A Proportionality Assumption and Measurement
Biases in the Factor Content of Trade
Laura Puzzello∗
Monash University
Abstract
This paper revisits Trefler and Zhu’s (2005, 2010) (TZ) empirical examination of
the factor content of trade in the presence of international differences in production
techniques and trade in inputs. In this framework, knowing the bilateral details of
each country’s input-output structure is key to the correct calculation of the factor
content of trade. Because input-output tables typically lack this detail, TZ impute
the relevant input-output coefficients by making a proportionality assumption. This
paper uses survey-based input-output coefficients from the Asian Input-Output
(AIO) tables that do provide bilateral details. Exploiting methodological differences
in the compilation of the AIO tables and the data underlying TZ studies, this paper
empirically assesses how well the TZ approach fits sourcing patterns of inputs and
finds that it understates countries’ use and relative use of foreign inputs, especially
in those sectors where they are most used. As a result countries’ use of domestic
factors is overstated. Biases generated on exported and imported factor services
cancel each other out. The net effect on the measured factor trade is small.
Keywords: Factor content of trade; Proportionality assumption; International differences
in production techniques.
JEL classification: F1; F11; F14
Address: Monash University, Department of Economics, Caulfield Campus, Caulfield East, VIC
3145; e-mail: [email protected]; phone: +61-3-9903-4517; fax: +61-3-9903-1128.
∗
1
Introduction
The Vanek (1968) proposition states each country is a net exporter of the services of those
factors with which it is relatively well-endowed. Early empirical studies found scarce
support for Vanek’s original formulation.1 One of the reasons relates to the measurement
of traded factor services. To see how, assume the Philippines produces cars by combining
labor, capital and steel. Exported cars incorporate direct factor services (i.e., labor and
capital employed in the car industry) and indirect factor services used in making steel.
Hence, to measure the factor exports of the Philippines one needs to know how both cars
and steel are made. If all countries share common techniques, making this calculation is
relatively easy because the origin of the steel is irrelevant. But if, as evidence suggests,
countries produce steel using different techniques,2 (e.g., U.S. steel is capital-intensive
while Chinese steel is labor-intensive), knowing the source of steel in cars is key to properly
measuring the amount of the factors embodied in Philippino cars.
In the older factor content literature, authors either assumed a common technology
or applied the producers’ technology to inputs and outputs.3 Recently, Trefler and Zhu
(2005, 2010) (TZ), and Reimer (2006) provide and apply algorithms that measure factor
content properly for an arbitrary number of countries and in the case of two countries, respectively. These algorithms weight goods flows, whether final or intermediate, using the
producing country’s technology while reconstructing the entire production chain of traded
goods. Their results find an improved empirical performance of the Vanek proposition.
An issue in TZ arises as they do not observe input usages by source country and using
industry. TZ impute these values by applying, consistently with the literature, a proportionality assumption.4 According to their approach, if 30% of the Chinese absorption of
1
Factor trade is largely overstated by the theory and, while rich countries are scarce in most factors,
poor countries are abundant in most factors (Trefler, 1995).
2
That countries’ production techniques are intensive in their abundant factors is supported by the
empirical evidence (see Dollar, Wolff, and Baumol, 1988; Maskus and Nishioka, 2009; among others).
3
The latter approach is equivalent to assuming inputs are not traded, which is what Davis and
Weinstein (2001) assume.
4
Even though Reimer (2006) focuses only on two regions, the United States and an aggregate Rest
of the World, the input-output data he uses are also imputed by making the same proportionality
assumption. The empirical work of this paper is based on the multi-country framework developed by
Trefler and Zhu. This is why the focus throughout the paper is almost exclusively on Trefler and Zhu’s
studies.
2
electronics is sourced from Japan, 30% of any Chinese sector’s use of electronics originates from Japan. Recently, more accurate estimates of countries’ input-output structures
have been made available in the Asian Input-Output (AIO) tables. These tables exist for
China, Indonesia, Korea, Japan, Malaysia, Philippines, Singapore, Taiwan, Thailand and
the United States. The AIO tables improve on commonly available input-output data as
all the countries covered conduct national firm-level surveys to distinguish the origin of
their input purchases between foreign and domestic. Some of the countries included also
carry out complementary surveys to distinguish their use of foreign inputs by country of
origin.5
This paper uses the AIO tables to perform two exercises. The first one assesses
how well the proportionality assumption in TZ fits sourcing patterns of inputs. The
comparison between the AIO data and the data constructed using the TZ approach
reveals large differences. The proportionality assumption understates the use and relative
use of foreign inputs, especially in those sectors where they are most used. The second
exercise sheds light on the implications of using the proportionality assumption to measure
factor content. By understating countries’ use of foreign inputs, the TZ approach makes
countries’ techniques more intensive in their own factors. Biases generated on exported
and imported factor services cancel each other out, and the net effect on measured factor
trade is small. As a result, the Vanek proposition performs similarly well when factor
trade is measured using the AIO data or the data constructed from the TZ approach.
In assessing the proportionality assumption this paper is closely related to Winkler
and Milberg’s (2009) work where detailed German data on the use of domestic and foreign inputs are exploited to measure service and materials offshoring. Observed offshoring
measures are very different from the ones obtained by applying the proportionality assumption. Importantly, the proportionality approach significantly biases the estimated
effect of offshoring on German employment.
