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Do State Borders Matter for U.S. Intranational Trade? The Role of
History and Internal Migration
Daniel L. Millimet
Southern Methodist University
Thomas Osang∗
Southern Methodist University
August 2005
Abstract
Empirical evidence of the impact of borders on international trade flows using the gravity equation ap-proach abounds. This paper examines the empirical relevance of state borders in U.S. interstate trade forvarious specifications of the gravity equation. We find a large and economically significant subnationalborder effect for some specifications. However, two model specifications drastically reduce (if not elimi-nate) the border effect: (i) dynamic panel specifications controlling for past levels of trade and (ii) modelsconditioning on internal migration.
JEL: C23, F14, F16, J61Keywords: Border Effect, Intranational Trade, Migration, Dynamic Panel Data Models
∗The authors thank Holger Wolf for sharing his state-to-state distance data. We also thank Nathan Balke, Charles Engel,
Tom Fomby, Russell Hillberry, Essie Massoumi, Hiranya Nath, Stephen Smith as well as seminar participants at SMU, the
Southeastern Economic Theory and International Trade Conference, and the Texas Camp Econometrics for helpful comments
and suggestions. Correspondence: Thomas Osang, Department of Economics, Southern Methodist University, Box 750496,
Dallas, TX 75275-0496, USA; Email: [email protected]; Tel. (214) 768-4398; Fax: (214) 768-1821.
1 Introduction
The importance of the border — or, alternatively, the home market — for international trade flows has been
documented in a number of empirical studies. Using a gravity equation model, McCallum [38] finds that,
even after controlling for the usual determinants of bilateral trade flows such as scale and distance, trade
between Canadian provinces is significantly larger (by a factor of 22) than cross-border trade with U.S.
states. Using post-NAFTA data for the period 1994 — 1996, Helliwell [27] finds that the border effect
declined by almost 50% compared to McCallum’s pre-NAFTA estimate. However, using Helliwell’s data
and controlling for unobserved time invariant attributes, Wall [48] estimates a U.S.-Canada border effect
that is 40% larger than that reported by McCallum. Anderson and Van Wincoop [2], relying on a more
structural specification of the gravity equation, report a border effect much smaller than McCallum. Still,
the authors claim that national borders reduce trade between Canada and the U.S. by about 44%; roughly
30% for other industrialized countries.1
Given the decline in formal barriers to trade over the recent decades, the existence of a substantial
home bias is puzzling. Obstfeld and Rogoff [40] label the border effect on trade flows one of the “six major
puzzles in international macroeconomics.”2 Even more puzzling than the existence of a large border effect
on international trade flows are recent studies, such as Wolf [50], that report significant home market effects
for trade flows at the subnational level. Wolf finds a statistically and economically significant border effect
for trade flows within the 48 contiguous U.S. states using data from the 1993 Commodity Flow Survey
(CFS) (see also [31]). Given the absence of formal and informal trade barriers (such as language or cultural
barriers) at the subnational level, Wolf suggests that other factors must account for the home bias.3 Before
1In a related literature, Engel and Rogers [16] and Parsley and Wei [42] find a substantial effect of national borders on
spatial price variation. Engel and Rogers calculate that the amount by which the border adds to price variation across
U.S. states and Canadian provinces is equivalent to a border that is 75,000 miles wide. Parsley and Wei estimate that the
U.S.-Japan border is equivalent to over 43,000 trillion miles.2One possible explanation is provided in Feenstra et al. [18]. The authors show that the home market effect is consistent
with models featuring trade in either homogeneous or differentiated goods. However, if home markets with homogeneous
goods have greater barriers to entry, one should expect a lower domestic income elasticity for exports of homogeneous goods
than of differentiated goods. Thus, the home market effect should be smaller for homogeneous goods with restricted entry, a
proposition for which the authors find empirical support.3Aside from intellectual curiosity, there are other motivations for understanding the large border effect at the U.S. sub-
national level. Back of the envelope calculations suggest that the border effect estimated in Wolf [50] implies a large loss in
welfare due to a reduction in trade. Many gravity-type models interpret the estimated border coefficient as equal to the prod-
uct of the elasticity of substitution and ad valorem border cost. As the majority of estimates of the elasticity of substitution
lie between two and ten, Wolf’s border coefficient of approximately 1.5 implies an ad valorem border cost of between 15% and
75% (see Hillberry [32] and Obstfeld and Rogoff [40] for similar calculations).
1
reaching such a conclusion, however, it is important to assess the robustness of Wolf’s findings.
Consequently, the aim of the present analysis is to expand the current literature on subnational trade
flows along several important fronts. First, we check the stability of Wolf’s [50] results over time by
estimating the author’s baseline gravity equation model using the more recent 1997 wave of the CFS.
Second, using both the 1993 and 1997 CFS data (the only years available), we estimate several extended
versions of the gravity equation that include controls for spatial price and wage variation (Bergstrand [7];
[8]). Third, in contrast to Wolf who reports cross-sectional results only (his analysis pre-dates the release of
the 1997 CFS data), we utilize the panel nature of the data to estimate a variety of models controlling for
a time invariant unobservables, as well as several straightforward dynamic specifications. Finally, building
on the literature relating international migration to cross-national trade flows (Girma and Zu [19]; Gould
[20]), we examine the possible interaction between subnational trade flows and internal migration. To this
end, we include measures of state-to-state migration (in- and outflows) as additional regressors, controlling
for the potential endogeneity of migration flows using an innovative technique proposed in Lewbel [36].
Our empirical investigation of the home bias effect on intranational trade yields several findings that
are particularly interesting and novel. To begin, our analysis reveals that the general finding in Wolf
[50] of a substantial subnational border effect is robust to a number of extensions including controls
for unobserved time invariant attributes, additional controls reflecting prices and wages, and alternative
measures of internal state distance. More importantly, though, is our finding that two specifications refute
the conclusion of a home bias effect on intranational trade.
First, incorporating migration inflows and outflows as additional (exogenous) explanatory variables to
proxy for unobserved network effects (in spirit of Rauch [43], [44]) in the static gravity equation models
controlling for time invariant unobservables diminishes or eliminates the border effect. Furthermore, we
find that each migrant (incoming and outgoing) ‘offsets’ between ten and 180 feet in terms of the distance
between states. These results are consonant with outgoing migrants increasing the demand for goods from
the state from which they left — either due to preferences or informational advantages — and incoming
migrants increasing sales to individuals in the state they formerly resided.
Second, panel models conditioning on past levels of trade also eliminate the average state border
‘width.’ This result holds when lagged trade flows are treated as exogenous (the norm in previous models
of dynamic trade flows; e.g., Anderson and Smith [5]; Eichengreen and Irwin [15]; Gould [20]), but is
even stronger when previous trade flows are treated as endogenous (using lagged exogenous covariates as
instruments). Moreover, in models incorporating both internal migration and lagged trade flows — treating
all as endogenous — we find that the border effect continues to disappear and lagged trade flows is the
dominant determinant of current trade patterns.
2
The fact that the subnational border effect disappears in the majority of specifications that include
lagged shipments and internal migration, both of which may proxy unobserved networks effects, indicates
that network ties may be a key omitted variable in many empirical specifications of the gravity equation.
This result is consistent with previous empirical studies using the gravity equation to analyze the trade
and migration issue at the international level and documenting significant effects of international migration
on export flows (Gould [20] for the U.S.; Head and Ries [24] for Canada; and recently, Girma and Yu [19]
for the U.K.). Moreover, in a recent paper, Combes et al. [12] investigate the impact of social and
business networks on trade flows between French regions. The authors also conclude that the border effect
is substantially diminished — though not eliminated — once they control for migration and inter-regional
plant connections.
The approach and findings of this paper are potentially interesting to those studying trade patterns in
other countries or regions. Similar studies for other EU countries may further shed light on the determinants
of trade patterns in general and the border effect puzzle in particular.
2 Theoretical Foundations and Empirical Methodology
As noted by Deardorff [14], the basic specification of the gravity equation — bilateral trade flows as a
function of gross output in the origin and destination country (state) as well as a measure of geographical
distance — can be derived from all major theoretical models of trade: the H-O-V model with impediments to
trade; Armington-based approaches with country-specific product differentiation (Bergstrand [7]; Anderson
[1]); and monopolistic competition models (Helpman [30]; Krugman [35]; Helpman and Krugman [29])).
Given the vast theoretical support for the gravity model, it seems appropriate to anchor our empirical
investigation of the home bias effect on subnational trade flows in the gravity equation approach.4 In
particular, we initially estimate an augmented version of the basic gravity equation. This specification
(hereafter referred to as the baseline model) is similar to the baseline model in Wolf [50]:
baseline model : ln(Shipmentsij) = α+ β1 ln(Yi) + β2 ln(Yj) + β3 ln(Dij)
+β4 ln(Remoteij) + β5 ln(Remoteji) + β6Adjacentij + β7Homei + uij (1)
where Shipmentsij is exports from state i to state j, Yi(j) is gross output in state i (j), Dij is the
geographical distance between state i and j, Adjacentij is a dummy variable equal to one for shipments
4Since the basic specification of the gravity equation is everybody’s child, it is also nobody’s child. Or, as Deardorff ([14],
p12) states: “... just about any plausible model of trade would yield something very like the gravity equation, whose empirical
success is therefore not evidence of anything, but just a fact of life.”
3
to a bordering state, and Remoteij and Remoteji are measures of how remote states i (j) and j (i) are
vis-a-vis all other states.5,6 We estimate the baseline model separately for each cross-section of data.
The expected signs for both gross output coefficients are positive as exports from state i to state j
should rise with output in the origin and the destination state, while the distance measure is expected to
have a negative effect due to greater transportation and other transaction costs affected by distance. The
two remoteness measures are anticipated to have positive coefficients as trade volume is likely to rise when
the two states are remote relative to alternative trading partners. Neighboring states are also expected to
trade more with each other, mainly due to the absence of a large alternative supplier separating the two
states (Stouffer [47]).
