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Federal Reserve Bank of Chicago

Real Exchange Rate Fluctuations and
the Dynamics of Retail Trade
Industries on the U.S.-Canada Border
Jeffrey R. Campbell and Beverly Lapham

WP 2002-17

Real Exchange Rate Fluctuations and the Dynamics of
Retail Trade Industries on the U.S.-Canada Border∗
Jeffrey R. Campbell†

Beverly Lapham‡

November 2002

Abstract
Consumers living near the U.S.-Canada border can shift their expenditures between
the two countries, so real exchange rate fluctuations can act as demand shocks to border
areas’ retailers. Using annual county-level data, we estimate the effects of real exchange
rates on the number of establishments and their average employment in border counties
for four retail industries. In three of the four industries we consider, the number of
operating establishments responds either contemporaneously or with a lag of one year,
so “long-run” changes in net entry in fact occur quickly enough to matter for short-run
fluctuations.
∗

The opinions expressed herein are those of the authors and are not necessarily those of the Federal

Reserve Bank of Chicago or the Federal Reserve System. We thank Lisa Barrow, Martin Boileau, Lars
Hansen, Allen Head, John Rogers, Chad Syverson, and Oved Yosha for helpful comments on previous versions
of this paper. 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. The latest versions of this paper and its technical appendix are available
on the World Wide Web at http://www.nber.org/˜ jrc. Please direct correspondence to Campbell at
Economic Research, Federal Reserve Bank of Chicago, 230 South LaSalle Street, Chicago, Illinois 60604.
†
Economic Research, Federal Reserve Bank of Chicago and NBER
‡
Department of Economics, Queen’s University

This paper estimates the effects of real exchange rate fluctuations on the number of
establishments and their average employment in U.S. retail trade industries located near
the U.S.-Canada border. It is widely known that there are large and persistent deviations
from purchasing power parity between these countries, and Engel (1999) and Engel and
Rogers (1996) have documented that these deviations largely arise from violations of the
law of one price for traded goods. For retailers near these countries’ common border, real
exchange rate movements represent changes in the price of a substitute good. Thus, they
have effects similar to an ordinary demand shock. For each of four retail industries, we
estimate a panel-data vector autoregression using annual county-level data on the number
of retail establishments and their average employment from the ten contiguous states that
border Canada. The model’s explanatory variables include current and lagged real exchange
rates interacted with a measure of the local importance of the Canadian market.
The analysis increases our understanding of the relative importance of intensive and
extensive margins of adjustment in retail industries in response to demand shocks. We find
that in three of the four industries we examine — Food Stores, Gasoline Service Stations,
and Eating Places — fluctuations in the real exchange rate induce a change in the number of
stores either contemporaneously or with a lag of one year. That is, “long-run” changes in
the number of establishments occur quickly enough to contribute to these industries’ shortrun fluctuations. In the one industry we examine in which adjustment of net entry plays
no significant role in short-run fluctuations, Drinking Places, producers enjoy well-known
licensing restrictions on entry. Border counties account for a trivial fraction of economic
activity in the U.S., and the amount of trade facilitated by cross-border shopping is small
relative to either the U.S. or Canadian economy. Our results nevertheless offer insight into the
nature of aggregate fluctuations, because they exemplify these important retail industries’
responses to other demand shocks that are more widespread.
The real exchange rate is a market-determined price, and its movements reflect unknown
structural disturbances that could directly affect retailers’ costs. We do not expect these cost

1

effects to differ between border and non-border retailers, because all retailers face substantial
barriers to the international flow of wholesale goods and labor. Therefore, we can control for
changes in retailers’ costs that are correlated with the real exchange rate using observations
from counties off of the U.S.-Canada border. The estimator we use can be viewed as an
extension of the familiar difference-in-differences procedure that accommodates autocorrelation in the model’s disturbance terms. Our application of it uses variation in counties’
proximity to the Canadian market to identify the demand-shifting effects of real exchange
rates. In all of the industries we study, we find that these effects are significant.
In the next section, we briefly describe the trading arrangements between the U.S. and
Canada that make it relatively easy for consumers to import small quantities of retail goods
for personal use. Section II describes the data, our empirical model, and the GMM estimation
procedure we use. Section III presents the estimation results, and Section IV contains
concluding remarks regarding their implications for future research.

I

Barriers to Trade and Cross-Border Shopping

Our empirical analysis will rely on two assumptions. First, movements in the real exchange
rate do not present arbitrage opportunities that would cause U.S. border retailers’ costs
to systematically differ from those of their counterparts in the country’s interior. Second,
these same movements induce border area consumers to shift their expenditures between
U.S. and Canadian border retailers. In this section, we provide evidence supporting these
assumptions.
U.S. and Canadian consumers can legally cross their common border for recreational
purposes subject only to a (usually) brief customs inspection. Furthermore, these consumers
can import small quantities of goods purchased abroad for personal use. Figure 1 illustrates
that consumers in both countries take advantage of international price differences to shift
their expenditures towards the low-price country. Its top panel depicts the Canada-U.S.

2

real exchange rate between 1977 and 1996, normalized to equal 1 in 1977. Over the same
time period, its bottom two panels each plot the number of one-day trips by Canadians and
Americans to the other country. This variable is the official measure of cross-border shoppers
used by Canadian government agencies.
During the appreciation of the Canadian dollar between 1986 and 1992, the number
of Canadian one-day trips increased dramatically. It reached a peak of approximately 59
million trips during 1991. The estimates of Canadian expenditures in the U.S. during that
year reported in Ford (1992) range from 4 to 11 billion Canadian dollars. These values
are small relative to either the Canadian or U.S. economies, but the studies on cross-border
shopping commissioned by local and provincial Canadian governments during that time, such
as New Brunswick (1992) and Ontario (1991), indicate that their perceived impact on border
communities was substantial. The flow of cross-border shoppers reversed direction when the
Canadian dollar subsequently depreciated: American one-day trips to Canada climbed from
19 million in 1992 to nearly 24 million in 1996. The spike in American trips in 1980-1981
came at a time when the Canadian National Energy Policy subsidized petroleum’s import
and taxed its export. These policies greatly reduced the price of gasoline in Canada relative
to its price in the U.S., and American consumers took advantage of the opportunity to export
low-cost gasoline in their automobile tanks tax-free. Because the export tax was much more
easily enforced against large tanker trucks, the same price difference presented no arbitrage
opportunity to wholesalers.
The extent and timing of cross-border shopping indicates that wholesale arbitrage does
not eliminate international price differences near the U.S.-Canada border. The resulting
inference that it is considerably easier for consumers to shift their expenditures on retail
goods and services than it is for retailers to shift their expenditures on inputs is consistent
with these countries’ bilateral trading institutions. The U.S. and Canada have enjoyed
a free trade agreement since 1989. The Canada-U.S. Free Trade Agreement (FTA) and its
successor, NAFTA, guarantee mutual tariff-free market access for most domestically produced