5
The countries with complementary surveys are: China, Indonesia, Malaysia, Singapore and Thailand.
3
1
Measuring the Factor Content of Trade
1.1
Theory
Under restrictive assumptions the original Vanek proposition relates trade in factor services linearly to countries’ factor endowments.6 Let Fi be a vector that describes for
each factor f = 1, . . . , K the amount of its services embodied in the net trade of country
i = 1, . . . , N, and si be country i’s share in world spending. Let Vi and V w be country i
and the world’s vectors of factor endowments, respectively. The Vanek proposition states
that a country is a net exporter of the services of factor f , Fif > 0, if and only if country
P
i is relatively abundant in that factor, Vf i / N
j=1 Vf j > si . More compactly the Vanek
proposition is represented as follows: Fi = Vi −si V w , with Fi and Vi −si V w being referred
to as the measured and the predicted factor content of trade, respectively.
The intuition behind factor content calculations is simple. U.S. net trade, Tus , defined
as the difference between U.S. exports and imports, Xus −Mus , embodies both direct factor
services (e.g. labor, capital used in direct production of traded goods) and indirect factor
services entering production through inputs. The U.S. factor content, Fus , just measures
the total amount of factor services employed worldwide to produce U.S. net trade.
The standard assumptions of the Heckscher-Ohlin-Vanek (HOV) model imply that
both factor and commodity prices are equalized worldwide. Thus, firms in industry
g = 1, . . . , G, irrespective of their geographic location, make the same choices in terms
of primary factors and inputs for production. In other words, countries around the
world are characterized by the same (KxG) matrix of direct factor unit requirements,
D ≡ Dus , and (GxG) input-output table, B ≡ Bus . Knowing the origin of inputs is
then not relevant to factor content calculations. While this reduces the computational
burden, measuring factor content still requires keeping track of the inputs directly used
in the production of Tus , Bus Tus , and of the inputs in turn used directly to produce them,
2
Bus
Tus , and so on. Considering that the total requirement of inputs in the production
P
n
of Tus is ∞
n=1 Bus Tus , the total factor content of U.S. net trade is the amount of factor
P
n
−1
−1
services embodied in Tus + ∞
is the
n=1 B Tus , or Dus (I − Bus ) Tus , where (I − Bus )
6
The Vanek proposition is robust to a series of amendments of the original assumptions. See Trefler
and Zhu (2010) for a full characterization.
4
well-known Leontief inverse. In the same context, country i’s factor content is measured
as follows: Fi ≡ Dus (I − Bus )−1 Ti .
More realistically, countries produce with different techniques, i.e., firms in the same
industry employ factors in different proportions depending on their location.7 In this case
Trefler and Zhu (2010) show the Vanek proposition is valid if each country’s consumption
of any other country’s good is a fixed proportion of the world consumption for that
good. The computation of the factor content now becomes more complicated, requiring
knowledge not only of what intermediate inputs are (directly and indirectly) used in the
production of traded commodities, but also of where these inputs come from. Trefler and
Zhu (2005, 2010) develop an algorithm to compute factor trade in a world with many
countries. Reimer (2006) provides it for the two country case. While both algorithms
measure country i’s factor content following a familiar formula: Fi ≡ D(I − B)−1 Ti , the
size of the problem becomes proportional to the number of countries, N. In fact the
matrix D is now a (KxNG) matrix obtained by concatenating each country i’s matrix
of direct factor requirements, Di , and Ti is the (NGx1) vector of country i’s trade with
imports detailed at the bilateral level. Importantly, the input-output matrix B attains
size (NGxNG) as follows:

B11
B12
...
B1N





 B21 B22 . . . B2N 

B≡
 ..
..
.. 
..
 .
.
.
. 


BN 1 BN 2 . . . BN N
with elements Bji (g, h) representing the unit requirement of country j’s good g in country
i’s output of good h.
The elements of the world matrix B are important beyond factor content calculations
for two interrelated strands of the literature. The first aims to quantify the extent of global
production networks and their effect on an economy’s wage structure (Hummels et al.,
2001; Feenstra and Hanson, 1995, 1999). The second examines the value added content
of trade, which depends on a country’s participation in global production chains and,
direct and indirect absorption of domestic output (Johnson and Noguera, forthcoming).
7
In the discussion that follows it does not really matter whether that is due to international differences
in production technologies, factor prices, or traded input prices.
5
1.2
Empirical Challenges
In the presence of international differences in production techniques, the elements of the
world B matrix are crucial to the proper measurement of trade in factor services. To
retrieve these values TZ adopt the proportionality assumption the OECD and GTAP employ for distinguishing the domestic from the foreign origin of a country’s input purchases.
Accordingly, if 30% of the Chinese absorption of electronics is sourced from Japan, 30%
of any Chinese sector’s use of electronics is assumed to originate from Japan. More formally, the amount of country j’s good g used to produce one unit of country i’s output
of good h, Bji (g, h), is imputed as follows:
TZ
Bji
(g, h) =
Mij (g)
∗ B̄i (g, h)
Qi (g) + Mi (g) − Xi (g)
j 6= i
(1)
where B̄i (g, h) is the amount (observed in national input-output tables) of good g used
per unit of country i’s output of h;8 Mij (g) is i’s imports of good g from the partner j;
Qi (g), Mi (g) and Xi (g) are i’s total output, imports and exports of good g, respectively.