As in Wolf [50], the important feature of the baseline specification is the inclusion of a dummy variable
for intrastate trade, Homei. Given the absence of formal and informal trade barriers at the subnational
level, one might expect a statistically insignificant coefficient estimate on the border (or home bias) dummy.
In addition to the statistical significance of the border effect, we are also interested in its economic relevance.
The size of the home effect — the anti-log of the coefficient on the home dummy — is typically used as a
measure of the economic relevance of the border effect. We report this measure along with its p-value.
Furthermore, along the lines of Engel and Rogers [16] and Parsley and Wei [42], we also construct a measure
of the average ‘width’ of each state border. In our model, as in Parsley and Wei, the average ‘width’ is
given by D∗ [exp{−β3/β7}− 1], where D is the sample mean for distance.7 In contrast to previous studies,
we not only report the border ‘width,’ but its statistical significance as well.8
To assess the robustness of the home bias effect, we extend the static baseline model in three ways.
First, we estimate a generalized model which includes additional controls for price and wage indices. Second,
we estimate static and dynamic panel models that utilize the time series dimension of the data.9 And third,
5As in Wolf [50], Remoteij =P48
k=1,k 6=jDikGSPk
. Similarly, Remoteji =P48
k=1,k 6=iDjkGSPk
. In general, a state located in the
middle of a country will be less ‘remote’ than coastal or international border states (on average, Iowa is the least remote, while
Oregon is the most remote).6The baseline model utilized here differs from Wolf [50] only in that Wolf codes intrastate shipments as adjacent as well
(i.e., Adjacentij equals one for contiguous neighbors and for within-state trade).7The implied border width is calculated as the distance from the mean one needs to travel in order to yield the same
negative effect on trade flows as that yielded by crossing the border. In other words, we solve for d∗ from
β3 ∗£ln(D + d∗)− ln(D)
¤= −β7
which results in d∗ = D ∗ [exp(−β7/β3)− 1].8The variance of the border ‘width’ is derived via the delta method and given by [ ∂d
∂β3, ∂d∂β7]V (eβ)[ ∂d
∂β3, ∂d∂β7]0, where V (eβ) is
the variance-covariance matrix of β3 and β7 (see Greene [21], p. 297).
9Due to data limitations, the time dimension of our panel data set encompasses only two periods, 1993 and 1997.
4
we estimate a migration model that accounts for the internal migration pattern in the U.S.
The theoretical justification for the generalized model, that is the inclusion of price variables in the
gravity equation, comes from theoretical trade models with Armington preferences and country-specific
product differentiation (e.g., Bergstrand [7]; [8]). Due to the complexity and non-linearity of the expressions
involving price variables in the theoretical models on the one hand, and data availability problems on the
other hand, the use of price and wage indices, GSP deflators, and import and export unit value indices
can only be interpreted as an approximation of the ‘true’ price effects predicted by the model:
additional controls in generalized model : β8RCPIi + β9RCPIj + β10Wi + β11Wj
+β12PGSPi + β13PGSPj + β14Xi + β15Mi (2)
where RCPIi(j) denotes the regional consumer price index for each state i (j), Wi(j) is the average wage
per job in state i (j), PGSPi(j) denotes the gross state product (GSP) deflator in state i (j), and Xi (Mi)
denotes the unit value index for exports (imports) by state i.10 Again, we estimate the generalized model
separately for each cross-section of data.
There are several justifications for the use of panel specifications. To begin, a panel framework allows
the inclusion of fixed effects in the gravity equation with home dummy, as recently suggested by Wall [48]
and Cheng and Wall [11]. The authors argue that specifications of the gravity equation that do not account
for the unobserved time heterogeneity at the level of pairwise trade flows (i.e., specifications of the gravity
equation without pairwise fixed effects) are biased and, in the case of the international trade flows, lead
to estimates of the border effect that are too small. Inclusion of fixed effects also addresses the critique
posed in Anderson and van Wincoop [2] that the controls for remoteness in the baseline and generalized
specifications do not properly control for the size of a given state’s internal market. Using fixed effects we
can control for time invariant state-specific unobservables and time-specific unobservables common to all
states:
additional controls in panel models: β16Tt + β017OFEi + β018DFEj + β019PFEij (3)
where Tt is a dummy variable equal to one in 1997 (zero otherwise), OFEi denotes a vector of origin fixed
effects, DFEj denotes a vector of destination fixed effects, and PFEij is a vector of pairwise fixed effects,
where PFEij 6= PFEji (as in Wall [48]). Note that the inclusion of pairwise fixed effects prevents the
inclusion of all time invariant control variables (Dij , Adjacenti, Homei, OFEi, and DFEj). .
Furthermore, a panel framework enables us to estimate several simple dynamic panel specifications.
Eichengreen and Irwin [15] argue strongly in favor of a dynamic specification of the gravity equation;
10Due to data limitation, the export and import unit value indices are only available for 1997. See Gould [20] for similar
price controls in a gravity model of international trade.
5
in particular, conditioning on lagged trade flows.11 Anderson and Smith [5], building on Rauch’s [43]
theoretical model, and Bun and Klaassen [10] also advocate the inclusion of lagged trade as a proxy
for past trade shocks and/or the establishment of information networks. We estimate the baseline and
generalized gravity equations with either (i) lagged control variables or (ii) lagged trade flows and current
control variables:
control variables in dynamic panel models: eβ0Zt−1or β20 ln(Shipmentsij,t−1) + eβ0Zt (4)
where Zt−1(Zt) is a vector of lagged (current) control variables that includes all regressors from the baseline
or generalized models, eβ is the corresponding vector of coefficients, and Shipmentsij,t−1 is the lagged value
of shipments from state i to j. In the present context, there is an additional benefit of including lagged trade
flows: since data on U.S. intranational trade contain shipments of wholesale and final goods (as discussed
in Section 3), any resulting bias of the border effect will be removed as long as this bias is constant over
time. Thus, we estimate several specifications conditioning on lagged trade flows. In addition, since lagged
trade flows will be endogenous if either the error term is autocorrelated or if there exist time invariant
unobservables that are correlated with bilateral trade flows, we report instrumental variables estimates in
addition to OLS estimates.
Several plausible theories provide a link between trade and migration flows. Migrants may form trade
networks in their new country (state), thereby reducing the (informational) transaction costs associated
with trade (Rauch [43], Gould [20]). Building on this logic, Combes et al. ([12]) extend the well-known
Dixt-Stiglitz-Krugman trade model of monopolistic competition to derive a gravity equation with social
(migrant) and business network effects. Alternatively, migrants may stimulate trade by reducing the
information deficit about foreign (out-of-state) goods among native consumers (Gould [20]). Both of
these effects may be more pronounced the higher the skill (income) level of the migrants (Gould [20]).
Furthermore, migration will stimulate trade if migrants continue to consume the goods they used to
consume in their former home country (state); and, wealthier migrants may be more likely to import
consumption items from their previous residence. Finally, models with Armington preferences and products
differentiated by country (state) of origin (Bergstrand [7]) as well as modified versions of the H-O-V model
(Markusen [37]) also predict that migration will lead to an increase in trade. In contrast, some models
— such as the standard H-O-V model — predict that trade and migration flows are substitutes rather
than compliments. Although theoretically ambiguous, Hazledine [23] and Helliwell and Verdier [28] note
that the deleterious effect of distance on trade is too large to be explained by transportation costs alone.
Thus, migration may be crucial to understanding trade patterns. We therefore extend the baseline and
11Eichengreen and Irwin ([15], p. 56) conclude their paper vowing to “... never run another gravity equation that excludes
lagged trade flows.”
6
generalized models by including variables that account for internal migration patterns in the U.S.:
additional controls in migration models : β21InMigrantij + β22InMigrantij ∗ InMedianij
+β23OutMigrantij + β24OutMigrantij ∗OutMedianij(5)
where InMigrantij is the number of migrants entering state i from state j, InMedianij is the median
income of all migrants entering state i from state j, OutMigrantij is the number of migrants leaving state
i for state j, and OutMedianij is the median income of all migrants moving from state i to state j.12 Using
the resulting estimates, the distance ‘offset’ per migrant is calculated using the same logic as the formula
in Parsley and Wei [42] for computing the average border ‘width.’ Specifically, in the models omitting the
interactions between migrant flows and the median income of migrants, the ‘offset’ per incoming migrant
is D ∗©exp{(−β21/β3) ∗ ln[M/(M + 1)]}− 1
ª(and similarly for each outgoing migrant), where M is the
sample mean of migration inflows. Including the interactions, the ‘offset’ is given by
D ∗©exp{(−β21/β3) ∗ ln[M/(M + 1)] + (−β23/β3) ∗ ln(Median) ∗ ln[M/(M + 1)]}− 1
ªStandard errors for the ‘offsets’ are obtained via the delta method.13
3 Data
The inter- and intrastate trade flow data are from the 1993 and 1997 U.S. Commodity Flow Survey (CFS),
collected by the Bureau of Transportation Statistics within the U.S. Department of Transportation. The
CFS tracks shipments — measured in dollars and in tons — between establishments by mode of transporta-
tion: rail, truck, air, water, and pipeline. The survey covers 25 two-digit SIC industries (codes 10 (except
108), 12 (except 124), 14 (except) 148, 20-26, 27 (except 279), 28-39, 41, and 50) and two three-digit SIC in-
dustries (codes 596 and 782). The 1993 (1997) survey randomly sampled 200,000 (100,000) establishments.
Total shipments from one state to another (or within state), Shipmentsij , are reported.
12For a theoretical justification of an expanded gravity equation incorporating internal migration, see Combes et al. [12].13The offset is calculated as the distance from the mean one needs to travel in order to offset the positive effect on trade
flows of adding one more migrant (above the mean). Thus, in the model omitting the interaction terms, we solve for d∗ from
β3 ∗£ln(D + d∗)− ln(D)
¤= −β21
£ln(M + 1)− ln(M)
¤or
β3 ∗£ln(D + d∗)− ln(D)
¤= −β22
£ln(M + 1)− ln(M)
¤In the model with the interaction, the formula is appropriately altered.
