Auburn University
kangmye@auburn.edu
mostafa.malki@utb.edu
University of Hartford
rassekh@mail.hartford.edu
Auburn University
thomph1@auburn.edu
Factor abundance is a bilateral concept in factor proportions
trade theory that has no definition when there are many countries and various
factors of production. The present paper
proposes a general definition, the Euclidean distance to the intersection of
abundance rays with unit hyperplanes.
“Distance factor abundance” is compared with other measures using a data
set from the literature.
Factor proportions
trade theory is based on the idea that differences in relative endowments of
productive factors across countries explain patterns of production and
trade. Countries would export products
using their abundant factor or factors intensively. A difficulty with empirical
application has been that the theory defines factor abundance for two countries
and two factors while the empirical investigator faces many countries and many
factors. The present paper proposes a
general definition that produces a unique ranking of countries for each factor
and collapses to the two dimensional definition.
Empirical studies of
factor proportions theory ideally would (but do not) include independent
measures of factor abundance and factor intensity, as pointed out by Bowen, Leamer, and Sveikauskas (1987)
and Leamer (1994). There is no measure of factor abundance, for
instance, in the classic studies of Leontief
(1953) and Baldwin (1971). Horiba (1974) develops a
method to apply bilateral concepts to many countries but does not provide a
general definition of factor abundance.
There are two measures of factor abundance in the applied trade
literature, share abundance based on the theory of Vanek (1968) and world abundance developed by Leamer (1980). The present paper introduces a “distance”
measure and compares it to the other two using the data set of Trefler (1995).
Distance factor
abundance is defined as the Euclidean distance from the unit value of a factor
to the intersection of a factor abundance ray with the unit factor
hyperplane. For each factor, countries
are ranked by distance abundance resulting in a measure that can be used in
direct estimations or applications of factor proportions theory. The ultimate empirical issue is the extent to
which countries tend to export the products that use their “abundant” factors
“intensively” at least in some senses with many countries and various
productive factors.
1. Factor Abundance Measures in the Literature
Factor abundance is
clearly defined for two countries or two productive factors. Let vij
represent the endowment of factor i
in country j. With two countries and two factors, country 1 (2) is abundant in factor 1 (2) if
(1)
v11/v21
> v12/v22.
Free trade would imply equal product prices
across the two countries. If there are
identical neoclassical production functions, factor price equalization (FPE)
follows and their input ratios would be identical. With homothetic production, country 1 would produce a higher ratio of
product 1 to 2. Countries with identical
homothetic utility functions would consume products in the same ratio and
export the product using their abundant factor intensively.
Vanek (1968) extends the two dimensional
factor content model to any number of factors.
Country 1 is more abundant in
factor m and country 2 is more abundant in factor n if
(2)
…> vm1/vm2
>…> vn1/vn2 >…
Factor abundance can similarly be defined when
there are many countries and two factors.
Share abundance rests
on the special set of assumptions in Vanek (1968) including FPE. Let sk
be the share of country k in
world income, sk = yk/yw. Given free
trade and identical homothetic preferences, country k would have to consume a share of the world output xjw of each
product j according to its income
share, cjk = skxjw. Country
k is share abundant in factor i if its endowment of factor i relative to the world is greater than
its share of world income, vik/viw
> sk or
(3)
vik -
skviw > 0.
Trefler
(1995) calculates share abundance with data on nine factors and 33
countries and furnished the present data set.
The less developed countries in the sample have very small income shares
due to low wages and cheap nontraded products and as a result are share abundant
in many factors.
Leamer (1980) develops
the world abundance measure. Country k is world abundant in factor m relative to factor n if
(4)
vmk/vnk
> vmw/vnw.
World abundance is equivalent to a ranking of
world endowment shares as in vmk/vmw
> vnk/vnw.
Thompson (1999)
shows that share and world abundance are identical to (1) when there are two
countries and two factors but with more countries or factors they are weaker
than the definition in (1). With many
countries and factors, world abundance might hold between pairs of countries
and factors when (1) does not. Share
abundance is the weakest condition and might hold between pairs of countries
and factors when world abundance does not.
2. A Distance Measure of Factor Abundance
Factor abundance is a
ratio that can be treated as a distance.