The superscript “TZ” indicates that (1) is used by TZ to calculate the world B matrix.
The use of domestic input g per unit of country i’s output of h is derived by subtracting
the foreign from the aggregate per unit usage of input g in sector h, BiiT Z (g, h) = B̄i (g, h)−
P
TZ
j6=i Bji (g, h), and it equals:
BiiT Z (g, h) =
Qi (g) − Xi (g)
∗ B̄i (g, h).
Qi (g) + Mi (g) − Xi (g)
(2)
Importantly, the end-use of bilateral imports is not relevant to the calculation of (1).
For instance, in our initial example, 30% of any Chinese sector’s use of electronics is
assumed to originate from Japan, irrespective of whether Japanese electronics imported
by China are purchased by final consumers, firms or both. This prediction works well
if every country is as competitive in making electronics for final consumption as it is in
making electronics for any production use. Under these circumstances the import share
of Japanese electronics in China is the same in the final and intermediate goods markets.
8
In other words, B̄i (g, h) is country i’s requirement of input g (summed over both national and
international sources of supply) per unit of good h. The notation used in equations (1), (2) and (3)
follows exactly Trefler and Zhu (2010).
6
However, this prediction is problematic if inputs differ from final goods in their sensitivity
to trade costs or embodied factor proportions.
More readily, consider the relative use of imported inputs, RUI, which is derived by
taking the ratio of (1) to (2):
TZ
Bji
(g, h)
Mij (g)
=
.
TZ
Qi (g) − Xi (g)
Bii (g, h)
(3)
Then, according to the TZ approach, the relative use of imported inputs depends on total
bilateral imports of good g but not at all on the using industry h, i.e., the incentive to
use imported or domestic products is independent of end-use.
This paper uses the AIO tables to calculate the world B matrix. These tables, collected in a joint project by the Institute of Developing Economies (IDE) and the Japanese
External Trade Organization (JETRO), exist for the United States and nine East Asian
countries. The IDE-JETRO project requires participating countries to undertake national surveys with the explicit aim to refine existing estimates of input-output data on
two margins.
The first margin involves distinguishing a country’s input purchases into foreign and
domestic. The responsible national agencies of all the countries in the project conduct
surveys on firms’ use of imported and domestic materials by sector.9 This set of surveys
provides, for each country, i, an accurate estimate of the country’s per unit use of foreign
input g in sector h, BiF,survey (g, h).
The second margin involves the distinction of foreign input purchases by country of
origin. An initial measure of country i’s per unit usage of country j’s good g in sector h
is obtained by applying a trade based factor to BiF,survey (g, h) as follows:
AIO
Bji
(g, h) =
Mij (g)
∗ BiF,survey (g, h)
Mi (g)
j 6= i.
(4)
The trade data employed to measure the coefficients in (4) are detailed at least at the
9
Firms are sampled from each of the AIO sectors. They are chosen depending on their size, level
and intensity of input usage. Response rates vary by country, which may reduce the universality of the
surveys. For instance, in China 176 enterprises of the 586 contacted actually responded. These firms
represent 51 out of 76 Asian IO sectors in 2000. The manufacturing sector, especially electronics, is well
represented. Unfortunately, mining and agriculture are not.
7
8-digit HS level with the exception of Singapore, which uses SITC data. Such fine detail
allows an accurate identification of the end-use of imports.10 All the countries in the
project were requested to adjust the quantities from (4) by conducting additional surveys
on a subsample of respondents from the first round of surveys. Only China, Indonesia, Malaysia, Singapore and Thailand complied by having selected firms list the source
country of the main inputs.
The differences between AIO and TZ input requirements could be pronounced in
two cases. First, many sectors such as the auto or electronics industries are broadly
defined so as to encompass both final and intermediate inputs. Suppose China imports
equal values of auto parts from Korea, and final cars from Japan. In any Chinese sector
that uses auto industry products as an input, the TZ method imputes equal inputoutput coefficients for Japan and Korea. Meanwhile, the AIO data register a large input
coefficient for Korea and a zero value for Japan. Second, two different industries may
both employ imported electronic inputs but from different sources. Suppose the Chinese
auto industry uses Japanese electronic inputs while the Chinese computer industry uses
Korean electronic inputs. The TZ methodology cannot distinguish end-use; rather it
notes only the distribution of total electronic imports and so assigns positive coefficients
to both Japanese and Korean electronics for both Chinese auto and computer industries.
The next section discusses how pronounced the differences between AIO and TZ input
requirements really are.
1.2.1
Empirical Assessment of the Proportionality Assumption
In order to assess the proportionality technique a simple exercise consists of comparing
the elements of the world B matrix, Bji (g, h), taken from the AIO and from constructed
TZ data. The latter are derived applying equations (1) and (2) to the countries’ aggregate
input-output coefficients from the AIO tables. The AIO data contain detailed information
on trade by end-use between 11 exporters and 10 importers in 2000.11 Each Bji (g, h)
10
Methodological work has shown the proportionality approach in (1) applied to fewer sectors (536
versus 6,800) reduces the amount of imports that are classified as intermediates by 6% (see the OECD
documentation, 2002). Similarly the proportionality assumption in (4) provides a more accurate identification of imported inputs by country of origin the finer the disaggregation of the trade statistics.
