                                                 Preliminary Draft: Please Do Not Recirculate


 Real Exchange Rate Fluctuations and the Dynamics of

       Retail Trade Industries on the U.S.-Canada Border∗

                         Jeﬀrey R. Campbell†               Beverly Lapham‡

                                              June, 2001


                                                Abstract

            This paper estimates the eﬀects of real exchange rate ﬂuctuations on retail trade

         industries located on the U.S.-Canada border. Consumers living near this border can

         shift their expenditures between the two countries, so real exchange rate ﬂuctuations

         can act as demand shocks to border areas’ retail trade industries. Using county level

         data, we estimate the eﬀects of real exchange rates on the number of establishments

         and their average payroll in ﬁve retail industries. To isolate the expenditure-shifting

         eﬀect of exchange rates, our estimation uses observations from counties oﬀ the border to

         control for the economy-wide eﬀects of the unobserved structural shocks. In three of the

         industries, the number of operating establishments responds either contemporaneously

         or with a lag of one year to real exchange rate movements.

   ∗
       We thank Allen Head for helpful discussions. The National Science Foundation supported Campbell’s
research through grant SBR-9730442, “Business Cycles and Industry Dynamics.” The Social Science and
Humanities Research Council of Canada supported Lapham’s research. Emin Dinlersoz provided expert
research assistance at an early stage of this project. The latest version of this paper is available on the
World Wide Web at http://home.uchicago.edu/~ jcampbe. Please direct correspondence to Campbell at
Department of Economics, University of Chicago, 1126 East 59th Street, Chicago, Illinois 60637.
  †
    Department of Economics, University of Chicago
  ‡
    Department of Economics, Queen’s University
   This paper estimates the eﬀects of real exchange rate ﬂuctuations on the number of

establishments and their average payroll in retail trade industries located on the U.S.-Canada

border. It is widely known that there are large and persistent deviations from purchasing

power parity (PPP) (see Rogoﬀ (1996) for a survey). Engel (1999) and Engel and Rogers

(1996) have documented that deviations from the law of one price for traded goods can

account for most of the observed deviations from PPP between the U.S. and Canada, and

that these price diﬀerences even characterize otherwise similar goods sold on diﬀerent sides

of these countries common border. Because consumers who live near the border can shift

their expenditures towards the cheaper country, movements in the international relative price

of goods may act as a demand shock for retail producers located near the border. Using

county level data for several retail industries, our empirical analysis estimates the impact

of industry-speciﬁc real exchange rate ﬂuctuations on net entry and average store size in

border counties. In three of the ﬁve industries we consider, a real exchange rate appreciation

causes the number of establishments to decline contemporaneously or with a lag of one year.

Therefore, the “long-run” changes in the number of establishments that theory predicts occur

in fact very quickly.

   Di Matteo and Di Matteo (1993,1996) provide compelling evidence that movements in

the real exchange rate between the U.S. and Canada does induce the type of expenditure

shifting behavior on the part of consumers that we have described above. In addition, Ford

(1992) provides survey data which indicates that the primary reason that Canadians shop

in the U.S. is lower prices. Figure 1 summarizes this evidence. Its top panel depicts the

nominal exchange rate (Canadian dollars per U.S. dollar) and the aggregate real exchange

rate constructed using aggregate CPIs from 1972-1998, and its bottom two panels plot a

measure of cross-border shoppers, same-day automobile trips by U.S. vehicles into Canada

and by Canadian vehicles into the U.S. The ﬁgure demonstrates that the appreciation of the

Canadian dollar from 1986-1992 was accompanied by a large increase in trips by Canadians

and a slight decrease in trips by Americans. The subsequent depreciation of the Canadian


                                              1
dollar from 1992-1998 was accompanied by a large decrease in trips by Canadians and a large

increase in trips by Americans. The spike in U.S. trips in 1980-1981 came at a time when

the Canadian National Energy Policy dramatically reduced the price of gasoline in Canada

relative to the U.S.

   The real exchange rate is an endogenous variable, determined by structural shocks that

themselves can have direct eﬀects on consumers’ purchasing decisions and retailers’ costs. To

address this issue, we ﬁrst present a model economy of cross-border shopping which predicts

a relationship between the real exchange rate for an industry and the average size of ﬁrms

and the number of ﬁrms operating in the industry. The results of this model motivate our

empirical speciﬁcation. To identify the expenditure shifting eﬀects of real exchange rates on

border counties’ retail trade industries, our estimation uses observations from retail trade

industries in counties that do not share a border with Canada to control for the direct

eﬀects of unobserved structural shocks. Our estimation procedure, based on Blundell and

Bond’s (1998) GMM estimator of a univariate panel-data autoregression, also accounts for

unobserved county-speciﬁc means of the observable variables, autocorrelation in county-

speciﬁc disturbances to demand and cost, and diﬀerences between prices in a given area and

their national aggregate counterparts.

   Our empirical analysis shows that real exchange rate ﬂuctuations have a signiﬁcant im-

pact on retail trade activity in border counties. In Food Stores and Eating Places, a real

exchange rate appreciation causes the number of operating establishments to fall contem-

poraneously, while in Gasoline Service Stations the number of establishments falls after one

year. In these industries, we also estimate that our measure an economically signiﬁcant de-

cline in our measure average establishment size, average payroll. However, this decline is not

statistically signiﬁcant. In Drinking Places, average payroll drops precipitously following a

real appreciation, but the number of establishments does not change. In only one of our ﬁve

industries, Apparel and Accessory Stores, we measure no statistically signiﬁcant impact of

exchange rates on industry activity. However, the point-estimates for this industry are large,


                                              2
suggesting that our estimation procedure has little power when applied to this industry’s

data. We believe that these results are interesting because the response of border counties’

retail trade industries to this particular demand shock yields insight into how retail industries

throughout the U.S. respond to other demand shocks that are more diﬃcult to measure.

    The rest of this paper is organized as follows. In the next section, we present a model

of retail industry dynamics with cross-border shopping, and we use it to characterize the

expenditure-shifting eﬀects of exchange rates. Section II derives the estimating equations we

use from the model and describes our data estimation procedure in more detail. Section III

presents the results of our estimation, and Section IV discusses the relationship of our work

with the relevant literature from international macroeconomics and industrial organization.

Section V contains concluding remarks regarding our results’ implications for future research.


I    A Cross-Border Shopping Model

In our empirical analysis, we examine the eﬀects of movements in industry-level relative

prices between the U.S. and Canada. These relative prices are endogenous variables so we

require a model economy to clarify how our estimation identiﬁes the expenditure-shifting

eﬀects of movements in these prices on border-counties’ retail trade industries. Furthermore,

we expect heterogeneity across counties on the border with respect to their exposure to

cross-border shopping. The model provides a measure of exposure which we incorporate

into our empirical analysis.

    In the model, there are two countries, the United States (U ) and Canada (C), each of

which is composed of distinct counties. A county can be located on the border between

the two countries, or it can be an interior county. Each county has a retail-trade sector

that produces diﬀerentiated goods in a monopolistically-competitive market with free entry.

Each country has a domestic currency and prices of all goods sold in a country are denomi-

nated in the local currency. Deviations from PPP arise from diﬀerences in the two countries’


                                               3
retailers’ marginal costs. One potential cause of such cost diﬀerences is wholesale price stick-

iness.Another source of cost diﬀerences, suggested by the experience of the National Energy

Policy, is regulatory diﬀerences between the countries that cannot be legally exploited by

wholesale arbitrageurs. We analyze the response of a border county’s retail-trade industry to

relative cost shocks, focusing on the behavior of variables we observe in our data, the number

of establishments and their average payroll. Firms enter and set prices after observing costs.

Diverging costs lead to price diﬀerences across international producers and this induces some

of the consumers living in border counties to shift their expenditures towards the country

with lower prices.

    In what follows, we consider consumers and producers in county U located in country U

and producers in county C located directly across the international border in country C.


A     Consumers

There are Sj consumers in county j and a fraction, λ, of those consumers purchase from both

domestic and foreign retailers. We refer to these consumers as travellers. The remainder

of consumers in a county only purchase from domestic retailers and are referred to as non-

travellers. Consumers have the following preferences:
                                                                            γ
                                            NU                 NC           ν

                           U = d1−γ              xν dj +
                                                  jU                xν di
                                                                     iC         ,
                                        0                  1


where d is consumption of an outside homogeneous good, xjU is consumption of diﬀerentiated

good j sold in county U , and xiC is consumption of diﬀerentiated good i sold in county

C. For non-travellers, consumption of goods sold by foreign retailers equals zero. The

number of distinct goods oﬀered for sale in county j is Nj and is determined in equilibrium.

