# GRAVITY WITH GRAVITAS: McCallum’s gravity equation

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.

To a large extent the contribution of this paper is methodological. Our specification can be applied in many different contexts in which various aspects of implicit trade barriers are the focus. Gravity equations similar to McCallum’s have been estimated to determine the impact of trade unions, monetary unions, different languages, adjacency, and a variety of other factors; all can be improved with our methods. Gravity equations have also been applied to migration flows, equity flows and FDI flows. Here there is no received theory to apply, consistently or not, but our results suggest the fruitfulness of theoretical foundations.

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The remainder of the paper is organized as follows. In Section II we will provide some results based on McCallum’s gravity equation. The main new aspect of this section is that we also report the results from the U.S. perspective, comparing interstate trade to state-province trade. In section III we derive the theoretical gravity equation. The main innovation here is to rewrite it in a simple symmetric form, relating bilateral trade to size, bilateral trade barriers and multilateral resistance variables. Section IV discusses the procedure for estimating the theoretical gravity equation, both for a two-country version of the model, consisting of the U.S. and Canada, and for a multi-country version that also includes all other industrialized countries. The results are discussed in section V. Section VI performs sensitivity analysis and the final section concludes.