7
Before proceeding there are two important limitations of the CFS data worth noting. First, the CFS
tracks all shipments, not just shipments to the final user. For example, shipments of a single good from
a factory to a warehouse and then to a retail store would each be included in the data. The fact that
wholesale trade is included in the CFS data will likely affect inferences pertaining to the existence and size
of the state border effect (Hillberry [32]). Second, Hillberry [32] and Hillberry and Hummels [33] argue
that utilization of the aggregate CFS data may affect the interpretation of the border effect. However, as
the emphasis of this paper is not the size of the border effect per se, but rather its robustness (in terms
of significance and magnitude) to various model specifications, these limitations are less problematic.
Moreover, as argued in more detail below, the bias generated by the flaws in the data should be mitigated
in the models conditioning on lagged shipments.
The main distance measure utilized, Dij , is borrowed from Wolf [50].14 The distance between any
two (of the 48 contiguous) states is the minimum driving distance in miles between the largest city in
each state. Driving distances are used as the majority of all shipments are shipped via truck. The U.S.
Department of Transportation reports that trucks accounted for 75.3% (71.7%) of the commodity value
shipped in 1993 (1997).15 Proper measurement of intrastate distance, Dii, has received much attention
recently in the literature. Wolf’s measure is computed as one-half the distance between a state and its
closest neighboring state, where distance to neighboring states is measured as indicated above (Wei [49]
also utilizes a similar definition for internal distances). However, Nitsch [39] and Helliwell and Verdier [28]
question the validity of such calculations. Thus, we assess the robustness of this measure below.
Data on GSP, Yi, come from the U.S. Bureau of Economic Analysis (BEA). For the generalized gravity
specifications, we utilize three price variables: (i) regional consumer price indices (RCPIi), available for
four regions — West, East, South, Midwest — from the U.S. Bureau of Labor Statistics; (ii) average wage
per job for each state (Wi), available from the BEA; and, (iii) state-specific GSP deflators, calculated as
(NGSPt/RGSPt)/(NGSP89/RGSP89), t = 1993, 1997, where NGSP denotes nominal GSP and RGSP
denotes real GSP (all measures taken from the BEA). In addition, we construct export (import) unit
values, measured as the dollar value of total state exports (imports) per ton of exports (imports). We
then construct an export (import) index equal to the weighted averages of the export (import) unit values,
using GSP as the weight. The change in the indices from 1993 to 1997 is used as an approximation for
the change in export and import prices for each state in 1997. Due to the lack of trade flow data prior to
1993, the export (import) unit value index is not available for 1993.
Lastly, internal migration flows are measured using data from the U.S. Internal Revenue Service. The
14The authors are grateful to Holger Wolf for providing this data.
15See http://www.bts.gov/ntda/cfs/docs/CFS99-PressRelease.pdf.
8
IRS tracks tax returns filed by state and computes measures of internal migration based on the number of
filers residing in state i who filed in state j in the previous year. Intrastate ‘migration’ (i.e., InMigrantii
and OutMigrantii) are measured as the number of filers who did not change states of residence.16 We use
data based on 1992 and 1996 tax records. Giving the timing of the IRS data, this implies that the total
inflow (outflow) of migrants in 1993 is the total number of households who moved from state i (j) between
February 1, 1992 and January 31, 1993 (similarly for 1997). Hence, we utilize the 1992 and 1996 IRS tax
records as the timing is more consistent with the 1993 and 1997 CFS data on trade flows. We should note
that the IRS internal migration statistics are based on the number of tax returns, not individual migrants.
Thus, to the extent that households file joint tax returns, our migration measure is a lower bound on the
total flow of individuals.17
Summary statistics for all variables are provided in the Appendix, Table A1. In addition, Table A2
breaks down the percent of all shipments — measured in dollars and tons — remaining in-state for each state
by year, as well as the change across the two waves. In terms of value shipped, California, Florida, and
Texas are the only states to ship within state at least 60% of the total commodity value shipped in both
years. Delaware (16%) and New Hampshire (13%) ship the smallest amount (measured in dollars) within
state in 1993 and 1997, respectively. The biggest changers were South Dakota and Vermont. Vermont
increased their share of shipments remaining in-state by over 14%, while South Dakota reduced their share
of shipments remaining in-state by nearly 14% (again, measured in dollars). Measured by weight, California
shipped within state over 90% of the total commodity weight shipped in both years. Wyoming has the
smallest percentage of shipments by weight remaining in-state in each year (17% in 1993 and 14% in 1997).
The largest changers, measured by weight, were Connecticut and Oklahoma, with Oklahoma increasing
their intrastate shipment share by over 14% and Connecticut reducing its share by 15%.
4 Empirical Results
4.1 Baseline Model Results
Table 1 contains the first set of estimates, corresponding to the baseline gravity specification in (1) for 1993
and 1997. We report three specifications for each year. Model I represents the simplest gravity equation:
trade flows as a function of origin and destination GSP, distance, and the home bias effect. Models II
16On average, 3.6% of households migrate out-of-state each year, with a minimum of 2% (Wisconsin) and a maximum of
7% (Wyoming), with this percentage remaining fairly constant across the two rounds of data.17The IRS data do contain the total number dependents claimed on all tax returns. However, since many dependents are
children who presumably have little to no influence on trade flows, we utilize the total number of tax returns to proxy for
internal migration.
9
and III condition on the origin and destination measures of remoteness and neighbor (adjacency) status,
respectively. The results for 1993 are essentially identical to those reported by Wolf ([50], Table 1). In
particular, we find the elasticities of shipments with respect to origin and destination GSP to be close
to unity, the elasticity with respect to distance is approximately one in absolute value, and there is a
substantial and statistically significant home bias. Furthermore, states are more likely to trade with
adjacent neighbors, and while shipments are increasing in the destination state’s remoteness, they are
decreasing in the origin state’s remoteness. Finally, all three specifications have a high degree of explanatory
power; the adjusted-R2 ranges from 0.84 to 0.86.
The size of the home bias effect in 1993 ranges from 4.90 (Model III) to 7.14 (Model I). This implies
that ceteris paribus intrastate trade is roughly five to seven times greater than interstate trade. Using the
coefficient estimates and the formula from Parsley and Wei [42] yields an implied average border ‘width’ of
at least 6,400 miles. Utilizing the delta method to obtain the standard errors of the border ‘width’ estimates
indicates that one easily rejects the null hypothesis that the ‘true’ border ‘width’ is zero (t-statistics range
from 5.04 to 6.12).
As with the 1993 data, the explanatory power of the three baseline specifications is also high in 1997;
the adjusted-R2 ranges from 0.83 to 0.85. Moreover, the coefficient estimates for 1997 are comparable in
size and significance to those for 1993. Nonetheless, given the sample size and the precision of the estimates,
Chow tests for parameter stability clearly reject the null hypothesis of exact equality of estimates across
the two waves of data (p=0.00 in all three models). In particular, the magnitude of the home bias effect
is larger in 1997, with values ranging from nearly six to over eight, an increase of roughly 20% for each
model from 1993.18 The larger home bias effect, coupled with a marginally lower elasticity with respect to
distance, yields an average border ‘width’ in excess of 10,000 miles in 1997. Using the results from Model
III, the average border ‘width’ nears 14,000 miles and represents a 90% increase from 1993. Thus, while the
effect of distance on trade appears to have declined over the 1990s, the role of state borders has increased.
In the interest of brevity the remaining models build solely on the original baseline gravity specification
widely employed in the literature.
18The larger subnational home bias effect in 1997 contrasts with some studies of the impact of borders on international
trade. For example, Helliwell [27] and Head and Ries [25] argue that the U.S.-Canada border effect has diminished since 1988
and the 1960s, respectively. On the other hand, Anderson and Smith [5] report a stable border effect over the 1988 — 1996
period.
10
4.2 Generalized Model Results
We now turn our focus to the generalized gravity equation given in (2). This specification is similar to Model
III in Table 1 with the addition of controls for prices and wages. Table 2 reports the coefficient estimates on
distance and the home dummy.19 Both coefficients change little as we add the additional controls despite
the fact that the price and wage variables enter the gravity equation as statistically significant (and the
overall fit of the models is marginally improved). However, while the inclusion of the price and wage indices
does not change the statistical significance of the border effect, it does reduce its magnitude from 4.90 to
4.57 and 5.91 to 5.42 in 1993 and 1997, respectively. The implied average border ‘widths’ are also reduced;
from approximately 7,200 to 5,200 miles in 1993 and from almost 14,000 to roughly 8,000 miles in 1997.
This represents a drop of almost 30% (over 40%) in 1993 (1997). These changes arise from the fact that
the omission of price controls biases the coefficient on distance (the home dummy) down (up) in absolute
value. Both of these small changes work in the direction of overestimating the border effect in the baseline
specification.
4.3 Panel Model Results
The next set of specifications pool the two waves of the CFS and control for various levels of unobserved
time invariant attributes. The first set of estimates, corresponding to the specification in (3), are reported
in Table 3. Models I and III are for the baseline model (omitting the price and wage measures) and
Models II and IV correspond to the panel version of the generalized gravity model (including price and
wage controls). Specifically, Models I and II include origin and destination fixed effects only; Models III
and IV contain pairwise fixed effects. All models also include a time dummy to capture changes over time
that affect all trade flows. As noted earlier, once pairwise fixed effects are included (Models III and IV),
all pairwise-specific, time invariant variables drop out of the model. Hence, the home effect cannot be
estimated directly. To circumvent this, we utilize the two-step approach of Wall [48]. The author suggests
estimating the gravity model including the pairwise fixed effects, obtaining estimates of the fixed effects,
and then regressing the estimated fixed effects on a constant, (log) distance, and a home dummy. The
coefficients from this second-stage regression can then be used to construct the home bias effect and the
implied border ‘width.’
19Even after adding the various price and wage controls, the coefficients on the scale, distance, remoteness, and adjacancy
variables remain similar to those reported in Table 1. The coefficients for the price and wage variables are predominantly
negative and statistically significant (the major exception being own regional CPI, where the coefficient is either positive and
significant, or insignificant). The coefficients on the export and import unit value index in 1997 are statistically insignificant.