All consumers are endowed with ω units of the outside good which they use to ﬁnance

consumption expenditures.

    The price of the manufactured good in country j, qj , is exogenous to consumers and pro-

ducers. The law of one price holds for this good so the nominal exchange rate is determined

                                                   4
as follows:

                                                                      qU
                                                            e=
                                                                      qC

We let pij denote the price of retail good i oﬀered in county j denominated in the local

currency. The budget constraint of a consumer in county U denominated in that country’s

currency is
                                    NU                      NC
                                         piU xiU di +            (epiC )xiC di + qU d = qU ω
                                0                       0

The consumer in county C faces an analogous budget constraint.

    Consumers in each county choose consumption of each relevant good to maximize their

period utility subject to their budget constraints. The solutions to these optimization prob-

lems give the following Marshallian demands. The demands of a traveller in county U for

retail goods are given by
                                                    1
                                            ν−1
                                   (γqU ω) piU
                          xT
                           iU    =                                                i ∈ [0, NU ]
                                       PT
                                   (γqU ω) (epiC )1/(ν−1)
                          xT
                           iC    =                                                i ∈ [0, NC ]
                                            PT
               NU      ν/(ν−1)              NC
where P T =   0
                    plU          dl +      0
                                                 (eplC )ν/(ν−1) dl. The demands of a non-traveller in county

U are given by
                                                        1
                                                    ν−1
                                           (γqU ω) piU
                                 xS
                                  iU     =                                    i ∈ [0, NU ]
                                               PS
                                 xS = 0
                                  iC                                         i ∈ [0, NC ]

                  NU    ν/(ν−1)
where P S =      0
                       plU          dl. The Marshallian demands for travellers and non-travellers of

county 1 have expressions symmetric to these.


B    Technology

A retail producer employs a ﬁxed amount of labor and capital each period to maintain the

store. This costs φ units of the manufactured good with a fraction, δ, of that ﬁxed cost paid

                                                                  5
to labor and the remainder to capital. She also uses labor and materials to produce ﬁnal

output, x, using a constant returns to scale technology. The fraction of fraction of variable

costs which is paid to labor equals α. With this production speciﬁcation, nominal payments

to labor (payroll) of ﬁrm i located in county j in units of the local currency is equal to


                                               α(cj )(xij ) + qj δφ


where cj is unit variable costs denominated in the local currency. Hence, payroll in units of

the manufactured good of ﬁrm i located in county j is given by


(1)                                        Wj ≡ α(cj /qj )(xij ) + δφ.


C         Free-Entry Equilibrium

The retail production technology is available to two large pools of potential entrants, one

pool in each country. The nominal prices of the outside homogeneous good, qU and qC , and

nominal costs, cU and cC , are random variables that are exogenous from the perspective of

a single county’s retail sector. After observing these variables, potential entrants simultane-

ously decide whether or not to irreversibly incur the ﬁxed cost φ and produce. Those that

enter choose their nominal retail prices to maximize proﬁts. In equilibrium, further entry is

not proﬁtable in either location. For simplicity, we suppose producers must incur the ﬁxed

cost φ every period, so a border county’s retail-trade sector is characterized by the inﬁnite

repetition of this free-entry game1 .

        The isoelasticity of consumers’ Marshallian demand curves implies that producers’ proﬁt

maximizing prices will follow the familiar constant percentage mark-up over marginal cost
    1
        We make the assumption that each establishment incurs the ﬁxed-cost φ each period only for convenience.
With minor modiﬁcations, our analysis carries through if we instead assume that φ is a sunk cost of entry
and that incumbent establishments each face a probability δ of having to pay this cost again or exit the
industry.


                                                        6
rule:
                                                     cj
(2)                                         pij =
                                                     ν
Because producers earn zero proﬁts, it must be the case that

(3)                                 (pij − cj ) xij − qj φ = 0.

Substituting (2) into (3) and rearranging yields the equilibrium output of a representative

retail producer in county j:
                                                   qj φν
(4)                                     xij =              .
                                                cj (1 − ν)
      Substituting this expression for xij into (1) gives equilibrium payroll per producer in

units of the manufactured good:
                                                αφν
(5)                                    Wj =         + δφ.
                                                1−ν
Note that this equation implies that payroll per ﬁrm is constant and does not depend on

cost or nominal exchange rate shocks. Instead, the industry responds to these disturbances

by changing the number of producers on both sides of the border.

      To determine the number of retail producers on both sides of the border, we equate the

output per producer that is consistent with free-entry from (4) with the output demanded

by consumers at the prices given by (2). Let r ≡ (epC /pU ) denote the relative price of

retail trade goods in the two countries, which we henceforth refer to as the industry real

exchange rate. The equilibrium market clearing conditions for retail trade producers in the

two counties are
                          (1 − λ) SU     λ (SU + SC )            φ
(6)                                  +             ν/(ν−1)
                                                           =
                              NU       N U + NC r            γω (1 − ν)
                          (1 − λ) SC     λ (SU + SC )            φ
(7)                                  +      ν/(1−ν) + N
                                                           =
                              NC       NU r             C    γω (1 − ν)
The ﬁrst term on the left-hand side of (6) is the quantity demanded from a retail producer

in county U by that county’s non-travellers, while the second term reﬂects that producer’s

demand from both county’s travellers.

                                                 7
      If there were no cross-border shopping, then λ = 0 and ﬁnding the values of NU and

NC that satisfy (6) and (7) is straightforward. In the case of interest where λ > 0, these

conditions form a system of two quadratic equations in the variables NU and NC . If r = 1

then it is straightforward to show that these equations have the same solution as they do

when λ = 0.

                                     ¯        γω (1 − ν)
                                     NU = S U
                                                  φ
                                     ¯        γω (1 − ν)
                                     NC = S C
                                                  φ

That is, in the absence of ﬂuctuations in r, the retail trade sector in a border county should

be no diﬀerent from its counterpart in an interior county.

      The objective of our analysis is to determine the responses of NU and NC to changes in

r, which are induced by changes in ecC /cU . To do so, we suppose that r is close to one and
                                                                       ¯    ¯
take a log-linear approximation of (6) and (7) around the point r = 1, NU , NC . Doing so

and solving the resulting system of log-linear equations yields

                              ¯            νλ             SC
(8)                    ln NU /NU =                               ln(r)
                                     (1 − ν)(1 − λ)     SU + S C
                              ¯           −νλ             SU
(9)                    ln NC /NC   =                             ln(r)
                                     (1 − ν)(1 − λ)     SU + S C

      These equations imply that when a change in ecC /cU causes r to fall, the number of

producers operating in county U , which is relatively more expensive, falls. Simultaneously,

the number of producers in county C, which is relatively cheaper, rises. Recall that (5)

gives each producer’s payroll, which does not depend on r. Therefore, this model has the

stark prediction that all of a retail-sector’s response to real exchange rate movements occurs

through changes in the number of producers and average producer size is unaﬀected. If

we relaxed the assumption that producers’ entry decisions are made after observing r, and

replaced it with the assumption that entry decisions must be made prior to realizing r, then

the solutions for NU and NC are very similar to (8) and (9) with E [ln r] taken with respect

to the information at the time of entry replacing ln r. In this case, establishments’ average

                                              8
payroll is no longer constant but instead varies with (ln r − E [ln r]) × [SC / (SU + SC )] in

county U and with (ln r − E [ln r]) × [SU / (SU + SC )] in county C. The technical appendix

describes this extension of our model in more detail.

     Because diﬀerent border counties have diﬀerent home and foreign populations, (SU and

SC ), the second term in brackets in equations (8) and (9) will vary across border counties.

We refer to this term as the county’s exposure measure. The exposure measure has the

intuitive property that it is increasing in the population of foreign consumers and decreasing

in the population of domestic consumers. Hence a heavily populated U.S. county located

next to a sparsely populated Canadian area will have a relatively low exposure measure

because the presence of foreign consumers has only a small eﬀect on the domestic industry.

The converse is true for a lightly populated U.S. county located near a large concentration

of Canadians. The measurement of each border county’s exposure to cross-border shopping

is an important component of our estimation.


II      Data and Estimation

The model of retail industry dynamics with cross-border shopping is useful for clarifying

the sense in which real exchange rates can be thought of as a demand shock for border

counties and for suggesting how to estimate a county’s exposure to cross-border shopping.

