We assume that the trade costs are borne by the exporter. We have in mind information costs, design costs and various legal and regulatory costs as well as transport costs. The new empirical literature on the export behavior of firms (Roberts and Tybout [1995]; Bernard and Wagner [1998]) emphasizes the large costs facing exporters. Formally, we assume that for each good shipped from i to j the exporter incurs export costs equal to t*j — 1 of country i goods. The exporter passes on these trade costs to the importer. The nominal value of exports from i to j (j’s payments to i) is x*j = p*jc*j, the sum of the value of production at the origin, p*c*j and the trade cost (t*j — 1)p*c*j that the exporter passes on to the importer. Total income of region i is therefore yi = ^2j xij-
The nominal demand for region i goods by region j consumers satisfying maximization of (4) subject to (5) is

where Pj is the consumer price index of j, given by

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We will refer to this price index as multilateral trade resistance as it depends positively on trade barriers with all trading partners. Market clearance implies:

A tractable gravity model approach may be based on estimating a stochastic version of (6) subject to the constraints (7) and ( 8). The set of scaled prices {PiPij are solved, up to a factor of proportionality, as implicit functions of the +’s and I’s from the system of market clearing constraints. Given some procedure for identifying the trade barriers, estimation can proceed. But we achieve a very useful simplification by assuming that the trade barriers are symmetric, that is, lij ‘ !ji- Under symmetry it can be shown that the implicit solution to

with 0i = yi/уw the ith region’s share in world income, is a solution to (7)-(8). (9) is solved not only for relative prices, but also for absolute prices, so it imposes an implicit normalization. Equation (9) has a simple intuition. First, a large Wi implies a large value of sales, which for a given preference parameter qi is induced by a low goods price pi. Second, high trade barriers, reflected by high multilateral resistance Pi, lower demand for region i’s goods, reducing its supply price pi. Continue reading →

The empirical literature cited above pays no more than lip service to theoretical justification. We show in this section how taking the theory seriously provides a different model to estimate with a much more useful interpretation.
Anderson [1979] presented a theoretical foundation for the gravity model based on constant elasticity of substitution (CES) preferences and goods that are differentiated by region of origin. Subsequent extensions (Bergstrand [1989,1990], Dear-dorff [1998]) have preserved the CES preference structure and added monopolistic competition or a Hecksher-Ohlin structure to explain specialization. A contribution of this paper is our manipulation of the CES expenditure system to derive an operational gravity model with an elegantly simple form. On this basis we derive a decomposition of trade resistance into three intuitive components: (i) the bilateral trade barrier between region i and region j, (ii) i’s resistance to trade with all regions, and (iii) j’s resistance to trade with all regions. Continue reading →

Border — Canada is the exponential of the Canadian dummy variable coefficient, a5, which gives us the effect of the border on the ratio of inter-provincial trade to state-province trade after controlling for distance and size. Similarly, Border — US is the exponential of the coefficient on the US dummy variable, which gives the effect of the border on the ratio of inter-state trade to state-province trade after controlling for distance and size. Continue reading →

McCallum [1995] estimated the following equation:

Here %ij is exports from region i to region j, + and +j are gross domestic production in regions i and j, is the distance between regions i and j, and By is a dummy variable equal to one for inter-provincial trade and zero for state-province trade. For the year 1988 McCallum estimated this equation using data for all 10 provinces and for 30 states that account for 90% of U.S.-Canada trade. In this section we will also report results when estimating (1) from the U.S. perspective. In that case the dummy variable is one for interstate trade and zero for state-province trade. We also report results when pooling all data, in which case there are two dummy variables. The first is one for interprovincial trade and zero otherwise, while the second is one for interstate trade and zero otherwise. Continue reading →

Two factors contribute to making McCallum’s ceteris paribus ratio of interprovincial to province-state trade so large. First, his estimate is based on a regression with omitted variables, the multilateral resistance terms. Estimating McCallum’s regression for 1993 data we find a ratio of 16.4, while a consistent estimate based on the theoretical gravity equation implies a ratio of 10.7. Second, the magnitude of both ratios largely reflects the small size of the Canadian economy. If we estimate McCallum’s regression with US data, we find that trade between states is only a factor 1.5 times trade between states and provinces. The intuition is simple in the context of the model. Even a moderate barrier between Canada and the rest of the world leads to high multilateral resistance for the provinces because it affects trade barriers between a province and almost all of its potential trading partners. This significantly raises interprovincial trade, by a factor 6 based on our estimated model. In contrast, the multilateral resistance of US states is much less affected by a border barrier since it does not affect the barrier between a state and the rest of the large US economy. Therefore trade between the states is not much increased by border barriers. Continue reading →

While gravity equations used in empirical applications are known for their strong fit to the data, the estimated equations do not correspond to those derived theoretically. The theory, first developed by Anderson [1979], tells us that after controlling for size, trade between two regions is decreasing in their bilateral trade barrier relative to the average barrier of the two regions to trade with all their partners. Intuitively, the more resistant to trade with all others a region is, the more it is pushed to trade with a given bilateral partner. We define a theoretically appropriate average barrier below and call it multilateral resistance. McCallum did not include multilateral resistance variables in his analysis. Most of the subsequent literature does include a form of multilateral resistance in the form of an atheoretic remoteness variable related to distance from all bilateral partners. But the remoteness inde does not include national border barriers, even though these are the focus of this literature, and its functional form is at odds with the theory. Continue reading →

ABSTRACT
The gravity model has been widely used to infer substantial trade flow effects of institutions such as customs unions and exchange rate mechanisms. McCallum [1995] found that the US-Canada border led to trade between provinces that is a factor 22 (2,200%) times trade between states and provinces, a spectacular puzzle in light of the low formal barriers on this border. We show that the gravity model usually estimated does not correspond to the theory behind it. We solve the “border puzzle” by applying the theory seriously. We find that national borders reduce trade between the US and Canada by about 44%, while reducing trade among other industrialized countries by about 30%. McCallum’s spectacular headline number is the result of a combination of omitted variables bias and the small size of the Canadian economy. Within-Canada trade rises by a factor 6 due to the border. In contrast, within-US trade rises 25%. Continue reading →