The full set of results are available from the authors upon request.
11
The results show that the inclusion of time, origin and destination fixed effects have a substantial
impact on many of the coefficients. In particular, it appears that most of the GSP (scale) effects are
subsumed by the fixed effects. To the extent that real GSP does not change dramatically over such a short
time span, this is perhaps not overly surprising. The same is true for the price and wage variables. While
the majority of these variables are statistically significant in the cross-sectional models (Table 2; although
the coefficients are not reported), many become insignificant in the models containing fixed effects. Again,
this is probably due to a lack of variation over such a short period. However, it is interesting to note that
both remoteness measures are now positive, as predicted, and statistically significant. Recall that in the
models failing to control for unobserved time invariant attributes, origin state remoteness had a somewhat
puzzling negative coefficient. This is no longer the case.
While adding origin and destination fixed effects alters many of the other gravity model controls, the
distance and home dummy coefficients only change marginally. However, as the distance effect is reduced
and the home effect increases, the net result is a substantially larger home bias effect and average border
‘width.’ The fact that the home bias effect increases is consistent with the results presented in Wall
[48] for U.S.-Canada trade. Specifically, we find that the home bias effect increases from roughly five
in the generalized models in Table 2 to 6.13 in Model II of Table 3. Controlling for unobserved time
invariant pairwise attributes in the generalized model (Table 3, Model IV) yields an even larger home bias
effect (7.06) relative to the models including only origin and destination fixed effects. Compared to the
generalized models in Table 2, the home bias increases by roughly 41%, a result reminiscent of the 40%
increase found in Wall. In terms of the average border ‘width’, the increase is approximately 600%, from
roughly 6,500 miles (Table 2) to nearly 45,000 miles in the model containing origin and destination fixed
effects (Table 3, Model II). However, the average border ‘width’ is reduced to a mere 31,000 miles when
we utilize pairwise fixed effects (Table 3, Model IV).20
Table 4 contains several simple dynamic panel estimates of the baseline (Models I, III, and V) and
generalized gravity equations (Models II, IV, VI and VII). Specifically, Models I and II replace the contem-
poraneous values of the various controls with their lagged counterparts. Models III — VII include current
controls, but lagged trade flows as an additional covariate, with Models III and IV estimated via OLS and
Models V — VII estimated using instrumental variables (IV) and Generalized Method of Moments (GMM).
In the models estimated via GMM, we utilize lagged origin and destination GSP and lagged origin and
destination remoteness as instruments. Several diagnostic tests are conducted to assess the reliability and
efficiency of the GMM estimates. First, since the number of instruments exceeds the number of endogenous
20In the second-stage regression (regressing the estimated fixed effects on a constant log distance, and a home dummy) for
Model IV, the coefficient on distance is -0.59 (t=-14.64) and the home dummy coefficient is 1.96 (t=10.89).
12
regressors, we present the results of Hansen’s J statistic, an overidentification test for the validity of the in-
struments. Second, we conduct the Pagan-Hall [41] test of heteroskedasticity of the errors. It is well-known
that GMM, as opposed to standard IV estimation, is more efficient in the presence of heteroskedasticity of
unknown form, but potentially less reliable in finite samples if the errors are homoskedastic (e.g., Baum et
al. [6]). Third, since it is also well-known that IV estimates based on weak instruments are biased toward
the OLS estimates (e.g., Bound et al. [9]), we conduct several additional tests. First, we report F -tests
for the joint significance of the instrument set in each first-stage regression. Second, we report Shea’s [45]
partial-R2 measure. Third, we conduct the test proposed in Hall et al. [22] for instrument relevance. The
test examines whether the smallest sample canonical correlation between the instrument set and the vector
of endogenous variables is significantly different from zero. Finally, we compute Stock and Staiger’s [46]
measure of the maximum squared bias of the IV estimates relative to the OLS estimates (Bmax in their
notation; equation (3.6), p. 566).
The first set of results, for Models I and II, are not qualitatively different from the analogous models
using contemporaneous values of the control variables. In particular, the estimates from Model I in Table
4 are very similar to the estimates of Model III for 1997 in Table 1; the estimates from Model II in Table
4 are consonant with the results from 1997 generalized gravity model in Table 2. For example, the home
bias effect (average border ‘width’) in Model I, Table 4 is 5.93 (14,900 miles), whereas the corresponding
estimate from Model III (1997), Table 1 is 5.91 (13,600 miles). For the generalized gravity equation in
Model II, Table 4, the home bias effect (average border ‘width’) is 5.47 (9,100 miles) versus 5.42 (8,000
miles) in the final 1997 model in Table 2.21 Thus, the use of current or lagged controls within a gravity
approach is, at least in the present case, inconsequential.
While conditioning on the lagged exogenous variables of the model has little impact on the estimates,
including lagged trade flows as a covariate does alter the estimates. As stated previously, the norm
in previous dynamic gravity models is to treat lagged trade flows as exogenous. Models III (baseline
specification) and Model IV (generalized specification) follow this lead. Doing so reveals a dramatically
altered estimate of the home bias effect and the impact of distance on subnational trade flows.22 In
particular, the estimated home bias effect is reduced to below two in both models (a decline of roughly 70%)
and the coefficient on distance, while still negative and statistically significant, is reduced by approximately
21Note that the comparisons utilizing the final 1997 generalized gravity model from Table 2 are not exact since the final
1997 specification in Table 2 also includes controls for export and import unit value indices. Despite this minor difference, the
results are still virtually unchanged.22Inclusion of lagged trade flows is consistent with a partial adjustment model. Thus, the coefficient on the home dummy
(and other covariates) may be interpreted as a short-term effect. The long-term effect can be obtained using the appropriate
transformation (Greene [21], p. 528), with standard errors derived via the delta method.
13
90% (80%) in the baseline (generalized) specification. In addition, the estimated average border ‘width’
is no longer statistically significant. Finally, many of the other coefficients are reduced and some become
statistically insignificant as lagged trade flows explain most of the variation in current trade patterns; the
elasticity with respect to lagged shipments exceeds 0.70 and remains highly statistically significant.
However, when we allow for the possibility that lagged shipments may be endogenous (either due to
time invariant unobserved attributes or autocorrelated errors), the coefficient estimates are further altered.
For the baseline specification (Model V), we first note that the overidentification test does not reject the
null of instrument validity (p=0.46) and the model fairs well in terms of the other diagnostic tests with
the exception of Shea’s Partial R2. In terms of the actual results, treating lagged shipments as endogenous
further reduces the home bias effect to close to unity and the estimate is no longer statistically significant.
The effect of distance is now positive and statistically significant at the 90% confidence level. Together,
these two coefficients imply a statistically significant average border ‘width’ of -960 miles! When we add
controls for regional CPI and average wages (Model VI), the point estimates change very little. Finally,
when we also control for original and destination GSP deflators (Model VII), the overidentification test
rejects the null of instrument validity. Hence, the results cannot be considered reliable.
The findings from Models III — VI support the conclusion in Anderson and Smith [5], Bun and Klaassen
[10], and Eichengreen and Irwin [15] that the inclusion of lagged trade flows may substantially change the
impact on trade flows attributed to certain control variables. One potential explanation for this result,
consonant with the work in Rauch [43], is that lagged trade flows proxy for unobserved network effects. It
is also consonant with the finding in Hillberry and Hummels [34] that wholesale activity drives much (but
not all) of the home bias effect documented in Wolf [50].
4.4 Migration Model Results
The final models incorporate migration flows into the gravity model, as in (5). Specifically, we re-estimate
several specifications of the baseline and generalized gravity equation — pooling both years and adding a
time dummy — including control variables for state-to-state migration. The results are displayed in Table
5. Models I and II re-estimate the baseline and generalized equations, respectively, including a measure of
migrant inflow and outflow along with origin and destination fixed effects. Models III and IV are analogous
to Models I and II except include pairwise fixed effects. Finally, Models V — VIII are identical to Models I
— IV except migration is interacted with the median income of the migrants. In all specifications, we test
for the equality of the two flow effects.
The effect of conditioning on internal migration is substantial. In the baseline gravity equation with
origin and destination fixed effects (Model I), the coefficients on the home dummy and distance are negative
14
and statistically significant. Thus, the home bias effect falls to 0.52 and the implied average border ‘width’
is less than -1,100 miles! Adding controls for spatial price and wage variation (Model II in Table 5), does
not alter the findings.23
In terms of the actual effect of migration flows, in both the baseline and generalized models migration
inflows and outflows both have a statistically significant impact on trade flows. The elasticity of shipments
with respect to each migration flow is approximately 0.22, and we fail to reject the equality of the two
migration coefficients in Models I and II (Model I: p=0.96; Model II: p=0.79). The implied distance ‘offset’
by each incoming (outgoing) migrant is at least 175 (167) feet; conversely, approximately 31 migrants (in
either direction) ‘offset’ one mile. The fact that migrant outflows matter for trade flows is consistent
with migrants having preferences for their former locally produced goods, or migrants bringing additional
information to their new location about goods produced elsewhere. The importance of migrant inflows is
consistent with migrants conveying information about goods produced in their new state to consumers in
their previous state.
Since migration within states (i.e., InMigrantii and OutMigrantii) is measured as the total number of
tax filers who resided in the state the year prior, these values are quite large since only a small percentage of
the population relocates in a given year (see footnote 16). Thus, the positive impact of migration captures,
to a large extent, the home bias effect. Note, however, that the inclusion of intrastate trade in the various
regressions in Table 5 does not drive the results. When we re-estimate the various specifications in Table 5
excluding observations on intrastate trade, we find very similar effects of migration flows and the distance
offset per migrant.24 Thus, the migration effect may be a missing feature in the standard gravity model
that has led to an erroneous home bias effect at the subnational level.25
Models V and VI are similar to Models I and II except that the migration measures are interacted
with the median income of in- and out-migrants. The positive coefficients on the interaction terms suggest
23Estimating a model similar to our Model II in Table 5 for French regions except without fixed effects, Combes et al.