For estimation, we extend the model to account for county-speciﬁc and economy-wide dis-

turbances to technology and demand as well as unobserved demand and cost heterogeneity

across counties. The resulting empirical model does not impose the restriction that only the

number of establishments responds to a demand shock. Instead, it allows for many patterns

of adjustment. This section extends the model in this way, describes the data we use in its

estimation, and summarizes our GMM estimation procedure. We begin with the model’s

extension.


                                              9
A      The Empirical Model

The variables we observe for each county are the number of establishments operating in an

industry and the U.S. dollar value of industry payroll. Gather these into the vector

                                     yt =   ln Nt ln At       .

Our data set provides annual observations of yt from 1977 through 1996 for six retail trade

industries in every county in the ten continental states that border Canada. In our data, Nt

is deﬁned as the number of stores operating at any time during the year, and At is the dollar

value of total industry payroll for the year.

    Deﬁne yit to be the value of yt for county i for a particular industry. Our model implies

that the logarithms of establishments and payroll satisfy

(10)                               yit = yi + ψ (si × ln rit ) ,
                                         ¯

where y i is the steady-state value of yit , rit is the relative retail price between county i and

its Canadian counterpart,

(11)                                ψ=          νλ            ,
                                            (ν−1)(1−λ)
                                                         0

and

                                                   SiC
(12)                                    si =              .
                                                SiU + SiC

Here, the population of U.S. county i is SiU , and the population of its Canadian counterpart

is SiC . If county i does not share a border with Canada, then we set SiC = 0. Below, we

discuss our measures of SiC for counties that do border Canada. We allow the intercept term

in (10), yi , to vary across counties because it is a function of parameters describing demand
         ¯

and cost that potentially vary across counties, such as ω and φ.

    The location-speciﬁc price data needed to construct rit are not available to us, so we

replace rit with its observable national-level counterpart, rt , which is the industry-level rela-

tive price constructed using national price-indices for the U.S. and Canada and the nominal

                                                 10
exchange rate. We further discuss our measure of rt in Section C below. To replace rit with

rt , we suppose that the linear projection of rit on rt has a slope coeﬃcient of one for each

border county. That is

(13)                                      ln rit = ai + ln rt + ζit ,

where

                                         E [ζit ln rt ] = E [ζit ] = 0,

{ζit } is a covariance-stationary stochastic process that is independent across counties.2 Using

(13) to replace ln rit in (10) yields

                                yit = yi + ψsi ai + ψ (si × ln rt ) + ψsi ζit .
                                      ¯

       To incorporate movements in yit that are not the consequence exchange-rate ﬂuctuations,

we suppose that the demand curves and cost functions in each county are subject to both

county-speciﬁc and economy-wide disturbances. Towards that end, let φit denote the ﬁxed

cost incurred by producers that choose to enter county i at time t and let ωit denote per-

capita income in county i at time t. Denote the logarithmic deviations of φit and ωit from

their steady state values with fit and zit , and group these together in the vector

                                            xit =       fit zit       .

The modiﬁcation of (10) that allows for ﬂuctuations in xit is

(14)                        yit = yi + Γxit + ψsi ai + ψ (si × ln rt ) + ψsi ζit ,
                                  ¯

where (5) and (6) and (7) imply that
                                                                 
                                                −1 1 
                                             Γ=      .
                                                  1 0
   2
       If the assumption that the slope coeﬃcient in (13) equals b = 1, then our deﬁnition of the parameter
matrix β in (22) should be multiplied by b. All other aspects of our analysis remain unchanged.

                                                        11
      We suppose that xit is the sum of an economy-wide disturbance that is common to all

counties and a county-speciﬁc disturbance, which follows a stationary ﬁrst-order autoregres-

sion.3


(15)                                          xit = xt + uit
                                                    ¯

(16)                                        Γuit = ΛΓuit−1 + vit


The roots of |I − ΛL| lie outside of the unit circle, and


                                              E [vit ] = 0

                                           E [vit viτ ] = 0 if t = τ.


Furthermore, we assume that {vit }∞                            T
                                  t=−∞ is independent of {vjt }t=1 if i = j. Our estimation

procedure requires no further assumptions on the disturbance process aside from the standard

technical regularity conditions for GMM. In particular, the second moments of vit may vary

over time and across counties.

      If we replace xit in (14) using (15) and multiply both sides of the resulting equation by

(I − ΛL), we get


(17)                yit = αi + µt + Λyit−1 + ψ (si × rt ) − Λψ (si × ln rt−1 ) + εit ,


where


(18)                                    αi = (I − Λ) (¯i + ψsi ai ) ,
                                                      y

(19)                                    µt = (I − ΛL) Γ¯t
                                                       x


and


(20)                                    εit = vit + si (I − ΛL) ψζit


This is a panel-data vector autoregression in yit with additional explanatory variables.
  3
      Extending the analysis to the case of higher-order autoregressions is straightforward.


                                                      12
    To get our ﬁnal estimating equation, we relax the common factor structure in (17) that

imposes non-linear constraints on the model’s parameters. Gather rt and its ﬁrst lag into

the vector


(21)                                  et =    rt rt−1    ,


and deﬁne the coeﬃcient matrix


(22)                                  β =     ψ −Λψ       .


With this notation, (17) can be written as


(23)                       yit = αi + µt + Λyit−1 + β (si × et ) + εit


This is our ﬁnal estimating equation. When estimating the parameters of (23), we do not

impose the non-linear constraints on β and Λ that the model implies. This allows the

empirical model to encompass a wide variety of responses of yit to rt . We now turn to the

discussion of the observations of yit , et , and si we use in our estimation.


B      Observations of Retail Trade Industries

Our source of retail trade industry observations is the United States Census’ annual publi-

cation, County Business Patterns (CBP). We construct our data set from twenty years of

this publication from 1977 through 1996. For each retail trade industry, the CBP reports

each county’s total employment, the number of establishments with employees, ﬁrst quarter

payroll, and annual payroll. In addition, the CBP reports the total number of establishments

falling into several predetermined employment size classes. The establishment counts give

the number of establishments that had paid employment at any time during the year, while

the employment counts measure employment during a mid-March pay period. Because this

data is based on administrative payroll tax records, its quality is very high. Our empirical

work uses the establishment count observation for Nit and uses annual payroll divided by


                                               13
the establishment count for Ait .4

       To estimate our model, we must determine which counties in our sample are exposed to

cross-border shopping and which ones are not. Our discussion above has presumed that only

those counties that share a border with Canada are exposed to cross-border shopping. For

some retail trade industries, this is clearly not the case. For example, Ford (1992) surveyed

Canadian consumers in Toronto, Hamilton, and the Niagara-St. Catherines region regarding

their shopping destinations in the U.S. Many consumers reported shopping outside of the

New York border counties of Erie and Niagara, particularly if the shopping trips were for

durable goods such as furniture and electronics. Conversely, U.S. consumers from counties

without a Canadian border can shop in Canada if they are willing to travel. However, Ford’s

(1992) survey data indicates that purchasers of food and gasoline, the two most frequently

purchased items by cross-border shoppers, tended to shop very near the border. For this

reason, we restrict our analysis to retail trade industries that Ford’s (1992) data and our

own experience as cross-border shoppers indicate consumers are unwilling to travel far to

purchase. The industries we consider are Food Stores (SIC 54), Gasoline Service Stations

(SIC 554), Apparel and Accessory Stores (SIC 56), Eating Places (SIC 5812), and Drinking

Places (SIC 5813). Of these industries, Apparel and Accessory Stores is the one most likely

to violate our assumption that only stores in border counties are exposed to cross-border

shopping. We include it in our analysis simply because Ford (1992) ﬁnds that clothing is

one of the most frequently purchased items by Canadians in the U.S.

       The Census bureau’s disclosure policy creates a potential problem with our data. The

Census Bureau withholds the employment and payroll information for any county-industry

observation where that data may disclose information about any individual producer. The

Census Bureau never withholds the establishment counts by size category. There is no
   4
       We use annual payroll instead of employment to construct our measure of average establishment size
because both it and the establishment count observations reﬂects the industry’s activity over an entire
calendar year.


                                                    14
precise rule that the Census uses to determine which observations must be withheld, but these

disclosure cases tend to occur in counties with small populations and few establishments. For

some counties, the census withholds data in almost every year of our sample period, while for

others this only occurs occasionally. To produce a balanced panel of employment and payroll

observations across counties, we estimate payroll per establishment for establishments in each

size category for all establishments in counties with withheld data using state level data. We

replace the withheld payroll observations with their forecast values using our estimates and

the published establishment counts. This paper’s technical appendix describes this data

replacement procedure in greater detail.