11
The exporters are the ten countries for which the AIO tables exist plus an aggregate Rest of the
World. Trade directed to the rest of the world is not distinguished by end-use.
8
corresponds to the use of good g produced by exporting country j, used in industry
h within importing country i (e.g., how much steel from the Philippines is used per
unit of auto output in China). When a domestic industry is the source of inputs, the
input requirements are denoted Bii (g, h). Each ji(g, h) corresponds to an observation,
so for 11 exporters, 10 importers, and 34 supplying and using industries, there are a
total of 11x10x34x34 or 127,160 observations to compare. The comparison excludes unit
requirements for the Rest of the World (ROW). These are in fact imputed by making
proportionality assumptions in both the AIO and the constructed TZ data.12
The IDE-JETRO project aims to improve the calculation of a country’s input requirements on two margins: the total use of foreign inputs, and the use of foreign inputs
by country of origin. To check how well it fares on both margins table 1 shows descriptives for the AIO and TZ distributions of countries’ domestic (Bii (g, h)), foreign
(BiF (g, h)) and bilateral (Bji (g, h)) input requirements, and relative use of imported inputs (Bji (g, h)/Bii (g, h)). For each distribution, table 2 summarizes statistics of the ratio
AIO
TZ
between matched observations in the two data samples, e.g., Bji
(g, h)/Bji
(g, h).
The basic statistics for unit requirements in table 1 are not too dissimilar across
datasets. A very different picture emerges when inspecting the incidence of zeros (last column) and the relative use of imported inputs (last two rows) in the same table. While for
the use of domestic inputs roughly 22 percent of observations are zeros in both datasets,
for the imported input requirements, the incidence of zeros is dramatically higher in the
AIO dataset. This is precisely what one would expect if the proportionality assumption in TZ data wrongly conflates flows of final goods and intermediates, and countries’
comparative advantage varies with end-use.13 Focus now on the relative use of imported
inputs. An observation is missing when a sector either does not use a given input at
all, or it only uses foreign varieties of that input. The larger sample size of TZ data
thus suggests the proportionality assumption overstates countries’ use of domestic intermediates. A glance at the means corroborates this finding: the relative use of imported
12
ROW’s unit requirements for the world matrix B AIO are derived by applying the proportionality
assumption in equation (3) on the ROW’s import matrix from the GTAP database. ROW’s unit requirements for the world matrix B T Z are obtained by applying equations (1) and (2) to the ROW’s aggregate
input-output table from the GTAP database.
13
In light of the concluding remarks in section 1.2, this finding is consistent with consumers demanding
goods from many sources and firms buying customized inputs from a much narrower set of suppliers.
9
inputs is much smaller in the TZ dataset. The fact that the AIO median is smaller than
the TZ one further suggests that relative demands of imported inputs are much larger in
the AIO sample when imported inputs are more important in production. Finally, the
large discrepancy in the dispersion of the distributions14 is due to the limited number of
values the relative use of imported inputs can take in the TZ data. In fact, as shown
in (3), the proportionality assumption implies that the relative use of imported inputs is
independent of end-use.
Many unit input requirements take on very small values. Large differences between
AIO and TZ data could then be big in relative terms but tiny in levels. At the same
time, having accurate information on the sourcing of inputs is most relevant for input
intensive sectors. To account for both issues the following comparison analysis focuses
mostly on those observations that fall in the top quartile of the distribution of the total
per unit usage of inputs, B̄i (g, h). Call this sample ‘1r’ as only one restriction is being
imposed. The sub-sample of sample 1r containing observations in the top decile of the
unit requirements of total foreign inputs, BiF,survey (g, h), is also examined (sample 2r).
Figure 1 shows a pair of plots for the ratio of matched unit uses of foreign inputs,
BiF,survey (g, h)/BiF,T Z (g, h).15 Each graph shows the density and the cumulative distribution of those observations falling in sample 1r and 2r, respectively. In table 2, the last two
rows of panel B report statistics for each of the distributions in figure 1. Figure 2 repeats
the exercise in figure 1 but for matched unit input requirements of foreign inputs by counAIO
TZ
AIO
TZ
try of origin, Bji
(g, h)/Bji
(g, h). In figure 2, each distribution of Bji
(g, h)/Bji
(g, h)
for samples 1r and 2r is plotted for both the full sample (AIO) and the five countries in
the IDE-JETRO project that conduct complementary surveys to distinguish their use of
foreign inputs by country of origin (Best 5 AIO), respectively. In table 2, the last two
rows of panels C.a and C.b summarize statistics for each of the distributions in the top
and the bottom graphs of figure 2, respectively.
The evidence is striking: there are large differences in the distribution of unit input requirements of imported inputs across datasets. Importantly, the distributions of matched
14
The measure of dispersion reported in table 1 is the coefficient of variation, CV.
B̄i (g, h) is the same in both AIO and TZ datasets. Thus, knowing the distribution of total foreign
input requirements is sufficient for that of domestic input requirements.