3

goods. Both agreements guarantee free trade in gasoline between the two countries, so we
expect wholesale arbitrage to have tempered retail gasoline price differences (net of excise
and sales taxes) near the border since 1989. However, the FTA and NAFTA have not joined
the United States and Canada into a customs union with free mobility of all goods and
factors of production. Instead, they contain numerous exceptions to the general rule of free
trade. For example, Canada continues to maintain severely limiting import quotas on dairy
products, poultry, and eggs; and the United States’ sugar quotas limit imports of food items
composed of more than ten percent sugar. These and other remaining restrictions on trade
in agricultural products make it infeasible for a grocery retailer or restaurant to rely on a
foreign grocery wholesaler or food-service distributor. Alcohol distribution is also subject
to considerable regulation in both countries that serves as a non-tariff barrier to wholesale
trade.1
The existing barriers to trade in wholesale goods suggest that proximity to the border
does not endow a retailer with easier access to less-expensive foreign goods. Both countries’
existing immigration restrictions for low-skilled workers lead to the same conclusion regarding
labor. The FTA and NAFTA have both made it easier for professional workers to move
between the U.S. and Canada, but they have not enabled workers in the retail sector to do
so. Taken together, these institutional features of U.S-Canada trade imply that movements in
the real exchange rate do not present arbitrage opportunities that would cause U.S. border
retailers’ costs to systematically differ from those of their counterparts in the country’s
interior.
The extent to which the demand-shifting effects of exchange rates differentially affect
retailers near the border depends on the distance that consumers are willing to travel to
obtain a discount. Even if all cross-border shoppers make their purchases in border areas,
1

See Taylor (1988) for a description of the restrictions on the export of alcohol, dairy products, poultry,

and eggs to Canada before and after the FTA, and see Wilson (1993) for a brief synopsis of the ongoing
trade dispute between the two countries over trade in beer.

4

exchange rate movements affect the demand of interior retailers when they induce interior
residents to shop abroad. Ford’s (1992) survey of Canadian consumers’ shopping decisions at
the peak of Canadian cross-border shopping in the early 1990’s indicates the extent to which
this occurs. She surveyed consumers in three cities: Niagara-St. Catherines (very close to
the border), Hamilton (about 30 minutes drive from the border) and Toronto (about 1 hour
from the border). Her respondents from Toronto tended to shop in the U.S. twice a year
for electronics and appliances and those from Hamilton shopped quarterly for those items
as well as apparel and linens. About 70% of her respondents from Niagara-St. Catherines
shopped in the U.S. These shoppers averaged two trips per month, primarily to buy food
and gasoline. Furthermore, 96% of her survey respondents who purchased food and gasoline
in western New York did so in the two border counties of Erie and Niagara. If we extrapolate
these results to the entire U.S.-Canada border, U.S. gasoline and grocery retailers located
in border communities faced increases in demand for their goods during the appreciation of
the Canadian dollar and decreases in demand during the subsequent depreciation. If U.S.
consumers’ travel habits mimic those of Canadians, then these demand changes were not
shared by food and gasoline retailers located in interior counties.
As our discussion indicates, Food Stores (SIC 54) and Gasoline Service Stations (SIC
554) share three characteristics that are salient for our analysis. First, wholesalers’ ability to
arbitrage the industry’s inputs between the two countries is limited, so any cost disturbances
associated with real exchange rate movements will be common to all counties in the U.S.
Second, consumers can and do shift their purchases between the two countries relatively
easily. Third, the value of a typical purchase is low relative to the cost of travel, so the
demand effects of cross-border shopping are confined to border counties. Together, these
imply that we can use observations from these industries in interior counties to control for
unobserved common cost shocks and thereby identify the demand-shifting effects of real
exchange rates. Our own experience as cross-border shoppers suggests that Eating Places
(SIC 5812) and Drinking Places (SIC 5813) share these characteristics. We restrict our

5

empirical analysis to these four retail trade industries.

II

Data and Estimation

This section describes the data we use, presents our panel-data VAR model, and discusses
the GMM procedure we use for its estimation. We begin with the data.

A

Observations of Retail Trade Industries

Our observations of retail trade industries come from the United States Census’ annual
publication, County Business Patterns (CBP ). We construct our data set from twenty years
of this publication, from 1977 through 1996. We focus on counties in the ten contiguous
states that border Canada so that the sample’s interior counties are as otherwise as similar
as possible to the border counties. For each retail trade industry the CBP reports each
county’s mid-March employment and the total number of establishments with employment
during the year, among other variables. From these observations, we construct for each
industry
(1)

yit =

·

ln Nit ln Ait

¸0

,

where Nit is the number of stores operating at any time during the year divided by the 1990
population of county i (establishments), and Ait is average number of employees at those
stores (average employment).
Our data set is incomplete because the Census withholds the employment information
for any county-industry observation where that datum may disclose information about an
individual producer. The Census does not reveal how it determines which observations must
be withheld, but these disclosure cases tend to occur in counties with small populations and
few establishments. To produce a balanced panel of employment observations across counties,
we use data in the CBP on each state’s employment and the number of establishments

6

by employment size class to forecast and replace the withheld observations. This paper’s
technical appendix describes this data replacement procedure in greater detail.
The counties on the U.S.-Canada border range greatly in size. It is unrealistic to expect
any parametric model to describe the evolution of both oligopolies in rural counties and
monopolistically competitive industries in urban areas, so we confine our analysis to counties
with relatively large numbers of establishments using two selection criteria. First, we consider
counties with populations greater than 20, 000 people, as measured in the 1990 decennial
census. There are 256 such counties in the ten contiguous border states, 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, 1.2% of our county-industry-year observations have imputed
employment data. As noted above, disclosure withholding primarily affects counties with
few producers, so our resulting sample is of unconcentrated industries.2
Our county selection criteria produce different samples for each industry we consider.
Table 1 provides summary statistics for each industry’s sample of counties.3 Its first column
2

Our data set also omits a handful of county-industry records because of apparent clerical errors in

the CBP data. The data file and printed CBP publication both contain observations of employment for
counties in some years that are extremely high. In these observations, the CBP reports the existence of a
extraordinarily large establishment in the county, and the reported employment far exceeds its values in the
data set’s other years. For observations from Food Stores, we have replaced these employment observations
with their values in the Bureau of Labor Statistics’ Covered Employment and Wages (ES-202) data based
on unemployment insurance records. In the other three industries, all observations from a county-industry
pair with one of these erroneously high employment observations are deleted from our final data set. This
results in the loss of three interior counties in Eating Places, two interior counties in Drinking Places, and
five counties in Gasoline Service Stations. Two of that industry’s five lost counties are border counties. See
this paper’s technical appendix for more information regarding this data replacement.
3
The statistics in Table 1 use the raw establishment counts from the CBP. These have not been scaled
by the county’s 1990 population.