   The sample of all counties in states that border Canada range from very small counties,

such as Divide County, North Dakota to very large, urban counties, such as Erie County,

New York. Our model economy describes competition between a large number of producers,

so it is unrealistic to expect our model to describe the retail industry dynamics in very small

counties. For this reason, we conﬁne our analysis to counties with relatively large numbers of

establishments using two selection criteria. First, we consider only counties with populations

greater than 20,000 people, as measured in the 1990 decennial census. There are 256 such

counties in the ten continental states that border Canada, and nineteen of these counties

share a border with Canada. Second, we drop all observations from any county-industry pair

with ten or more observations withheld by the Census Bureau. This criterion lessens the

dependence of our results on our data replacement procedure. For the resulting sample of

counties, less than 4% of our county-industry-year observations have imputed payroll data.

However, these imputed observations are heavily concentrated in a single industry, Apparel

and Accessory Stores. As noted above, disclosure withholding primarily aﬀects counties with

few producers, so our resulting sample is of relatively unconcentrated industries in relatively

populated counties.

   Our county selection criteria produce diﬀerent samples for each industry we consider.

Table 1 provides summary statistics for each industry’s sample of counties. Its ﬁrst column


                                              15
reports the number of counties included in each sample, and its remaining three columns

report the ﬁrst quartile, median, and third quartile, across counties, of the average number of

establishments, across years, serving that industry. None of the 256 counties with populations

greater than 20,000 had ten or more of their establishment and payroll observations withheld

for ten or more years in Food Stores or Gasoline Service Stations. Our disclosure criterion

eliminates between 10 and 30 counties from the remaining industries’ samples. For Apparel

and Accessory Stores one of these eliminated counties is a border county, and in Eating Places

and Drinking Places ﬁve eliminated counties are border counties. The sample quartiles of

average establishment counts indicate the extent to which our selection procedures leave

relatively unconcentrated industries. For all industries but Drinking Places, the median

county has more than 25 establishments in an average year. For Drinking Places, the median

county has approximately 18 establishments. Again with the exception of Drinking Places,

the ﬁrst quartiles of the average establishment counts are all above 15. For drinking places,

the ﬁrst quartile is 12. It appears that our county selection procedure produced a sample of

relatively unconcentrated industries.

   Our data describe two margins along which an individual industry can vary its activity:

the number of establishments and their average payroll. To assess how these margins indi-

vidually contribute to local retail trade industries’ idiosyncratic ﬂuctuations, we regressed

each of these variables’ logarithms against a set of time dummies. We then tabulated the

sample standard deviations of that regression’s residuals for each county. Table 2 reports

the medians, across counties, of these standard deviations for each retail trade industry. In

practice, these medians are close to their corresponding means. Relative to many aggre-

gate time series, these median standard deviations are quite high for all of the industries.

The lowest are in Eating Places, 0.09 for establishments and 0.10 for average payroll. The

remaining industries display somewhat more variance, with Drinking Places displaying the

highest standard deviations, 0.17 and 0.22 respectively. In all industries, establishments’

median standard deviation is not much lower than that of average payroll, indicating that


                                              16
these industries’ structures are far from rigid.


C     International Relative Prices

Our measures of international relative prices are based on national price indices from the

United States and Canada for speciﬁc goods and the exchange rate between the two countries’

currencies. For each retail trade industry, we found matching consumer price indices for the

goods for sale by that industry from the two countries. Table 3 lists the U.S. and Canadian

CPI series used to construct the relative price series for each of the ﬁve industries we consider.

    The ﬁrst two columns of Table 4 report the sample standard deviation and ﬁrst auto-

correlation for the industries’ relative price series, expressed in logarithms. For all of the

industries but Service Stations, the standard deviations of the relative price series are all be-

tween 0.06 and 0.09. The standard deviation of the relative price of Gasoline is much higher

than this, 0.21. Most of this variance reﬂects ﬂuctuations in the years of the Canadian Na-

tional Energy Policy (NEP). In response to international oil price shocks in the 1970’s, the

Canadian federal government implemented the NEP which, among other things, imposed

import subsidies and export taxes on petroleum products. Thus while gasoline prices rose

considerably in the U.S. in response to these shocks, Canadian gasoline prices did not and

the relative price of gasoline between the two countries exhibited considerable ﬂuctuation.

    Unsurprisingly, the relative price series are all highly persistent, with ﬁrst order auto-

correlations between 0.74 and 0.88. Table 4’s ﬁnal column reports the contemporaneous

correlation between each industry’s relative price series and that constructed with the aggre-

gate CPI’s for all goods less energy. The relative prices for Apparel and Accessory Stores,

Eating Places, and Drinking Places are all highly correlated with this aggregate real ex-

change rate. The relative prices of food purchased at stores and gasoline have somewhat

lower correlations.


                                               17
D     Measures of Exposure to Cross-Border Shopping

Our model predicts that the elasticity of retail trade activity on the U.S. side of the border

with respect to the real exchange rate depends on the share of the border area’s consumers

that are Canadian, si = SiC / (SiU + SiC ). Consumers’ strong preferences for product diver-

sity directly produce this result, but it accords well with the intuition that being located next

to Canadian land is irrelevant for a border county’s retail industry if there are no nearby

Canadians.

    To measure SiU , we use data on each county’s population in the 1990 decennial census.

Measuring SiC is less straightforward, because there is no natural or political geographic

partition of Canada that indicates which Canadians are potential cross-border shoppers for

which counties. It is possible to measure SiC as the number of Canadians living within

a particular distance of county i, however this measure of SiC is unsatisfactory because it

does not account for potential geographic obstacles and obstacles to travelling between these

Canadians’ homes and county i. For instance, travel bottlenecks such as bridges may make

even a short distance costly to travel, while an adequate highway leading to the border may

make such trips very convenient.

    Our preferred measure of SiC uses observations of the number of Canadians who cross the

international border into county i to estimate the number of Canadians who are potential

cross-border shoppers. Using interview data from border crossing points, Statistics Canada

tabulates the number of U.S. and Canadian travellers that travel through each oﬃcial border

crossing point while either embarking upon or returning from a trip lasting one-day or less

to the other country. Statistics Canada does not keep track of travellers’ identities, so an

individual making multiple trips to or from Canada in a year will contribute to the count

of travellers on each trip. This data is available from 1990 through 1999. We average the

data across these years to measure the average number of U.S. and Canadian travellers for

county i, which we denote with TiU and TiC .

    Our model implies that the number of Canadians crossing the border on one-day trips is

                                               18
λSiC , but our model implies nothing about the frequency of cross-border shopping during one

year for a travelling consumer. To construct a measure of SiC based on TiC , we assume that

the average number of trips taken by a travelling consumer, θ, is constant across locations.

Given prespeciﬁed values of λ and θ, we can then measure SiC with TiC / (λθ). The resulting

measure of county i’s exposure to cross-border shopping is
                                                         TiC
(24)                                          si =               .
                                                     λθSiU + TiC
       As this expression for si makes clear, the problem of choosing λθ is one of expressing

county i’s population in units of travellers. For our baseline measure of si , we assume that all

U.S. travellers entering Canada for one-day trips from county i are residents in that county,

and use the average of TiU /SiU across border counties to measure λθ. The resulting value of

λθ is 7.49.5

       In general, our empirical results are not very sensitive to our choice of λθ, but we wish

to examine the implications of using other exposure measures. One alternative measure

of si dispenses with population data altogether by using TiU = λθSiU to rewrite si as

TiC / (TiU + TiC ). We refer to this as our trips-based exposure measure. The other mea-

sure of si we consider is a naive one based only on population data. For this, we measure

SiC with the number of Canadians living within a radius of ﬁfty miles of county i’s central

point, as deﬁned by the U.S. Bureau of the Census. The Canadian population data comes

from that country’s 1991 census. We refer to this measure of si as our population-based

exposure measure.

       The ﬁrst two columns of Table 5 report the sample means and standard deviations of the

three measures of si that we use in estimation across the 19 border counties in our sample. Its
   5
       We have also considered calibrated values of λ and θ based on Ford’s (1992) survey data of Canadian
consumers’ cross-border shopping habits. The calibrated values of λ and θ are 0.71 and 25, so that λθ = 17.75.
This is far diﬀerent from our baseline measure of λθ, but the resulting exposure measure is almost perfectly
correlated with our baseline measure.The cross-sectional correlation coeﬃcient between the two measures
equals 0.98. The empirical results we obtain with this alternative measure of si are nearly identical to our
baseline results, so we do not report them.

