NBER WORKING PAPER SERIESA MODEL OF INTERNATIONAL CITIES:IMPLICATIONS FOR REAL EXCHANGE RATESMario J. Crucini
Hakan Yilmazkuday
Working Paper 14834
http://www.nber.org/papers/w14834

NATIONAL BUREAU OF ECONOMIC RESEARCH
1050 Massachusetts Avenue
Cambridge, MA 02138
April 2009

We especially thank Mary Amiti, Eric Bond, Paolo Pesenti and Robert Vigfusson for valuable comments
and criticisms. We grateful to seminar participants at the California State University -- Long Beach,Federal Reserve Banks of Dallas and New York, Utah State University, Temple University, Universityof Tennessee at Knoxville and Vanderbilt University; conference participants at the 2008 Midwest
International Economics Meeting at The Ohio State University, the 2008 Midwest Annual Meeting
participants in Chicago, IL, the Wegman's Conference at the University of Rochester, and the Murray
S. Johnson Memorial Conference, The University of Texas at Austin. The authors gratefully acknowledge
the financial support of the National Science Foundation (SES-0136979, SES-0524868). The views
expressed herein are those of the author(s) and do not necessarily reflect the views 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.
© 2009 by Mario J. Crucini and Hakan Yilmazkuday. 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.

A Model of International Cities: Implications for Real Exchange Rates
Mario J. Crucini and Hakan Yilmazkuday
NBER Working Paper No. 14834
April 2009
JEL No. F0,F15
ABSTRACTWe develop a model of cities each inhabited by two agents, one specializing in manufacturing, theother in distribution. The distribution sector represents the physical transformation of all internationallytraded goods from the factory gate to the final consumer. Using a panel of micro-prices at the citylevel, we decompose the long-run variance of LOP deviations into the fraction due to distribution costs,
trade costs and a residual. For the median good, trade costs account for 50 percent of the variance,
distribution costs account for 10 percent with 40 percent of the variance unexplained. Since the sample
of items in the data are heavily skewed toward traded goods, we also decompose the variance basedon the median good on an expenditure-weighted basis. Now the tables turn, with distribution costs
accounting for 43 percent, trade costs 36 percent and 21 percent of the variance unexplained.

Mario J. Crucini
Department of Economics
Vanderbilt University
Box 1819 Station B
Nashville, TN 37235-1819
and NBER
mario.j.crucini@vanderbilt.edu
Hakan Yilmazkuday
Department of Economics
Vanderbilt University
Box 1819 Station B
Nashville, TN 37235-1819
skuday@gmail.com

1. Introduction
According to the U.S. National Income and Product Accounts, expenditure by consumers at
the retail level is about twice what producers receive for the same goods and services. Thisdi¤erence has come to be called the distribution margin. The distribution margin includes
transportation costs from the factory gate to the …nal point of consumption as well costs
and markups at the wholesale and retail stage.
Most existing international models abstract from the distribution sector entirely and focus
on the fraction of transportation costs attributable to international shipments. Abstractingfrom the distribution sector is problematic for three reasons. First, the distribution sector
may help us to understand the large and persistent deviations from the Law-of-One-Price(LOP) and Purchasing Power Parity. Second, the general equilibrium interaction of the
distribution sector and the production sector is not well understood. Given the prominentrole of the dichotomy between traded and non-traded goods in international …nance, this is
an important omission. Recent evidence also suggests that information technology and scaleeconomies in distribution have altered the e¢ ciency and markup structure of the distributionsector (e.g., the Walmart e¤ect). These developments may have fundamentally altered pricedispersion and dynamics, both across locations within countries and across countries. Third,
the distribution sector includes the …nancial, legal, medical and education sectors. These
sectors have grown immensely in economic importance over time. Much of the economic
activity engaged by these sectors is geographically segmented due either to the arms-length
nature of the exchange, public policy decisions or some combination of the two. Since theshares of expenditure attributable to these sectors tend to rise with the level of development,
their economic importance continues to rise globally.
We have two related goals in this paper. The …rst is to develop a tractable stochastic
general equilibrium model of production and distribution at the microeconomic level ofindividual goods and services across cities. The second is to use the theory to specify aregression model to estimate microeconomic parameters of a cost function, speci…c to anindividual retail good or service, which includes the cost of distribution as well as the more
traditional inputs of capital and labor embodied in traded inputs. This cost function is used3

to conduct a variance decomposition of prices across cities into a distribution margin, a trade
cost margin and a residual, good-by-good. The distribution margin is further parsed into thein‡uences of labor and retail infrastructure costs across cities. The Economist Intelligence
Unit (EIU) retail price data along with supplementary sources for wages at the city levelare used in the empirical work. Since the model assumes perfect competition and abstracts
from o¢ cial barriers to trade, the residual in the regression equation is expected to include
markups, o¢ cial barriers to trade and measurement error.
In the model, each city is inhabited by two representative agents, a manufacturer anda retailer. The manufacturer produces a single homogeneous good using labor as the only
input. The manufactured good is shipped to all other cities of the world and deviationsin the prices of these traded goods re‡ect only shipping costs from the factory door to thereceiving dock at the retail establishment. The retailer transforms these goods by combining
them with her labor and a …xed factor; she may also produce pure services which require no
traded inputs at all. The …xed factor is intended to capture retail infrastructure, broadly
de…ned to include land, buildings, equipment and public infrastructure.
The advantage of drilling down to the level of individual goods and services at the citylevel is that we can learn a great deal about production structure from the cross-sectionalvariance in the data. What distinguishes the manufacturing sector from the distributionsector is intimately related to what distinguishes a personal computer from a haircut. Aggregating the data tends to obscure these di¤erences.

For example, if trade costs are

symmetric, aggregating across imports and exports has the e¤ect of understating their role.
Having cities as the locations allows both greater attention to the spatial dimensions of manufacturing specialization and a more precise measure of the distance between production andconsumption locations.
We have two sets of results, one for the sources of LOP variance for the median good,
the other for the di¤erences in the sources of variance across goods in the cross-section.
For the median good in the EIU sample, trade costs account for about 50 percent of LOP
deviations, the distribution margin accounts for about 10 percent and the remaining 40
percent is unaccounted for. Because the median good in the EIU has a distribution shareof only 0.2, well below the aggregate value of 0.5 in the U.S. National Income and Product4

Accounts, we also report results centered on this value. Now the tables turn, with distribution
costs accounting for 43 percent, trade costs 36 percent percent and 21 percent of the variance
unexplained.
The relative importance of trade and distribution is fairly stable across sets of locations
that include high and low income countries and when comparing within country and crossborder city pairs. The absolute level of cross-sectional variance rises when a border is crossed
as one would expect or when comparisons are made between cities with vastly di¤erent wealthlevels. One exception is the division of the variance accounted for by the distribution sector
into the cost of labor and capital. Variance across low income countries is dominated bydi¤erences in the capital component, with labor playing a small role. For other countries,
the division of the distribution margin across labor and capital is closer to equality.
Turning to di¤erences in geographic price dispersion across goods, we …nd substantial
heterogeneity consistent with Crucini, Telmer and Zachariadis (2005) who focused on European Union capital cities using Eurostat micro-price data. The structure of the modeland methodology allow us to say more about the underlying sources of this heterogeneity.
In the international data, the distribution margin accounts for 50 percent of cross-sectionalvariance in LOP deviations for the good with the highest distribution share and this fraction
falls to a mere 10 percent as we move to the good with the lowest distribution share. Retailinfrastructure accounts for more than 30 percent of the cross-sectional variance in LOP deviations across Canada and the United States for the good with the highest infrastructure
intensity, while accounting for virtually none of the variance for the good with the lowest
infrastructure intensity.
Our theoretical model is closest to Giri (2009) who adds a good-speci…c distribution
cost to the Eaton-Kortum (2002) model. In Giri’s model distribution services are in …xed
proportion to the physical units of the base good as in Burstein, Neves and Rebelo (2003)(BNR) with e¢ ciencies drawn from a distribution with a country-speci…c mean and common
world-wide variance. In contrast, we assume that the technological parameter for distribution
inputs is good–speci…c while the productivity of the distribution sector is city-speci…c. Given
that this margin is measurable in the NIPA, we view this as a more tractable way to model the
distribution sector than the random e¢ ciency approach. Our model shares with Alvarez and5Lucas (2007), Atkeson and Burstein (2007), Eaton and Kortum (2002), and Kanda Naknoi(2008) an interest in the role of traditional trade costs. However, to the extent these papers
incorporate a distribution sector, it is a common wedge across all goods in the retail basket,
which assumes away any cross-sectional variance in price deviations due to the distribution
margin. We …nd this heterogeneity to be essential for improving our understanding of LOP
deviations.