7

reports the number of counties included in the 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. All 256 counties are in our sample
for Food Stores. The sample for Gasoline Service Stations excludes 5 counties, two of which
border Canada. The samples for Eating Places and Drinking Places exclude 14 and 23
counties. For each of these industries, five of the excluded counties are border counties.
The first sample quartiles of average establishment counts indicate the extent to which
our selection procedures leave relatively unconcentrated industries. 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 11.5. It appears that our county selection procedure
produced a sample of unconcentrated industries.
To assess how variations in the number of establishments and their average employment
each contribute to retail trade industries’ county-specific 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
of these standard deviations for each retail trade industry separately for border and interior
counties. In practice, these medians are close to their corresponding means. Relative to
many aggregate time series, these median standard deviations are quite high. For interior
counties, the lowest are in Eating Places, 0.09 for establishments and 0.10 for average payroll.
Drinking Places has the highest median standard deviations, 0.17 and 0.22 respectively.
Overall, establishments’ median standard deviations are not much lower than those of average
employment, indicating that these industries’ structures are far from rigid. The median
standard deviations for border counties do not differ substantially from those of interior
counties.
Figure 2 provides a visual impression of our data for one industry, Gasoline Service
Stations. Its left panel plots the logarithm of the number of establishments in all of our
sample’s border and interior counties, and its right panel plots the logarithm of these two

8

groups’ average employment. Both panels also contain the logarithm of the relative price of
gasoline between the U.S. and Canada, and all of these series have been normalized so that
their values in 1977 equal zero.
Between 1977 and 1981, the relative price of gasoline fell 44%. Establishment counts fell
much more rapidly in border counties over this period. There were 30% fewer establishments
in border counties in 1981 than there were in 1977, and the corresponding number for interior
counties is 20%. In contrast, average employment in border and interior counties were nearly
identical for these five years. Thus, it appears that retail gasoline industries in border counties
shrank and recovered through this period by adjusting net entry, leaving establishments’
average size constant. Between 1985 and 1991, when gasoline became relatively cheap in the
U.S., the number of establishments in border counties grew by approximately 10%, while
the number in interior counties shrank 3%. Average employment grew in both border and
interior counties through this period, but it grew by much more (40% versus 20%) in border
counties. Overall, Figure 2 shows that changes in both average establishment size and in
the number of establishments were used in border counties’ retail gasoline industries to
accommodate the demand shifts due to cross-border shopping. Movements in the number
of establishments were particularly important during the period of inexpensive Canadian
gasoline.

B

International Relative Prices

The international relative price of gasoline used in Figure 2 equals the ratio of the two
countries’ consumer price indices for gasoline multiplied by their nominal exchange rate.
That is
(2)

rt =

pCt
nt ,
pUt

where pCt and pUt are the two countries’ national-level price indices and nt is the price of
a Canadian dollar in U.S. dollars. Hence, an increase in the real exchange rate reflects an
9

depreciation from the U.S. perspective. We constructed our measures of international relative
prices for the other three industries in a similar fashion using industry-specific consumer price
indices.4 Table 3 lists the U.S. and Canadian CPI series used to construct the relative price
series for each of the four industries we consider.
The first two columns of Table 4 report the sample standard deviation and first autocorrelation 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 between 0.07 and 0.09. The standard deviation of the relative price of Gasoline is much higher
than this, 0.21. Unsurprisingly, the relative price series are all highly persistent, with first
order autocorrelations between 0.75 and 0.88. Table 4’s final column reports the contemporaneous correlation between each industry’s relative price series and that constructed with the
aggregate CPI’s for all goods less energy. The relative prices for Eating Places and Drinking
Places are both highly correlated with this aggregate real exchange rate. The relative prices
of food purchased at stores and gasoline have somewhat lower correlations.

C

Canadian Market Size

Exposure to Canadian shoppers and competitors differs across border counties. For example,
the number of one-day trips by Canadians returning from Whatcom County, Washington
and returning from Niagara County, New York during 1990 were 13,414,110 and 7,274,940
respectively. The populations of those counties in that year were 127,780 and 220,756. This
suggests that the size of the Canadian market relative to the local market was much larger for
Whatcom county than for Niagara county. Accordingly, we expect retail activity to respond
more to real exchange rate changes in Whatcom county.
Our model accounts for these observable differences across border counties by specifying
the effect of rt on yit to be a function of the share of customers for county i’s retailers that
are Canadian in a typical year. If we let SiU be the population of county i and let SiC be
4

For Drinking Places, relative price data is not available until the third year of our sample.

10

the Canadian population “close” to county i, then this share is
(3)

si =

SiC
.
SiU + SiC

For interior counties, we define SiC and si to equal zero. This measure 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 act as either customers or competitors.5
Measuring SiC for border counties is not straightforward, because there is no natural or
political geographic partition of Canada that indicates which Canadians are potential crossborder shoppers for county i. It is possible to measure the number of potential cross-border
shoppers as the number of Canadians living within a particular distance of county i, but
this measure is unsatisfactory because it does not account for potential geographic obstacles
to travel. 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 shopping 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 for that county. Using interview data from border crossing points,
Statistics Canada tabulates the number of U.S. and Canadian travelers 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 travelers’
identities, so an individual making multiple trips to or from Canada in a year will contribute
to the count of travelers on each trip. This data is available from 1990 through 1999. We
average the data across these years to measure the average annual number of U.S. and
Canadian travelers for county i, which we denote with TiU and TiC .
To construct a measure of SiC based on TiC , we assume that the average number of
5

In Campbell and Lapham (2001), we present a simple two-country, two-county model of cross-border

shopping with free entry in which the elasticities of average store size and the number of stores in the U.S.
county with respect to the real exchange rate were proportional to this proposed ideal measure of si .

11

trips taken per consumer, ψ, is constant across locations. Given a value for ψ, we can then
measure SiC with TiC /ψ. The resulting measure of si is
(4)

si =

TiC
.
ψSiU + TiC

As (4) makes clear, the problem of choosing ψ is one of expressing county i’s population in
units of travelers. For our baseline measure of si , we assume that all U.S. travelers entering
Canada for one-day trips from county i are residents of that county, and use the average of
TiU /SiU across border counties to measure ψ. The resulting value of ψ is 7.49. Across the
nineteen border counties, the mean and standard deviation of this baseline measure of si are
0.60 and 0.27. In Section III we examine the implications of measuring si differently.

D

The Empirical Model

Our empirical model provides a framework for using our observations to estimate the demandshifting effects of real exchange rate movements. The specific autoregressive equation we
estimate is
yit = αi + µt + Λyit−1 + β 0 (si × et ) + εit .

(5)

In (5), αi is a random county-specific intercept, µt is a time-specific effect common to all
counties,
(6)

et =

·

ln rt ln rt−1

¸0

is a vector containing the current and lagged exchange rate, εit is a disturbance term with
(7)

E [εit ] = 0,

and Λ and β are (2 × 2) matrices of unknown coefficients.6
6

The fixed effects in (5) allow us to use unscaled observations on the number of establishments rather than

the per capita measure we use. We chose the latter specification, however, because the GMM estimation
procedure described below treats αi as a component of the model’s error rather than as a parameter to be
estimated. Scaling establishments by population reduces the overall error variance.