                                                       19
ﬁnal column reports the sample correlation of the alternative measures of si with our baseline

measure. By construction, all of our exposure measures are between zero and one. Our

baseline measure’s mean is 0.60, which is between the other two measures’ means, 0.57 and

0.70. These means are close to their (unreported) corresponding median values. The baseline

measure’s standard deviation is 0.27, which is very close to the standard deviation of the

population-based measure. The standard deviation of the trips-based measure is somewhat

lower than this, 0.14. Both alternative exposure measures have positive correlations with

the baseline measure, 0.59 and 0.57.


E      GMM Estimation

The estimation of panel-data vector autoregressions similar to (23) without the explanatory

variables si × et is a well-studied problem. To estimate (23), we use a GMM estimator based

on Blundell and Bond (1998), which uses moment conditions derived from the lack of serial-

correlation in εit and an assumption that yit is mean-stationary. A novel complication that

arises in our analysis is the presence of the measurement error ψsi ζit due to the replacement

of ln rit with ln rt . We have placed no restrictions on the serial correlation properties of ζit , so

this measurement error’s presence invalidates Blundell and Bond’s (1998) moment conditions

when applied to observations from border counties. However, si equals zero for the majority

of our sample counties, so their moment conditions remain valid if we impose them only on

observations from counties without a Canadian border. The appropriately modiﬁed moment

conditions which we use in our GMM estimator are


(25)                      E [I {si = 0} ∆εit yit−s ] = 0, t = 3, . . . , T, t > s ≥ 2,

(26)              E [I {si = 0} (αi + εit ) ∆yit−1 ] = 0, t = 2, . . . , T.


We can impose additional restrictions by assuming that yi has a zero mean, which is merely
                                                       ¯

a normalization given the presence of µt in (23). This constrains the error term’s level to


                                                   20
have a zero mean, conditional upon not being a border county.


(27)                            E [I {si = 0} (αi + εit )] = 0, t = 2, . . . , T


       Taken together, the moment conditions in (25), (26), and (27) are more than suﬃcient

for identifying and estimating the 4 autoregressive parameters and the 2 (T − 1) year-speciﬁc

intercepts for T = 20. However, these conditions clearly leave β unidentiﬁed. Because we

have assumed that both vit and ζit have zero unconditional means, it must be the case that


(28)                                   E [∆εit si ] = 0, t = 3, . . . , T.


These 2 (T − 2) moment conditions allow us to estimate β along with the model’s other

parameters.6

       The GMM estimator we use is based on the moment conditions in (25), (26), (27), and

(28).7 We use a one-step GMM estimator, in which the weighing matrix is a version of

that used by Blundell and Bond (1998) appropriately modiﬁed to account for the additional

moment conditions in (27), and (28). We use a one-step estimator rather than an asymptot-

ically eﬃcient two-step estimator because the number of moment conditions we use exceeds

the number of cross-sectional observations in our sample. This implies that the usual con-

sistent estimator of the optimal weighting matrix’s inverse is singular, and so non-invertible.

Existing Monte Carlo results for panel data VAR estimation typically consider estimation of

a single-equation with a small value of T , so that this issue does not arise. For this reason,

we investigated the estimator’s properties in a sample of the size we use in a Monte Carlo

experiment. We found that the estimator displayed very little bias and that the asymptotic

distributions of t-statistics and χ2 tests provided reliable guides for inference. The technical
   6
       Note that because we have allowed ai to potentially have a non-zero mean in (13), we cannot claim that
E [αi si ] = 0, which would be necessary for adding the moment condition E [(αi + εi2 ) si ] = 0.
   7
     For Drinking Places, relative price data is not available until the third year of our sample. This slightly
changes the set of available moment conditions. The technical appendix describes these changes in more
detail.


                                                       21
appendix describes the estimation procedure and this Monte Carlo experiment in much more

detail.


III       Estimation Results

Our baseline empirical analysis of retail trade industry dynamics for the ﬁve industries we

consider produces estimates of ten autoregressive equations’ parameters for each industry.

To conserve space, we report complete results for one industry, Food Stores, as an example.

For the remaining industries, we report the estimates of the coeﬃcients on current and

lagged relative prices and summarize our estimates of the autoregressive coeﬃcients. Table

6 presents the GMM estimates of the coeﬃcients in (23) for Food Stores. Before estimation,

we divided si by its mean value, so that the coeﬃcients on current and lagged relative prices

can be interpreted as elasticities at a county with the mean value of si , 0.60. Below each

estimate is its heteroskedasticity-consistent standard error. The Table’s ﬁnal row reports

the value of a Wald test of the null-hypothesis that the international relative prices can

be excluded from that equation. These tests are asymptotically distributed as χ2 random

variables with two degrees of freedom. The relevant 5% critical value for this test is 5.99.

   The estimates in Table 6 indicate that ﬂuctuations in the U.S.-Canada relative price of

food purchased in stores signiﬁcantly impacts the Food Stores industries in counties that bor-

der Canada. In the establishments equation, β0 equals −0.101. This has the sign predicted

by our model and is statistically signiﬁcant at the 5% level. The corresponding estimate β1

is very close to zero and is not signiﬁcant. The Wald exclusion test statistic for the establish-

ments equation equals 10.70, which far exceeds the 5% critical value. The point estimates

of β0 and β1 for the average payroll equation are similar to those from the establishment

equation, but they are not statistically signiﬁcant at conventional levels. The Wald exclusion

test statistic for this equation is 4.37, and its probability value is 0.11.

   Recall that the instantaneous-entry model presented in Section I predicts that the ex-


                                                22
penditure shifting eﬀects of an exchange-rate appreciation decrease the number of stores in a

border county but should leave their average sizes unchanged. These results are statistically

consistent with this view. However, the estimated magnitude of average payroll’s response

to the current relative price and the relatively high probability value for that equation’s ex-

clusion test suggest the more conservative conclusion that the Food Stores industry responds

to relative price movements by changing both the number of stores and their average size.

At our point estimates, about 2/5 of the reduction in total payroll comes from reducing the

number of stores, and the remaining 3/5 comes from reducing stores’ average payroll.

   Finally, note that the autoregressive parameter estimates indicate that both the number

of establishments in a county and their average payrolls are persistent time series, with

establishments displaying somewhat more persistence than payroll. The diagonal elements

of Λ are both positive and signiﬁcant, while its oﬀ-diagonal elements are much smaller.

These parameters are tightly estimated. The other four industries’ estimated autoregressive

coeﬃcients are very similar to Food Stores. Finally, note that the estimates of Λ and β

together do not satisfy the common-factor restriction of the instantaneous entry model. For

this reason, we investigate richer parameterizations of our model below.

   To better gauge the economic signiﬁcance of our estimates for Food Stores, we have

plotted the responses of ln Nit and ln Ait to a persistent innovation in the current relative

price. Figure 2 displays these impulse-response functions over a ten-year horizon for Food

Stores. Its top panel plots the response of ln Nit , whereas its bottom panel plots the response

of ln Ait . For both panels, we assumed that ln rt follows an AR(1) process

                                  ln rt = κ + 0.87 ln rt−1 + υt

where υt is an i.i.d. disturbance term with mean zero and standard deviation 0.037. With

these parameter values, the unconditional standard deviation of ln rt equals its sample value

of 0.075. Each panel’s solid line plots the response to a one standard deviation positive

impulse to υt . The dashed lines plot the upper and lower limits of pointwise 95% conﬁdence

intervals for the impulse response function. These conﬁdence intervals reﬂect sampling un-

                                               23
certainty regarding the model parameters Λ and β, but they do not reﬂect uncertainty about

the true process for ln rt .

   Both variables’ impulse response functions display considerable persistence. This reﬂects

both the persistence in ln rt and the large deviation of the estimated model from one with

a common-factor representation. As the parameter estimates imply, the number of estab-

lishments falls during the period of the shock and then continues to fall. The instantaneous

impact is about four tenths of one percent, and the impact at a horizon of ﬁve years is slightly

less than two percent. As the test statistics suggest, the pointwise conﬁdence intervals for

these responses never include zero. For establishments’ average payroll, the instantaneous

impact of the shock is about six tenths of one percent, and its impact after ﬁve years is

around one percent. The impact of the shock on average payroll after one year is negative

and statistically signiﬁcant. The relevant pointwise conﬁdence intervals for the shock’s im-

pact at other horizons all include zero. Thus, over short horizons of a year or less, it appears

that both the number of establishments and their average sizes change following a shock

to the relative price. Over the long-run, however, the industry accommodates the shock

primarily by through entry and exit.

