Aggregation
and Applied Trade Theory
Abstract. Data aggregation affects
properties of applied trade theory.
Aggregation can have a direct impact on the direction of trade, factor
intensity, factor abundance, factor substitution, product differentiation, and
intra-industry trade. This paper
develops some propositions for applied trade theorists on the effects of
aggregation.
Explaining
the observed trade patterns with only homogenous products requires too much
fine tuning
of
technology to be convincing. The broad
structure of world trade is more naturally explained
with
the aid of product differentiation than without it. Elhanan Helpman
(1999)
A
preliminary issue for applied trade theorists is the choice between models with
homogeneous and heterogeneous products.
The level of data aggregation would ideally describe the issue at hand
with minimal theoretical structure.
Aggregation leads to simpler data sets but creates distortions by
including increasingly dissimilar products in the same categories.
In
the applied trade literature, the observation of intra-industry motivates the
theory of product differentiation.
Intra-industry trade, however, occurs for the simple reason that even
the finest categories in standard industrial classifications contain different
products. There are other distortions
due to aggregation. Data on factors of
production is highly aggregated and regional aggregation can disguise
underlying patterns of production and trade.
Aggregation
clarifies various issues that arise in applications. Examples in the present paper develop a
series of working propositions on aggregation and applied trade theory.
Aggregation & Product Differentiation
Suppose we start with the unrealistic
assumption that products are separated at the ideal level with the product
vector Pn = {gi}, i = 1,…,n. A red 2002 Ford F150 pickup truck with a
regular cab, 2-wheel drive, 120 inch wheelbase, V6 4.2 liter engine, style side
body, manual 5 speed transmission with overdrive, air conditioning, front and
rear antilock brakes, and cloth seats would be in a separate category from a
blue one. The order n of the
product vector Pn is large but finite. Assume products are ranked next to their
closest substitute in consumption, with beef closer to pork than leather. Each product is a perfect substitute with
itself and a closer substitute for products closer to it in Pn.
Let cPn represent a
partition of Pn into c categories. A partition is a collection of disjoint
subsets. The standard in macroeconomics
is 1Pn or simply Pn, useless for
trade theory because there must be at least two products to trade. For trade theory, 2Pn
might be {{exports}, {imports}} or {{goods}, {services}}.
Consider partitions that do not skip products. With two products, there is only one
partition. With three products, there
are three partitions
1P3 =
{g1, g2, g3},
(2P3)1 = {{g1,
g2}, g3} (1)
(2P3)2 = {g1,
{g2, g3}}.
Note
there is no {g1, g3} aggregate because g2
is between them in P3.
Given a desire to aggregate, (2P3)1
would be chosen if g2 is a closer substitute for g1
than g3. Suppose
country 1 exports g1 and g2 to
country 2 in exchange for g3. There is only interindustry trade with (2P3)1
but there is intra-industry trade with (2P3)2
as pictured in Figure 1.
(2P3)1
g1
g2
country 1 country
2
g3
(2P3)2
Figure
1. Aggregation: Interindustry (2P3)1
or Intra-industry (2P3)2 Trade
Proposition 1. Intra-industry trade depends directly on
aggregation.
With
four products, there are six partitions
1P4 =
{g1, g2, g3, g4}
(3P4)1 = {{g1,
g2}, g3, g4}
(3P4)2 = {g1,
{g2, g3}, g4}
(3P4)3 = {g1,
g2, {g3, g4}} (2)
(2P4)1 = {{g1,
g2, g3}, g4}
(2P4)2 = {g1,
{g2, g3, g4}}.
If
two countries trade the four products in (2), many different patterns of
interindustry or intra-industry trade could arise based on the choice of
partition or aggregation.
With n products in Pn there are n2
- (1 + 2 + … + n) possible partitions. The OECD collects SITC (Standard Industrial
Trade Classification) data for 68 products, implying 2,278 possible
partitions. There is also SIC (Standard
Industrial Classification) data available for trade in 1008 products at the
4-digit level, implying 7,158,527 possible partitions. The choice of partition will affect observed
intra-industry trade.