12

The time-specific intercepts, µt , capture the effects of economy-wide demand and cost
shocks that affect all counties’ equally. A structural shock that influences the real exchange rate will affect an interior county’s industry entirely through changing µt . The term
β 0 (si × et ) in (5) captures the additional demand-shifting effects of this shock on a border
county.
D.1

GMM Estimation

The estimation of panel-data vector autoregressions similar to (5) without the explanatory
variables si × et is a well-studied problem. To estimate (5) we use a GMM estimator based
on Blundell and Bond (1998) which uses moment conditions derived from the lack of serialcorrelation in εit and an assumption that yit is mean-stationary. To apply these moment
conditions, we assume that the roots of |I − ΛL| lie outside of the unit circle and that if
si = 0 and t 6= τ , then
(8)

E [εitεiτ ] = 0.

That is, for an interior county εit is the fundamental error (in the sense of the Wold decomposition theorem) for yit − (I − ΛL)−1 µt . We furthermore assume that for interior counties
(9)

E [αi ] = 0.

Given the presence of µt in (5), this is only a normalization.
We restrict the assumption of serially uncorrelated disturbance terms in (8) to interior
counties, because county-specific shocks might cause the real exchange rate between a particular U.S. border county and its Canadian counterpart to persistently deviate from the
real exchange rate measured using national level price indices. Such deviations contribute
to the error term in (5) for that border county, causing (8) to fail. Similarly, the time-series
averages of establishments per capita and average employment in border counties may differ
systematically from their counterparts in interior counties, violating (9).

13

The appropriate moment conditions used by our GMM estimator are
E [I {si = 0} ∆εit yit−τ ] = 0, t = 3, . . . , T, t > τ ≥ 2,

(10)
(11)

E [I {si = 0} (αi + εit ) ∆yit−1 ] = 0, t = 3, . . . , T,

(12)

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

Taken together, the moment conditions in (10), (11), and (12) are more than sufficient for
identifying and estimating the 4 autoregressive parameters and the 2 (T − 1) year-specific
intercepts for T = 20.7 However, these conditions clearly leave β unidentified. Because (7)
applies to border counties, it must be the case that
(13)

E [∆εit si ] = 0, t = 3, . . . , T.

These 2 (T − 2) moment conditions identify β. The GMM estimator we use is based on the
moment conditions in (10), (11), (12), and (13). 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 (12), and (13).
D.2

Comparison with Difference-in-Differences Estimation

Although we estimate Λ, β, and the values of µt jointly, it is possible to estimate Λ and µt
using data from only interior counties and the moment conditions (10), (11), and (12). These
estimates can then be substituted into a second stage GMM estimator that uses only data
from border counties and (13) to estimate β. Considering such a sequential estimator clarifies
the relationship between the GMM procedure we use and the more familiar difference-indifferences scheme.
If we use (5) to replace ∆εit in (13), the resulting moment conditions are

7

E [(∆yit − Λ∆yit−1 − ∆µt − βsi ∆et) si ] = 0, t = 3, . . . , T.

The derivation of (11) requires an additional assumption: The initial value, yi1 − (I − Λ)−1 αi must have

zero covariance with αi . This paper’s technical appendix discusses this assumption and other aspects of the
estimation procedure in greater detail. See also Blundell and Bond (1998).

14

The second-step GMM estimator of β replaces Λ and ∆µt with their estimated values from
the first step, Λ̂ and ∆µ̂t ,and makes the sample analogues of the resulting approximate
moment conditions as close to zero as possible.
The relationship between our estimator and difference-in-difference estimators can be
most easily seen by considering the case where T = 3 and lagged real exchange rates are
excluded from (5), so that et equals ln rt . In this case, the GMM estimator is simply that
obtained from regressing ∆yi3 − Λ̂∆yi2 − ∆µ̂3 on si ∆ ln r3.
³
´
P
∆ ln r3 N
s
−
Λ̂∆y
−
∆µ̂
∆y
i3
i2
3
i=1 i
(14)
β̂ =
2 PN
2
(∆ ln r3)
i=1 si

If we dismissed the possibility that yit displays autocorrelation, then we could constrain Λ̂
to equal zero and choose µ
bt to satisfy the sample analogue of (12). The resulting value of µ
bt

equals the sample average of yit across interior counties. If we furthermore redefined si to

be a simple indicator variable that equaled one for all border counties, then the expression
for β̂ in (14) would reduce to the difference in the growth rates of ∆yi3 between border and
³³P
´ P
´
N
N
interior counties scaled by ∆ ln r3 ,
s
∆y
s
−
∆b
µ
/
i3
3 /∆ ln r3 . This correi=1 i
i=1 i

sponds exactly to the difference-in-differences estimator used by Card and Krueger (1994)
in which the border counties play the role of the treatment group and the interior counties

serve as the control group. In this sense, our GMM estimator can be viewed as an extension
of the difference-in-differences estimator that accounts for serial correlation in the dependent
variable and observable heterogeneity of individuals’ treatment effects.

III

Estimation Results

Our baseline empirical analysis for the four industries we consider produces estimates of eight
autoregressive equations’ parameters. 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, β, and summarize our estimates of
Λ and µt .
15

A

Food Stores

Table 5 presents the GMM estimates of Λ and β in (5) for Food Stores. 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. Figure 3 plots the estimates of µt along with the logarithm of the
real exchange rate for that industry.
The estimated elements of Λ indicate that both the number of establishments in a county
and their average employment are persistent time series. Its diagonal elements are both large
and positive, while its off-diagonal elements are much smaller and statistically insignificant.
The other three industries’ estimated autoregressive coefficients are very similar to Food
Stores’, with the notable exception that the coefficient on lagged establishments in the average employment equation is positive and statistically significant in the other three industries.
Turning to estimates of the time-specific effects depicted in Figure 3, we note that the
estimates for establishments and the estimates for average employment have a strong negative
comovement with each other. The figure also indicates that the estimates of µt covary with
the real exchange rate, at least until the implementation of the FTA in 1989. This suggests
that movements in these time-specific effects may be correlated with disturbances associated
with real exchange rate movements. To assess this covariance more formally, we regressed
the estimated coefficients against the current and lagged real exchange rate’s logarithm. We
could not reject the null hypothesis that the real exchange rate had no power to explain
the estimates of µt . This was also the case when we repeated this procedure for Eating
Places and Drinking Places, but the real exchange rate for Gasoline Service Stations does
help predict the estimates of µt for that industry.
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. The estimates in Table 5 indicate that in the Food Stores industry, the number
16