   For the sake of brevity, we report only the estimates of β and the values of the exclusion

tests for the remaining industries. Table 7 reports the estimates of β and the exclusion

tests for all ﬁve of the industries we consider, and Figures 3–6 graph the impulse response

functions for the remaining industries. In those exercises, we assumed that the relevant

industry-speciﬁc real exchange rate followed a ﬁrst-order autoregression parameterized to

match the reported statistics in Table 4 and simulated the industry’s response to a one-

standard deviation positive shock.

   In Gasoline Service Stations the lagged gasoline-based real exchange rate has a negative

and statistically signiﬁcant coeﬃcient while the coeﬃcient on the current relative price is

insigniﬁcant. Thus, in this industry the number of establishments responds to real exchange-

rate shocks only after one year. Just as with Food Stores, the Wald test rejects the exclusion


                                              24
restriction for establishments, but not for average payroll. However, the Wald test statistic

for the average payroll equation is not very small, and the point estimates in that equation

are larger than those for the establishments equation, so it seems premature to conclude that

Gasoline Service Stations’ average payroll does not respond to a real exchange rate shock.

The impulse-response functions for Gasoline Service Stations reﬂect the delayed response of

net entry to the exchange rate shock. In the year of the shock, average payroll falls more

than 1%, while the number of establishments rises very slightly. The reduction in average

payroll persists, while the number of establishments falls. After ﬁve years, the number of

establishments has declined approximately 2%. These results resemble the textbook descrip-

tion of the transition from the short-run to long-run response to a demand shock. Initially

the number of establishments is held ﬁxed and the industry responds to a negative demand

shock by decreasing their average size. If the demand shock persists as it does in our simu-

lation, then the number of establishments decreases, either by reducing entry or increasing

exit.

   In Apparel and Accessory Stores, the estimated coeﬃcients on the contemporaneous

real exchange rate are large and negative in both equations, but they are not statistically

signiﬁcant. The Wald tests also oﬀer no evidence that these coeﬃcients are statistically

signiﬁcant. These estimates’ standard errors are somewhat larger than those for Food Stores

and Gasoline Service Stations, so it is diﬃcult to determine whether these estimates indicate

the absence of any eﬀect or simply an absence of statistical power to reject the null hypothesis.

As noted previously, this industry may be one in which a signiﬁcant portion of cross-border

shopping occurs in interior counties, particularly at discount outlet centers. This may provide

a partial explanation for our ﬁndings of little eﬀect of relative price movements in this

industry.

   The results for Eating Places are very similar to those for Food Stores, but the statistical

strength of the results is somewhat weaker. In the establishments equation, neither of the

coeﬃcients are individually signiﬁcant, and the Wald test’s probability value is 0.072. The


                                               25
corresponding Wald test statistic for the average payroll equation is close to its median

value under the null hypothesis. The impulse response functions for Eating Places show

that ﬂuctuations in the number of establishments play a central role in the responses to real

exchange rate disturbances. The contemporaneous responses of establishments and average

payroll to the exchange rate shock are nearly equal. After impact, average payroll quickly

returns to its pre-shock value, while the number of establishments remains persistently low.

Of the ﬁve industries we consider, Eating Places most resembles the stark behavior of our

model with immediate entry.

   Our ﬁnal industry is Drinking Places. These estimates are quite diﬀerent from those of

the other industries. The estimated coeﬃcients for the establishments equation are close to

the corresponding estimates for Eating Places, but their standard errors are much larger.

In contrast, the coeﬃcient on the contemporaneous real exchange rate in the average pay-

roll equation is −0.775. This is by far the largest absolute value of any of our estimated

coeﬃcients, and it is statistically signiﬁcant at the 5% level. The Wald exclusion test also

indicates that real exchange rate ﬂuctuations have a strong impact on the average payrolls of

Drinking Places in border counties. The impulse response functions reﬂect the importance

of establishments’ average payroll in responding to exchange-rate shocks. In the year of the

shock, the number of establishments falls slightly and remains low. However, the response of

establishments to the shock is not statistically signiﬁcant at any horizon. In contrast, Drink-

ing Places’ average payroll falls nearly 4% in the period of the shock, and it only slowly rises

back to its pre shock level.

   To determine the robustness of our conclusions to our choice of exposure measure, we

have re-estimated (23) using both of the alternative exposure measures discussed above.

Table 8 reports estimated coeﬃcients and exclusion tests for our estimates that use the

trips-based exposure measure, and Table 9 reports the analogous results for the population-

based exposure measure. The results using the trips-based exposure measure are very similar

to those from our baseline exposure measure, although the standard errors tend to be larger


                                              26
and the statistical signiﬁcance of the results tends to be weaker. The estimates which use the

population-based exposure measure are quite diﬀerent from those that use either of the other

two exposure measures. The only Wald tests which reject the null hypothesis of exclusion are

those for establishments in Food Stores and for average payroll in Gasoline Service Stations.

With the notable exception of this latter equation, the point estimates for the remaining

equations are all very diﬀerent from those of our baseline estimation. We believe that these

diﬀerences reﬂect the inaccuracy of measuring the number of Canadians that are potential

customers for a U.S. county’s retail trade industry with the number of Canadians living

within ﬁfty miles of the county’s center. Because the decision to enter a county reveals that

one is willing to cross-border shop, we believe that our baseline and trips-based exposure

measures more accurately measure the size of each U.S. market’s relevant Canadian customer

base. This accuracy is reﬂected in our baseline estimates’ greater magnitude and statistical

signiﬁcance.


IV      Related Literature

Much of the theory of industrial organization assumes that entry responds to persistent

shocks only in the long run. The implications of sluggish entry are well-known: When entry

takes time, incumbent producers can temporarily earn economic proﬁts following a favorable

aggregate demand or cost shock. Baumol, Panzar, and Willig (1982) show that the opposite

assumption of very rapid entry with no sunk costs implies that incumbents never earn positive

proﬁts and that price always equals average cost. In spite of this theoretical importance, little

is known about the speed with which entry can take place following a demand shock. Using

a cross-section of rural retail and service industries, Bresnahan and Reiss (1991) examined

a long-run free-entry model’s prediction that the number of producers is proportional to

market size. That analysis reveals no evidence of barriers that permanently exclude potential

entrants, but it says nothing about the speed with which entry can respond to demand shocks.


                                               27
Our analysis suggests that entry into retail trade industries responds very quickly to demand

shocks. Only in Drinking Places, where alcohol licensing restrictions may indeed present a

barrier to entry, does the real exchange rate aﬀect industry activity without changing the

number of establishments. The number of establishments responds contemporaneously to a

real exchange rate shock in Food Stores and in Eating Places, and it responds after one year in

Gasoline Service Stations. In these industries, either potential entrants, potential exiters, or

both must respond very quickly to demand shocks. In our model economy and its extension

discussed in Footnote 1 that incorporates sunk costs of entry and long-lived producers, all

ﬂuctuations in the number of producers reﬂect the decisions of potential entrants. This is a

very robust theoretical result that only depends on the cost of entry being invariant to the

number of entrants and their identities.8 Thus, our results strongly suggest that potential

entrants can aﬀect their decisions very quickly following demand shocks.

       Although real exchange rate ﬂuctuations are substantial, their nonﬁnancial eﬀects have

been diﬃcult to detect. Baxter and Stockman (1989) examine data from several OECD coun-

tries and ﬁnd that the characteristics of a country’s business cycle ﬂuctuations do not depend

on whether or not it has adopted a ﬁxed exchange rate. Conversely, Frankel and Rose (1995)

survey a large literature that concludes that macroeconomic quantities do not contribute to

better forecasts of real exchange rates. This paper belongs to a literature which attempts

to identify the real eﬀects of exchange rate ﬂuctuations. For example, Gourinchas (1998)

regresses job creation and destruction rates from export-intensive and import-intensive man-

ufacturing industries on real exchange rates. That estimation shows little eﬀect of exchange

rates on the level an industry’s activity, but it does indicate that real appreciations increase

the reallocation of employment across an industry’s plants. Several diﬀerences between this

estimation and ours can account for the diﬀerences in our results. First and foremost, our pa-
   8
       Campbell and Fisher (1996) present a perfectly competitive industry dynamics model with idiosyncratic
producer risk, sunk costs of entry, and exogenous exit. In that model, demand shocks only contemporaneously
impact the number of entrants.


