GRAVITY WITH GRAVITAS: Regulatory costs

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
GRAVITY WITH GRAVITAS: Regulatory costsw8079-6
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:
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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
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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.
Substituting (9 ) into the export demand system (6) yields the gravity equation
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An implicit solution for the price inde es as a function of trade barriers can be found by substituting (9) in (7):
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Our basic gravity model is (10) subject to (11).