of establishments responds to movements in the relative price of food purchased from stores
after one year. In the establishments equation, the coefficient multiplying si × ln rt equals
−.087 and is not statistically significant while that on si × ln rt−1 equals 0.165. This latter
estimate has the expected sign and is statistically significant at the 5% level. The Wald
exclusion test statistic for the establishments equation equals 5.93, which has a probability
value of 0.052. The individual coefficient estimates for the average employment equation are
not statistically significant at conventional levels. However, the Wald exclusion test statistic
for this equation equals 10, indicating that the real exchange rate affects Food Stores’ average
employment at a very high level of confidence.
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 relative price.
Figure 4 displays these impulse response functions over a ten-year horizon. Its top panel
plots the response of ln Nit , whereas its bottom panel plots that 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 and first autocorrelation of
ln rt equal their sample values. 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 uncertainty regarding the model parameters Λ and β, but they do not reflect uncertainty about the true process for ln rt . When calculating these impulse response
functions, we do not allow υt to influence µt at any horizon. Thus, they reflect only the
demand-shifting effects of a real exchange rate shock arising from cross-border shopping.
Both impulse response functions in Figure 4 display little contemporaneous effect of exchange rates on either variable, but eventually real depreciations (from the U.S. perspective)
affect both of them positively. As the point estimates in Table 5 indicate, the initial response
17

of establishments to a real exchange rate shock is small and negative. At a horizon of one
year, the impulse response function crosses zero. Although neither of these estimated effects
is individually statistically significant, the Wald test of the hypothesis that they both equal
zero has a probability value of 0.057.8 The response of establishments reaches its peak value
of 0.74% six years after the initial shock. Average employment’s impulse response function
builds more rapidly. It equals 0.72% after one year and reaches its peak of 0.90% after two
years. It appears that the Food Stores industry responds to a shock to its relative price by
changing both its average establishment size and the number of establishments.

B

Other Industries

Table 6 reports the estimates of β and the exclusion tests for all four of the industries we
consider, and Figures 5, 6, and 7 graph the other industries’ impulse response functions.
Just as with Food Stores, the responses in these figures are to a persistent real exchange rate
shock from an autoregression parameterized to match the reported statistics in Table 4.
The results for Gasoline Service Stations are similar to those for Food Stores. In particular, the lagged gasoline-based real exchange rate has a positive 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 after one year.
The Wald test rejects the exclusion restriction for establishments at the 1% level. Exclusion of the real exchange rates from the average employment equation cannot be rejected at
any conventional significance level. However, the point estimates and Wald test statistic for
that equation are not very small; so it may be premature to conclude that Gasoline Service
Stations’ average employment does not respond to real exchange rate shocks. 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 employment rises more than 1%,
8

We have conducted these tests for all of the impulse-response functions reported in this paper. These

test statistics’ values are nearly identical to the corresponding statistics in Table 6, discussed below.

18

while the number of establishments falls very slightly. Thereafter, the increase in average
employment persists as the number of establishments rises. After five years, the number of
establishments has increased by approximately 2%.
For Eating Places, fluctuations in the number of establishments play a central role in its
responses to real exchange rate disturbances. Although neither of the estimated coefficients
in the establishments equation are individually significant, the Wald test’s probability value
is relatively low, 0.026. The corresponding Wald test statistic for the average employment
equation has a very high probability value. Establishments’ impulse-response function hits
its peak value, 0.86%, two years after the shock, and this response is statistically significant
at the 5% level. Average employment’s response is small and statistically insignificant at
all horizons. Apparently, long-run industry analysis, in which the free-entry/zero-profit
condition determines producers’ sizes and changes in the number of producers accommodate
shifts in demand, characterizes Eating Places’ short-run fluctuations. The period of time
over which the number of producers in Eating Places is fixed is at most one year.
Our final industry is Drinking Places. These estimates are quite different from those
of the other industries. The standard errors of the estimated coefficients for the establishments equation are much larger than in the other industries we consider. Furthermore, the
coefficient on the contemporaneous real exchange rate in the average employment equation
is 0.597. This is by far the largest absolute value of any of our estimated coefficients, and
it is statistically significant at the 10% level. The Wald exclusion test also indicates that
real exchange rate fluctuations have a strong impact on the average employment of Drinking
Places in border counties. The response of establishments to the shock is not statistically
significant at any horizon. In contrast, Drinking Places’ average employment rises nearly 3%
in the period of the shock, and it slowly falls back to its pre-shock level.

19

C

Alternative Canadian Market Size Measures

The construction of si required a choice of ψ in (4), so we wish to examine the implications
of taking alternative approaches to its measurement. We have also calibrated ψ based on
Ford’s (1992) survey of Canadian consumers’ cross-border shopping habits. The calibrated
value of ψ is much larger than our baseline choice, 17.75. The empirical results we obtain
using it are nearly identical to our baseline results. We do not report them here.
Table 7 reports the estimates obtained from two other measures of si . The table’s upper
panel reports the result of using the fraction of total one-day trips across the border at
county i that are made by Canadians:
si =

TiC
.
TiU + TiC

This trips-based measure requires no choice of ψ, but it replaces SiU with a noisy proxy,
TiU . The table’s lower panel reports the results of setting si equal to the fraction of local
residents who are Canadian:
si =

SiC
,
SiU + SiC

where SiC is measured using Canada’s 1991 census as the number of Canadians living within
fifty miles of county i’s central point, as defined by the U.S. Census. As we noted above
in Section II, this population-based measure takes no account of the potential difficulties in
traveling between these Canadians’ homes and county i.
In spite of these potential shortcomings, the results from these two alternative measures
of si are similar to each other and to our baseline results. The point estimates from using the
trips-based measure are comparable to our baseline estimates, and the pattern of inference is
identical to that based on the test statistics in Table 6. Using the population-based measure
generally lowers the measured impact of real exchange rates. With two exceptions, in the
establishments equation for Food Stores and in the average employment equation for Gasoline
Service stations, the point estimates and the Wald test statistics tend to be closer to zero.
However, these estimates still indicate that establishments in Food Stores, Gasoline Service
20

Stations, and Eating Places, respond within one year to real exchange rate disturbances.

D

OLS Estimation

To gain a sense of how our results depend on our GMM estimation procedure, Table 8 reports
results from estimating a version of our model using ordinary least squares. These estimates
are only consistent as the number of time periods in the sample becomes large for a fixed
number of counties, an assumption that poorly characterizes our sample of 256 counties over
20 years. Nevertheless, the estimated coefficients on the real exchange rate are not far from
those reported in Table 6. The standard errors are comparable to those from the GMM
estimation, and the inferences based on these exclusion tests are similar to those that use
the GMM based tests. However, the exclusion tests’ probability values rise to 0.220 and
0.092 for the coefficients in Food Stores’ and Eating Places’ establishments equations, while
the test’s probability value falls to 0.026 for Gasoline Service Stations’ average employment
equation. It appears that our results manifest themselves even in a simple OLS regression.