2. The Model
Each city, indexed by j, is inhabited by two representative agents. As is usual in representative agent frameworks, these two agents should be viewed as stand-ins for a large number of
atomistic agents of each type, since we will be assuming perfect competition in all factor and…nal goods markets throughout. One agent specializes in the production of a single traded
good, indexed by i, while the other specializes in retail trade and production of non-traded
services. Production in the manufacturing sector is proportional to labor input, the factor
of proportionality is a random productivity variable. Retail production requires both laborand capital. Capital is …xed and is broadly de…ned to include land, buildings, equipment
and public infrastructure. Productivity varies across cities in both the traded goods sector
and the retail sector.
Traded goods are subject to iceberg transportation costs which are good and destination
speci…c. Final goods and local inputs (retailer labor and retail capital) are not traded beyond
the city limits. While hours and consumption are both choice variables, the assumptions wemake in the model imply constant hours in all sectors in all locations, reminiscent of theLong and Plosser (1983) multi-sector, closed economy, real business cycle model.

Retailinfrastructure, including land, capital and equipment, is in …xed supply (denoted Kj ).
The good index, i, distinguishes physical objects from the identities of agents and locations only when needed to avoid confusion. In describing the ‡ow of goods from one location
to another, the source is the …rst subscript and the destination is the second subscript. Thus,
Xsd refers to the shipment of good X, from city s to city d. Given the assumption that individuals at each location specialize, s also indexes the good and the individual to whom6

the income ‡ows, while d indicates the expenditure side of the equation.

sd is the iceberg

shipping cost from the source to the destination. Since there are no durable goods or assets
in the model, adding time subscripts is innocuous: they are omitted here since the focus ison the steady-state properties of the model and long-run deviations from the LOP.
The full solution for quantities and prices is given in the appendix. This section presents
the complete model and parts of the equilibrium solution relevant for pricing implications,which is the focus of our empirical work.
2.1. Consumers
Agents preferences are log-additive over consumption and leisure:
U CjA ; LAj

) log CjA + log LA
j , A = m; s.

(1

(2.1)

CjA is aggregate consumption and LA
j is hours of leisure, for an individual working in cityj. There are two individuals in each city, indexed by A = m; s; one is engaged in the
manufacture of a single good (m) and the other is engaged in retailing and service activities(s).
The consumption aggregate is CES over varieties of manufactured goods produced worldwide:
CjA =

M
X

( i)

1
"

i

CijA

" 1
"

!""1

.

(2.2)

CijA is the consumption of good i in city j by worker of type A; " > 0 is the elasticity of
substitution across goods,iis a good speci…c taste parameter and M is the number ofmanufactured goods in existence. M is also the number of cities given our specialization
assumption.
The two agents inhabiting city j, maximize utility (2.1) subject to their respective budget
constraints:X

Pij CijA

WjA NjA + 'A Hj Kj

(2.3)

i

where Pij is the price of good i in destination city j. These prices will be the same for all
agents in the same location, but di¤er across locations for reasons described below. Each of
the two residents of city j earn labor income from their production activities and split the7rental income accruing to the retail infrastructure in their city ('m + 's = 1), the stock ofwhich is assumed to be …xed at Kj . The rental price of retail infrastructure is denoted Hj .
The consumer’s problem may be solved in two stages. In the …rst stage, the consumer
chooses aggregate consumption and leisure, subject to a budget and time allocation constraint. In the second stage, the consumer minimizes expenditure across goods. Here wecollapse the problem to a single stage for brevity. The key equations from the solution to
the consumer’s problem are:
"

Pij
CjA
i
Pj
A A
W j N j + ' A H j Kj=
Pj
H j Kj= 1'A
WjA
H j Kj=+ 'A
WjA

CijA =

(2.4)

CjA

(2.5)

NjA
LA
j

(2.6)
(2.7)

Aggregate real consumption is nominal consumption de‡ated by the ideal de‡ator Pj
1PP
1 " 1 "
, which ensures i Pij Cij = Pj Cj as well as a theoretical mapping from
(P
)
ij
i i

price indices to welfare.

The …rst equation determines consumption demand for a particular good as a functionof the relative price of the good paid by the …nal consumer in their home market and that
individual’s aggregate consumption level. It is important to note that, Pij is the retail priceof good i, in city j; it embodies the cost of local retail services paid to the retailer in addition
to the traditional iceberg trade costs of the imported item. The price index, is a weighted
average of these retail prices, the closest empirical counterpart would be the CPI index. The
second equation is aggregate consumption of an agent, which is equal to her real income.
Real income is the sum of nominal wage and rental income, de‡ated by the local price level,
Pj .
The last two equations determine hours of work and leisure. In the absence of rental
income, the two agents would work the same number of hours, independent of their relative
wage, due to the o¤setting income and substitution e¤ect of wages on e¤ort with CobbDouglas preferences. In the presence of rental income the requirement for constant e¤ort
in equilibrium is that the ratio of rental income to labor income be constant. Most growth8models impose restrictions on tastes and technology to ensure constancy of hours per capita
in the presence of trending productivity.1
2.2. Manufacturers
The production function for manufactured good, i, is:Yi = Ai Nim(2.8)

where Ai is the productivity level and Nim is hours of work.
Manufacturers choose labor inputs to maximize pro…ts:
Wim Nim ) .

max(Qii Yi
m
Ni

(2.9)

The manufacturer receives the factor gate price, Qii , for every unit produced, no matter where
the goods end up being sold. Given the assumptions of constant returns to scale, perfectcompetition and one factor of production, the factory gate price equals the manufacturing
wage divided by productivity:
Wim
.
Qii =
Ai

(2.10)

Given specialization, the productivity level in this expression is good and city-speci…c. The
presence of a nation-speci…c component could easily be incorporated by allowing Ai to havea common factor across cities located within the same country.
Retailers in each city purchase the manufactured goods and pay a proportional shippingcost. Thus the retail purchase price is the factory-gate price marked up by a proportional
shipping cost:
Qij = (1 +whereij ) Qii = (1 +mij ) Wi =Ai(2.11)

ij > 0 is the net transportation cost from city i to j. Qij is the price the retailer paysin the destination city. The empirical counterpart to this would be a wholesale price. The
local manufacturing plant is close enough to the city to ignore local transportation costs sothat1ii = 0.

E¤ectively this cuts out one intermediary, the wholesaler, and the retailer is

Details of these restrictions in the context of the one sector stochastic growth model may be found in

King, Plosser and Rebelo (1988).

9viewed as operating next to the factor gate. The destination price of the manufactured gooddepends: i) positively on both the manufacturing wage and the trade cost; and ii) negatively
on manufacturing productivity.
2.3. Retailers
The retailer in each city optimally chooses how much of each manufactured good to purchasefrom various cities of the world. The retailer transforms these goods using a fraction of her
time endowment and some amount of the local retail infrastructure. The retailer then sells
the resulting composite good in the local retail market. The production function for good i,sold in city j is:Rij =Bj Nijsi(Kij )1i

1i(Gij ) i(2.12)

Gij is the amount of the manufactured good imported from city i, by a retailer in city
j. Nijs is the fraction of the retailer’s time endowment allocated to the transformation ofimported good i for local consumption in city j and Kij is the amount of retail infrastructure
allocated to retail good i in city j. Bj is labor-augmenting productivity speci…c to the city(equivalently, the retailer), common to all goods sold there.2
While the production function is restricted to be common to all locations, it is very
‡exible across goods.
equal to zero andIt captures pure labor services (e.g., baby-sitting services) withii equal to one; internet purchases (e.g., Amazon.com book purchases),iequal to one, and all points in between.
The retailer in city, j, maximizes pro…ts from the sale of each good, i, by optimallychoosing the three inputs needed to produce the good: i) the amount of the traded input,
Gij , to import ii) the fraction of her time to devote to the good, Nijs ; and iii) how much local
infrastructure to allocate to the activity, Kij :max (Pij Rij

s ;K ;GNijijij

Wjs Nijs

Hj KijQij Gij )(2.13)At the optimum, the unit price equals marginal cost. Given constant returns to scale andthree factors of production, the retail price of good i sold in location j, is a Cobb-Douglas
2

In principle one could add good-speci…c productivity of retailers to account for di¤erent levels of com-

petency across goods, but we lack productivity data to operationalize this idea.

10

aggregate of the price (inclusive of trade cost) that the retailer paid to acquire the traded
input, Qij , the retailer’s market wage, Wjs , and the rental price of retail infrastructure, Hj :Pij = M Cijs =
1
i

i

i

i

(1

Wjs =Bji) ( i)ii(Hj )(1
(1
i)

(1

i)

i)

(1

(1

i)

(Qij ) ii)(2.14)(2.15)The retail price in city j is rising in input prices and falling in retail productivity, Bj .
2.4. Equilibrium
The appendix contains the tedious algebra necessary to arrive at the equilibrium allocations
discussed in this section. In the remainder of the paper the consumption aggregator isrestricted to Cobb-Douglas to arrive at closed form solutions.
In the global general equilibrium, all the optimality conditions of partial equilibrium must
hold for consumers, retailers and manufacturers. In addition, the supply of each good must
equal its total demand, including the resources lost to iceberg shipping costs.
Yi =X

Gij (1 +

j

=

X

Gij +

j

ij )

X

Gij ij(2.16)(2.17)j= Gi + Ti(2.18)

In words: the production of good i, Yi , is exhausted between the global demand for that
good by retailers aggregated across destinations, Gi , and physical loses due to iceberg costs,
Ti .
Each individual has a …xed amount of time to devote to hours of work and leisure, here,
normalized to unity. The time constraints for the manufacturers and the retailers are thus:mLm= 1
j + NjX
Lsj +Nijs = 1 .

