# Collapsing trade in a Barbie world

In recent months, several analysts have argued that the unprecedented trade collapse the world is currently experiencing is linked to the vertical disintegration of production. Every time the US buys one fewer Barbie doll, trade declines not only by the value of the finished doll, but by the value of all the intermediate trade flows that went into creating it.

Not being a theorist, I have been puzzled by the argument for a while, but I now think I may understand.

The puzzlement comes from the following thought experiment. Consider a world in which total trade consists of 100 Barbie dolls. Imagine that income declines by 1%, and that this leads to one fewer Barbie doll being exported and imported. Now imagine two states of the world. In the first state of the world, there is no vertical disintegration. One Barbie doll no longer gets shipped, and thus trade has declined by 1%. The elasticity of trade with respect to GDP is 1. In the second state of the world, there is vertical disintegration, and each time a Barbie gets traded this sets in motion intermediate trade flows of equivalent size. Thus, when one fewer Barbie gets shipped, trade now falls by 2. But since initial trade was 200, this is still a 1% decline, and the elasticity of trade with respect to GDP is still 1.

On the other hand, imagine a third state of the world, in which 50 Barbies are produced in a vertically disintegrated manner (leading to a total trade flow of 100), and in which 50 Kens are produced the old fashioned way, producing a trade flow of 50. Total initial trade is thus 150. If the impact of a 1% fall in world income is that 1 fewer Barbie gets shipped, then trade falls by 2, which is 1.33% of 150. The elasticity of trade with respect to GDP is now higher than before. And if initial trade had involved only 1 Barbie, and 99 Kens, and again declining income led to one less Barbie being shipped, the elasticity would be almost 2, or nearly twice what it was in the original state of the world.

Of course, if the marginal impact of falling income was to lower trade in Kens rather than in Barbies, the conclusions would be very different.

So: in the context of a world where goods either are vertically disintegrated or not, vertical disintegration can help to explain the higher elasticity of trade with respect to GDP that we are experiencing today, providing that (a) marginal trade disproportionately involves vertically disintegrated goods; and (b) not all trade is vertically disintegrated. Indeed, given that (a) holds, the ability of vertical disintegration to explain higher trade elasticities in such a world increases as vertical disintegration becomes less important (in the sense of accounting for a smaller share of initial trade)!

In the real world, different goods involve differing degrees of vertical disintegration, and marginal declines in income trigger falling consumption of and trade in not just cars and Barbies, but primary commodities and other more traditional products. The general point presumably will remain valid: non-linearities of one sort or another are crucial in making the vertical disintegration story work.

## 6 replies on “Collapsing trade in a Barbie world”

John Fitzgeraldsays:

A move from a world where countries produce final products from basic inputs to one where there is vertical disintegration has produced a high elasticity of trade with respect to GDP over recent decades. If data were available for world trade in consumer goods – final products – the elasticity would be much lower.
The consequence of this is also that for a given change in world trade the impact on domestic value added is falling. Much of the increase in exports is accounted for by imports.
In the case of Ireland, input output tables from 1969 till 1985 show that the import content of exports rose steadily from 40% to 50%. Since then, while there has been some further increase, it has been limited.

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US researchers say trade statistics can mislead as much as inform. For every \$300 iPod sold in the US, the politically volatile US trade deficit with China increases by about \$150 (the factory cost). Yet, the value added to the product through assembly in China is probably a few dollars at most.

In 2007, a teardown analysis of the 451 parts, which made up the 30-gigabyte video iPod, was used to to track the value-added from the US, across Asia and back to the US:

http://pcic.merage.uci.edu/papers/2007/AppleiPod.pdf

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