E

Canada-U.S. FTA Subsample Estimation

The FTA substantially integrated the market for wholesale gasoline, so we may expect that
our model’s parameters for Gasoline Service Stations changed in 1989. Although the FTA did
not completely integrate the wholesale goods markets that supply the other three industries,
the possibility that it could have affected them in a way that changes our model’s parameters
is clear. Table 9 addresses this possibility. Its top panel reports estimates of β obtained using
only data from the pre-FTA period of 1977 through 1988, and its bottom panel reports the
analogous estimates obtained from the last 8 years of our sample.
As expected, the standard errors of the subsample estimates are considerably larger than
those from the full sample. In Gasoline Service Stations, coefficient estimates for the establishment question are indeed sensitive to the subsample chosen. In the earlier sample,
the coefficient multiplying si × ln rt is close to zero, that for si × ln rt−1 is positive and not
21

statistically significant, and the Wald test statistic has a probability value of 0.068. Using
the later sample, these coefficients are −0.385 and 0.413. Both of these coefficients are statistically significant at the 5% level, but the Wald test statistic is almost exactly equal to
its value in the earlier sample. The negative and statistically significant estimate from the
later sample is difficult to interpret because it does not have the expected sign. We speculate that because wholesale gasoline is more easily arbitraged between border counties and
Canada following the FTA’s implementation, real exchange rate fluctuations after 1989 may
be associated with systematic retail cost differences between border and interior counties.
For the other three industries, there are two notable differences between the subsample
and full sample estimates. First, there is little evidence in either subsample that the number
of Eating Places responds to the real exchange rate. We attribute this to a lack of statistical
power to reject the null hypothesis in a smaller sample. Although the subsample point
estimates from that equation are similar to those from the full sample, their associated
standard errors are much larger. Second, the estimated timing of the response of the number
of Food Stores to a real exchange rate shock depends greatly on the time period used for
estimation. Using either the full sample or the post FTA period, the contemporaneous
impact of a shock to the real exchange rate on the number of Food Stores is relatively small
and negative, while its effect after one year is larger and positive. In the earlier subsample,
the contemporaneous impact equals 0.415 and is statistically significant at the 1% level.
The coefficient multiplying the lagged real exchange rate is large, negative, and statistically
significant at the 1% level. Its magnitude is such that the estimated response of the number
of establishments after one year to a completely transitory real exchange rate movement is
approximately zero.

F

Results Summary

Drinking Places conforms to the short-run/long-run dichotomy from basic microeconomic
theory. Immediately following a demand shock, activity increases at each producer, while
22

the number of producers does not change. Food Stores and Gasoline Service Stations do
not fit this familiar description of industry evolution as well, because both the number of
establishments and their average size increase following a demand shock. In Eating Places,
there is no evidence that average producer size changes after a demand shock. Instead, that
industry’s short-run dynamics better match a long-run industry analysis in which demand
only influences the number of producers.
While we find aspects of the most simple long-run analysis compelling for Eating Places’
short-run fluctuations, it is incomplete because it abstracts from size differences between
producers. Entering and exiting establishments tend to be smaller than the average continuing incumbent, so if all else is held equal an increase in entry or a decrease in exit will
tend to decrease average producer size. This suggests that our estimates of the response of
average employment to the real exchange rate may reflect both an increase in the average
size of incumbents and an increase in the number of small establishments.

IV

Conclusion

Much of the theory of industrial organization assumes that entry responds to persistent
shocks only in the long run, so that 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. Only in Drinking Places, where alcohol licensing
restrictions might present a barrier to entry, does the real exchange rate affect industry
activity without changing the number of establishments. In the other three industries we
consider, either potential entrants, potential exiters, or both respond relatively rapidly to
demand shocks. In models of perfect or monopolistic competition with instantaneous entry

23

subject to a sunk cost, demand shocks change the equilibrium decisions of potential entrants,
not those of exiting incumbents. 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.9 Thus,
our results strongly suggest that potential entrants can affect their decisions shortly after
demand shocks.
This paper’s examination of retail industries’ responses to demand shocks also sheds light
on previous empirical work that documents their responses to cost disturbances. Card and
Krueger (1994) estimate that the imposition of New Jersey’s minimum wage in 1992 actually increased employment in their sample of fast food outlets relative to a control sample
from Eastern Pennsylvania over an eight-month period. They find these employment gains
following a minimum wage increase to be at odds with the basic theoretical prediction of
downward sloping labor demand. Fast food outlets belong to one of the industries we have
considered, Eating Places. Our finding that the number of establishments serving that industry responds to demand shocks very quickly suggests that a long-run analysis may reconcile
Card and Krueger’s observations with competitive economic theory. Because the location
of the average cost curve’s minimum can either decrease, remain unchanged, or increase
following a factor price change; the effect of a minimum wage increase on an individual
producer’s long-run size is ambiguous. To the extent that greater output is associated with
greater employment, Card and Krueger’s finding that employment increased in their panel
of incumbent producers can be interpreted as an increase in the location of the average cost
curve’s minimum. In this interpretation, industry-wide output and employment fell following the minimum wage increase because a drop in entry reduced the number of producers.
Determining how well this theory characterizes Eating Places’ responses to minimum wage
changes is on our agenda for future research.10
9

See, for example, Campbell and Fisher (1996). They present a perfectly competitive industry dynamics

model with idiosyncratic producer risk, sunk costs of entry, and endogenous exit. In that model, demand
shocks only contemporaneously impact the number of entrants.
10
Card and Krueger (1994) discuss this possibility and examine it by estimating the relationship between

24

Our results also present a challenge for the branch of international macroeconomics which
focuses on the puzzle of persistent deviations from purchasing power parity (PPP), such as
Betts and Devereux’s (2000) and Chari, Kehoe, and McGrattan’s (2002) general equilibrium
analyses. The failure of consumer prices to respond to nominal exchange rate movements
and the infrequency with which individual retailers change their prices suggest that sticky
nominal retail prices play a central role in generating and maintaining deviations from PPP.
Our observation that real exchange rate fluctuations affect the number of establishments
serving border counties’ retail trade industries presents two difficulties for the view that
deviations from PPP arise from retail-level price stickiness. First, it is difficult to imagine
that some retailers’ prices are fixed for a longer period than it takes to open or close an entire
establishment in their industry.11 Second, sticky prices are by definition those of incumbent
producers. Because an incumbent’s artificially low price reduces the payoff to entry, periods
in which U.S. retailers’ prices are low relative to those of Canadian retailers should not be
periods of increased entry in the U.S. Our future research will assess the severity of these
difficulties for models of real exchange rates and monetary non-neutrality that rely on sticky
prices.

minimum wage changes and the openings of new McDonald’s restaurants. They find no significant effect
of minimum wage changes on McDonald’s entry, but McDonald’s may not be representative of potential
entrants.
11
Bils and Klenow (2002) measure the average duration of retailers’ prices for a variety of items. Those
sold in Eating Places and Drinking Places have average durations of between 7 and 10 months, while the
durations of those sold by Food Stores and Gasoline Service Stations are between 1 and 2 months.