(2.19)(2.20)i

The summation in the second time constraint re‡ects the fact that the retailer must divide
her time across the M di¤erent retailing activities. The notation implicitly sets the numberof goods at the retail level equal to the number of goods in the manufacturing sector. Nothing11

we derive requires this: we could have some activities that use no traded inputs at all inwhich case the number of retail goods would exceed the number of manufacturing goods by
the number of pure services produced by ‘retailers’in each city.
The city’s retail infrastructure is exhausted across uses:
Kj =

X

Kij .

i

3. The data
Our focus is retail price dispersion across international cities at the microeconomic andmacroeconomic level. The data source for prices is the Economist Intelligence Unit (EIU)
worldwide retail price survey. The survey spans 123 cities, located in 79 countries. Most of
the cities are national capitals. The larger number of cities than countries is due to the factthat the survey also includes multiple cities in a few countries. Noteworthy are the 16 U.S.
cities included in the survey; the next largest number of cities surveyed equals 5 in Australia,
China and Germany. Up to data availability for particular years and cities, the number ofgoods and services priced is 301. The available sample is 1990 to 2005.
Our goal is to understand the sources of variation in LOP deviations. The Cobb-Douglas
functional forms in our model rationalize the use of logarithms of LOP deviations acrossbilateral city-pairs:
qijk;t = ln(Sjk;t Pij;t =Pik;t ) .

(3.1)

while our long-run focus further suggests the use of time-averaged deviations:qijk = T 1

Xtqijk;t .

(3.2)

Crucini and Telmer (2007) derive a variance decomposition which is very useful for splitting
the total variance of LOP deviations into long-run deviations and time series ‡uctuations:
V arjk;t (qi;jk;t j i) = V arjk (Et [qi;jk;t j i; jk]) + Ejk [V art (qi;jk;t j i; jk)]

(3.3)
(3.4)

Vi = Ti + Fi :The …rst term, Ti , which is meant to remind the reader of trade costs broadly de…ned, isthe focus of this paper. It is the variance of the deviations from the LOP across all location
12

pairs remaining after time-averages of the data have been taken. The role of time-averaging
is to eliminate the time series component of the variation, which is valid when the data
are stationary and su¢ ciently long time samples are available, which is the case here. The
second term, Fi , which is to remind the reader of ‡uctuations, is the focus of the international…nance literature, often featuring short-run ‡uctuations of LOP due to local currency pricestickiness. One of the novel …ndings of Crucini and Telmer is that the ratio of the varianceof the long-run deviations to the total (i.e., Ti =Vi ) is very large for the average good: 0.51
for U.S.-Canada intranational pairs and 0.69 for all international city pairs in the EIU data.
In other words, the variance component this model focuses upon is at least as important inan accounting sense as the focus of business cycle models.
One way to visualize this property of the data is to estimate LOP distributions using
kernel estimation. Figure 1 has eight such kernel estimates. Each chart contains two lines,
one for the distribution of time-averaged LOP, qijk , and one for the distribution of the timeseries deviations from the long-run means, qijk;t qijk . The upper two charts are distributions
for U.S. city pairs and the lower two are international pairs. The left column uses non-traded
goods prices and the right column uses traded goods prices. The dominance of the long-run
sources of variation relative to the short-run (time series) sources of variation in most cases
is evident in the wider dispersion in the LOP distributions represented by the solid lines
than those represented by the dashed lines in each chart. The role of borders in increasing
price dispersion is evident in comparing the top and bottom panels and the role of the typeof good, as summarized by the classical dichotomy, is apparent by comparing charts in aparticular row across columns.
Table 1 presents summary statistics relating to these …gures. The least amount of pricedispersion is found in U.S. traded goods, 0.29 and the greatest amount is found in the caseof non-traded goods involving border crossings, 1.07. More surprising is the fact that nontraded goods in the U.S. have less price dispersion than do traded goods internationally,
0.54 compared to 0.68. Interquartile di¤erences yield similar measures of price dispersion.
As discovered by Crucini and Telmer (2007), the time series variation is always less thanthe long-run variance, with the possible exception of traded goods across U.S. cities andeven there one of the two measures (interquartile di¤erence) also gives this ranking. Notice13

also that the distinction between traded and non-traded goods is obvious in the long-run
measure, but ambiguous in the time series measure. Given our emphasis on trade costs,
broadly de…ned and abstraction from stochastic variation due to shocks interacting withsticky prices, this observation is another reason to focus on the time averaged data with ourmodel.
The EIU survey o¤ers little in the way of wage data. Supplemental wage data at thecountry level come from the International Labor Organization (ILO) survey of occupationaland sectoral wages and at the city level from the Union Bank of Switzerland (UBS) survey.
The ILO data are averages for countries. They span 49 sectors, 162 occupations and 137
countries. The sample period is annual from 1983 to 2003. The complete list of these sectors,
occupations, and countries is found in Oostendorp (2003). In the raw ILO data, the mostcommon period is the month, followed by the hour, but some countries report weekly pay,others give daily rates for some occupations, and so on. In order to have a comparable wage
data across countries, the standardized version of ILO survey by Oostendorp (2003) is used:in cases in which the wage data are reported as hourly or daily, then these wages were made(roughly) comparable with monthly wages by multiplication by 160 and 20 respectively. In
order to have the largest panel of wage data that are comparable across countries, the monthly
wages in US dollars that have been obtained by country-speci…c and uniform calibration in
Oostendorp (2003) are used.
Wage data at the city level is more appropriate given the EIU retail price data is city
based and the intent of the model. International cities were surveyed by the UBS in 2006.
These are hourly wages in US dollars, spanning occupations in 71 international cities, 60of which are also surveyed by the EIU. Among the 60 EIU cities there are four cities from
Brazil, Canada, China, France, Italy, Spain and Switzerland; four cities from Germany, andfour cities from the U.S. The hourly wages have been obtained by dividing the income per
year in each occupation by the city level hours of work in a year, where the latter we collectedby a survey, also conducted by the UBS.
Bureau of Labor Statistics (BLS) city wage data from the Occupational Employment
Statistics (OES) Survey in 2006 are used to complement UBS data. These wage data arehourly wages in US dollars for the same 16 US cities found in EIU retail price survey.
14

The combination of UBS and BLS wage data, then, provides wage data for 72 EIU cities,
comprised of 16 from the BLS and the remainder (non-U.S. cities) from the UBS. Withinthese 72 EIU cities, in terms of intranational cities, we have two cities from Brazil, Canada,
China, France, Italy, Spain and Switzerland; three cities from Germany, and 16 cities fromthe US.3
In a preliminary part of the analysis, the BLS city wage data are used for broader wage
dispersion analysis. These data cover two industries, namely production and sales, for 400
cities (on average) within the U.S. in terms of hourly wages from 1999 to 2006.
A number of trade-o¤s present themselves in terms of the model focus and the available
data. Country-level wage data is generally available for longer periods of time, but fewer
locations than city-level wage data. Since the model is explicitly constructed to mimic citylevel aggregation and steady-state features, ideally one would want long time series at thecity level. Unfortunately these are simply not available. These trade-o¤s are discussed asthey arise below.
Land prices and rents are even more di¢ cult to come by than are wages and prices. We
use the EIU survey data item: “Typical annual gross rent for top-quality units, 2,000 square
meters, suitable for warehousing or factory use.”4
The other two pieces of information are sectoral estimates of the distribution shares, 1,

which are calculated from a combination of U.S. NIPA data and input-output tables. The
NIPA data extend to 57 sectors, while the input-output data span 33 sectors. The NIPA
shares are computed as the value the producers receive relative to the value consumers pay
for the output of a particular sector. The distribution margin, 1, includes transportation

costs, retail and distribution costs and markups. Sectors involving arms-length transactions,such as medical services are recorded in the NIPA as though the producer and consumer
valuation is equal. While this is literally true in some cases, this accounting fails to distinguish3

In an earlier version of this paper we used PWT per capita annual income data covering the annual

period from 1990 to 2004 to proxy for real wages. These data span all 79 EIU countries. The results werequalitatively similar to those reported here.
4
One additional commerical rental price is available in the EIU, “Typical annual gross rent for a 1,000
square meter unit in a Class A building in a prime location.” Results are very similar with this alternative
measure.