15
10
unit input requirements in figures 1 and 2 shift to the right once the second constraint
is added. The shift just reflects the tendency of TZ data to understate the use of foreign
inputs where they are most important. The statistics in table 2 confirm this finding.16
The results for the unit input requirements of foreign inputs by country of origin are
qualitatively similar for the “AIO” and the “Best 5 AIO” samples. In other words, the
“Best 5 AIO” countries do not drive the results from the full sample. Thus, the IDEJETRO project does improve the calculations of a country’s input requirements on both
the margins it aims to for countries with and without complementary surveys.
In conclusion, differences between the AIO and the TZ unit requirements of intermediates are large and relatively more important for imported inputs when these are most
used. These findings have potentially important implications for factor content calculations. By understating the use and relative use of foreign inputs in those instances where
imported intermediates are more important, the TZ methodology could bias a country’s
techniques of production in favor of its own factors.
2
2.1
Empirical Evidence on the Vanek Proposition
Testing the Vanek Proposition
In this section the Vanek proposition is assessed for two factors, capital and labor, in
nine East Asian countries, the United States and one aggregate ROW. The nine Asian
countries plus the United States are the countries covered by the IDE-JETRO project.
Henceforth, they are collectively referred to as “AIO countries”. All data are for 2000.17
Data on endowments Vi and factor usages by industry Di are obtained from various
sources. Employment data by industry are from the IDE-JETRO employment matrices for the AIO countries and from a combination of Occupational Wages around the
World (OWW) with GTAP data for the ROW.18 UNPop data on the economically active
16
From (unreported) histograms for the ratio of matched observations of the relative use of imported
inputs, and panels D.a and D.b in table 2, similar conclusions follow.
17
This year reduces the number of sources underlying the dataset. Importantly, IDE-JETRO employment matrices are available exclusively in 2000.
18
In the spirit of Reimer (2006), data from the OWW are used to find the employment distribution
of a country representative of the ROW (Italy). This distribution is then applied to the ROW’s total
employment to obtain labor employment by sector.
11
population older than 15 define the world labor endowment. ROW’s labor endowment
is calculated as the difference between the world and the AIO countries’ labor endowments. Data on physical capital stock are from the GTAP database for 2001. These data
are adjusted to their 2000 values by integrating investment information from the GTAP
database for the ROW, and from the AIO tables for the AIO countries, and investment
quantities and price changes from the Penn World Tables (PWT) 6.2. Following Reimer
(2006), capital use by industry is calculated dividing the industry’s payments to capital
by the country’s average cost of capital. Industry payments to capital are taken from
the AIO tables for the AIO countries and from GTAP for the ROW. In the latter case
the real payments are assumed to be stable over time. Integrating AIO and GTAP data
reduces the sectors to 34.19
Under standard HOV assumptions, each country’s factor content is measured using the
U.S. choice of techniques. When production techniques are different across countries, the
Trefler and Zhu (2010) algorithm is applied. In this case the proportionality assumption
bias is quantified examining the Vanek proposition performance when factor contents are
measured using the AIO rather than the constructed TZ data in the world matrix B.
Tests results for the Vanek proposition are shown in table 3. With 11 countries and
two factors, 22 data points are available to test the models. In order to express factors in
comparable units and account for country size, each fi observation of Ff i = Vf i − si Vfwi is
scaled by σf i ≡ σf sµi , where σf is the cross-country standard deviation of Ff i − Vf i + si Vfwi
and, consistently with Antweiler and Trefler (2002), µ equals 0.9.20 Table 4 summarizes
some of the results by factor.
The Vanek proposition under standard HOV assumptions fares poorly. Measured
and predicted factor contents of trade match in sign roughly 60% of the time, but not
significantly so. The Spearman correlation between Ff i and Vf i − si Vfwi is positive but
statistically insignificant. The estimated slope from the regression Ff i = α + βVf i −
si Vfwi + ǫf i is not different from zero. Reading Trefler’s (1995) ‘missing trade’ statistics,
the variance of the measured factor content is only 0.03 times that of the predicted.
19
The complete list of sectors and further details on data construction can be found in supplementary
material for this paper available at http://users.monash.edu.au/∼ laurap/research.php or upon request.
20
This strategy ensures the unit-variance of country-factor specific deviations of the measured from
the predicted factor content (Trefler, 1995).
12
Consistently with the literature, factor trade is largely overstated by the theory.21
Turning to the Trefler and Zhu (2010) definition of factor content, the performance
of the Vanek proposition improves substantially.22 Row 2 in table 3 shows the results
for when the B matrix consists of the AIO data. Despite the sign test insignificance,
the Spearman correlation is now significant at 0.65. The regression slope is significantly
different from zero. Trade is still missing, but the variance of the predicted factor content
of trade is now “only” ten times that of the measured. These results are consistent with
previous studies and especially close to Trefler and Zhu’s (2005) findings.