25

References
Baumol, William J., John C. Panzar, and Robert D. Willig. (1982) Contestable Markets and
the Theory of Industry Structure. New York, Harcourt Brace Jovanovich.
Betts, Caroline and Michael Devereux. (2000) Exchange Rate Dynamics in a Model of
Pricing-to-Market. Journal of International Economics 50, 215-244.
Bils, Mark and Peter J. Klenow. (2002) Some Evidence on the Importance of Sticky Prices.
NBER Working Paper 9069.
Blundell, Richard and Stephen Bond. (1998) Initial Conditions and Moment Restrictions in
Dynamic Panel Data Models. Journal of Econometrics, 87(1), 115—143.
Campbell, Jeffrey R. and Jonas D.M. Fisher. (1996) Aggregate Employment Fluctuations
with Microeconomic Asymmetries. NBER Working Paper 5767.
Campbell, Jeffrey R. and Beverly Lapham. (2001) Real Exchange Rate Fluctuations and
the Dynamics of Retail Trade Industries on the U.S.-Canada Border. NBER Working Paper
8558.
Card, David and Alan Krueger. (1994) Minimum Wages and Employment: A Case Study
of the Fast Food Industry in New Jersey and Pennsylvania. American Economic Review,
84(4), 772-793.
Chari, V.V., Patrick J. Kehoe, and Ellen R. McGrattan. (2002) Can Sticky Price Models
Generate Volatile and Persistent Real Exchange Rates? Review of Economic Studies, 69(3),
533—563.
Engel, Charles. (1999) Accounting for U.S. Real Exchange Rate Changes. Journal of Political Economy, 107, 507-538.
Engel, Charles and John Rogers. (1996) How Wide is the Border? American Economic
Review, 86(5), 1112-1125.

26

Ford, Theresa. (1992) International Outshopping Along the Canada-United States Border:
The Case of Western New York. Canada-United States Trade Center Occasional Paper No.
12, State University of New York at Buffalo
New Brunswick, Government of. (1992) A Discussion Paper on Cross Border Shopping.
Fredericton: Department of Economic Development and Tourism.
Ontario, Government of. (1991) Report on Cross-Border Shopping. Toronto: Standing
Committee on Finance and Economic Affairs.
Taylor, Teresa. (1988) The U.S.-Canada Free Trade Agreement: Winners and Losers in the
Northeast-Midwest Region. Northeast Midwest Institute Center for Regional Policy.
Wilson, Arlene. (1993) The Canada-U.S. Free Trade Agreement: Lessons for the NAFTA.
Congressional Research Service Report for Congress 93-153 E.

27

Table 1: Quartiles from Sample Counties of Average Establishment Counts
Counties(i)

First Quartile(ii)

Median(ii)

Third Quartile(ii)

Food Stores

256

27.0

45.5

94.8

Gasoline Service
Stations

251

18.5

28.0

51.5

Eating Places

242

39.0

73.8

152.0

Drinking Places

233

11.5

18.0

38.0

Industry

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.

28

Table 2: Median Within-County Standard Deviations(i)

Industry

Establishments
Average Employment
Interior Counties Border Counties Interior Counties Border Counties

Food Stores

0.11

0.09

0.13

0.11

Gasoline Service
Stations

0.13

0.16

0.15

0.20

Eating Places

0.09

0.08

0.10

0.11

Drinking Places

0.17

0.15

0.22

0.20

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 those regressions
were tabulated for each county. The values reported in the table are the medians, across
interior counties and across border counties, of these statistics. See the text for further
details.

29

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

U.S. CPI(i)

Canadian CPI(i)

Food Stores

Food at Home

Food Purchased from Stores

Gasoline Service Gasoline
Stations

Gasoline

Eating Places

Food Away from Home Food Purchased from Restaurants

Drinking Places

Alcoholic Beverages
Away from Home

Served Alcoholic Beverages

Note: (i) For each industry, the column headed U.S. CPI reports the name of the U.S.
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.

Table 4: Summary Statistics for Relative Price Series(i)

Industry

Correlation with Aggregate
Standard Deviation First Autocorrelation
Real Exchange Rate

Food Stores

0.075

0.87

0.63

Gasoline Service
Stations

0.214

0.88

0.47

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 19771996. 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.
30

Table 5: Estimates for SIC 54, Food Stores(i),(ii)
Dependent Variable
Establishments Average Employment
0.788∗∗∗
(0.026)

−0.078
(0.047)

Lagged Average Employment,
ln Ait−1

0.015
(0.020)

0.496∗∗∗
(0.045)

Current Real Exchange Rate,
si × ln rt

−0.087
(0.059)

0.036
(0.129)

Lagged Real Exchange Rate,
si × ln rt−1

0.165∗∗
(0.072)

0.140
(0.149)

Exclusion Test for
Real Exchange Rate(iii)

5.93
(0.052)

10.00
(0.007)

Lagged Establishments,
ln Nit−1

Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each
coefficient estimate. (ii) The superscripts ∗, ∗∗, and ∗ ∗ ∗ indicate that the estimate is
statistically 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.

31

Table 6: Baseline Estimation Results(i)(ii)
Industry

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

Average Employment
si × ln rt si × ln rt−1 χ2 Test(iii)

Food Stores

−0.087
(0.059)

0.165∗∗
(0.072)

5.93
(0.052)

0.036
(0.129)

0.140
(0.149)

10.00
(0.007)

Gasoline Service
Stations

−0.041
(0.042)

0.127∗∗
(0.052)

9.30
(0.010)

0.128
(0.089)

−0.024
(0.062)

3.38
(0.184)

Eating Places

0.111
(0.092)

0.041
(0.071)

7.32
(0.026)

0.035
(0.097)

−0.018
(0.092)

0.14
(0.931)

Drinking Places

0.145
(0.147)

−0.056
(0.144)

1.41
(0.493)

0.597∗
(0.325)

−0.098
(0.292)

6.63
(0.036)

Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each
coefficient estimate. (ii) The superscripts ∗, ∗∗, and ∗ ∗ ∗ indicate that the estimate is
statistically different from zero at the 10%, 5%, 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.

32

Table 7: Estimation Results using Alternative Sensitivity Measures(i)(ii)
si =Canadian Trips/Total Trips

Industry

si × ln rt

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

Average Employment
si × ln rt si × ln rt−1 χ2 Test(iii)

Food Stores

−0.101
(0.068)

0.174∗∗
(0.081)

4.88
(0.087)

0.075
(0.156)

0.121
(0.169)

8.32
(0.016)

Gasoline Service
Stations

−0.042
(0.044)

0.132∗∗
(0.056)

7.55
(0.023)

0.130
(0.094)

−0.021
(0.066)

3.13
(0.209)

Eating Places

0.110
(0.131)

0.050
(0.093)

6.85
(0.033)

0.051
(0.113)

−0.027
(0.108)

0.23
(0.891)

Drinking Places

0.184
(0.194)

−0.100
(0.190)

1.24
(0.537)

0.809∗∗
(0.338)

−0.161
(0.306)

8.59
(0.014)

si =Canadian Population/Total Population

Industry

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

Average Employment
si × ln rt si × ln rt−1 χ2 Test(iii)

Food Stores

−0.133∗
(0.070)

0.223∗∗
(0.087)

7.42
(0.024)

−0.040
(0.108)

0.017
(0.115)

0.26
(0.879)

Gasoline Service
Stations

0.015
(0.034)

0.031
(0.048)

4.11
(0.128)

0.127∗∗
(0.055)

−0.009
(0.054)

10.02
(0.007)

Eating Places

0.053
(0.081)

0.034
(0.066)

6.66
(0.036)

−0.043
(0.070)

0.088
(0.076)

1.47
(0.480)

Drinking Places

−0.030
(0.104)

0.112
(0.100)

2.93
(0.231)

0.206
(0.208)

−0.135
(0.189)

1.00
(0.607)

Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each
coefficient estimate. (ii) The superscripts ∗, ∗∗, and ∗ ∗ ∗ indicate that the estimate is
statistically different from zero at the 10%, 5%, 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.