The proposed definition is based on the distance from the unit value of
a factor to the intersection of an abundance ray with its unit hyperplane. Figure
1 illustrates the distance measure with two countries and two
factors. Rays m and n represent
endowments of two countries. Consider
the unit value of factor 1, v1j
= 1, and its intersections with the two abundance rays. Country m is abundant in factor 1 since the distance d1m = v2m/v1m to the unit axis from ray m is
less than the distance d1n =
v2n/v1n from
ray n. Any number of countries
can be ranked by their abundance in factor 1.
The model with three factors
illustrates the generality of distance abundance. Figure
2 pictures the distance measure for country m. On the left, the three
factors are measured along axes v1m,
v2m, and v3m. Consider the v1m = 1 plane and its intersection with endowment ray m
at point M. The right side of
Figure 2 is the v1m = 1
plane with its origin at point 1 and endowment point M. By the Pythagorean theorem, the Euclidean
distance from point M to the origin 1 is
(5)
d1m = ((n2m/n1m)2 + (n3m/n1m)2)1/2.
Across any number of factors, the Euclidean
distance for factor 1 in country k would be
(1)
d1k = ((v2k/v1k)2 + … + (vrk/v1k)2)1/2.
To standardize by an arbitrary factor h, divide endowments of each factor i in country k by vhk to
find the distance abundance,
(2)
dhk = (Siąh(vik/vhk)2)1/2.
This procedure produces a ranking of countries
for each factor. Distance abundance collapses
to (1) in the two dimensional model. The
next step for theory would be to establish a link between distance abundance
and production but there are no necessary links between factor endowments and
production with more than two factors even in the special situation of
universal, identical, homothetic, constant returns production functions. As an example, Thompson (1985) uncovers 7 possible Rybczynski
comparative static sign patterns of endowments differences on outputs in the model
with only 3 factors and 2 products. If
production is not necessarily linked to factor endowments in a unique manner,
neither is trade. Measuring factor
abundance might appear pointless without such necessary theoretical links but
applied trade theorists face the challenge of applying the concepts of factor
proportions theory. The empirical issue
is the extent to which factor abundance, at least under some interpretation,
explains trade.
3. A Comparison of Factor Abundance Measures
This section compares
the three measures of factor abundance using the data set of Trefler (1995). All abundance measures are scaled to a
maximum of 1 and a minimum of 0 for comparison.
The factors of production are listed in Table 1.
Table 2 reports share abundance. Due to its large share of world income, the
US has the lowest share abundance of all factors except capital and
manufacturing labor. At the other extreme,
the LDCs have small shares of world income and high share abundances for a
number of factors. For instance,
Bangladesh, Columbia, Indonesia, Pakistan, Sri Lanka, Thailand, and Yugoslavia
have higher than average abundance in professional labor. Capital, clerical, and manufacturing labor
share abundances are skewed right with most countries below the mean and a thin
long tail of countries with above average abundance. The other factors are skewed left with most
countries above the mean and a long tail of scarce countries. All distributions except manufacturing labor
are highly leptokurtic with narrow high peaks and many countries close to the
mean. The coefficient of variation is
the standard deviation relative to the mean and it indicates a very high degree
of dispersion for capital and manufacturing labor. The least dispersed endowments are cropland
and pastureland.
Table 3 reports world abundance, each
country’s share of the world endowments of each factor. In direct contrast with share abundance, the
US has the highest world abundance of every factor except agricultural labor
and pastureland. The US has the largest
portion of world capital, other countries having an average of about 10% of the
US level and Japan the closest at 55.8%.
In contrast to share abundance, the LDCs generally have low world
abundances except for agricultural labor, cropland, and pastureland. World abundances are all skewed to the right
with most countries below the mean and a long tail of abundant countries, in
contrast to the left skews of most of the share abundances. All of the distributions except pastureland
are highly leptokurtic with narrow high peaks and many countries close to the
mean. Coefficients of variation indicate
a higher degree of variation than share abundance except for capital, clerical,
and manufacturing labor. The least
variation occurs with cropland. Share
and world abundance generate very different measures for particular
factors. Comparing pastureland, for
instance, there is a higher mean, less dispersion, more countries above the
mean, and more countries close to the mean with share abundance.