15

local inputs from traded inputs used in the production of services. For these sectors we use
the input-output tables to determine the distribution share. These sectoral measures fromthe NIPA complement the good-level parameters estimated using a regression framework
discussed below.
Finally, the greater circle distance between cities in the EIU sample is used to estimate
the trade cost component of the LOP deviations at the retail level.5

4. Microeconomic sources of long-run variation in wages
In the model, wage deviations arise across the retail and manufacturing sectors and acrosscities. The amount of labor income accruing to the manufacturer relative to the retailer incity j is,P
Njm Wjmi=P(1
Njs Wjs
i

i i
i)

(4.1)
i i

Which is intuitive: the numerator is an expenditure share weighted average of labor’s shareof manufacturing and the denominator is the counterpart in retailing. The appearance ofthe parameteri in the denominator accounts for the fact that retail production involves

some retail infrastructure, unlessi = 1, in which case retail production is labor-only.

Note,also, that the ratio is the same in all cities.
As the primary interest is wage variation across cities as an explanation for cost andprice variation across cities, we would like to understand the wage ratio and e¤ort ratios
separately. The equilibrium relative sectoral wage is given by:
Wjm
'm (1
=
Wjs
1 'm (1

)
)

Njs
Njm

Thus, given …xed shares of rental income across agents in the city, relative wages and relative
hours move inversely as one would expect. The appendix shows that the equilibrium e¤ort
5

Hummels (2001) provides the most comprehensive estimates of sectoral trade costs using import unit

values, a more direct method than employed here. Unfortunately these estimates are available for a limited
number of countries and are more aggregated than our retail data.

16

levels are:
(1

Njm =

(1

0

1

1 (1
+ 's (

Njs =

where

0

P

i (1

i)

i and

0 ) (1) + 'm (

P

i (1

1

)
1)

0

)
1)

0

i i.

i)

E¤ort in both sectors is declining inthe share of rental income allocated to the agent (a wealth e¤ect), and in the preference forleisure ( ), as one would expect.
Substituting these expressions into the wage ratio leads to the following expression for
relative wages:

= ( 0

A
Wjm
1 'm (10) + '
=
Wjs
'm
'A )
1 + (11 ).

As the retail sector becomes more labor intensive (thus reducing rental income), ( 01)converges to zero and the model reverts to the labor-only version with a common fraction ofavailable hours worked by both agents, equal to (1
to:

Wjm
1
=
s
Wj

0
0

) and the sectoral wage ratio converges
P

i

i i

i (1

i)

=P

i

which is exactly the same expression as labor income shares in the more general case (seeequation (4.1)).
Turning to wage di¤erences across cities things are much simpler even in the general
case:
Wjs
=
Wks
Wjm
=
Wkm

j

j

k

k

j

j

k

k

(4.2)
.

(4.3)

The cross-city wage di¤erential is the same in both sectors and is determined by the productof the taste and technology parameters in the two locations being compared. The intuition
for this result is as follows. Consider, …rst, the special case in which all goods use traded
inputs in the same proportion,j=. Wages are higher in locations that produce the17goods most preferred by consumers, given by the comparison ofj ande¤ect. Next, consider the case with symmetric tastes across goodsj =k , a demand-side; then wages are

the highest for producers of manufactures requiring the least amount of input from retailers(i.e., the lowest 1). Essentially, the higher the distribution share, the less productive isan hour allocated to production of the manufactured good in terms of delivering a unit ofconsumption to …nal consumers. This lowers the equilibrium real wage.
Wage data are available by occupation or sector of employment. Our model focuses on
the distinction between goods and services, suggesting the production sector de…nition ismore appropriate. However, we use both labor classi…cations as a robustness check.
The more comprehensive of the sources used is the ILO survey of wage levels acrosscountries. These data span 49 sectors, 162 occupations and 137 countries. The sample
period is annual from 1983 to 2003.6 Because the model is intended to be based on city-level
data, the preferred measure is wage data from the UBS that span 14 occupations and 71
international cities for the year 2006.
According to the model, if the retail sector uses only labor and traded goods, the ratioof manufacturing wages to service wages provides on estimate of the overall scale of theP, = i i i . Since we lack consumption expenditure
distribution sector Wjm =Wjs = =1

shares at the present time, we associate this with the distribution share alone since using thesymmetric taste version of the model we have:= . A direct way to measure the overall

size of the distribution sector is to use U.S. NIPA data and input-output data. Crucini and
Shintani (2008) do exactly this and …nd= 0:57. The advantage of their calculation is thatis it based on expenditure weighting of sectoral ’s.
Table 2 reports the sectoral wage ratio averaged across locations as well as the impliedvalue for . It turns out that the direct and indirect (model-based) estimates are equal when
U.S. wages in production sector relative to the sales sector are used. The wage ratio in theinternational data is consistent with a valueof 0.52. While this is a modest di¤erence fromthe U.S. value, the implied manufacturing wage premium is quite dramatically a¤ected: it
is a factor of 5 smaller than the U.S. case. It could be that relative productivity di¤erences
are the cause. Another possibility is that the U.S. and international agencies have di¤erent
6

Useful technical documentation is found in Remco H. Oostendorp (2003).

18

classi…cation systems for the sectors.
As the theory is a two-sector model, any sectoral variation in wages in a particular city
is attributable to wage di¤erences across the manufacturing and service sectors. Variationin wages across sub-sectors are abstracted from entirely. Thus, it is important for the theory
that wages di¤er signi…cantly across locations and less so across sectors other than the two
sectors emphasized by the model (retail and manufacturing). And this is what is found.
Table 3 conducts a variance decomposition by sector and country for time-averaged wages
in the case of the ILO survey and an analogous decomposition by sector and city for wages
in 2006 for the UBS survey data. Since the answer may depend on the set of sectors andlocations used, we consider three location groups and allow for many sectors throughout.
The location groups are the entire world, the OECD and the LDC.
Based on the ILO wage data: locations account for between 72 and 85 percent of thecross-sectional variation in wages, sectoral di¤erences account for less than 10 percent. The
dominance of location in accounting for wage dispersion is somewhat less pronounced when
the data is organized by occupation: location e¤ects drop to between 38 and 65 percent.
Most of di¤erence is not attributed to a pure sectoral component, but rather an interactionof location and sector. The UBS tell a similar story to the ILO for location e¤ects, with theoccupation e¤ect rising in contribution due to a lower interaction with location compared to
the ILO.
In sum, location is a key component of wage dispersion with the precise fractions depending somewhat on the set of locations examined and the precise de…nition of wage categories.

5. Microeconomic sources of long-run variation in real exchange
rates
We turn, now, to the main focus, price dispersion. In the model, prices consumers actually
pay may di¤er from factory gate prices for two reasons. The …rst is the trade cost to import
the good from the foreign production location. The second is the value added by the retailer.
To simplify the notation, all international prices have been converted to common currency
units (it does not matter which numeraire is chosen). The ratio of the price of good i in city19

j relative to k, based on the theory is:
Pij
=
Pik

Wjs =Bj
Wks =Bk

i (1

i)

(1

Hj
Hk

i )(1

i)

i

Qij
Qik

.

Noting that the last term reduces to the ratio of trade costs from the single source of good ito each of the destinations, j and k and taking logs, de…nes the Law-of-One-Price deviation
across a city pair:qijk = (1i ) [ i ! jk + (1=i hjk +

i ! jk +i ) hjk ] +

(5.1)

i ijk

i ijk .

The retail margin is the …rst term in square braces; it is a weighted average of the productivityadjusted wage and the rental price di¤erential faced by retailers in the two cities. The weights
attached to the relative input prices in the retail sector depend on

i . The entire retail com-ponent gets weighted by its overall share in the production of the …nal good, (1i ). The

second term is the relative trade cost. The last line, used to specify our regression approach,expresses the relationship in terms of the three key cost ratios, retail wages, rental prices
and trade costs.
The aggregate real exchange rate in our theory follows directly from equation (5.1) since
the consumption aggregator is Cobb-Douglas (i.e., " = 1):
qjk =X! jk + hjk +i
Xi ),i i (1
i

i

(5.2)

i ijk

X

i

i (1

i )(1

i)

The aggregate real exchange rate has a number of interesting features. The distribution
component of the PPP deviations are driven by exactly the same wage and rental price differentials as was true of the LOP deviations, the impact factors are consumption-expenditureweighted production parameters,

and . The trade cost component is more convoluted

because the expenditure shares, production coe¢ cients, and trade costs are good speci…c.
However, it seems plausible that the individual deviations could average out across goods
since theijk are expected to vary in sign across goods.

205.1. Regression speci…cation
This section conducts a variance decomposition of retail prices into the channels describedby the equilibrium model. Adding a measurement error term to the theoretical equation for
the LOP deviation, gives:
qijk =

i ! jk +i hjk +

i ijk + "ijk

(5.3)

Data on retail prices, wages and rent, are available, but no data on retail productivity or
trade costs exist for this cross-section of locations, at this level of disaggregation. The raw
wage ratios are used in place of ! jk and a two-stage estimation approach is used to infer the
impact of trade costs.
The …rst-stage regression is:qijk =
where

1i ! jk +1i hjk +

ijk .

(5.4)

ijk is an estimated residual, which, according to the theory, is the LOP deviation in

the traded component of cost.