33

Table 8: OLS Estimation Results(i)(ii)
Industry

si × ln rt

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

Average Employment
si × ln rt si × ln rt−1 χ2 Test(iii)

Food Stores

−0.127
(0.092)

0.190
(0.110)

3.02
(0.220)

0.075
(0.110)

0.088
(0.136)

4.88
(0.087)

Gasoline Service
Stations

−0.051
(0.062)

0.146∗∗
(0.062)

14.46
(0.000)

0.127
(0.095)

−0.009
(0.093)

7.28
(0.026)

Eating Places

0.133
(0.082)

0.006
(0.093)

4.78
(0.092)

0.022
(0.149)

0.034
(0.132)

0.38
(0.831)

Drinking Places

0.151
(0.174)

−0.054
(0.178)

0.64
(0.53)

0.622∗∗
(0.295)

−0.074
(0.328)

12.52
(0.002)

Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each
coefficient estimate. (ii) The superscripts ∗, ∗∗, and ∗ ∗ ∗ indicate that the estimate is
statistically different from zero at the 10%, 5%, and 1% levels. (iii) This test statistic has
an asymptotic χ2 distribution with 2 degrees of freedom as T → ∞. Probability values from
this distribution appear in parentheses below each test statistic. See the text for further
details.

34

Table 9: Subsample Estimation Results(i)(ii)
Before the FTA, 1977—1988
Establishments
si × ln rt−1 χ2 Test(iii)

Average Employment
si × ln rt si × ln rt−1 χ2 Test(iii)

Industry

si × ln rt

Food Stores

0.415∗∗∗
(0.140)

−0.346∗∗∗
(0.155)

9.64
(0.008)

0.129
(0.185)

0.403∗
(0.231)

13.01
(0.001)

Gasoline Service
Stations

−0.005
(0.056)

0.080
(0.082)

5.37
(0.068)

0.139
(0.103)

0.017
(0.052)

4.73
(0.094)

Eating Places

0.076
(0.185)

−0.020
(0.121)

0.21
(0.899)

0.107
(0.172)

−0.088
(0.195)

0.41
(0.816)

Drinking Places

0.305
(0.277)

−0.255
(0.395)

1.23
(0.541)

0.774
(0.519)

0.227
(0.473)

4.58
(0.101)

After the FTA, 1989—1996

Industry
Food Stores

Establishments
si × ln rt si × ln rt−1 χ2 Test(iii)
−0.097
(0.177)

Average Employment
si × ln rt si × ln rt−1 χ2 Test(iii)

0.243
(0.172)

7.14
(0.028)

0.164
(0.225)

−0.088
(0.259)

2.76
(0.252)

Gasoline Service −0.385∗∗
Stations
(0.174)

0.413∗∗
(0.177)

5.44
(0.066)

0.102
(0.246)

0.154
(0.229)

3.61
(0.165)

Eating Places

0.105
(0.116)

0.153
(0.200)

2.79
(0.248)

−0.213
(0.146)

0.083
(0.171)

2.28
(0.320)

Drinking Places

−0.125
(0.222)

0.285
(0.334)

1.12
(0.571)

0.599
(0.443)

−0.126
(0.492)

4.70
(0.095)

Notes: (i) Heteroskedasticity-consistent standard errors appear in parentheses below each
coefficient estimate. (ii) The superscripts ∗, ∗∗, and ∗ ∗ ∗ indicate that the estimate is
statistically different from zero at the 10%, 5%, 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.

35

Real Exchange Rate
(1977=1)
Canadian Same-Day Trips
(Millions)
U.S. Same-Day Trips
(Millions)
10

15

20

25

30

60
55
50
45
40
35
30
25
20
15

.75

.8

.85

.9

.95

1

1976

1976

1976

1980

1980

1980

1984

1984

1984

Year

1988

1988

1988

1992

1992

1992

1996

1996

1996

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

-.5

-.5
Year

-.25

-.25
1992 1996

0

0

1988

.25

.25

1984

.5

.5

1980

.75

.75

1976

1

1

Border Counties
Interior Counties
Relative Price of Gasoline

Establishments

Logarithm
(1977=0)

1976

1980

1984

Year

1988

1992 1996

Border Counties
Interior Counties
Relative Price of Gasoline

Average Employment

Figure 2: Gasoline Service Stations in Border and Interior Counties

Figure 3: Estimated Coefficients on Time Dummies for SIC 54: Food Stores

0.2

Real Exchange Rate
Establishments, µt
Average Employment, µt

Logarithm (1978=0)

0.15
0.1
0.05
0
-0.05
-0.1
-0.15
-0.2
1978

1980

1982

1984

1986

1988

Year

1990

1992

1994

1996

Figure 3: Impulse Response Functions for SIC 54, Food Stores

Percentage Points

Establishments
2

1
0

−1

0

1

2

3

4

5

6

7

8

9

10

8

9

10

Percentage Points

Employees/Establishment
2

1
0

−1

0

1

2

3

4

5

6

Years After Shock

7

Figure 4: Impulse Response Functions for SIC 554, Gasoline Service Stations

Establishments
Percentage Points

4
3
2
1
0
−1
−2
0

1

2

3

4

5

6

7

8

9

10

8

9

10

Employees/Establishment
Percentage Points

4
3
2
1
0
−1
−2
0

1

2

3

4

5

6

Years After Shock

7

Figure 5: Impulse Response Functions for SIC 5812, Eating Places

Percentage Points

Establishments
2
1.5
1
0.5
0
−0.5
−1
−1.5
0

1

2

3

4

5

6

7

8

9

10

8

9

10

Percentage Points

Employees/Establishment
2
1.5
1
0.5
0
−0.5
−1
−1.5
0

1

2

3

4

5

6

Years After Shock

7

Figure 6: Impulse Response Functions for SIC 5813, Drinking Places

Percentage Points

Establishments
6
5
4
3
2
1
0
−1
0

1

2

3

4

5

6

7

8

9

10

8

9

10

Percentage Points

Employees/Establishment
6
5
4
3
2
1
0
−1
0

1

2

3

4

5

6

Years After Shock

7

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