From the last row of table 3 it is evident that measuring factor trade with the constructed TZ data improves the Vanek proposition performance further but slightly so. To
see why that is, focus on the first columns of table 5, which report the signs of FfAIO
and
i
of the common prediction Vf i − si Vfwi , and the percentage difference in measured factor
23
contents, 100 ∗ (FfAIO
− FfTiZ )/FfAIO
Except for Taiwanese labor, FfAIO
and FfTiZ have
i
i .
i
always the same sign. But whenever the Vanek prediction is met in sign, the TZ data
inflate the measured factor trade in absolute value, with inflations ranging only between
0.57 and 8.02 percentage points. Take Singapore, it is a correctly measured net exporter
of capital and the TZ data overstate its net capital trade by just 4.43 percentage points.24
A glance at column 3 in table 5 indicates that the bias the proportionality approach
creates on the measured factor trade is very small. This is at odds with the large differences between the AIO and the TZ data documented in section 1.2.1. In order to
reconcile these findings, the next section examines the biases the TZ approach generates
on the domestic and the foreign components of the measured trade in factors.
2.2
Proportionality Assumption and Measured Factor Trade
Consider a world with only country i and a foreign region j. If i and j produce with
different techniques, country i’s factor content is Fi = [Di Dj ](I − B)−1 [Xi − Mji ]′ ,
21
The results in the first row of table 4 reveal a particularly poor performance for labor. Once Singapore
and Malaysia are dropped from the sample this ceases to be the case. Results are available upon request.
22
That is true also at the factor level too (see table 4).
23
In table 5 the normalization of the factor content of trade by σf i is dropped, and then, the Vanek
prediction is the same irrespective of the data used for B.
24
Table 5 reveals that Taiwan is an important observation. Results are robust without Taiwan.
13
which, letting B ij be the ij-th element of (I − B)−1 , can be written as:
h
i
Fi = Di (B ii Xi − B ij Mji ) + Dj (B ji Xi − B jj Mji )
(5)
The first term on the right hand side of equation (5) measures the total amount of
domestic factor services embodied in country i’s net exports (Domestic component). In
particular, Di B ii Xi measures the total domestic factor services that country i contributes
to its factor content through the 1st, 2nd, 3rd,... stages of domestic production before
exporting; Di B ij Mij is the total amount of domestic factor services embodied in imports
from country j. Imported goods from j are in fact produced with inputs sourced from
i. The last term in (5) is the Foreign component and it measures the total amount of
foreign factor services embodied in country i’s net trade.25
Plugging the data into (5) it turns out that the domestic component is always positive,
i.e., countries are net exporters of their factors and the foreign component is always
negative, i.e., countries are net importers of foreign factors. Thus, hereafter Finx and Finm
indicate the domestic and the foreign components of country i’s factor trade, respectively.
The percentage difference in country i’s factor content measured using the AIO instead
of the TZ data for the elements of B can be then decomposed as follows:
h F nx,AIO − F nx,T Z F nm,AIO − F nm,T Z i
FfAIO
− FfTiZ
fi
fi
fi
fi
i
∗ 100 =
+
∗ 100.
AIO
AIO
AIO
Ff i
Ff i
Ff i
(6)
The last two columns in table 5 show the decomposition results by country-factor pair.
With the exception of Malaysian labor, the TZ data significantly inflate, in absolute value,
both countries’ net exports of domestic factors and their net imports of foreign factors.
In other words, the proportionality assumption biases countries’ production techniques in
favor of their own factors.26 This is exactly what one expected from section 1.2.1 where
the TZ data are shown to understate the use and relative use of foreign inputs, especially
in the production processes that use them the most. In conclusion, the proportionality
assumption bias on the measured factor content of trade is small only because the biases
25
The intuition behind the decomposition can be obtained by solving the simple case of two countries,
one factor and one good; or by inspecting the coefficients of Ti , BTi , B 2 Ti and so on.
26
In the interest of space results by subcomponent are not reported. Implications are consistent.
14
on exports and imports of factor services cancel each other out.
3
Conclusions
This paper uses survey-based input-output coefficients from the AIO tables to assess
the proportionality assumption commonly made in the literature to split a country’s
purchases of intermediates by country of origin. The proportionality assumption turns
out to understate countries’ use and relative use of imported inputs, especially in those
sectors where they matter the most. Thus, countries’ use of domestic factors is overstated
and net trade in factor services is biased upward only slightly. In fact, if, on the one
hand, countries export more of their factors, on the other hand, they import more foreign
factors. As a result, the Vanek proposition performs similarly well when factor trade is
measured using input-output coefficients from the AIO tables or those imputed applying
the proportionality assumption.
The fact the proportionality assumption does not fare well in quantifying input trade
implies a country’s comparative advantage depends on end-use. While this is not problematic if one is interested in measuring trade in factor services, it could be if one wants
to appraise the effects of trade on a country’s wage structure or technology know-how.
Acknowledgements
I am extremely grateful to David Hummels for his many questions, invaluable comments
and constant support. The insightful comments of the editor, Daniel Trefler, greatly
improved this paper. I thank two anonymous referees, Chong Xiang, Vova Lugovskyy,
Sirsha Chatterjee, Anca Cristea, Jakob Madsen, Tasneem Mirza, Kevin Mumford, Iryna
Topolyan, Justin Tobias and many seminar participants for helpful comments and suggestions. I am indebted to Yoko Uchida for help with the Asian data and Terry Walmsley
for granting me access to the GTAP database. All remaining mistakes are my own.
15
References
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Paper 11221.
