Lecture 7: Factor Content
Elhanan Helpman
Fall 2016
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Lecture 7: Factor Content
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Factor Content
Suppose that instead of predicting the pattern of commodity trade, we
attempted to predict the net factor content of trade.
Net exports of factor j in country k is given by
Fjk =
or
F k = AT k ,
∑i aji (w ) Tik ,
where T k = X k
Ck.
With homothetic preferences C k = s k ∑l X l and factor market clearing
requires AX k = V k .
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Vanek Equations
Therefore:
F k = AT k = A X k
Ck
= Vk
s k V , where V =
∑ Vl.
l
It follows that Fjk > 0 if and only if Vjk > s k Vj .
Furthermore, suppose that we rank factors such that
Vk
Vk
V1k
Vk
Vk
> 2 > ... > l > s k > l +1 > ... > m .
V1
V2
Vl
Vl + 1
Vm
Then we must have Fjk > 0 for all factors j
j > l.
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Lecture 7: Factor Content
l and Fjk < 0 for all factors
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The Leontief Paradox Reconsidered
Leamer (1980) noted that Leontief’s paradoxical …nding is only paradoxical in
a world of two inputs, but not necessarily paradoxical in a world of more than
two inputs.
Moreover:
He noted that in 1947, the U.S. exported both capital and labor services.
The capital-labor ratio in production was higher than in consumption. which
reveals capital abundance.
The U.S. had a large trade surplus, which would make it a net exporter of
more inputs than predicted by the Vanek equations.
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First Test of HOV: Bowen, Leamer and Sveikauskas (1987)
Bowen et al. (1987) conducted the …rst test of the Vanek equations, which
they rewrote as:
Vjk
Fjk
= k
1 for all j and k.
s k Vj
s Vj
They used data on 12 factors and 27 countries in 1967.
They performed two types of tests:
Sign tests: for what fraction of the observations is
!
Vjk
Fjk
sign
=
sign
s k Vj
s k Vj
Rank tests: for what fraction of the observations is
!
Fjk0
Vjk
Fjk
sign
=
sign
s k Vj
s k Vj 0
s k Vj
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Lecture 7: Factor Content
!
1 ?
Vjk0
s k Vj 0
!
?
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Bowen, Leamer and Sveikauskas (continued)
The table below shows these tests by factors:
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Bowen, Leamer and Sveikauskas (continued)
The table below shows these tests by country:
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The Case of Missing Trade: Tre‡er (1995)
Tre‡er (1995) studies systematic deviations of the data from the theoretical
predictions of the Vanek equations.
The Vanek equations imply:
Fjk = Vjk
s k Vj .
For 33 countries (accounting for about 80% of world income) and 9 inputs in
1983, he constructs the following measures of deviation from the Vanek
equations:
εkj = Fjk
Vjk s k Vj .
The main …ndings are that:
1
2
3
εkj is approximately equal to
Vjk
s k Vj , which implies that the factor
content measures are biased toward zero, Fjk
0 (“Missing Trade”).
In poor countries there is a predominance of εkj < 0 while in rich countries
there is a predominance of εkj > 0.
The above imply that poor countries tend to be abundant in most factors while
rich countries tend to be scarce in most factors (“Endowments Paradox”).
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Tre‡er (1995) (continued)
The missing trade is illustrated in the following …gure:
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Tre‡er (1995) (continued)
These features may result from productivity di¤erences, which he examines
next.
First, consider Hicks neutral technological di¤erences; π kj = δk for all j, k.
Then
0
0
(1)
Fjk = δk Vjk s k ∑k 0 δk Vjk .
This can help because it increases the e¤ective supply of factors in rich
countries.
This is di¤erent from his 1993 exercise, because equation (1) need not hold
exactly and can therefore be estimated.
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Tre‡er (1995) (continued)
The estimated δs are positive and they are highly correlated with income per
capita (90%).
Tre‡er also allows a set of poor countries to have a common factor-bias
e¢ ciency parameter φj on top of their individual Hicks-neutral terms.
Using a model-selection criterion he concludes that the Hicks-neutral
speci…cation performs better.
Finally, he models Home bias in consumption and shows that the data prefers
this more general model.
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Tre‡er (1995) (continued)
The resulting estimates are:
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No Conditional FPE
Using a common technology matrix to calculate F k when in fact di¤erences
in factor prices imply di¤erent As across countries, biases F k toward zero
(see Helpman 1999).
The factor content of k’s gross imports from country ` is
,`
Fjk,IMP
=
∑i aji
w ` Mik ,` ,
where Mik ,` is gross imports of i by k from `.
Now consider a world of two countries H and F and two factors VK and VL .
Suppose Home is capital abundant. Then wKH < wKF and wLH > wLF .
The factor price di¤erences =) aLi w H
aKi
wH
()
> aKi
wF
< aLi w F
and
for all i.
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No Conditional FPE (continued)
The actual capital content of H’s net exports is
FKH =
∑i aKi
w H MiF ,H
∑i aKi
w F MiH ,F > 0.
This is larger than both
and
∑i aKi
w H MiF ,H
∑i aKi
w H MiH ,F
∑i aKi
w F MiF ,H
∑i aKi
w F MiH ,F ,
the capital contents obtained from using either A w H
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Lecture 7: Factor Content
or A w F .
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No Conditional FPE: Davis and Weinstein (2001)
Davis and Weinstein correct for intermediate inputs, nontraded goods and
Hicks-neutral technology di¤erences.
They also allow for di¤erences in factor composition that lead to a failure of
FPE.
Using input-output tables of 10 OECD countries they estimate
log ajik = αk + βji + γj K k /Lk + εkji ,
and con…rm that γK > 0 and γL < 0 (αk = log δk , from the Hicks-neutral
technology di¤erences).
They construct the factor content of trade with the estimated input
requirements.
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Davis and Weinstein (2001) (continued)
The plot of predicted versus actual factor content measures now looks as
follows (their Figure 7):
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Tre‡er and Zhu (2010)
They carefully develop a calculation of factor content that accounts for each
country’s use of intermediate inputs from all over the world. Under these
circumstances the matrix A in calculating F k = AT k is a construct that
accounts for these intermediate products.
In constructing the matrix of intermediate inputs they follow the OECD in
assuming that an industry in country k uses an imported intermediate in
proportion to its use of the intermediate input, i.e., the fraction of an imprted
intermediate is the same in all sectors.
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Tre‡er and Zhu (2010) (continued)
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