[12] report a comparable decline in the border effect relative to their benchmark model (roughly 63%). In addition, their
reported estimates for the two migration measures are similar to ours, with one effect smaller in magnitude and statistically
insignificant.24For example, in Model I, the distance offset per migrant inflow is 196.02 feet (t=4.72) and per migrant outflow is 197.66
feet (t=4.78).25A possible alternative explanation of the migration effect is that since migration is negatively correlated with distance,
the migration effect may simply be capturing a non-linear effect of distance. However, inclusion of higher order distance terms
in the baseline model (without migration), suggest that the relationship between shipments and distance is log-linear. To be
exact, when we include ln(dist)2 and ln(dist)3 as regressors, while the parameters on the higher order terms are statistically
significant, the plot of ln(shipments) against ln(dist) is approximately linear over the range containing the majority of the
data (95% of the observations). Moreover, inclusion of the higher order terms in the migration models has little effect.
15
that the effects of migration — even at a subnational level — depend on the income (skill-level) of the
migrants (similar to the results found in Gould [20] at the international level). However, all four migration
parameters are statistically insignificant (presumably there is too little variation in the data); thus, we
do not wish to overstate this finding. Nonetheless, the remainder of the results in Models V and VI are
virtually unchanged from Models I and II; the coefficients on the non-migration variables as well as the
implied migrant offsets are nearly identical to the previous specifications omitting the interactions.26
Models III (baseline) and IV (generalized) are equivalent to Models I and II (omitting the migration
interactions), but now include pairwise fixed effects. The change in coefficient estimates is profound. Now,
we do find evidence of a home bias effect, and the implied border ‘width’ is roughly 5,000 feet in the
generalized model; the border ‘width’ continues to be negative in the baseline model. The larger home bias
effect in the generalized versus baseline specification when pairwise fixed effects are included is consonant
with the findings reported in Table 3. Moreover, even though the border ‘width’ remains positive in the
generalized model in Table 5, the addition of the migration variables reduces the border ‘width’ by over
80% (from about 31,000 to 5,100 miles). In terms of the migration coefficients, only the coefficients on
migrant outflows are statistically significant once we include pairwise fixed effects, although we do not reject
equality between the coefficients on migrant inflows and outflows (Model III: p=0.23; Model IV: p=0.50).
Thus, despite the demands placed on the data, we continue to find support for a role of migration flows in
the explanation of trade patterns. Finally, the results are virtually unchanged when we add interactions
between the migration and the median income variables (Models VII and VIII).
In the end, as this is one of the first studies that examines the role of migration on trade flows at a sub-
national level, clearly there exists enough support to further examine the role of migration in determining
trade flows at both the national and subnational level in the future. The results here are consonant with
previous results obtained at the national level in Gould [20] and Girma and Zu [19] and at the subnational
level for French regions in Combes et al. [12]: preferences for home goods and/or the informational ad-
vantage obtained via migrants play a substantial role in explaining trade flows. Moreover, the fact that
the subnational border effect either disappears entirely or is substantially reduced when we condition on
lagged shipments and internal migration, both of which proxy unobserved networks effects, indicates that
network ties may be a key omitted variable in many empirical specifications of the gravity equation.
26The similarity between the estimated border ‘width’ in the models controlling for both migration flows and unobserved
heterogeneity (Table 5, Models I, II, V, and VI) and the models including (endogenous) lagged trade flows (Table 4, Models
V — VII) is quite striking. This suggests that lagged trade flows on the one hand and the combination of migration and
unobserved heterogeneity on the other may be both capturing the same underlying determinants of subnational trade.
16
5 Sensitivity Analysis
Before proceeding to the conclusion of the paper, it is worthwhile to examine the robustness of the preceding
findings to some alternative measurement schemes proposed in the literature.
5.1 Baseline Model
In the interest of brevity, Table A3 presents the coefficients on (log) distance and the home dummy from
11 alternative specifications of the baseline model. Specification (1) measures the dependent variable,
shipments, by weight rather than value. Not surprisingly, the results yield effects of distance and borders
that are larger in absolute value relative to those reported in Table 1 since shipping costs have a more
detrimental effect on shipments measured by weight. The home bias effect nearly doubles from 4.90 to 9.78
in 1993, and rises by over 90%, from 5.91 to 11.25 in 1997. Specifications (2), (3), and (4) use population
rather than GSP to measure scale and/or population as weights in obtaining the remoteness measures.
Both changes have little impact on the estimated coefficients.
Specification (5) scales the dependent variable (measured in dollars) by the product of origin and
destination GSP, as suggested in Wolf [50]. Again, no qualitative change results. Next, we address a recent
criticism proposed in Evans [17]. The author claims that using origin GSP is not the appropriate measure
of scale since not all domestically produced goods are available for export. Evans proposes that origin GSP
should be replaced with the total value added of all goods actually exported. In this spirit, we replace
origin GSP with the total value of all commodities shipped ‘abroad’ from each state (i.e., the value of
shipments that are not consumed locally) in specification (6). This change has little substantive effect.
Specifications (7) — (11) examine the sensitivity of the home bias effect to the measurement of internal
state distance, Dii. While Wei [49] and Wolf [50] approximate internal distances as one-half the distance
between the largest city and nearest border, Nitsch [39] and Helliwell and Verdier [28] criticize such calcu-
lations. As an alternative, Nitsch, based on geometric calculations, argues that Dii = k ∗√Areai offers a
good approximation of the average internal distance, where k = 0.56 if populations are uniformly distrib-
uted within each state and Areai is the land area of state i. If populations are not uniformly distributed,
then k = 0.56 will overstate the average internal distance (and, hence, overestimate the home bias since
k and the home bias are positively related). To arrive at a more precise measure of internal distance
for Canadian provinces, Helliwell and Verdier embark on an intensive data exercise of estimating internal
distance as a population-weighted average of intra-city and inter-city distances, as well as distances to and
within rural areas. While obtaining similar estimates for the U.S. would be an exhaustive process, Nitsch
notes that (for Canada) the average internal distance obtained in Helliwell and Verdier is equivalent to
17
k = 0.31.27 As a result, specifications (7) — (10) use k = 0.5, 0.4, 0.3, and 0.2; k = 0.41 yields an average
internal state distance equal to the mean of Wolf’s measure.
Examining the results shows that the home bias effect and k are positively related, as mentioned above,
and the size of the home bias effect is sensitive to the choice of k. Nonetheless, for ‘reasonable’ values
of k (e.g., k = 0.31) the home bias effect still exists, and for k = 0.41 the home bias effect is larger
than that obtained under Wolf’s internal distance measure.28 Finally, rather than settling for simply
choosing values of k ad hoc, we propose a new method to estimate state-specific k’s, similar in spirit to
Helliwell and Verdier [28], although much simpler to execute. Specifically, since the value of k is designed
to reflect deviations from a uniform spatial distribution of the population within a state (k = 0.56 assumes
a uniform distribution, k = 0 assumes everyone is located at one centralized location), we estimate state-
specific values of k, ki, using the Gini coefficient calculated for each state based on the distribution of
the state population across counties. We then note that if a state has its entire population located in
one county, the Gini coefficient will equal unity; if a state has an equal share of its population in each
county, the Gini coefficient will be zero. Consequently, we estimate ki = 0.56(1−Gi), where Gi is the Gini
coefficient, and then define each state’s internal distance as Dii = ki√Areai.
29
According to this procedure, Gi ranges from 0.32 to 0.78, with a mean of 0.55; ki then ranges from
0.12 to 0.38, with a mean, k, of 0.25. Interestingly, the k obtained here for the average U.S. state is
not that different than the average k obtained for Canadian provinces in Helliwell and Verdier (k = 0.31,
as reported in Nitsch [39]; see footnote 27). Specification (11) reports the results using this measure of
internal distance. The home bias effect is 1.27 (1.50) in 1993 (1997). While smaller than those obtained
in Table 1 using Wolf’s distance measure, the results are still statistically and economically significant, as
intrastate trade exceeds interstate trade by a factor of 3.6 (4.5).
5.2 Panel and Migration Model Results
Given the previous findings in the dynamic panel data and migration models, our final two sensitivity
tests combine these models, thus asking a lot of the data. First, we re-estimate the dynamic specifications
in Models V and VII in Table 4 including the (exogenous) migration variables as additional covariates.
However, since one might suspect that migration and trade flows respond to common idiosyncratic shocks,
implying that migration is endogenous, we re-estimate these models treating both lagged trade flows
27To be clear, Helliwell and Verdier [28] do not report the fact that k = 0.31 in their published paper, but Nitsch [39] refers
to this as being mentioned in an earlier draft of Helliwell and Verdier’s paper.
28For 1993 (1997), k = 0.18 (k = 0.12) yields a coefficient on the home bias of unity.29Note that this procedure allows internal state distance to be time-varying since the Gini coefficient will change from year
to year.
18
as well as migration as endogenous. We attempted various instruments from outside the model (e.g.,
measures of crime rates, provision of public goods, racial composition, etc.), but were unable to find non-
weak instruments from outside the model that did not fail the overidentification test. To circumvent this
problem, we rely on a novel IV solution to the bias resulting from measurement error in righthand side
variables when there are no instruments available from outside the model proposed in Lewbel [36]. The
solution exploits skewness in the data by devising instruments based on higher order moments of the data.
In our case, the instruments utilized are the migration variables demeaned and squared; lagged migration
inflows and outflows are used as instruments for lagged trade flows.
Results are displayed in Table A4. Models I — IV (V — VIII) treat migration as exogenous (endogenous).
The models treating migration as exogenous confirm the previous results in Tables 4 and 5. Specifically, we
find an economically and statistically significant impact of lagged trade flows (although now the coefficient
on lagged trade flows is strictly less than unity), the home bias effect is less than one, and the average
border ‘width’ is either negative or statistically insignificant. Moreover, there continues to be strong
evidence suggesting the importance of migration patterns in explaining trade flows.
