International Trade — The Gravity Model and Global Value Chains

International Trade — Who Trades With Whom Is Not Settled by Comparative Advantage Alone

Chapters 1–4 used models to show why trade brings gains and whose surplus a tariff moves. Actual bilateral trade data follow a simpler rule: large countries trade more with each other, and so do nearby countries. On top of that, when intermediates cross borders several times, gross exports drift away from value-added exports.

1. The gravity equation is a metaphor of mass and distance

Basic gravity

X_{ij} = G Y_i^a Y_j^b / D_{ij}^c

X is exports from country i to country j, Y is economic size, and D is a proxy for trade costs such as distance, borders, language and tariffs.

Taking logs gives $\ln X_{ij} = \mathrm{const} + a \ln Y_i + b \ln Y_j - c \ln D_{ij} + \cdots$ . Empirically, $a$ and $b$ are often near 1 and the distance elasticity $c$ around 0.7–1.5. A partner with twice the GDP trades almost twice as much, and doubling distance cuts trade substantially.

To claim that “distance is the cause”, the equation must control for multilateral resistance — how close the other markets are. Trade between Korea and Chile depends not only on the distance between the two countries but also on how close Korea is to the Chinese and US markets. This is the point Anderson and van Wincoop made.

With distances of 1,000 km and 2,000 km and an elasticity of 1, trade halves, other things equal. Whether a 10% tariff raises trade costs by that much depends on the elasticity of substitution and customs costs, so it is not the same number as the distance coefficient.

2. Gross exports count intermediates several times

If Korea designs and fabricates a semiconductor, has it assembled abroad, then reimports it to put in a mobile phone, the same value added shows up repeatedly in export statistics. Exports/GDP on a gross basis can overstate openness.

The same phone, different trade numbers
Measure	What it captures	What it misses
Gross exports	Every amount that crosses the border	The share of imported intermediates
Value-added exports	Value newly created at home	Lags and industry classification in some data
Intermediate share	Depth of GVC participation	Who captures the profit

If a 100-dollar export contains 60 dollars of imported intermediates, domestic value added is 40 dollars. Export dependence is 100/GDP in gross terms and 40/GDP in value-added terms. That a tariff on intermediates makes the effective rate of protection differ from the tariff on final goods links back to chapter 3.

3. How gravity and GVCs change policy statements

A tariff cut for a distant market has a different effect from a tariff cut for a neighbour already tied in through supply chains. Rules of origin can decide participation more than the nominal tariff. The statement “growing industries with a comparative advantage raises exports” is complete only when it also says at which stage of value added that industry sits.

This course takes comparative advantage, factor endowments, trade policy, worked numerical examples and empirical patterns as the skeleton of undergraduate international trade. Strategic trade policy and firm heterogeneity (the Melitz model) are topics these five chapters do not cover.

Check your understanding

If Korea’s gross exports are 40% of GDP and imported intermediates make up 50% of exports, what is value-added exports/GDP roughly? 0.40×0.50 = 0.20. If the intermediate share differs by industry, this product is only an approximation.

References

James Anderson and Eric van Wincoop, “Gravity with Gravitas,” American Economic Review (2003)
OECD, Trade in Value Added (TiVA)
WTO, World Trade Report