In practice it will incorporate other sources of deviations

as well. In an attempt to purge these other factors from the pure trade cost component,
the estimated residuals are projected on bilateral distances. To accomplish this, de…ne thedirection-of-trade indicator function:

where

ijk = qijk

1i ! jk8< 1 ifIijk =: 1 ifijk > 0(5.5)

ijk < 01i hjk from the …rst-stage regression. In words: imports (exports)

are assumed to be relatively expensive (inexpensive) at the destination (source).
Consider, now, the more elaborate equation for stage two:qijk =

2i ! jk +

2i

= (1

i) i

2i

= (1

i )(1

& 2i =

2i hjk + & i2 Iijk djk + "ijk

(5.6)
(5.7)

i)

(5.8)
(5.9)

i i

with the trade cost replaced by Iijk i djk . The indicator function ensures the sign of theimplied trade cost is consistent with the sign of the residual estimated in stage one. The
21

greatest circle distance between locations j and k is the empirical counterpart to djk andgoods are allowed to have di¤erent trade cost elasticities with respect to distance,

i.

The

bene…t of projecting the prices on wages, rents, and the indicator function multiplying distance is that we relegate any sources of variation in retail prices not correlated with wages,
rental prices or distance to the error term. This gives us more con…dence that the wage,
rental, and trade cost components are capturing what the model says they should.
The model is best suited to describe the long-run properties of real exchange rates since
we abstract from nominal exchange rate variation and sticky prices. While we have a long
panel of EIU retail price data from which to construct time-averages and target long-run pricedispersion, as noted earlier, we lack comparable city-level panel data on wages. Moreover,
the argument could be made for estimating the parameters with a single cross-section. Our
benchmark estimation and variance decomposition uses time-average data as available (i.e.,
for qijk and hjk ) and wage data for a single cross-section in 2006. Wage data from the UBS
is used for cities outside of the U.S. and wage data from the BLS is used for U.S. cities.
Preliminary experimentation with alternatives does not seem to alter the main thrust of theresults.
We see in Table 4, that the empirical model captures the majority of long-run retail pricedispersion across locations for all groupings of the data. The range of variance accounted
for is between 70 percent and 90 percent for the median good when pooling all international
cities or just those in North America. The …t of the model is excellent over much of the
distribution of goods. The lowest quartile for the R2 is a very respectable 0.67 (the OECD
cross-border pairs). In summary, the empirical model …ts well across sub-set of locations
and across goods ranging from haircuts to personal computers.
5.2. Variance Decomposition
Using the estimated equations motivated by the theory, we are able to provide a crosssectional variance decomposition analysis according to the following equation (we suppress
the residual and covariance terms here for expositional convenience; also the parameters
used in computations will be those from the second stage estimation, though we suppress

22the subscript denoting this as well in what follows):
2i ) Dijk +varjk (qijk ) = (12i dijk .

According to the theory, geographic price dispersion at the level of an individual good,i, is a weighted average of the geographic dispersion in distribution costs, Dijk , and thegeographic dispersion of destination prices for traded inputs, dijk . The relative contributionof distribution costs and trade costs for a particular good hinges on the value taken by the
distribution share,i , ranging from close to zero for a personal computer to close to 1 for ahaircut.
Recall that the distribution cost component is a weighted average of the dispersion inwages and rental prices:
Dijk[ 2i varjk (! jk ) + (12i ) varjk (hjk )] .

Finally, the quantitative role of trade costs depends on the relationship between trade costs
and distance interacting with the direction of trade:dijk =

2i varjk [Iijk djk ].

Table 5 presents estimates of the variances of retail prices, wages and rental prices forvarious location groups: i) intranational city pairs (which given the data, is dominated by
U.S. city pairs), and ii) cross-border city pairs (using three groupings, OECD, LDC andWorld).
The conventional wisdom is that factor markets are close to perfectly integrated intranationally, while the immobility of labor and possibly capital prevents this from occurringinternationally. This seems to be a reasonable assumption of labor markets since we …nd
wage dispersion of 3 or 4 percent, for intranational pairs. It appears not to be true of rental
prices, where dispersion is about 30 percent. These numbers are fairly robust of inclusion of
intranational city pairs outside of North America.
Turning to cross-border city pairs, consistent with expectations, we see less of a tendency
toward factor-price equalization than within countries. In fact, there is an approximate
tripling of the variance of wages as a consequence of crossing the U.S.-Canadian border.
23

The border width appears less dramatic when we look at rental prices, where the variancemerely doubles. When we expand the set of international comparisons to the OECD, we…nd virtually no impact on wage dispersion, but a large impact on rental price dispersion.
Expanding the geography further to include both the OECD and non-OECD (the row labelled WORLD), wage dispersion increases considerably more than rental price dispersion.
The main implication for retail price dispersion, though, is that factor price dispersion rises
by a factor of about 30 for both wages and rental prices as we move from intranational city
pairs to international city pairs. Distribution costs, therefore, are expected to be signi…cant contributors to the absolute level of LOP deviations at the retail level, particularly forcross-border pairs since factor prices are far from being equalized internationally. Moreover,
the relative contribution of distribution costs relative to trade costs will shift across goods
according to the distribution share parameter,i.

We turn now to the details of the variance decomposition. The analysis considers botha variance decomposition for the median good and results good-by-good. In each case wecontrast interesting geographic groups. For the discussion that follows, it is useful to referto the full variance decomposition:
varjk (qijk ) = [(12i ) i ] varjk (! jk ) + [(1

i )(1

2
2
i )] varjk (hjk ) + ( i i ) varjk [Iijk djk ]+varjk ["ijk ] + cov terms
Consider a good which uses no traded inputs at the retail level ( i = 0). The prediction
simpli…es reduces to:varjk (qijk ) =2
i varjk (! jk ) + (12i ) varjk (hjk ) + cov terms

We key insight here, is that price dispersion is entirely due to retail costs associated withwage and rental price dispersion, varjk (! jk ) and varjk (hjk ), respectively. These numbers
naturally depend on the locations pooled in the estimation for the reasons discussed earlier.
Borders matter.
At the opposite end of the continuum is a good with no retail costs at all (e.g., a good
available on the internet that trades up to a shipping cost everywhere in the world ( i = 1)).
Now the expression for the predicted price dispersion reduces to:varjk (qijk ) =2
i varjk [Iijk djk ]24

This is an intriguing expression. The coe¢ cient out front is the elasticity of trade cost withrespect to distance (recall, the empirical model assumes a log-linear proportional trade costfunction as is typical in the gravity literature). The variance of distance is a function of theset of locations under examination. As bilateral distance become less symmetric (less equal),
trade cost matters more for price deviations.
The variance decomposition results are given in Table 6. For the median good, distribution costs account for between 5 and 20 percent of overall price dispersion, depending on
the locations used. The wage component tends to account for more of this dispersion than
the rental component. An exception is the LDC group where the rental component accounts
for 12.6 percent of the dispersion, compared to only 2.5 percent for wages.

Trade costs

dominate the picture throughout the table, accounting for as much as 60 percent of the pricedispersion for cross-border OECD pairs, to a lower, but still very substantial, 36.1 percent
across the Canada-U.S. border. Approximately 30 percent of the variance is left unaccounted
for by the model. This variation could be due to a combination of markup variation, o¢ cialbarriers to trade or measurement error. The covariance across e¤ects is typically less that 5
percent. The bottom line of the analysis of the median good are that trade costs dominate
independent of the location or border crossing and that distribution margins are importantenough not to ignore.
Variation across goods within the cross-section, is interesting. Figure 2 shows the variancedecomposition at the individual good level as a function of the traded input share,i.

Tomake these easier to read we have smoothed the pro…les by taking centered moving averagesof the variance share across 10 goods. Starting with all international cross-border pairs andthe good with the lowest traded input share (roughly 0.4), wage dispersion accounts forabout 45 percent of price dispersion. As we move to goods with the highest traded input
share (roughly 0.97), wage dispersion accounts for almost none of the price dispersion. Of
course if this good had literally no non-traded inputs the contribution would necessarily
be exactly zero. The OECD group tells a similar story with about 30 percent of pricedispersion accounted for by wage dispersion at one end of the continuum of goods and lessthan 10 percent contributed for goods embodying mostly traded inputs. The Canada-U.S.
pairs have a lower contribution from wage dispersion as we would expect given the similar
25

wage levels of the two countries, the contribution of this component also declines as

rises,

though not as smoothly as the other groups. In most cases, the falling contribution of wage
di¤erences is associated with a rising role for trade costs. The intranational pairs show lessheterogeneity in the proportion of variance explained by various components as the tradeshare of …nal good production varies. Partly this re‡ects the lower variance of wages andrent across cities within countries. Nonetheless, the contribution of distribution costs is not
negligible for the intranational pairs either.
Figure 3 displays the same variance decomposition by good plotted against the labor
share of total retail cost,i.