16
Trefler, D., Zhu, S.C., 2010. The structure of factor content predictions. Journal of
International Economics 82(2), 195-207.
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Winkler, D., Milberg, W., 2009. Errors from the “proportionality assumption” in the
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Paper 2009-12.
17
Table 1: Descriptives of the Elements of the Global Matrix B: AIO vs. TZ.
Bii (g, h)
AIO
TZ
BiF (g, h)
AIO
TZ
Bji (g, h)
AIO
TZ
RU I
AIO
TZ
N
Median
Mean
CV
Zeros
11560
11560
0.0008
0.0008
0.0124
0.0125
2.96
2.95
2620
2553
11560
11560
8.95e-06
0.00007
0.0038
0.0037
5.67
5.21
4660
2827
115600
115600
0
2.53e-07
0.0004
0.0004
12.17
11.01
63764
43568
89400
90070
0.0002
0.0029
0.1508
0.0792
55.64
14.44
38042
18059
Note. CV stands for coefficient of variation. RUI stands for relative use of imported intermediates, Bji (g, h)/Bii (g, h).
The statistics shown are calculated excluding the Rest of World as an importer from the sample.
18
Table 2: Per unit use of inputs: AIO vs TZ.
N
Zeros
Top-coded
Median
Mean
CV
AIO
TZ
Panel A. Bii
(g, h)/Bii
(g, h)
All
IV-q B̄i (g, h)
IV-q B̄i (g, h) and X-d BiF,survey (g, h)
9015
2988
993
75
5
5
225
32
15
1.022
1.005
0.936
1.2594
1.0524
0.9297
1.85
0.51
0.61
Panel B. BiF,survey (g, h)/BiF,T Z (g, h)
All
IV-q B̄i (g, h)
IV-q B̄i (g, h) and X-d BiF,survey (g, h)
8733
2923
997
1841
215
0
398
122
82
0.597
0.886
1.155
1.2028
1.0962
1.6228
4.01
1.84
1.33
72032
23226
8974
20220
2032
209
3689
1534
751
0.424
0.793
1.097
1.2024
1.5464
2.1805
9.61
6.83
7.14
41203
13915
6547
13470
1355
143
1818
899
478
0.490
0.903
1.111
1.0742
1.3437
1.6351
11.18
3.75
3.63
71377
23171
8919
20020
2032
209
6023
2538
1736
0.356
0.752
1.198
4.5105
3.1840
6.4192
65.60
10.86
8.58
40718
13882
6514
13327
1355
143
3674
1757
1319
0.392
0.887
1.240
4.9633
2.8724
4.8849
78.26
8.57
7.27
AIO
TZ
Panel C. Bji
(g, h)/Bji
(g, h)
(a) All AIO countries
All
IV-q B̄i (g, h)
IV-q B̄i (g, h) and X-d BiF,survey (g, h)
(b) Best 5 AIO
All
IV-q B̄i (g, h)
IV-q B̄i (g, h) and X-d BiF,survey (g, h)
Panel D. RU I AIO /RU I T Z
(a) All AIO countries
All
IV-q B̄i (g, h)
IV-q B̄i (g, h) and X-d BiF,survey (g, h)
(b) Best 5 AIO
All
IV-q B̄i (g, h)
IV-q B̄i (g, h) and X-d BiF,survey (g, h)
Note. CV stands for coefficient of variation. RUI stands for relative use of imported intermediates, Bji (g, h)/Bii (g, h).
The cut-off for the top quartile of B̄i (g, h) is 0.0101. The cut-off for the top decile of BiF (g, h) is 0.0070.
19
Table 3: Empirical Performance of the Vanek Proposition
Slope
R2
MT
Obs.
0.1790
0.0153
0.0070
0.0335
22
(0.429)
(0.425)
(0.711)
TZ FCT Definition,
0.6363
0.6533
0.1905
0.3839
0.0945
22
AIO Data
(0.229)
(0.001)
(0.002)
TZ FCT Definition,
0.6818
0.6544
0.1954
0.3840
0.0994
22
TZ Data
(0.113)
(0.001)
(0.002)
HOV standard
Sign
Spearman
Test
Corr.
0.5909
Note. P-values in parenthesis. FCT stands for factor content of trade. TZ indicates that Trefler and
Zhu’s (2010) algorithm is applied to measure factor contents of trade. MT is the Missing Trade statistics.
With two factors and 11 countries the total number of observations is 22. Each fi observation is scaled
by σf i ≡ σf sµi , where σf is the cross-country standard deviation of Ff i − Vf i + si Vfwi and µ = 0.9.
Table 4: Empirical Performance of the Vanek Proposition by Factor
Capital
HOV standard
Labor
2
Slope
R
0.1948
0.2556
MT
N
Slope
R2
MT
0.1485
11
0.0005
0.0095
0.00003
0.8431
0.0436
0.8431
0.0456
(0.113)
TZ FCT Definition,
0.4123
AIO Data
(0.043)
TZ FCT Definition,
0.4273
TZ Data
(0.042)
(0.776)
0.3816
0.4456
11
0.1918
(0.000)
0.3838
0.4757
11
0.1962
(0.000)
Note. P-values in parenthesis. FCT stands for factor content of trade. TZ indicates that Trefler
and Zhu’s (2010) algorithm is applied to measure factor contents of trade. MT is the Missing Trade
statistics. Each fi observation is scaled by σf i ≡ σf sµi , where σf is the cross-country standard deviation
of Ff i − Vf i + si Vfwi and µ = 0.9.