Table 4
reports the proposed distance measure, inverted and rescaled for comparison
with 1 the most abundant and 0 the least abundant country. Singapore is the most abundant country in
capital as well as in more skilled labor groups due to its lack of cropland and
pastureland. The US is relatively scarce
in capital and most types of labor due to its abundant pastureland. Japan has higher than average distance
abundance for capital and all types of labor.
Countries with above average capital abundances are Singapore, Hong
Kong, Japan, the Netherlands, and Belgium.
Distance abundance measures are skewed to the right with very high peaks
and most countries below the mean, similar to world abundance. Coefficients of variation are relatively low
except for agricultural labor, cropland, and pastureland. Capital and most types of labor are highly
leptokurtic with high peaks while agricultural labor, cropland, and pastureland
are more evenly spread across countries.
Table 5 reports correlations between the three
abundance measures. Notation is S for
share, W for world, and D for distance abundance. Correlations are typically small and over
half are negative. Only 4 of the 27
correlations are greater than 0.5. World
abundance is negatively correlated with distance abundance for most
factors. The three measures are most
consistent for agricultural labor.
Clearly these abundance measures measure different things and tests of
factor proportions theory would vary depending on the measure utilized.
Table 6
reports the signs of US factor contents from Trefler (1995) with positive (negative) signs
indicating net factor exports (imports).
Factor content calculations based on US input coefficients as in this
data set are not necessarily appropriate for other countries. The US is a net importer of capital and all
types of labor except agricultural, and is a net exporter of cropland and
pastureland. Table 6 also reports
“signs” of the three US abundance measures.
The sign of the original share abundance measure is reported. For world and distance abundance, the US is
compared to world means with a positive (negative) sign indicating above
(below) average abundance.
Abundance measures completely agree only for the scarcity of
agricultural labor but the US is a net exporter of agricultural labor due to
its capital intensive agricultural production.
Distance scarcities of capital and manufacturing labor correctly predict
those net imports in direct contrast to the other two measures. For pastureland, only share abundance has the
wrong prediction. Both share and
distance abundance correctly anticipate net imports of professional, clerical,
sales, and service labor. World
abundance anticipates US factor content for only 2 of the 9 factors and share
abundance for 4 of the 9. Distance
abundance is correct for 7 of the 9 factors, missing only agricultural labor
and cropland due to the capital intensive production techniques of US
agriculture.
5. Conclusion
Bilateral concepts of
factor proportions theory fall short empirically when facing data with many
countries and various factors of production.
Share abundance is questionable in practice because it relies on a
special set of theoretical assumptions including factor price equalization. Having both developed and developing
countries in the same sample is especially troublesome when one applying share
abundance. World abundance produces more
sensible rankings but is biased due to country size. The European Union, for instance, is more
world abundant in every factor than any of its individual countries.
Empirical economists
can adopt one of the two following approaches.
In the first approach, they formulate a model as close to the
specifications of the theory as possible and estimate the model using real
world data to determine the applicability (not the accuracy) of the
theory. This is the approach adopted by Rassekh and Thompson (1997)
for the Stolper-Samuelson theorem. The
second approach involves searching for model specifications that best explain
observed trade. Davis and Weinstein (1998) adopt this approach
in explaining the factor content of capital and labor. Both approaches are scientifically valid.
Empirical international
economists using either approach want a reliable independent measure of factor
abundance. The proposed distance
abundance measure is a step in the direction of a more complete realization of
the empirical scope of factor proportions trade theory.
Baldwin, Robert (1971) “Determinants of
the Commodity Structure of U.S. Trade,” American
Economic Review 61.
Bowen, Harry P., Edward E. Leamer, and
Leo Sveikauskas (1987)“Multicountry, Multifactor Tests of the
Heckscher-Ohlin-Vanek Model,” American
Economic Review 77,
791-809.
Davis, Donald and David Weinstein (1998)
“An Account of Global FactorTrade,” NBER
Report, available online at www.nber.org
Leamer, Edward E. (1994) “Testing Trade
Theory,” in David Greenaway and L. Alan Winters (ed.) Surveys in International Trade, Cambridge: Basil Blackwell, 1994.