We see the dramatic e¤ect of this parameter on the split of

distribution margin variance across labor and rent. As we move across goods based on thisparameter, the contribution of rent goes from zero to about 40 percent in the Canada-U.S.
panel and from zero to about 20 percent in the world grouping (for cross-border city pairs).
The contribution of wage dispersion tends to follow the same pattern in reverse, maintaining
the total share of price dispersion due to distribution costs. The OECD is anomalous in thesense that the distribution share contributes about 10 percent without much variation acrossgoods until we reach very high labor intensities in distribution. Turning to the intranational
pairs, the overall contribution of wage dispersion is rising in its cost share as one would
expect.
The results for the median good in the EIU cross-section seem to downplay the role of
distribution costs relative to trade costs. Given the dramatic di¤erences in how the variancedecomposition plays out across goods, the natural question that arises is how representative
the EIU sample is of the CPI basket. A second issue is the extent to which the estimateddistribution share matches up with the direct measures in the NIPA data.
Regarding the second issue, the average estimated value of the distribution share acrossgoods we use in the estimation is 0.2. This value is signi…cantly below, 0.5, the average
we get when we merge our micro-data with the U.S. NIPA and use the sectoral values ofthe distribution share from that source. Moreover, the di¤erence between the regression
estimates of the distribution share and the direct NIPA measure is not due to a few outliers:
151 out of 160 regression coe¢ cients values are below their NIPA counterparts. This suggeststhat our good-level estimates of the distribution shares are downward biased.
26

To account for this estimation bias and make the results relevant for aggregate consumption, we recompute our variance decomposition using goods with distribution shares in theneighborhood of= 0:5, the expenditure weighted average of the distribution shares foundin the U.S. NIPA data. What we do is average the decomposition results across 5 goods
on either side of this value. Table 7 reports these …ndings. We see that the contributionof the distribution margin is much more signi…cant. Wage dispersion alone now accounts
for more than one-third of retail price dispersion when all cross-border city pairs are pooled(WORLD). The role of wages for the OECD and LDC groupings is more limited suggesting the city pairs that straddle high and low income countries are the reason for the much
elevated wage component. It is interesting to note that for the Canada-U.S. pairs, wage dispersion plays a signi…cant role as well. Keep in mind, however, that the absolute dispersion
of prices across North American cities is about one-…fth of that existing across cities of theworld, thus the signi…cant role of wage dispersion in North America is partly due to the factthat there is little in the way of price dispersion to explain in North America relative to thebroader international sample.

6. Conclusions
Consumers face prices that are to a varying degree, location-speci…c. Our model of production and distribution across cities shows how these di¤erences are shaped by the distances
separating cities due to trade costs, the good-speci…c share of retail distribution and its division between local labor and rental costs. While we found trade costs dominated distribution
costs by a factor of 5 to 1 for the median good in the sample, their relative contribution
varies greatly across goods. For …nal goods that involve mostly non-traded inputs, distribution margins dominate trade costs. Given that most of the goods in the EIU have low
distribution shares, these unweighted averages understate the role of distribution margins
in the aggregate consumption basket. Using the aggregate distribution share and estimatesof the variance decomposition for individual goods with that share, the tables are turn:
distribution costs now clearly dominate trade costs.
In future work we will undertake analysis of PPP using our model and empirical method-27

ology. We expect the distribution margin will dominate trade costs in this case we well.
These …ndings point to the importance of incorporating a distribution sector into existing
international trade and macroeconomic models.

7. References
Alvarez, Fernando and Robert E. Lucas, “General Equilibrium of the Eaton-Kortum Modelof International Trade, Journal of Monetary Economics, September 2007, 54(6), 1726-1768.
Atkeson, Andrew and Burstein, Ariel. “Pricing-to-Market in a Ricardian Model of International Trade,”American Economic Review. 2007, 97(2), 362-367.
Burstein, Ariel, Joao Neves and Sergio Rebelo, “Distribution Costs and Real Exchange
Rate Dynamics During Exchange-Rate Based Stabilizations,” Journal of Monetary Economics, September 2003.
Crucini, Mario J., Chris I. Telmer and Marios Zachariadis, “Understanding European
Real Exchange Rates.”American Economic Review. 2005, 95(3), 724-38.
Crucini, Mario J. and Motostugu Shintani, “Persistence in Deviations from the Law-ofOne-Price: Evidence from Micro-Data.” Journal of Monetary Economics. 2008, Vol. 55,
Issue 3, 629-644.
Crucini, Mario J. and Telmer, Chris I. “Microeconomic Sources of Real Exchange Rate
Variation.”Vanderbilt University, mimeo, September 2007.
Eaton, Jonathan and Samuel Kortum. “Technology, Geography and Trade.”Econometrica. 2002, 70(5), 1741-1779.
Giri, Raul. “Local Costs of Distribution, International Trade Costs and Micro Evidence
on the Law of One Price.”February 2009, unpublished manuscript.
Hummels, David. “Toward a Geography of Trade Costs.”2001, unpublished manuscript.
King, Robert K., Charles I. Plosser and Sergio Rebelo. “Production, Growth and Business Cycles: I. The Basic Neoclassical Model.” Journal of Monetary Economics. 21(2-3),
195-232.
Long, John and Charles I. Plosser. “Real Business Cycles.”Journal of Political Economy.
1983, 91, 39-69.

28

Naknoi, K. “Real Exchange Rate Fluctuations, Endogenous Tradability and Exchange
Rate Regimes.”Journal of Monetary Economics. 2008, 55, 645-663.
Oostendorp, Remco H. (2003), “The Standardized ILO October Inquiry 1983-2003,”
mimeo, Free University Amsterdam, Tinbergen Institute, Amsterdam Institute for International development.

29

Table 1. Kernel Density Summary Results
Long-run LOP deviations
Standard

Interquartile

First

Third

Deviation

Range

Quartile Quartile

Traded goods

0.294

0.385

-0.1610.224

Non-traded goods

0.543

0.616

-0.2500.366

Traded goods

0.681

0.796

-0.3650.431

Non-traded goods

1.069

1.092

-0.497

0.595

U.S. cities

International cities

Short-run LOP deviations
Standard

Interquartile

First

Third

Deviation

Range

Quartile Quartile

Traded goods

0.250

0.295

-0.1510.144

Non-traded goods

0.258

0.295

-0.1510.144

Traded goods

0.412

0.417

-0.2090.209

Non-traded goods

0.488

0.430

-0.215

0.215

U.S. cities

International cities

Note: Long-run LOP deviations are time-averaged LOP deviations, short-run LOP deviations are the di¤erence between the raw LOP series and the long-run means.

30

Table 2. Mean sectoral wage di¤erentials
Wjm =Wjs

World Manufacture to Sales (ILO)

1.07

Implied

0.52

U.S. Production to Sales (BLS)
1.34
0.57
Note: For details on the data sources, see the data appendix.

31

Table 3. Variance of wage di¤erentials across sectors and locations
Industry (ILO)

Occupation (ILO)

Location

Sector

Error

Location

Sector

Error

0.85

0.04

0.10

0.65

0.01

0.34

46

19

136

113

0.84

0.06

0.64

0.03

27

12

26

113

0.72

0.08

0.38

0.04

36

19

109

113

World
Proportion of varianceObservations

OECD
Proportion of varianceObservations

0.10

0.33

LDC
Proportion of varianceObservations

0.20

0.58

Occupation (UBS)
World
Proportion of varianceObservations

0.66

0.19

56

14

0.51

0.31

32

14

0.48

0.29

24

14

0.15

OECD
Proportion of varianceObservations

0.18

LDC
Proportion of varianceObservations

Notes: A panel has been selected such that the total number ofobservations is maximized.

32

0.23

Table 4. Explanatory power
First quartile

MedianThird quartile

Panel A: International cities, cross-border pairs
CANADA-US

0:83

0:90

0:94

OECD

0:67

0:71

0:74

LDC

0:70

0:73

0:75

WORLD

0:69

0:72

0:75

Panel B: Intranational cities, no border
CANADA-US

0:72

0:77

0:81

OECD

0:71

0:76

0:79

WORLD

0:70

0:75

0:79

LDC

0:70

0:73

0:75

33

Table 5. Variance of prices across locations
RetailRentalPricesWages

PricesPanel A: International cities, cross-border pairs
CANADA-US

0.07

0.13

0.61

OECD

0.25

0.17

3.05

LDC

0.42

0.59

11.18

WORLD

0.38

1.15

9.49

Panel B: Intranational cities, no border
CANADA-US

0.06

0.04

0.33

OECD

0.06

0.03

0.27

–

–

–

0.07

0.03

0.28

LDC
WORLD

34

= 0:8)

Table 6. Variance Decomposition (median across goods,
Total

Fraction of variance account for by:
Wages

Rental Prices

Trade cost

Error

Covariance

Panel A: International cities, cross-border pairs
CANADA-US

0.07

10.1

7.8

36.1

12.8

15.5

OECD

0.25

2.3

1.7

60.0

29.4

0.8

LDC

0.42

2.5

12.6

53.9

27.2

0.4

WORLD

0.38

7.7

3.4

50.7

28.1

5.1

Panel B: Intranational cities, no border
CANADA-US

0.06

4.8

5.9

53.8

24.8

2.3

OECD

0.06

5.1

3.7

51.4

26.5

3.0

–

–

–

–

–

–

0.07

5.2

4.9

55.8

26.1

1.7

LDC
WORLD

35

Table 7. Variance Decomposition (aggregate
Total= 0:5)

Fraction of variance account for by:
Wages

Rental Prices

Trade cost

Error

Panel A: International cities, cross-border pairs
CANADA-US

0.10

31.8

16.6

38.5

13.1

OECD

0.36

10.7

6.2

54.6

28.5

LDC

0.75

15.2

16.7

45.7

22.4

WORLD

0.66

36.4

6.8

36.0

20.9

Panel B: Intranational cities, no border
CANADA-US

0.12

10.0

8.5

57.2

24.3

OECD

0.13

6.6

11.0

56.0

26.3

0.10

8.6

6.3

59.7

25.4

LDC
WORLD

36

Figure 1. Kernel density estimates of price distributions.