A category becomes more “differentiated” when a product
is added. For example, if (3P4)1
is “aggregated” to (2P4)1 in (2) there
would be one less product category and a higher “degree” of product
differentiation in the category containing g1 and g2. There has to be more products in at least one
group of iPn compared to jPn when i
< j.
Proposition
2. The “degree” of product
differentiation depends on aggregation.
A high degree of product heterogeneity remains at the
finest level of standard industrial data.
One example is SITC Division 65, “textile yarn, fabrics, made-up
articles, and related products.” In the
more finely separated SIC data set, Category 5084 “Industrial machinery and
equipment” contains “fans, industrial wholesale” and “trucks, industrial
wholesale.” It should be little surprise
that even at the most disaggregated level of data most countries import and
export most categories of products.
Proposition
3. The finest categories in standard
industrial data contain what would be different products.
Chipman (1992) makes the point that intra-industry trade
would be eliminated with enough disaggregation.
With the perfectly separated
products in Pn, there would be no reason for
intra-industry trade apart from relative transport costs. Traders in fact distinguish between different
types of even the most basic commodities such as #2 red wheat or light crude
oil.
Proposition
4. With perfectly separated data, there
would be virtually no intra-industry trade.
While perfectly homogeneous products may not be
observable in practice, homogeneity may be a successful theoretical
assumption. The scientific issue is whether
the trade theorems based on homogeneous products stand as null hypotheses. Similarly, propositions based on theories of
heterogeneous products deserve the status of null hypotheses.
Aggregation and the Intra-industry Trade
Index
The level of intra-industry trade in a category of
differentiated products can be gauged by an index due to Grubel and Lloyd
(1971),
I = (X – M) /
(X + M) . (3)
If I
> 0 (< 0) the product is a net export (import). If the product is only exported, I =
1. If it is only imported I =
-1. The highest level of intra-industry
trade occurs when I = 0.
Table 1 presents index I in (3) for SITC Division
7 “machinery and transport equipment” along with its finer Division 78 “road
vehicles” for NAFTA, the EU, the
Table 1. Examples of 1996 OECD Intra-industry Trade
Div 7 Div78 Div7 Div 78
I I I’ I’
NAFTA .048 .0053 .163 .0049
US .097 .0101 .461 .0078
EU .010 -.0026 -.047 .0018
Proposition
5. Aggregation raises the intra-industry
trade index.
An alternative index I’ in Table 1 is a measure of
net trade relative to GDP. The EU is a
net importer of road vehicles in Division 78 but a net exporter of the
aggregate “other machinery and transport equipment” in Division 7. The
Proposition
6. The choice of standardization can
change the direction of trade and relative magnitudes of the intra-industry
trade index.
Aggregation and Factor Intensity
Aggregation of products can alter factor intensity as in
the following example from the 1999 US Census of Manufacturing. The products are
H = chemicals
E = electrical
machinery
R = rubber &
plastic.
The
factors of production are
C = craft workers
O = operators
T = technical
workers.
Factor
intensity rankings across the three pairs of factors are
aCE / aOE
= 0.77 > aCH / aOH = 0.50 > aCR / aOR =
0.28 (4a)
aTH / aOH
= 0.24 > aTE / aOE = 0.16 > aTR / aOR =
0.03 (4b)
aCR / aTR = 9.33 > aCE / aTE = 4.81 > aCH / aTH =
2.08, (4c)
where aij is the amount of factor i
per unit of product j. Consider
the aggregation of chemicals H and rubber & plastics R into a
product category “chemicals, rubber, plastics” P. Continuing with the ranking of factors across
products, with two products there is the simplified factor intensity scheme
aCE / aOE
= 0.77 > aCP / aOP = 0.39 (5a)
aTE / aOE = 0.16 > aTP / aOP = 0.13 (5b)
aCE / aTE = 4.81 > aCP / aTP = 2.89. (5c)
There
are some intensity relationships hidden by the aggregation from (4) to
(5). Consider the relative input of
technical workers T and operators O in (4b) and (5b). Chemicals H use operators the least
intensively in (4b) but its aggregate product P uses operators O
intensively in (5b). As another example,
rubber & plastic R uses technical workers T the least
intensively in (4c) but its aggregate product P uses technical workers T
intensively relative to craft workers C in (5c).