Turning to the models treating migration as endogenous, two important differences arise relative to
Models I — IV.30 First, the migration variables are no longer statistically significant. Second, the coefficient
on lagged trade flows once again becomes unity. Unchanged, however, is the fact that the home bias effect
is less than one and the average border ‘width’ is never positive and statistically significant. These results
appear credible despite the demands placed on the data as the diagnostic tests affirm the specifications,
especially in Models V and VI. In particular, the overidentification weak IV tests are all favorable.
6 Conclusion
Using data from the 1993 U.S. Commodity Flow Survey on intra- and interstate shipments, Wolf [50] shows
that even trade at the subnational level is characterized by a home bias that is statistically and economically
significant. As economists are extremely skeptical of such a finding, we extend Wolf’s analysis, combining
the 1993 and 1997 CFS surveys to examine the stability of Wolf’s results over time, as well as test a
number of additional specifications of the basic gravity model. We find that the home bias effect is robust
to a number of extensions including controls for unobserved time invariant attributes, additional controls
reflecting prices and wages, and alternative measures of internal state distance. More importantly, though,
30As pointed out by one of the referees, the assumption of exogeneity of the price variables may be misplaced. However,
given data limitation and the difficulties in finding suitable instruments for both lagged shipment and migration (the two most
important right hand side variables in the paper), we leave this task for future extensions.
19
is our finding that two specifications refute the conclusion of a home bias effect on intranational trade:
dynamic specifications conditioning on lagged trade and specifications conditioning on internal migration.
The latter result holds even when lagged trade flows and migration are treated as endogenous.
The absence of a home bias effect in these two specifications, both of which arguably control for
unobserved network effects (in the spirit of Rauch [43], [44]), suggests that the finding of a border effect on
international trade flows may simply be an artifact of model mis-specification. Since it is the presence of a
large international border effect that is particularly troublesome to policymakers and trade economists (as
it may imply genuine barriers to trade), inclusion of controls designed to proxy for such network effects, is
clearly warranted in future examinations of international bilateral trade flow data.
20
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24
Table 1. Baseline Gravity Equation: Static Results by Year.IndependentVariable
I II III I II IIIConstant -9.81 -9.67 -11.58 -9.88 -9.77 -11.81
(-31.40) (-30.49) (-35.09) (-31.45) (-29.52) (-34.42)ln(Y1) 1.03 1.02 1.03 0.96 0.96 0.97
(63.26) (63.07) (66.82) (59.36) (59.15) (62.89)ln(Y2) 1.00 1.00 1.01 0.99 0.99 1.00
(61.33) (61.70) (65.44) (60.93) (60.89) (64.88)ln(Distance) -1.03 -1.05 -0.82 -0.93 -0.94 -0.71
(-45.53) (-44.63) (-29.93) (-41.62) (-40.23) (-25.90)ln(Remote1) -0.41 -0.57 -0.37 -0.55
(-4.40) (-6.42) (-4.10) (-6.39)ln(Remote2) 0.60 0.44 0.47 0.29
(6.62) (5.04) (5.29) (3.41)Adjacent 0.92 0.94
(14.52) (14.90)Home 1.97 1.94 1.59 2.13 2.12 1.78
(16.20) (16.05) (13.50) (17.85) (17.71) (15.32)Adjusted R² 0.84 0.85 0.86 0.83 0.83 0.85Observations 2137 2137 2137 2091 2091 2091Home Effect 7.14 6.94 4.9 8.45 8.32 5.91
[p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00]Border 'Width' 6827 6450 7174 10561 10167 13626 In Miles (6.12) (6.11) (5.04) (5.69) (5.64) (4.42)Chow Test: F(5,4218)=23.40 F(7,4214)=8.32 F(8,4212)=13.61 Ho:β93= β97 [p=0.00] [p=0.00] [p=0.00]NOTES: 1. t-statistics in parentheses; p-values in brackets. 2. Shipments measured in millions of nominal US$. 3. A subscript on a control variable indicates orgin (1) or destination (2) state. 4. 'Home Effect' is calculated as exp(βhome); p-value tests null that the effect is equal to one. 5. Border 'width' calculated as (mean distance)*[exp(-βhome/βdist)-1]; t-statistic for border 'width' obtained via the delta method. 6. Chow test reports the p-value associated with the null that the coefficients in each model do not change from 1993 to 1997. See text for further detail.
Dependent Variable: ln(shipments)1993 1997
Table 2. Generalized Gravity Equation: Selected Coefficients by Year.AdditionalControls
ln(dist.) Home Bias ln(dist.) Home BiasCoeff. Coeff. Coeff. Coeff.
Regional CPI -0.88 1.54 -0.79 1.71deflators (origin (-32.77) (13.58) (-29.65) (15.47)& destination)
above controls + -0.89 1.54 -0.80 1.71Ave. wage per job (-33.80) (13.83) (-30.40) (15.75)(origin & destination)
above controls + -0.90 1.52 -0.83 1.69GSP deflators (-34.26) (13.74) (-31.45) (15.73)(origin & destination)
above controls + -0.83 1.69Export/Import (-31.07) (15.73)unit value index
Additional Results: Final Generalized Gravity EquationAdjusted R²ObservationsHome Effect
Border 'Width' In MilesNOTES: 1. t-statistics in parentheses; p-values in brackets. 2. Each regression also includes measures of scale (Y1
and Y2), measures of remoteness (Remote1 and Remote2), a dummy variable for adjacent states, and a constant, corresponding to Model III in Table 1. A subscript on a control variable indicates orgin (1) or destination (2) state.3. GSP deflators calculated as (NGSPt/RGSPt)/(NGSP89/RGSP89), t=1993, 1997, where NGSP = nominal gross state product and RGSP = real gross state product. 4. Export unit value index is calculated by first obtaining theratio of the value of shipments per ton from each state to each possible destination in 1997 to the same variable in 1993, and then by computing the weighted average for each state where the weights are the trade shares (defined in terms of total value). 5. Additional results in bottom panel are for final generalized specification (i.e., including all controls listed in the first column). 6. p-value for home effect tests null that the effect is equal to one. See text for further detail.
(5.75)
21374.57
[p=0.00]5260
Dependent Variable: ln(shipments)1993 1997
0.88
8048(5.50)
0.8720915.42
[p=0.00]
Table 3. Baseline & Generalized Gravity Equation: Panel Estimates.Controls
I II III IVln(Y1) -0.74 -0.44 0.16 0.67
(-2.47) (-1.34) (0.63) (2.42)ln(Y2) -0.60 -0.33 -0.06 0.43
(-2.03) (-1.04) (-0.26) (-1.58)ln(Distance) -0.50 -0.50
(-23.82) (-23.82)ln(Remote1) 17.01 17.00 6.76 1.82
(22.88) (22.76) (2.58) (0.51ln(Remote2) 11.27 11.35 2.01 -4.89
(15.17) (15.17) (0.78) (-1.35)Adjacent 0.83 0.83
(24.42) (24.49)Home 1.81 1.81
(30.66) (30.82)1997 Dummy 6.83 4.89 2.13 0.46
(28.15) (5.84) (2.38) (0.49)CPI1 0.08 0.002
(2.32) (0.06)CPI2 0.07 -0.04
(1.95) (-1.27)Wages1 -0.00002 -0.00002
(-1.04) (-1.71)Wages2 -0.00003 -0.00003
(-1.65) (-2.93)GSP Deflator1 -5.22 -5.27
(-5.58) (-7.70)GSP Deflator2 -0.60 -1.09
(-0.63) (-1.59)
Origin FEs Yes Yes No NoDestination FEs Yes Yes No NoPairwise FEs No No Yes YesObservations 4228 4228 3948 3948Home Effect 6.13 6.13 2.23 7.06
[p=0.00] [p=0.00] [p=0.00] [p=0.00]Border 'Width' 44677 44935 923 31023 In Miles (4.50) (4.50) (2.81) (2.35)NOTES: 1. t-statistics in parentheses; p-values in brackets. 2. A subscript on a control variable indicates origin(1) or destination (2) state. 3. Origin FEs refers to fixed effects for each exporting state (i.e., where the shipment originates); destination FEs refers to fixed effects for each importing state (i.e., where the shipment is shipped); pairwise FEs refers to fixed effects for each bilateral trading pair, allowing a separate fixed effect for shipments from state A to state B and for shipments from state B to state A. 4. Border 'width' in Models I -- II calculated as in Table 1; 'width' (and home effect) in Models III -- IV calculated using Wall's two-step approach (see the text -- section 4.3 -- for further details). 5. p-value for home effect tests null that the effect is equal toone.