                                                      28
per and his examine diﬀerent industries with diﬀerent production technologies. Second, the

econometric strategies for accounting for the direct eﬀects of unobserved structural shocks

on preferences and technology are substantially diﬀerent. Gourinchas includes a vector of

macroeconomic aggregates in his regression equations to proxy for unobserved aggregate

shocks, while we estimate a set of time-dummies using data from counties that do not bor-

der Canada. Gourinchas’ approach requires that some exchange rate variation is exogenous,

in the sense that it does not reﬂect changes to either tastes or technology. Our strategy

requires no such assumption. Finally, Gourinchas’ estimation pools data from several manu-

facturing industries. His estimation uses cross-industry variation in the industry-speciﬁc real

exchange rate ﬂuctuations to identify the parameters of interest. Our estimation pools data

from the same retail trade industry in diﬀerent counties and uses cross-sectional variation in

the counties’ locations relative to the U.S.-Canada border to identify the expenditure-shifting

eﬀects of exchange rates.

       The deviations from PPP that induce cross-border shopping form the central puzzle in

international macroeconomics. Another implication of our empirical results is that they may

provide insight into the source of these international relative price diﬀerences. One candidate

explanation for persistent deviations from PPP is nominal stickiness of producers’ prices

denominated in the currency of the consumer, as in Devereux and Engel (2000). Our model

assumed that all retailers prices are perfectly ﬂexible and that deviations from PPP reﬂect

diﬀerences in U.S. and Canadian retailers’ marginal costs. When they are considered more

generally, our empirical results reinforce the assumption of perfectly ﬂexible retail prices. If

we assume that the time required to plan and build a new store is no less than the time horizon

over which retailers’ prices are ﬁxed, then our estimates of net entry’s response place a bound

on the duration of retailers’ nominal price stickiness.9 In Food Stores and Eating Places, the

results suggest that the impact of real exchange rate appreciations on net entry is immediate,
   9
       Although we ﬁnd this assumption to be a reasonable description of retail trade technology, it does rule
out the contestability of retail markets, as that term is deﬁned by Baumol, Panzar, and Willig (1982).


                                                       29
indicating that nominal price stickiness and menu costs play little role in generating real price

diﬀerences between U.S. and Canadian grocery stores and restaurants. In Gasoline Service

Stations, where the presence of nominal retail price stickiness is particularly implausible,

there is a signiﬁcant response of net entry after one year. Our results suggest that for these

industries costs of changing retail prices play little role in generating deviations from PPP. In

the absence of regulation, retailers would exploit diﬀerences in the two countries’ wholesale

prices, eliminating the need of consumers in border areas to do so themselves. Therefore, the

observed deviations from PPP must arise from either time-varying retail markups,.diﬀerences

in U.S. and Canadian retailers’ costs of producing retail services, as in Burstein, Neves, and

Rebelo (2000), or from wholesale price diﬀerences, like those for gasoline the early 1980’s,

due to regulation and taxation.


V      Conclusion

The persistent deviations from PPP that our empirical work uses imply that residents of

border counties face diﬀerent prices than those who do not live on the border. Our empirical

work used these deviations and the resulting expenditure-shifting by border residents to

identify the eﬀects of real exchange rates on border counties’ retail trade industries. Although

this paper has focused on producers’ behavior, our results suggest that it is possible to also

learn about consumers’ behavior by comparing those who live on the U.S.-Canada border

with those who do not. For example, with sticky nominal wages, the real wages of those

living on an international border will diﬀer from those who do not, potentially allowing us to

estimate the wage elasticity of labor supply. There is clearly more work to be done examining

these price diﬀerences and their implications.

    Our results document how ﬁve retail industries respond to a particular demand shock

that arises from real exchange rate ﬂuctuations. In three of the ﬁve industries we consider,

the response of net entry to this demand shock is statistically and economically signiﬁcant.


                                               30
Our interest in these results arises from an assumption that these retail trade industries

respond similarly to other transitory demand shocks, such as large local income expansions

and contractions. Verifying this assumption directly is our agenda for future research. The

County Business Patterns data we used is available for all U.S. counties between 1977 and

1996. We believe that the modelling and estimation techniques developed for this paper

can be extended and fruitfully applied to this data more generally to measure, for example,

retail industry responses to local government spending shocks and the comovement of city

and suburban retail trade industries. This paper’s results give us reason to believe that the

net entry of establishments also plays an important role in these ﬂuctuations.


                                             31
References


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                                            32
Engel, Charles and John H. Rogers. (1996) How Wide is the Border?,” American Economic

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ature, 34(2), 647-68.


                                             33
        Table 1: Quartiles from Sample Counties of Average Establishment Counts

 Industry            Counties(i)    First Quartile(ii)   Median(ii)   Third Quartile(ii)


 Food Stores             256              26.7             45.0             93.3


 Gasoline Service        256              18.9             28.8             51.2

 Stations


 Apparel and             228              16.2             28.2             68.5

 Accessory Stores


 Eating Places           245              39.1             74.2             145.7


 Drinking Places         235              11.8             18.6             38.5


Notes: (i) Refers to the number of counties included in the estimation sample for each

industry. (ii) For each included county, the average number of establishments serving each

industry between 1977 and 1996 was calculated. ‘First Quartile’, ‘Median’, and ‘Third

Quartile’ refer to the quartiles of that statistic across all sample counties for that industry.

See the text for further details.


                                                 34
                  Table 2: Median Within-County Standard Deviations(1)

                     Industry            Establishments   Average Payroll


                     Food Stores               0.11            0.14


                     Gasoline Service          0.13            0.16

                     Stations


                     Apparel and               0.16            0.18

                     Accessory Stores


                     Eating Places             0.09            0.10


                     Drinking Places           0.17            0.22


Note: (i) For each industry, each of the variables was ﬁrst logged and regressed against a set

of time dummies. The sample standard deviations of the residuals from that regression was

tabulated for each county. The values reported in the table are the medians, across counties,

of these statistics. See the text for further details.


                                                35
               Table 3: Consumer Price Index Sources for Relative Price Series

 Industry            U.S. CPI                 Canadian CPI


 Food Stores         Food at Home             Food Purchased from Stores


 Gasoline Service    Gasoline                 Gasoline

 Stations


 Apparel and         Apparel and Upkeep       Clothing and Footwear

 Accessory Stores


 Eating Places       Food Away from Home      Food Purchased from Restaurants


 Drinking Places     Alcoholic Beverages      Served Alcoholic Beverages

                     Away from Home

Notes: For each industry, the column headed U.S. CPI reports the name of the consumer

price index series used in constructing the relative price, and the column headed Canadian

CPI reports the name of the analogous Canadian series. See the text for further details.


                                             36
                    Table 4: Summary Statistics for Relative Price Series

                                                                     Correlation with Aggregate

 Industry              Standard Deviation First Autocorrelation          Real Exchange Rate


 Food Stores                 0.075                    0.87                           0.63


 Gasoline Service            0.214                    0.88                           0.47

 Stations


 Apparel and                 0.064                    0.74                           0.96

 Accessory Stores


 Eating Places               0.070                    0.75                           0.93


 Drinking Places(ii)         0.085                    0.82                           0.92

Notes: (i) The ﬁrst two columns report the standard deviation and ﬁrst autocorrelation of

the relative price series used for the corresponding industry over the sample period 1977-

1996. The ﬁnal column gives the contemporaneous correlation between the relative price

series and the relative price of “all goods less energy”. (ii) Sample period for the relative

price series for Drinking Places begins in 1979. See the text for further details.


                                              37
        Table 5: Summary Statistics for Cross-Border Shopping Exposure Measures

                                              Standard        Correlation with

 Exposure Measure(i)              Mean(ii)   Deviation(ii)   Baseline Measure(ii)


 Baseline,                          0.60         0.27               1.00

 si = Ti1 / (7.49 × Si0 + Ti1 )


 Trips-Based Measure,               0.70         0.14               0.59

 si = Ti1 / (Ti0 + Ti1 )


 Population-Based Measure,          0.57         0.27               0.57

 si = Si1 / (Si0 + Si1 )


Note: (i) In the expressions under each entry, Si0 is county i’s population, from the 1990

census, Si1 is the Canadian population within 50 miles of county i’s central point, from the

1991 Canadian census, Ti0 and Ti1 are the average annual numbers of U.S. and Canadian

travellers crossing into Canada from county i while taking cross-border trips lasting a day

or less. (ii) All sample statistics are calculated across the 19 border counties in our sample.

See the text for further details.