Proposition 7.
Aggregation can reverse factor intensity.
Geographical Aggregation
Geographical aggregation can also introduce
distortions. National borders partition
the earth’s surface, and different partitions would result in different trade
patterns. Consider the changing
appearance of the “international” trade data due simply to the new national
borders of the
In Table 1,
Table 2. EU Trade in Meat with the
exports imports balance
US $270 $251 $19
NAFTA $291 $336 -$55
Proposition
8. Geographical aggregation can alter
the direction of trade.
In a world without national borders, applied trade theorists
could search for the geographical aggregation that would optimally explain the
pattern of trade. As an example,
regional or interstate trade in the
Aggregation of Factors
Data for factors of production are generally scarcer and
more aggregated than data for products.
There are fewer separate categories, unless factors are industry
specific. Clark, Hofler, and Thompson
(1985) find that the eight categories of skilled labor reported by the US
Census of Manufacturing are separate inputs that cannot be aggregated at
all.
Proposition
9. There are at least as many different
categories of skilled manufacturing labor as available in the most detailed
There is a vast literature on
the difficulty of estimating capital input and separating the influence of
technology. Some manufacturing data
includes estimates of capital structures and machinery & equipment. Capital input is often the residual of value
added after other estimated inputs are subtracted.
An unsettling property from applied production theory is
that factor aggregation alters the estimates of cross price substitution
between factors not involved in the aggregation, and in ways that are
impossible to predict. Substitution
involving the aggregated factors generally diminishes. Berndt and Christensen (1973) and Diewert
(1974) explore the links between aggregation and estimates of factor
substitution.
Proposition
10. Aggregation distorts estimates of
cross price factor substitution.
Factor aggregation may also reverse factor
intensity. Consider the aggregation of
clerical C and technical workers T into skilled labor S in
(4). With the two remaining factors,
there is a single factor intensity ranking across products
aSE / aOE = 0.93 > aSH / aOH = 0.74 > aSR / aOR =
0.31. (6)
Relative
to the electric machinery industry E, the chemicals industry H
uses technical workers T intensively relative to operators in (4a) but
uses operators intensively relative to the aggregate skilled labor S in
(6).
Proposition 11.
Aggregation of factors may reverse factor intensity.
Analogously, aggregation can reverse factor
abundance across countries.
Proposition
12. Aggregation of factors may reverse
factor abundance.
Conclusion
Trade
theory stresses efficiency gains that occur from specialization. Comparative advantage leads to gains from
trade in models with competition, constant returns, and homogeneous products. In models with imperfect competition,
increasing returns, or differentiated products, there can be various other
sources of gains from trade. Competition
and monopoly are industrial organizations that involve interindustry trade in
homogeneous products. The monopolistic
competition of Chamberlain (1933), Lancaster (1980), and Helpman and Krugman
(1985) is an industrial organization that involves intra-industry trade in
differentiated products. For applied trade
theory, the purpose and tastes of the researcher determine the choice of model
and industrial structure.
Some
theorists label factor proportions theory and its underlying competitive models
a failure based on empirical results from highly aggregated data. The “missing trade” discussed by Trefler
(1993) is due in part to missing detail in the data. Davis and Weinstein (1999) uncover missing
theoretical assumptions although they use highly aggregated input data.
Detailed disaggregated studies will ultimately supplement
intuition based on highly aggregated data.
Whether the broad structure of world trade is more naturally explained
with highly disaggregated homogeneous products and competition, or with product
differentiation and imperfect competition remains an open question.
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