Dependent Variable: ln(shipments)
Table 4. Baseline & Generalized Gravity Equation: Dynamic Panel Estimates.Controls
I II III IV V VI VIIln(shipments1993) 0.76 0.72 1.00 0.88 0.99
(52.46) (48.51) (13.00) (5.57) (5.99)ln(Y1) 0.97 1.13 0.19 0.26 -0.04 0.06 -0.05
(62.00) (41.74) (11.04) (10.28) (-0.49) (0.34) (-0.25)ln(Y2) 1.00 1.13 0.22 0.34 -0.01 0.16 0.04
(63.77) (42.12) (12.70) (13.56) (-0.10) (0.94) (0.25)ln(Distance) -0.69 -0.79 -0.07 -0.17 0.12 0.0001 0.08
(-24.94) (-30.26) (-3.43) (-7.45) (1.83) (0.00) (0.51)ln(Remote1) -0.49 -0.09 -0.09 0.11 0.04 0.12 0.23
(-5.58) (-0.96) (-1.50) (1.70) (0.61) (1.25) (2.42)ln(Remote2) 0.36 0.92 0.02 0.19 -0.07 0.03 -0.03
(4.08) (9.71) (0.38) (3.04) (-1.05) (0.20) (-0.23)Adjacent 0.97 0.80 0.25 0.20 0.04 0.1 -0.002
(15.28) (13.54) (5.90) (4.81) (0.55) (0.85) (-0.01)Home 1.78 1.70 0.56 0.59 0.19 0.35 0.19
(15.20) (15.72) (7.28) (7.89) (1.47) (1.43) (0.73)CPI1 -0.004 -0.01 -0.01 -0.01
(-0.73) (-1.96) (-3.04) (-2.52)CPI2 -0.02 -0.000002 0.002 0.004
(-3.45) (-0.00) (0.37) (0.75)Wages1 -0.0001 0.000001 0.000003 0.00001
(-7.86) (0.26) (0.31) (1.55)Wages2 -0.0001 -0.00002 -0.00002 -0.00001
(-6.23) (-4.38) (-2.56) (-1.95)GSP Deflator1 -1.00 -4.49 -4.07
(-1.02) (-7.23) (-5.73)GSP Deflator2 -3.80 -0.92 -0.08
(-3.89) (-1.53) (-0.09)Lagged/Current Controls Lagged Lagged Current Current Current Current CurrentPagan-Hall (1983) [p=0.00] [p=0.00] [p=0.00] Heteroskedasticity TestHansen's J-Statistic [p=0.46] [p=0.28] [p=0.01] (Overidentification Test)F-test of Joint Significance [p=0.00] [p=0.00] [p=0.00] of Instrument SetShea's Partial R² 0.04 0.01 0.01Hall et al. (1996) Test of Instrument Relevance ρ = 0.78 ρ = 0.78 ρ = 0.78Staiger-Stock (1997) [p=0.00] [p=0.00] [p=0.00] Measure of Maximum Bmax=0.003 Bmax=0.003 Bmax=0.003 Relative BiasObservations 2091 2091 1974 1974 1974 1974 1974Home Effect 5.93 5.47 1.75 1.80 1.80 1.43 1.20
[p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.14] [p=0.15] [p=0.47]Border 'Width' 14901 9086 2722611 40478 -960 -1198 -1085 In Miles (4.23) (5.27) (0.40) (1.49) (-2.05) -- (-1.22)NOTES: 1. t-statistics in parantheses. 2. A (non-year) subscript on a control variable indicates orgin (1) or destination (2) state. 3. Intruments used for lagged shipments in Models V -- VII are: ln(Y1,1993), ln(Y2,1993), ln(Remote1,1993), and ln(Remote2,1993). 4. p-value for home effect tests null that the effect is equal to one. See text for further detail.
GMMOLSDependent Variable: ln(shipments1997)
Table 5. Baseline & Generalized Gravity Equation: Exogenous State-to-State Migration.Controls
I II III IV V VI VII VIIIln(Y1) -0.69 -0.39 0.02 0.56 -0.74 -0.44 0.04 0.58
(-2.44) (-1.26) (0.07) (1.95) (-2.61) (-1.42) (0.16) (2.01)ln(Y2) -0.62 -0.34 -0.28 0.30 -0.68 -0.40 -0.29 0.28
(-2.21) (-1.15) (-1.07) (1.06) (-2.40) (-1.33) (-1.09) (1.00)ln(Distance) -0.20 -0.20 -0.19 -0.19
(-8.63) (-8.72) (-8.03) (-8.12)ln(Remote1) 13.31 13.29 6.96 2.31 13.34 13.32 6.79 1.84
(18.54) (18.43) (2.95) (0.64) (18.58) (18.46) (2.56) (0.50)ln(Remote2) 7.63 7.64 2.31 -4.40 7.68 7.68 2.67 -3.69
(10.63) (10.58) (0.89) (-121) (-10.70) (10.64) (1.02) (-1.00)Adjacent 0.42 0.42 0.42 0.42
(11.45) (11.46) (11.38) (11.40)Home -0.65 -0.64 -0.74 -0.73
(-5.43) (-5.42) (-5.69) (-5.68)1997 Dummy 5.14 3.61 2.30 0.57 5.17 3.65 2.35 0.62
(21.46) (4.58) (2.57) (0.61) (21.53) (4.62) (2.61) (0.65)CPI1 0.07 0.004 0.07 0.002
(2.11) (0.13) (2.09) (0.05)CPI2 0.05 -0.03 0.05 -0.03
(1.58) (-1.05) (1.57) (-0.94)Wages1 -0.00003 -0.00002 -0.00003 -0.00002
(-1.52) (-1.61) (-1.51) (-1.61)Wages2 -0.00003 -0.00003 -0.00003 -0.00003
(-2.14) (-3.06) (-2.19) (-3.04)GSP Deflator1 -5.11 -5.09 -5.09 -5.13
(-5.80) (-7.35) (-5.78) (-7.39)GSP Deflator2 -0.24 -0.97 -0.22 -0.93
(-0.27) (-1.40) (-0.24) (-1.35)Migration Inflow 0.22 0.23 0.07 0.05 0.10 0.09 0.01 -0.05 (from 2 → 1) (6.46) (6.62) (1.20) (0.74) (0.79) (0.78) (0.08) (-0.32)Inflow*Median Income 0.01 0.01 0.01 0.01 of In-Migrants (1.13) (1.23) (0.36) (0.63)Migration Outflow 0.23 0.22 0.17 0.10 0.19 0.19 0.29 0.24 (from 1 → 2) (6.58) (6.13) (2.76) (1.65) (1.60) (1.61) (1.76) (1.44)Outflow*Median Income 0.004 0.003 -0.01 -0.010 of Out-Migrants (0.39) (0.29) (-0.82) (-0.88)Origin & Destination FEs Yes Yes No No Yes Yes No NoPairwise FEs No No Yes Yes No No Yes YesHo:βinmig=βoutmig p=0.96 p=0.79 p=0.23 p=0.50 p=0.66 p=0.65 p=0.27 p=0.25Ho:βinmig*median= p=0.68 p=0.60 p=0.44 p=0.33 βoutmig*median
Home Effect 0.52 0.53 0.53 2.74 0.48 0.48 0.52 2.67[p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00]
Border 'Width' in Miles -1149 -1147 -447 5196 -1172 -1171 -452 4555 (-29.36) (-28.63) (-3.78) (2.49) (-56.84) (-54.57) (-3.93) (2.77)Distance Offset Per 174.75 181.60 8.66 12.19 180.07 186.15 7.65 9.05 Migrant Inflow in Feet (4.82) (4.93) (1.20) (0.74) (4.48) (4.57) (1.05) (0.56)Distance Offset Per 177.07 167.40 19.52 26.57 194.16 184.48 20.53 28.83 Migrant Outflow in Feet (4.90) (4.71) (2.74) (1.64) (4.73) (4.58) (2.86) (1.80)Observations 4228 4228 3948 3948 4226 4226 3948 3948NOTES: 1. t-statistics in parentheses. 2. All regressions pool the 1993 and 1997 cross-sections. 3. A subscript on a control variable indicates orgin (1) or destination (2) state. 4. Average distance offsets evaluated at the mean. 5. t-statistics for the distance offsets calculated via the delta method. 5. p-value for home effect tests null that the effect is equal to one. See text for further detail.
Dependent Variable: ln(shipments)
Table A1. Summary Statistics
Variable 1993 1997 Full SampleShipments 2666.71 3240.13 2950.10 (mills current US$) (12910.76) (16004.91) (14523.65)Shipments 4655.61 5700.29 5161.68 (1000s tons) (30292.45) (35975.61) (33167.15)Distance (miles) 1197.68 1197.68 1197.68
(717.21) (717.21) (717.13)Gross State Product 133481.50 168943.90 151212.70 (mills current US$) (154335.90) (191697.00) (174904.40)Population 5321.83 5530.35 5426.09 (1000s) (5661.77) (5856.62) (5760.34)Remoteness 1.19 0.95 1.07 (GSP-weighted) (0.24) (0.19) (0.25)Remoteness 0.03 0.03 0.03 (Population-weighted) (0.01) (0.01) (0.01)CPI (regional, 144.04 160.15 152.09 1982-1984 = 100) (4.57) (4.42) (9.22)Average Wage 26050.75 28954.21 27502.48 Per Job (current US$) (3702.02) (4594.85) (4417.35)Adjacent (1 = bordering 0.11 0.11 0.11 states) (0.32) (0.32) (0.32)Home (1 = intrastate) 0.02 0.02 0.02
(0.14) (0.14) (0.14)State-to-State Migration 39175.10 40892.26 40033.68 (Total Tax Returns, (379140.10) (390379.20) (384759.80) In Migration)NOTE: We only report summary statistics for one GSP-weighted remotesness measure and onepopulation-weighted remoteness measure since the mean of Remoteij is equal to the mean of Remoteji.