                                                38
                           Table 6: Estimates for SIC 54, Food Stores(i),(ii)


                                                          Dependent Variable

                                                   Establishments    Average Payroll


              Lagged Establishments,                      0.957∗∗∗              −0.017

              ln Nit−1                                     (0.011)              (0.018)


              Lagged Average Payroll,                     0.096∗∗∗              0.681∗∗∗

              ln Wit−1                                     (0.021)              (0.050)


              Current Real Exchange Rate,                −0.101∗∗               −0.155

              si × ln rt                                   (0.049)              (0.111)


              Lagged Real Exchange Rate,                   −0.001               −0.043

              si × ln rt−1                                 (0.070)              (0.139)


              Exclusion Test for                             10.70                 4.37

              Real Exchange Rate(iii)                      (0.005)              (0.112)


Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each

coeﬃcient estimate. (ii) The superscripts ∗, ∗∗, and ∗ ∗ ∗ indicate that the estimate is

statistically signiﬁcantly diﬀerent from zero at the 10%, 5%, and 1% levels. (iii) The Wald

exclusion tests are asymptotically distributed as χ2 random variables with 2 degrees of

freedom. Probability values from this distribution appear below each test statistic. See the

text for further details.

                                                  39
             Table 7: Estimation Results using Baseline Exposure Measure(i)(ii)

                                  Establishments                              Average Payroll

 Industry            si × ln rt    si × ln rt−1   χ2 Test(iii)   si × ln rt    si × ln rt−1   χ2 Test(iii)


 Food Stores        −0.101∗∗         −0.001         10.70        −0.155          −0.043          4.37

                     (0.049)         (0.070)       (0.005)       (0.111)         (0.139)        (0.112)


 Gasoline Service     0.033         −0.091∗            7.73      −0.121           0.029          2.89

 Stations            (0.044)         (0.047)       (0.021)       (0.089)         (0.058)        (0.235)


 Apparel and         −0.147           0.065            2.23      −0.215           0.050          0.93

 Accessory Stores    (0.099)         (0.106)       (0.328)       (0.237)         (0.260)        (0.629)


 Eating Places       −0.135           0.067            5.27      −0.117           0.098          1.28

                     (0.086)         (0.079)       (0.072)       (0.110)         (0.098)        (0.529)


 Drinking Places     −0.152           0.098            1.32      −0.775∗∗         0.322          6.68

                     (0.143)         (0.138)       (0.517)       (0.340)         (0.275)        (0.035)

Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each

coeﬃcient estimate. (ii) The superscripts ∗ and ∗∗ indicate that the estimate is statisti-

cally signiﬁcantly diﬀerent from zero at the 10% and 5% levels. (iii) Asymptotically, this

test statistic has a χ2 distribution with 2 degrees of freedom. Probability values from this

distribution appear in parentheses below each test statistic. See the text for further details.


                                                  40
            Table 8: Estimation Results using Trips-Based Exposure Measure(i)(ii)

                                  Establishments                              Average Payroll

 Industry            si × ln rt    si × ln rt−1   χ2 Test(iii)   si × ln rt     si × ln rt−1   χ2 Test(iii)


 Food Stores          −0.097         −0.001            5.34       −0.201          −0.016          5.97

                      (0.068)        (0.082)       (0.069)        (0.128)         (0.155)       (0.051)


 Gasoline Service      0.042        −0.095∗            5.57       −0.121           0.044          1.81

 Stations             (0.047)        (0.049)       (0.062)        (0.094)         (0.059)       (0.404)


 Apparel and          −0.090          0.006            0.96       −0.235           0.008          1.02

 Accessory Stores     (0.121)        (0.138)       (0.619)        (0.245)         (0.273)       (0.599)


 Eating Places        −0.133          0.061            3.69       −0.106           0.113          1.12

                      (0.119)        (0.108)       (0.158)        (0.128)         (0.108)       (0.571)


 Drinking Places      −0.192          0.144            1.11      −0.981∗∗∗         0.426          9.09

                      (0.197)        (0.193)       (0.575)        (0.356)         (0.289)       (0.011)

Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each

coeﬃcient estimate. (ii) The superscripts ∗ and ∗ ∗ ∗ indicate that the estimate is statis-

tically signiﬁcantly diﬀerent from zero at the 10% and 1% levels. (iii) Asymptotically, this

test statistic has a χ2 distribution with 2 degrees of freedom. Probability values from this

distribution appear in parentheses below each test statistic. See the text for further details.


                                                  41
        Table 9: Estimation Results using Population-Based Exposure Measure(i)(ii)

                                 Establishments                              Average Payroll

 Industry           si × ln rt    si × ln rt−1   χ2 Test(iii)   si × ln rt    si × ln rt−1   χ2 Test(iii)


 Food Stores         −0.003         −0.112            8.80      −0.123           0.110          1.45

                     (0.059)        (0.084)       (0.012)       (0.104)         (0.129)        (0.485)


 Gasoline Service    −0.026         −0.010            3.56      −0.134∗∗         0.014          9.21

 Stations            (0.034)        (0.042)       (0.169)       (0.062)         (0.054)        (0.010)


 Apparel and         −0.133          0.000            2.85      −0.186           0.061          1.12

 Accessory Stores    (0.110)        (0.119)       (0.240)       (0.178)         (0.174)        (0.571)


 Eating Places       −0.050          0.006            3.67       0.062          −0.080          0.73

                     (0.075)        (0.073)       (0.160)       (0.080)         (0.095)        (0.693)


 Drinking Places      0.002         −0.092            3.43      −0.340           0.213          2.35

                     (0.097)        (0.103)       (0.180)       (0.229)         (0.204)        (0.308)

Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each

coeﬃcient estimate. (ii) The superscripts ∗ and ∗∗ indicate that the estimate is statisti-

cally signiﬁcantly diﬀerent from zero at the 10% and 5% levels. (iii) Asymptotically, this

test statistic has a χ2 distribution with 2 degrees of freedom. Probability values from this

distribution appear in parentheses below each test statistic. See the text for further details.


                                                 42
                                              1.5


                                              1.4


                                              1.3


                                              1.2


                                 (1972=1)
                                              1.1


                                               1


         Real Exchange Rate
                                               .9
                                                    1972   1976   1980   1984     1988   1992   1996
                                                                           Year

                                              30

                                              28

                                              26

                                              24

                                              22

                                              20

                                              18

                                              16


                              (Millions)
                                              14

                                              12

                                              10


Canadian Same-Day Trips
                                               8
                                                    1972   1976   1980   1984     1988   1992   1996
                                                                           Year


                                              14


                                              12


                                              10


                                 (Millions)
                                                                                                       Figure 1: The Real Exchange Rate and Cross-Border Shopping


                                               8


       U.S. Same-Day Trips
                                               6
                                                    1972   1976   1980   1984     1988   1992   1996
                                                                           Year
                             Figure 2: Impulse Response Functions for SIC 54, Food Stores


                                                   Establishments
                     1
Percentage Points


                     0

                    −1

                    −2

                    −3

                    −4

                    −5
                         0       1      2      3      4      5      6      7     8      9   10


                                                   Payroll/Establishment
                     1
Percentage Points


                     0

                    −1

                    −2

                    −3

                    −4

                    −5
                         0       1      2      3      4      5      6      7     8      9   10
                                                     Years After Shock
 Figure 3: Impulse-Response Functions for SIC 5540, Gasoline Service Stations


                                         Establishments
                     2
Percentage Points


                     1

                     0

                    −1

                    −2

                    −3

                    −4

                         0   1   2   3      4      5      6      7   8   9   10


                                         Payroll/Establishment
                     2
Percentage Points


                     1

                     0

                    −1

                    −2

                    −3

                    −4

                         0   1   2   3      4      5      6      7   8   9   10
                                           Years After Shock
Figure 4: Impulse-Response Functions for SIC 56, Apparel and Accessory Stores


                                          Establishments
                      2
 Percentage Points


                      1

                      0

                     −1

                     −2

                     −3

                     −4

                          0   1   2   3      4      5      6      7   8   9   10


                                          Payroll/Establishment
                      2
 Percentage Points


                      1

                      0

                     −1

                     −2

                     −3

                     −4

                          0   1   2   3      4      5      6      7   8   9   10
                                            Years After Shock
                     Figure 5: Impulse-Response Functions for SIC 5812, Eating Places


                                             Establishments
Percentage Points


                     1


                     0


                    −1


                    −2

                         0   1    2      3      4      5      6      7      8     9     10


                                             Payroll/Establishment
Percentage Points


                     1


                     0


                    −1


                    −2

                         0   1    2      3      4      5      6      7      8     9     10
                                               Years After Shock
                     Figure 6: Impulse-Response Functions for SIC 5813, Drinking Places


                                             Establishments
Percentage Points


                     0


                    −2


                    −4


                    −6


                    −8
                         0   1    2      3      4      5      6      7      8      9      10


                                             Payroll/Establishment
Percentage Points


                     0


                    −2


                    −4


                    −6


                    −8
                         0   1    2      3      4      5      6      7      8      9      10
                                               Years After Shock