Leamer, Edward E. (1980) “The Leontief
Paradox Reconsidered,” Journal of Political
Economy 88, 495-503.
Leontief, Wassily W. (1953) “Domestic
Production and Foreign Trade: The American Capital Position Re-Examined,” Proceedings of the American Philosophical
Society,
97, 332-49.
Thompson, Henry (1985) “Complementarity in
a Simple General Equilibrium Production Model,” Canadian Journal of
Economics, 616-21.
Thompson, Henry (1997) “International
Differences in Production Functions and Factor Price Equalization,” Keio
Economic Studies, 1997, 43-54.
Thompson, Henry (1999) “Definitions of
Factor Abundance and the Factor Content of Trade,” Open Economies Review 10, 385-93.
Trefler, Daniel (1995) “The Case of the
Missing Trade and Other Mysteries,” American
Economic Review 85, 1029-46.
K = capital
P =
professional/technical labor
C = clerical labor
S = sales labor
R = service labor
A = agricultural labor
M = manufacturing
labor
T = cropland
U = pastureland
|
K |
P |
C |
S |
R |
A |
M |
T |
U |
Austria |
.038 |
.687 |
.179 |
.457 |
.906 |
.631 |
.053 |
.980 |
.980 |
Bangladesh |
.001 |
.814 |
.267 |
.671 |
1.00 |
.818 |
.256 |
.997 |
.997 |
Belgium |
.041 |
.717 |
.182 |
.448 |
.891 |
.625 |
.048 |
.974 |
.974 |
Canada |
.146 |
.756 |
.314 |
.439 |
.852 |
.589 |
.123 |
.912 |
.911 |
Columbia |
.022 |
.713 |
.182 |
.486 |
.934 |
.657 |
.078 |
.990 |
.990 |
Denmark |
.021 |
.709 |
.155 |
.451 |
.910 |
.633 |
.023 |
.985 |
.985 |
Finland |
.024 |
.712 |
.121 |
.451 |
.906 |
.635 |
.028 |
.986 |
.986 |
France |
.297 |
.740 |
.409 |
.391 |
.776 |
.548 |
.298 |
.829 |
.829 |
Greece |
.024 |
.712 |
.153 |
.466 |
.911 |
.645 |
.054 |
.989 |
.989 |
Hong Kong |
.012 |
.681 |
.159 |
.466 |
.921 |
.636 |
.068 |
.992 |
.992 |
Indonesia |
.111 |
.953 |
.522 |
1.00 |
.994 |
1.00 |
.651 |
.976 |
.976 |
Ireland |
.008 |
.702 |
.135 |
.461 |
.914 |
.641 |
.018 |
.996 |
.996 |
Israel |
.013 |
.721 |
.146 |
.454 |
.910 |
.636 |
.008 |
.993 |
.993 |
Italy |
.268 |
.760 |
.409 |
.435 |
.824 |
.584 |
.398 |
.876 |
.875 |
Japan |
.600 |
.337 |
1.00 |
.689 |
.608 |
.482 |
.993 |
.652 |
.651 |
Netherlands |
.060 |
.749 |
.188 |
.449 |
.882 |
.618 |
.049 |
.961 |
.961 |
New Zland |
.010 |
.700 |
.146 |
.458 |
.911 |
.639 |
.016 |
.994 |
.994 |
Norway |
.026 |
.709 |
.100 |
.452 |
.905 |
.633 |
.020 |
.986 |
.986 |
Pakistan |
.017 |
.855 |
.276 |
.602 |
.951 |
.782 |
.374 |
.992 |
.992 |
Panama |
.000 |
.695 |
.131 |
.458 |
.919 |
.643 |
.000 |
1.00 |
1.00 |
Portugal |
.019 |
.721 |
.227 |
.473 |
.926 |
.646 |
.081 |
.994 |
.994 |
Singapore |