Mean (Standard Deviation)
Table A2. Intrastate Shipment Share as a Percent of Total State Shipments
State 1993 1997 % Change State 1993 1997 % ChangeSouth Dakota 0.401 0.266 -0.136 Connecticut 0.770 0.620 -0.150Vermont 0.345 0.218 -0.127 Utah 0.908 0.778 -0.129New Hampshire 0.229 0.130 -0.100 Minnesota 0.679 0.566 -0.113Wyoming 0.411 0.333 -0.078 West Virginia 0.373 0.288 -0.085Washington 0.622 0.560 -0.061 Louisiana 0.707 0.626 -0.081West Virginia 0.277 0.243 -0.035 Nevada 0.813 0.732 -0.080Maine 0.353 0.319 -0.033 Washington 0.841 0.776 -0.066Oregon 0.494 0.465 -0.029 Vermont 0.720 0.655 -0.065Virginia 0.372 0.345 -0.027 Oregon 0.808 0.755 -0.053New Mexico 0.483 0.462 -0.022 Missouri 0.634 0.597 -0.037New Jersey 0.315 0.293 -0.022 Ohio 0.710 0.674 -0.037Michigan 0.486 0.466 -0.020 New Mexico 0.608 0.577 -0.030Wisconsin 0.351 0.332 -0.019 Wyoming 0.170 0.141 -0.029Arizona 0.437 0.419 -0.018 Virginia 0.734 0.712 -0.022Ohio 0.384 0.368 -0.016 Michigan 0.741 0.728 -0.013Louisiana 0.497 0.484 -0.013 Kansas 0.540 0.531 -0.009Texas 0.612 0.601 -0.011 Montana 0.504 0.496 -0.008Minnesota 0.406 0.395 -0.011 Texas 0.853 0.848 -0.006Pennsylvania 0.353 0.349 -0.005 California 0.916 0.912 -0.004California 0.617 0.614 -0.004 Colorado 0.766 0.763 -0.003Missouri 0.284 0.286 0.002 New York 0.779 0.783 0.004South Carolina 0.307 0.309 0.002 South Carolina 0.641 0.648 0.008Alabama 0.341 0.346 0.005 Iowa 0.655 0.668 0.013Rhode Island 0.227 0.233 0.006 Alabama 0.712 0.737 0.025Colorado 0.432 0.439 0.006 Massachussetts 0.725 0.752 0.027Florida 0.639 0.646 0.007 Georgia 0.729 0.761 0.032Iowa 0.352 0.361 0.010 Maryland 0.652 0.691 0.040Indiana 0.284 0.296 0.011 Wisconsin 0.695 0.735 0.040Oklahoma 0.347 0.360 0.013 Arkansas 0.591 0.633 0.043New York 0.413 0.426 0.013 Mississippi 0.562 0.609 0.047Idaho 0.335 0.357 0.022 Tennessee 0.609 0.657 0.048Kansas 0.265 0.291 0.026 North Carolina 0.698 0.755 0.057Massachussetts 0.338 0.370 0.031 Idaho 0.646 0.707 0.061Nebraska 0.291 0.324 0.033 Kentucky 0.511 0.576 0.064Montana 0.534 0.567 0.033 South Dakota 0.600 0.667 0.067Illinois 0.340 0.374 0.034 Florida 0.861 0.929 0.068Connecticut 0.220 0.256 0.036 Maine 0.732 0.810 0.079North Carolina 0.382 0.419 0.038 Indiana 0.567 0.652 0.085Tennessee 0.263 0.305 0.042 New Jersey 0.608 0.697 0.090Mississippi 0.289 0.334 0.045 Nebraska 0.524 0.618 0.094Georgia 0.332 0.384 0.052 Arizona 0.775 0.872 0.097Utah 0.395 0.448 0.053 Illinois 0.589 0.687 0.098Kentucky 0.249 0.313 0.063 Pennsylvania 0.628 0.746 0.119North Dakota 0.379 0.443 0.064 North Dakota 0.592 0.716 0.124Delaware 0.160 0.243 0.082 Oklahoma 0.553 0.696 0.144Arkansas 0.263 0.353 0.090 Delaware 0.314 - -Maryland 0.324 0.433 0.109 New Hampshire - 0.470 -Nevada 0.262 0.403 0.141 Rhode Island 0.806 - -
Value ($) Weight (tons)
Table A3. Alternative Static Baseline Specifications: Changes in Measurement.
ln(dist.) Home Bias ln(dist.) Home BiasCoeff. Coeff. Coeff. Coeff.
(1) Use weight, measured in 1000s -1.15 2.28 -1.09 2.42 of tons, as dependent variable (-24.30) (11.43) (-22.44) (11.93)
(2) Use population-weighted -0.83 1.58 -0.72 1.76 distance for remoteness measure (-30.10) (13.39) (-26.07) (15.15)
(3) Use population to measure -0.86 1.55 -0.75 1.74 scale (original remoteness measure) (-32.12) (13.53) (-28.10) (15.40)
(4) Use population to measure -0.85 1.56 -0.74 1.75 scale & population-weighted (-31.81) (13.68) (-27.82) (15.53) distance for remoteness measure
(5) Use Shipments/(Y1*Y2) -0.82 1.58 -0.70 1.78 as dependent variable (-30.41) (13.43) (-25.94) (12.54)
(6) Use Interstate Shipments -0.73 1.65 -0.66 1.81 to measure own scale (Y1) (-29.75) (15.60) (-26.72) (17.29)
(7) Use Nitsch (2000) distance -0.82 1.85 -0.71 2.01 measure (k=0.5) (-29.70) (15.93) (-25.71) (17.50)
(8) Use Nitsch (2000) distance -0.82 1.67 -0.71 1.85 measure (k=0.4) (-29.70) (14.23) (-25.71) (15.97)
(9) Use Nitsch (2000) distance -0.82 1.43 -0.71 1.64 measure (k=0.3) (-29.70) (12.03) (-25.71) (13.98)
(10) Use Nitsch (2000) distance -0.82 1.10 -0.71 1.36 measure (k=0.2) (-29.70) (8.98) (-25.71) (11.21)
(11) Use Nitsch (2000) distance -0.82 1.27 -0.71 1.50 measure (state-specific k's) (-29.48) (10.45) (-25.53) (12.54)
NOTES: 1. t-statistics in parentheses. 2. Each regression also includes measures of scale (Y1 and Y2) (except specification (6)), measures of remoteness (Remote1 and Remote2), a dummy variable for adjacent states, and a constant. See Table 1 for further details. 3. A subscript on a control variable indicates orgin (1) or destination (2) state.
Dependent Variable: ln(shipments)1993 1997
Alternative Specification
Table A4. Baseline & Generalized Gravity Equation: Dynamic Panel Estimates with State-to-State Migration.Controls
I II III IV V VI VII VIIIln(Distance) -0.01 0.05 -0.04 -0.04 0.15 0.11 0.20 0.16
(-0.08) (0.36) (-0.53) (-0.32) (2.45) (1.55) (2.20) (1.63)Home -0.22 -0.03 -0.19 -0.09 -0.13 0.01 -0.50 -0.34
(-2.19) (-0.25) (-1.63) (-0.72) (-1.26) (0.05) (-1.83) (-1.23)ln(shipments1993) 0.75 0.91 0.70 0.78 1.00 1.00 1.01 1.03
(6.85) (5.37) (5.82) (4.54) (10.92) (11.64) (10.24) (10.09)Migration Inflow 0.01 -0.01 -0.42 -0.61 0.03 0.03 0.16 -0.25 (from 2 → 1) (0.40) (-0.22) (-2.70) (-3.42) (0.58) (0.36) (0.21) (-0.36)Inflow*Median Income 0.04 0.06 -0.01 0.03 of In-Migrants (2.88) (3.49) (-0.13) (0.43)Migration Outflow 0.13 0.07 0.66 0.46 0.03 -0.001 -0.75 -0.52 (from 1 → 2) (2.98) (1.42) (3.49) (2.47) (0.44) (-0.01) (-0.91) (-0.67)Outflow*Median Income -0.05 -0.03 0.08 0.05 of Out-Migrants (-2.98) (-2.10) (0.99) (0.68)Expanded Control Set No Yes No Yes No Yes No Yes
Instrument Set A A A A B B B BPagan-Hall (1983) [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] Heteroskedasticity TestHansen's J-Statistic [p=0.88] [p=0.01] [p=0.81] [p=0.01] [p=1.00] [p=0.67] [p=0.28] [p=0.23] (Overidentification Test)F-test of Joint Significance [p=0.00] [p=0.00] [p=0.00] [p=0.01] [p1=0.00] [p1=0.00] [p1=0.00] [p1=0.00]
of Instrument Set [p2=0.00] [p2=0.00] [p2=0.00] [p2=0.00][p3=0.00] [p3=0.00] [p3=0.00] [p3=0.00]
[p4=0.00] [p4=0.00][p5=0.00] [p5=0.00]
Shea's Partial R² 0.02 0.01 0.02 0.01 0.54 0.37 0.06 0.080.33 0.31 0.05 0.060.03 0.04 0.06 0.07
0.05 0.050.03 0.03
Hall et al. (1996) Test of ρ = 0.75 ρ = 0.75 ρ = 0.75 ρ = 0.75 ρ = 0.42 ρ = 0.42 ρ = 0.26 ρ = 0.26 Instrument Relevance [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00] [p=0.00]Staiger-Stock (1997) Bmax=0.003 Bmax=0.003 Bmax=0.002 Bmax=0.002 Bmax=0.004 Bmax=0.003 Bmax=0.003 Bmax=0.73
Measure of Maximum Relative Bias
Ho:βinmig=βoutmig p=0.10 p=0.36 p=0.00 p=0.00 p=0.98 p=0.86 p=0.55 p=0.85Ho:βinmig*median= p=0.00 p=0.00 p=0.55 p=0.88 βoutmig*median
Home Effect 0.80 0.97 0.83 0.91 0.88 1.01 0.61 0.72[p=0.01] [p=0.80] [p=0.07] [p=0.45] [p=0.18] [p=0.96] [p=0.02] [p=0.14]
Border 'Width' in Miles -1198 1196 -1181 -1068 1615 -74 13000 9200 -- (0.21) (-8.12) (-0.94) (0.81) (-0.05) (1.30) (1.00)Distance Offset Per 412.45 35.33 -52.13 -114.52 -29.59 -40.63 -56.46 -45.88 Migrant Inflow in Feet (0.08) (0.21) (-0.30) (-0.27) (-0.59) (-0.37) (-1.00) (-0.59)Distance Offset Per 3740.38 -247.18 626.84 469.16 -27.51 0.84 -3.18 16.83 Migrant Outflow in Feet (0.08) (-0.32) (0.58) (0.34) (-0.40) (0.01) (-0.05) (0.20)Observations 1974 1974 1974 1974 1974 1974 1974 1974
NOTES: 1. t-statistics in parentheses. 2. All regressions pool the 1993 and 1997 cross-sections. 3. Each specification also includes controls for own anddestination GSP and remoteness, a dummy for adjacent states, and a 1997 dummy. 4. Expanded control set includes own and destination CPI, wages, andGSP deflator. 5. Instrument sets: A = ln(Y1,1993), ln(Y2,1993), ln(Remote1,1993), and ln(Remote1,1993); B = each migration variable demeaned squared plus
lagged own and destination migration. 6. Average distance offsets evaluated at the mean. 7. t-statistics for the distance offsets calculated via the delta method. 8. p-value for home effect tests null that the effect is equal to one.
Endogenous MigrationDependent Variable: ln(shipments)
Exogenous Migration