20
Table 5: Decomposition of Percentage Differences in Measured Factor Content of Trade
Country
Sign
Ff i
Sign
Vf i − si Vfwi
∆% Ff i
(in %)
Z
Ffnx,AIO
−Ffnx,T
i
i
Ff i
Z
Ffnm,AIO
−Ffnm,T
i
i
Ff i
(in %)
(in %)
(1)
(2)
(3)
(4)
Panel A. Decomposition of Measured Capital Content of Trade.
China
+
-1.67
-3.73
Indonesia
+
-0.70
-2.72
Japan
+
+
-1.51
-1.99
Korea
+
-6.31
-16.56
+
+
-1.53
-2.83
Malaysia
Philippines
+
+
-0.73
-7.47
Singapore
+
+
-4.43
-8.36
+
10.02
-18.71
Taiwan
Thailand
+
+
-0.76
-4.55
USA
+
-7.09
-8.44
ROW
+
-2.77
0.82
Panel B. Decomposition of Measured Labor Content of Trade.
China
+
+
-1.86
-2.04
Indonesia
+
+
-2.46
-3.07
Japan
-0.57
0.20
Korea
-8.02
9.92
Malaysia
+
+
-2.72
-2.08
Philippines
+
+
-3.20
-4.84
Singapore
0.29
10.47
Taiwan
+a
148.32
-106.89
Thailand
+
+
-1.43
-3.23
USA
0.43
0.50
ROW
+
-3.50
0.91
(5)
2.06
2.02
0.48
10.25
1.30
6.73
3.93
28.73
3.79
1.34
-3.6
0.18
0.61
-0.76
-17.95
−0.64
1.63
-10.18
255.21
1.81
-0.07
-4.40
nm
Note. Ffnx
i and Ff i indicate the domestic and the foreign components of country i’s trade in factor
f , respectively, as described in section 2.2. Interpretation of the numbers in columns 4 and 5 requires
nm
knowing the sign of FfAIO
as well as keeping in mind that Ffnx
< 0. For example,
i
i > 0 and Ff i
AIO
nx
Japan is a net importer of capital, FkJ < 0. The domestic component, FkJ , is positive, therefore
nx,AIO
nx,T Z
nx,AIO
nx,T Z a
AIO
(FkJ
− FkJ
)/FkJ
> 0 iff FkC
< FkC
. Taiwan is measured to be a net exporter of labor
according to the AIO data but a net importer of labor using the TZ data.
21
0
1
2
1
.8
.4
.6
Cumulative Distribution Function
1
Density
3
0
.2
.5
0
0
0
.2
.5
Density
1
.4
.6
Cumulative Distribution Function
.8
1
1.5
AIO
1.5
AIO
0
BiF_AIO/BiF_RTZ−−IVq Bi
1
2
3
BiF_AIO/BiF_RTZ−−IVq Bi and top 10% BiF
Figure 1: Foreign Inputs Usage: AIO vs. RTZ, sub-samples
Note. The distribution underlying the quartiles is that of the usage of inputs, B̄i (g, h). The cut-off for
the top quartile of B̄i (g, h) is 0.0101. The distribution underlying the top decile is that of the usage of
foreign inputs, BiF,survey (g, h). The cut-off for the top decile of BiF,survey (g, h) is 0.0070. For legibility of
the graphs, values above 3 are top coded 3. Statistics corresponding to each of the distributions plotted
in this figure are reported in the last two rows of panel B in table 2.
22
3
2
Density
1
1.5
.5
0
1
2
3
Best 5 AIO
2
3
2
Density
1
1.5
.5
0
Density
1
1.5
.5
1
0 .2 .4 .6 .8 1
Cumulative Distribution Function
Best 5 AIO
0
0
0
Bji_AIO/Bji_RTZ−−IVq Bi and top 10% BiF
0
Bji_AIO/Bji_RTZ−−IVq Bi
1
2
3
0 .2 .4 .6 .8 1
Cumulative Distribution Function
2
0 .2 .4 .6 .8 1
Cumulative Distribution Function
1
Bji_AIO/Bji_RTZ−−IVq Bi
2
0
AIO
0 .2 .4 .6 .8 1
Cumulative Distribution Function
0
.5
Density
1
1.5
2
AIO
Bji_AIO/Bji_RTZ−−IVq Bi and top 10% BiF
Figure 2: Foreign Inputs Usage by country of origin: AIO vs. RTZ
Note. The distribution underlying the quartiles is that of the usage of inputs, B̄i (g, h). The cut-off for
the top quartile of B̄i (g, h) is 0.0101. The distribution underlying the top decile is that of the usage of
foreign inputs, BiF,survey (g, h). The cut-off for the top decile of BiF,survey (g, h) is 0.0070. For legibility of
the graphs, values above 3 are top coded 3. Statistics corresponding to each of the distributions plotted
in the two top graphs are reported in the last two rows of panel C.a in table 2. Statistics corresponding
to each of the distributions plotted in the two bottom graphs are reported in the last two rows of panel
C.b in table 2.
23