤erent story. The distance coe¢cient is of
the wrong sign and statistically insigni…cant. Using the same interpretation as
we did for the international context we reject the Law-of-Price, but unlike the
international data distance plays no role at all.
Combining the two results there appears to be a border involving an increase
in the unconditional variance in price levels across locations and an increase (from
zero) in the impact of geographic distance on price di¤erences.
According to our retail model, though, income/productivity disparities play
an independent role. Re-estimating with the absolute value of the log of relative
income across bilateral pairs, we have:
jqjkj = 0:2537 ¡ 0:0022 log Djk+ 0:0447 jzjkj + "jk international (4.4)
(:0272)
(:0031)
(:0031)
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jqjkj = 0:130 ¡ 0:0044 log Djk + "jk intranational
(4.5)
(0:0433)
(0:0059)
where we have simply repeated our results for the intranational case because
we lack data on income levels across regions within countries (assuming that
income di¤erences are small across regions within countries, this should not be
too problematic, but we will rectify this for the U.S. where we know such data is
available).
The absolute deviations of the log of relative income has a positive coe¢cient
as expected. The distance coe¢cient is no longer not statistically signi…cant as
we would expect if the income ratio was e¤ective in picking up the impact of
non-traded goods, based on the ‘averaging out’ property for traded good prices.
It is also interesting to note that the reduction in the magnitude of the coe¢cient
on distance coe¢cient (it actually becomes negative) is consistent with a positive
correlation between distance and income di¤erentials.2
5. Properties of Cross-Sectional Variance
Next we examine the cross-sectional variance: V ari(qijkjjk) which, in the model,
is given by:
V ari(qijkjjk) = a0(zjk)2 + b0(log Djk)2.
(5.1)
a0 = V ar(®i) and b0 = vari n(1¡®i)Ii ¯
jk
io.
5.1. Balassa Samuelson E¤ects
Taking the Balassa Samuelson e¤ect in isolation of the trade cost give us:
V ari(qijkjjk) = a0(zjk)2 .
(5.2)
Thus the variance of Law-of-One-Prices around the mean is increasing in the
income/productivity gap. Thus if we select a location pair with very similar
incomes there will be very little variation in the size of the deviations across
goods. If we take location pairs with vastly di¤erent incomes we will …nd that
the Law-of-One_Price deviations are more heterogenous across goods. In other
2 This classic results is derived as follows. Let the true regression be: yi = bxi + czi + "i. If
we estimate: yi = bxi + czi + "i then the di¤erence between the OLS estimate bband the true
one is: bb¡b=(x0x)¡1x0zc. Inourcontext c>0andifx0z>0 the OLSestimate is upwardly
biased.
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