Note: The solid lines are kernel density estimates of the distribution of qijk , time averaged
LOP deviations over the period 1990-2005. The dashed lines are kernel density estimatesof the distribution of (qijk;tqijk ), time series deviations from these long-run values. Each

chart contains a di¤erent location and commodity grouping as indicated by the headers.

37Figure 2. Variance decomposition of price dispersion as a function of
costs (x-axis)

38

i the share of traded input

Figure 3. Variance decomposition of price dispersion as a function of
non-traded input costs (x-axis)

39

i the labor share of

8. Model Appendix
This appendix presents the function forms of the model, the …rst-order conditions and details
for the model solution.
8.1. Function forms

U (Cj ; Nj )
Cj =

(1
M
X
i

Pj

) log (Cj ) + log Lj
!""1

(8.1)

1 "
i (Pij )

(8.3)

" 1

1

(8.2)

( i ) " (Cij ) "

X
i

!11"

Yj = Aj Njm
Rij = (Gij ) i(8.4)
Bj Nijsi(Kij )1

i

1

i

(8.5)

8.2. Constraints

L j + Nj = 1
X
Pij Cij = Pj CjiX

Pij Cijm

Wjm Njm + 'Hj Kj

Pij Cijs

Wjs Njs + (1iX') Hj Kjiwhere ' 2 (0; 1) is the capital income share received by the manufacturer, (1') is thecapital income share received by the retailer, Hj is the price of capital, and Kj is the amountof capital.

40

8.3. Consumer and producer problems
maxf(1) log (Cj ) + log Lj +mj [Wj (1

Lj ) + 'Hj Kj

maxf(1) log (Cj ) + log Lj +sj [Wj (1

Lj ) + (1Cj

Cj

fQjj Aj Njm
maxm

Wjm Njm g

maxs fPij (Gij ) i

Bj Nijs

Nj

Gi ;Nji(8.6)

Pj Cj ]g') Hj Kj

(8.7)

Pj Cj ]g

(8.8)
(Kij )11

ii

Wjs Nijs

Qij Gij

Hj Kij g(8.9)

8.4. E¢ ciency conditions
=

Pij
Pj

"

CijA
CjA

WjA (1
=
Pj

)

i

CjA

(8.10)
NjA

1(8.11)' H j Kj
Wjm(1 ') Hj Kj= 1
Wjs' H j Kj=+
Wjm(1 ') Hj Kj=+
Wjs

Njm = 1

(8.12)

Njs(8.13)

Lmj
Lsj(8.14)(8.15)(8.16)

Nijs =(1i

Gij = Rij
Kij =

i Qij
Rij
Wjs

i)

(1

Bj Qij (1Wjs

Bj Qij (1Wjsii ) (1i ) Qiji

Hj

Qjj = M Cj =i)

( i 1) i

i

Rij

i)

( i 1) iii

Qij (1Hj

Bj Qij (1
Wjs

i

i)

( i 1)(1i)

i)(8.17)

i
i)(8.18)ii)( i 1) iii

Qij (1Hji ) (1i)( i 1)(1i)(8.19)

i(8.20)

Aj(Qij ) i

Wjs
Bj

i

(1

i) ( i)iii ) (1i ) (1

Wjm

Pij = M Cijs =Qij (1Hj( i 1)(1(Hj )(1
(1

i)

(1

i)

(1

i)

i)

(1

i)

(8.21)

8.5. Price relationships
Qji = (1 +41ji ) Qjj(8.22)

8.6. The retail …rm(1

Njs = 1

Gij = Rij') Hj Kj X s
=
Nij =
Wjs
i
Bj Qij (1
Wjs

i)

i

8
>
X < (1i( i 1) i

i ) i Qij
Wjsi

Bj Qij (1
i) i
Rij W
s
i
j
( i 1)(1
Qij (1
i )(1
i)
Hj
i

>
:

Qij (1Hjii ) (1i)( i 1)(1( i 1)
i)

i)

9
>
=
>
;

i

8.7. General equilibrium
8.7.1. Manufacturing Labor Market
The labor supply of the manufacturer is used in the manufacturing process, which implies:
Yj
=1
Aj

' H j Kj
Wjm

(8.23)

8.7.2. Goods Market
In the global general equilibrium all the conditions of partial equilibrium must hold. However
we also require that the supply of each good equals the demand for each good. This is where
the treatment of trade costs becomes crucial. We will assume that trade costs are of theiceberg variety, so the physical resource constraint for good j must satisfy:
Yj =X

Gji (1 +(8.24)ij )i

In words: the units produced equal the demand of traded inputs of retailers at the destinations plus a fraction lost to iceberg costs. The aggregate fraction lost will depend on theequilibrium allocations since the loss along any bilateral trade route is proportional to thevolume of trade along that branch:P
Gji ijTj=P i
Yji Gji (1 + ij )(8.25)

Returning to our global equilibrium, we substitute the optimal traded input choices of theretailers into the resource constraint to arrive at:
Yj =

X
i

Rji

Bi Qji (1
Wis

j)
j

j

( j 1) j

Qji (1
Hi

42

j)

1
j

j

!( j 1)(1

j

)
(1 +

ji )

Recall 8.23:' H j Kj
Wjm

Yj
=1
Aj
Combining these last two we get:
X

Rji

i

Bi Qji (1Wisj)( j 1) jj

Qji (1
Hi

j

j)

1

!( j 1)(1

j

j

j

)
(1 + (8.26)
ji )' H j Kj
Wjm

= Aj 1(8.27)The equilibrium of the retailer implies:
Rij = Cijm + Cijs =

"

Pij
Pj

i

Cjm + Cjs

Assuming that " = 1 (for the rest of the text), we have:
Rij = Cijm + Cijs =i

Pj Cjm + Pj Cjs =

Pij

Rji =

j

Pji

i

Njm Wjm + Njs Wjs + Hj Kj

Pij(Nim Wim + Nis Wis + Hi Ki )which says that the total income (sales) of the retailer from good i is equal to the share ofthat good in the budget of the region. Thus, we have
X

Rji

i

Bi Qji (1
Wis

X
i

>
>
:

( j 1) jj

Qji (1
Hi

j

j)

1

!( j 1)(1

j

j

j

)
(1 +

ji )

' H j Kj
Wjm

= Aj 1
8
>
>
<

j)

9
>
>
=

( j 1) j
Bi Qji (1
j) j
m
m
s
s
(N
W
+
N
W
+
H
K
)
s
i
i
i
i
i
i
Pji
Wi
j
( j 1)(1 j )j )(1Qji (1j)(1 + ji )
Hi
j
j

>
>
;

Recall the price set by the retailer:(Qij ) i

Wjs
Bj

i

(Hj )(1(1i) ( i)

i

(1

Pij =
i

i

i)

(1

(1
i)

i)

(Hi )(1j)' H j Kj
Wjm

= Aj 1i)(1i)

which is to say:
(Qji ) j
Pji =
j

j

(1

j)

Wis
Bi
(1

j

(1

j) j

j) j

(1

43

j)

1

(1

j

)

(1
j

j)

(1

j

)

Thus,

X
i

8
>
>
>
>
>
>
<

(Qji ) j
j

>
>
>
>
>
>
:

j

((1

i

j

Ws
i
Bi

(

! 1

1
) j )(

j

Bi Qji (1
Wis

j

)j

) j ((1

j) j

i

j

(1

)(1

j

)(1

j

1
))(

j

j

j

( j 1) jj

Qji(Nim Wim + Nis Wis + Hi Ki )Wm

By using Qjj = Ajj and Qji = (1 +X

(H i )

)

)(1

j

)

( j 1)(1

Qji (1
Hij )(1

j (1 +ji ) = Aj

j

)

j

)
(1 +

j

ji )

