Online Appendix for "Vertical Linkages and the Collapse of Global Trade" Rudolfs Bems

Robert C. Johnson

International Monetary Fund

Dartmouth College

Kei-Mu Yi Federal Reserve Bank of Minneapolis

This appendix presents algebraic details regarding the construction of the …nal versus intermediate goods trade decomposition.

Looking at trade from the import side,we can

rewrite the change in imports for each country as: imdi d d imm i dm IM IM i i + imi imi X dIi (t) X mIi (t) dd = q b (t), and IM qbid (t); = i i m d im im i i t t

di = IM

dm with IM i

(1) (2)

d where imm i and imi are total intermediate and …nal goods imports for country i, mIi (t) = P P P j6=i s mji (s; t), and dIi (t) = j6=i dji (t). There are two important di¤erences here be-

tween …nal and intermediate goods imports. First, …nal goods imports respond directly to changes in …nal demand (b qid (t)), while intermediate goods imports respond to changes in pro-

duction (b qi (t)). Second, the import weights placed on each sector may di¤er for intermediate and …nal goods. Aggregating across countries, the proportional change in world trade in …nal goods is P imdi d d IM i , and the proportional change in world trade in intermediate goods T^d = i Td 1

P P is T^m = i t

imm i Tm

P P m d d dm = i imm IM i . These proportional i , with T = i imi and T

changes can then be rewritten as: Tbd =

Tbm = where T m (t) =

P

i

X t

X t

T d (t) Td T m (t) T (t)

Tbd (t) with Tbd (t) =

X

Tbm (t) with Tbm (t) =

mIi (t) and T d (t) =

P

i

i

X i

dIi (t) T d (t)

qbid (t);

mIi (t) T m (t)

qbi (t);

(3) (4)

dIi (t). Note that the index t here identi…es the

sector in which the goods are imported, for either …nal or intermediate use. For …nal goods, the sector in which goods are produced is identical to the sector in which goods are imported by de…nition. For intermediate goods, goods produced in sector s can be imported by another sector t as intermediates.

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