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 approach abounds. This paper examines the empirical relevance of state borders in U.S. interstate trade for various specifications of the gravity equation. We find a large and economically significant subnational border effect for some specifications. However, two model specifications drastically reduce (if not eliminate) the border effect: (i) dynamic panel specifications controlling for past levels of trade and (ii) models conditioning on internal migration. JEL: C23, F14, F16, J61 Keywords: 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: tosang@mail.smu.edu; 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 1 In 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. 2 One 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. 3 Aside from intellectual curiosity, there are other motivations for understanding the large border effect at the U.S. subnational 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 product 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 flowsisthe 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 flowsasa 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-specificproductdifferentiation (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(shipments ij )=α + β 1 ln(y i )+β 2 ln(y j )+β 3 ln(d ij ) +β 4 ln(remote ij )+β 5 ln(remote ji )+β 6 Adjacent ij + β 7 Home i + u ij (1) where Shipments ij is exports from state i to state j, Y i(j) is gross output in state i (j), D ij is the geographical distance between state i and j, Adjacent ij is a dummy variable equal to one for shipments 4 Since 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 Remote ij and Remote ji are measures of how remote states i (j) andj (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, Home i. 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{ β 3 /β 7 } 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, 5 As in Wolf [50], Remote ij = P 48 k=1,k6=j D ik GSP k. Similarly, Remote ji = P 48 k=1,k6=i D jk GSP k. 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). 6 The baseline model utilized here differsfromwolf[50]onlyinthatwolfcodesintrastateshipmentsasadjacentaswell (i.e., Adjacent ij equals one for contiguous neighbors and for within-state trade). 7 The 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 which results in d = D [exp( β 7/β 3) 1]. β 3 ln(d + d ) ln(d) = β 7 8 The variance of the border width is derived via the delta method and given by [ d β 3, d β 7 ]V ( β)[ e d β 3, d β 7 ] 0,whereV( β)is e the variance-covariance matrix of β 3 and β 7 (see Greene [21], p. 297). 9 Due 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 : β 8 RCP I i + β 9 RCP I j + β 10 W i + β 11 W j +β 12 P GSPi + β 13 P GSPj + β 14 X i + β 15 M i (2) where RCP I i(j) denotes the regional consumer price index for each state i (j), W i(j) is the average wage per job in state i (j), P GSPi (j) denotes the gross state product (GSP) deflator in state i (j), and X i (M i ) 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 effectthataretoosmall. Inclusionoffixed 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: β 16 T t + β 0 17OFE i + β 0 18DFE j + β 0 19PFE ij (3) where T t is a dummy variable equal to one in 1997 (zero otherwise), OFE i denotes a vector of origin fixed effects, DFE j denotes a vector of destination fixed effects, and PFE ij is a vector of pairwise fixed effects, where PFE ij 6= PFE ji (as in Wall [48]). Note that the inclusion of pairwise fixed effects prevents the inclusion of all time invariant control variables (D ij, Adjacent i, Home i, OFE i,anddfe j ).. 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; 10 Due 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: β e0 Z t 1 or β 20 ln(shipments ij,t 1 )+ β e0 Z t (4) where Z t 1 (Z t ) is a vector of lagged (current) control variables that includes all regressors from the baseline or generalized models, β e is the corresponding vector of coefficients, and Shipments ij,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 11 Eichengreen 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 : β 21 InMigrant ij + β 22 InMigrant ij InMedian ij +β 23 OutMigrant ij + β 24 OutMigrant ij OutMedian ij (5) where InMigrant ij is the number of migrants entering state i from state j, InMedian ij is the median income of all migrants entering state i from state j, OutMigrant ij is the number of migrants leaving state i for state j, andoutmedian ij 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{( β 21 /β 3 ) 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{( β 21 /β 3 ) ln[m/(m +1)]+( β 23 /β 3 ) ln(median) ln[m/(m +1)]} 1 ª Standard 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 transportation: 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 industries (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), Shipments ij, are reported. 12 For a theoretical justification of an expanded gravity equation incorporating internal migration, see Combes et al. [12]. 13 The 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 or β 3 ln(d + d ) ln(d) = β 21 ln(m +1) ln(m) β 3 ln(d + d ) ln(d) = β 22 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, D ij, 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, D ii, 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, Y i, 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 (RCP I i ), available for four regions West, East, South, Midwest from the U.S. Bureau of Labor Statistics; (ii) average wage perjobforeachstate(w i ), available from the BEA; and, (iii) state-specific GSP deflators, calculated as (NGSP t /RGSP t )/(NGSP 89 /RGSP 89 ), 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 14 The authors are grateful to Holger Wolf for providing this data. 15 See 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 filedinstatej in the previous year. Intrastate migration (i.e., InMigrant ii and OutMigrant ii ) 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, notindividual 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 16 On 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. 17 The 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-r 2 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-r 2 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. 18 The 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 effectcannotbe 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. 19 Even 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 contemporaneous 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 20 In 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 instruments. 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-r 2 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 (B max 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 approach is, at least in the present case, inconsequential. Thus, the use of current or lagged controls within a gravity 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. in previous dynamic gravity models is to treat lagged trade flows as exogenous. As stated previously, the norm 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 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 21 Note 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. 22 Inclusionoflaggedtradeflows 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. In 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 firstnotethattheoveridentification 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 R 2. 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., InMigrant ii and OutMigrant ii ) 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 23 Estimating 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. 24 For 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). 25 A 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) againstln(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 subnational 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 advantage 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. 26 The 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