' H j Kj
Wjm

= Aj 1X

9>(Nim Wim + Nis Wis + Hi Ki ) >
>

j

j
m
ji ) Wj

(1 +

j

j

X

' H j Kj
Wjm

1

j (1 +ji ) =jX' H j Kj
Wjm

1

' H j Kj
Wjm

(Nim Wim + Nis Wis + Hi Ki ) = Wjm 1
j

>
>
>
>
>
>
;

ji ) Qjj , we can write(Nim Wim + Nis Wis + Hi Ki )

i

>
>
>
=

(Nim Wim + Nis Wis + Hi Ki ) = Wjm Njm(8.28)i

This is the …rst equation for the relation between N m W m , N s W s , and HK.
8.7.3. Retailing Labor Market
We have the following condition for the retailing labor market equilibrium:98( i 1)>>
Bj Qij (1(1i) ii ) i Qij=<XXR
Wjs ij
Wjs
i
i
s
s
Nj =
Nij =
( i 1)(1 i )Qij (1
>
>
i )(1
i)
;
i
i :
Hj

Njs =

8
>
>
>
>
X<
i

>
>
>
>
:

(1

i ) i Qij
Wjsii

Bj Qij (1Wjs(Njm Wjm +Njs Wjs +Hj Kj )(Qij ) i
i

i ((1

i) i

i

Ws
j
Bj

(1
i) i)
( i 1) i

i

!( 1

i) i

i ) i ((1Qij (1Hj

Njs Wjs = Njm Wjm + Njs Wjs + Hj Kj

(1

i )(1

(Hj )
i )(1

i ))

i )(1

i)

i

X

(1

(1

i)

9
>
>
>
>
=

i )(1
i)
>
( i 1)(1 i ) >
>

i)

i i

>
;

i

This is the second equation for the relation between N m W m , N s W s , and HK.

44(8.29)

8.7.4. Capital Market
We have the following condition for the capital market equilibrium:8( i 1)>
Bj Qij (1i) ii ) QijX
X < (1 i )(1
R
s
ij
Hj
Wj
i
i
Kj =
Kij =
( i 1)(1 i )Qij (1
>
i )(1
i)
i
i :
Hj

9
>
=

i

Hj Kj = Njm Wjm + Njs Wjs + Hj KjX(1i ) (1i)i>;(8.30)i

This is the third equation for the relation between N m W m , N s W s , and HK.
8.7.5. Implications for Wages, Rents, Wage Income, and Capital Income
Recall 8.28, 8.29, 8.30, which are:Njm Wjm =jjX(Nim Wim + Nis Wis + Hi Ki )i

Njs Wjs = Njm Wjm + Njs Wjs + Hj Kj
Hj Kj = Njm Wjm + Njs Wjs + Hj Kj

X

X

(1

i)

i i

i ) (1

i)

i

(1

i

i

Combine 8.29 and 8.30 to get:H j Kj=Njs WjsandHj Kj + Njs Wjs
and thusP(1iPi ) (1

i)

i)

i i

i (1

= Njm Wjm

i

P
i (1
P
(1
i (1

(8.31)i)P
Njs Wjs(1i) i iiP=mm
Nj W j
(1
i) i)
i (1

i
i)

i)

(8.32)(8.33)

which show that the sectoral wage incomes and capital incomes are all proportional to eachother within each city.
Recall the individual optimality condition for the retailer:
Njs = 1

(1') Hj Kj
Wjs

Njs Wjs = Wjs (1

)

(1

45

') Hj Kj

Combine this with 8.31 to get:H j Kj =Njs Wjs 1 +Njs Wjs

P
(1
P i
i (1

P
')
(1
P i
i (1

(1

i)

i ) (1i)P(1)
i ) i i ) + (1Njs = P( i (1i ) (1

i)

i

i i
i)

i

= Wjs (1)

i ) (1

i)

i i

i (1

)
Pi i i') ( i (1i)(8.34)

which shows that Njs is constant across regions. In a special case in which the share ofcapital is equal to zero in the retail production function (i.e.,

i = 0), or in which the shareof capital income received by the retailer is equal to zero (i.e., ' = 1), we have Njs = (1).

Combine 8.33 with 8.28 to get:Njs Wjs (1Pi (1Nks Wks (1
P
i (1

P

i (1

P

i) i

)

i) i ii (1i) ii) i i)=Njm Wjm=Nkm Wkm

j

j

k

k

=

Njs Wjs
Nks Wks

which show that the manufacturing wage income and the retailing wage income are proportional across cities. It is implied that:
Wjs
=
Wks

j

j

k

k

(8.35)

since Njs is constant across regions. If we also use 8.31, we obtain:
H j Kj=H k Kkjjkk(8.36)

where KA is the capital stock in city A = j; k.
Recall the individual optimality conditions for both the retailer and the manufacturer:

Wjm Njm = Wjm (1)' H j Kj

Wjs Njs = Wjs (1)(1') Hj Kj

These conditions can be combined to obtain:
Wjm
=
Wjs
(1

' (1
') (1

46

) 'Njs) (1 ') Njm

Recall 8.33:

P
Njm Wjm
(1
(1
i) i)
= P i
s
s
Nj W ji) i ii (1Combine the last two expressions to get:
Njm
Njm Wjm=
Njs WjsNjs (1
Njm
= (1

' (1
)
s
Nj
') (1

P
) 'Njs
(1
(1
i) i)
= P i
m
) (1 ') Nji) i i
i (1

' (1
') (1
'

X

(1

i)

i i

i

X

) 1

(1

i)

!

i

i

X

') Njm 1

(1

)

= (1

i

i i = 1

P

i (1

i)

i,

1

i

' ( 0
)
1 ) (1' ( 01 ) + (10)
) when ' = 0 or i = 1

Njm = (10i)

iwhich can be combined with 8.34 (i.e., Njs ) to obtain:

where
P

(1

!

P

i (1

i i,

i)

0

=

1

P

i (1

i ) (1i)i. 2

m
0 . This shows that Nj is constant and equal across cities. The level of e¤ort

is equal to the leisure share of expenditure, (1) when either rental income is zero for the

manufacturer (' = 0) or when retail production is labor-only

i = 1.

E¤ort is declining inasset income.
Njm
= 1
(1
)
Nm
@ (1 j )

@'

' ( 0
1)
' ( 0
1 ) + (1

=
=

( 0

1) d

( 0

1) d

1

1

0)

+' ( 01) d2[ 1 + 'd 1 ]

Nm

sign

@ (1 j )@'= sign [ 1 + 'd 1 ] since ( 0

' < d

Njm =

Njs =

(1
(1

0 ) (1)0) + '

( 0

1 (1

)

1 + (147') ( 0

1)

1)

1) d

1

>0

Wjm
=
Wjs
(1

(1
) (1

') (1

0) + '( 00) + ' ( 01)1)(1 ') ( 0') 1 + (1 ') ( 0

(1

1)
1)

8.8. Implications for Price Ratios across Cities
Recall the retail price of good i in city j and city k:
Pij =

i

i

((1

(1
i)

i)

i

i

((1

i) i

(1
i)

i)

i) i

i) i

(Hj )(1

((1

(1

Wks
Bk

(Qik ) i
Pik =

(1

Wjs
Bj

(Qij ) i

i )(1

(1
i ))

i ) (1i) i(Hk )(1

((1

i)

i )(1

i)

i )(1

i)

i)

(1
i ))

i ) (1i )(1Take their ratio to get:
Pij
=
Pik
By using Qij = (1 +

Wjs
Bj

(1

(Qij ) i

i) i

Wks
Bk

(1

(Qik ) ii) i(Hj )(1i )(1i)(Hk )(1i )(1i)

ij ) Qii , we can write the ratio of the price of good i across regions jand k as follows:
((1 +
Pij
=
Pik
((1 +

ij ))

i

ik ))

i

Wjs
Bj

(1

i) i

Wks
Bk

(1

i) i

(Hj )(1i )(1i)(Hk )(1i )(1i)

By using 8.35 and 8.36, the analytical solution for the price ratios can be written as:
Pij
=
Pik

Bk
Bj

i

(1

j

j

k

k

i)

1+
1+

ij
ik

i

Kk
Kj

(1

i )(1

i)

where Kj is the total amount of capital in city j.

9. Estimation Appendix
The derivation of the variance decomposition of equation 5.6 can be written as follows:
varjk [Et (qijk;t )] = varjk [(1 b i ) bi Et (! jk;t )] + varjk [(1 b i ) (1hibb+varjk b i Et Iijk;t i djk + varjk [Et (b"ijk;t )]+2cov ((1+2cov (1+2cov (1b i ) bi Et (! jk;t ) ; (1b i ) (1bi ) Et (hjk;t ))b i ) bi Et (! jk;t ) ; b i Et bIijk;tbi djk

b i ) (148bi ) Et (hjk;t )]bi ) Et (hjk;t ) ; b i Et bIijk;tbi djk

where b i ’s, bi ’s, bIijk ’s, bi ’s and b"ijk ’s are all estimated values for the relevant variables. Notethat the covariance terms including Et (b"ijk;t ) are equal to zero by OLS regression.

49