.011 |
.682 |
.137 |
.460 |
.912 |
.637 |
.015 |
.995 |
.995 |
Spain |
.107 |
.717 |
.263 |
.480 |
.893 |
.628 |
.260 |
.947 |
.947 |
Sri Lanka |
.008 |
.740 |
.187 |
.482 |
.927 |
.664 |
.065 |
1.00 |
1.00 |
Sweden |
.031 |
.805 |
.133 |
.446 |
.896 |
.624 |
.039 |
.972 |
.972 |
Switzland |
.050 |
.663 |
.141 |
.438 |
.886 |
.623 |
.030 |
.970 |
.970 |
Thailand |
.028 |
.806 |
.176 |
.579 |
.933 |
.850 |
.165 |
.989 |
.989 |
Trinidad |
.001 |
.688 |
.126 |
.457 |
.916 |
.641 |
.001 |
.999 |
.999 |
UK |
.179 |
1.00 |
.465 |
.378 |
.831 |
.543 |
.359 |
.849 |
.849 |
USA |
1.00 |
.000 |
.000 |
.000 |
.000 |
.000 |
1.00 |
.000 |
.000 |
Uruguay |
.003 |
.704 |
.151 |
.464 |
.923 |
.642 |
.012 |
.999 |
1.00 |
W. Germany |
.335 |
.456 |
.448 |
.400 |
.735 |
.534 |
.418 |
.803 |
.803 |
Yugoslavia |
.061 |
.829 |
.283 |
.474 |
.916 |
.661 |
.171 |
.984 |
.983 |
mean |
.108 |
.704 |
.239 |
.476 |
.864 |
.629 |
.187 |
.926 |
.926 |
variance |
.042 |
.029 |
.032 |
.096 |
.029 |
.023 |
.068 |
.032 |
.032 |
CV |
1.89 |
.241 |
.755 |
.298 |
.198 |
.233 |
1.40 |
.196 |
.197 |
skewness |
3.04 |
-2.30 |
2.45 |
.584 |
-4.10 |
-1.79 |
1.96 |
-4.19 |
-4.18 |
kurtosis |
12.4 |
10.4 |
10.3 |
10.1 |
20.5 |
12.0 |
6.18 |
21.0 |
21.0 |
|
K |
P |
C |
S |
R |
A |
M |
T |
U |
Austria |
.038 |
.025 |
.034 |
.033 |
.034 |
.010 |
.040 |
.009 |
.068 |
Bangladesh |
.004 |
.040 |
.035 |
.267 |
.139 |
.478 |
.130 |
.048 |
.020 |
Belgium |
.041 |
.040 |
.040 |
.031 |
.025 |
.004 |
.041 |
.004 |
.023 |
Canada |
.139 |
.125 |
.132 |
.116 |
.116 |
.021 |
.109 |
.242 |
.800 |
Columbia |
.023 |
.021 |
.025 |
.053 |
.056 |
.063 |
.047 |
.030 |
1.00 |
Denmark |
.023 |
.026 |
.024 |
.018 |
.031 |
.006 |
.023 |
.014 |
.008 |
Finland |
.025 |
.025 |
.015 |
.016 |
.020 |
.009 |
.025 |
.012 |
.005 |
France |
.277 |
.219 |
.236 |
.187 |
.197 |
.059 |
.236 |
.098 |
.426 |
Greece |
.025 |
.022 |
.020 |
.030 |
.022 |
.032 |
.036 |
.021 |
.175 |
Hong Kong |
.015 |
.010 |
.018 |
.026 |
.031 |
.002 |
.042 |
.000 |
.000 |
Indonesia |
.098 |
.105 |
.110 |
.702 |
.181 |
1.00 |
.332 |
.103 |
.398 |
Ireland |
.011 |
.010 |
.008 |
.013 |
.007 |
.007 |
.015 |
.005 |
.162 |
Israel |
.015 |
.020 |
.014 |
.010 |
.011 |
.002 |
.012 |
.002 |
.027 |
Italy |
.245 |
.169 |
.188 |
.169 |
.159 |
.071 |
.260 |
.065 |
.171 |
Japan |
.558 |
.317 |
.540 |
.825 |
.364 |
.202 |
.661 |
.025 |
.020 |
Netherlands |
.059 |
.065 |
.055 |
.053 |
.044 |
.009 |
.048 |
.005 |
.038 |
New Zland |
.012 |
.012 |
.013 |
.013 |
.008 |
.005 |
.015 |
.002 |
.500 |
Norway |
.027 |
.024 |
.011 |
.018 |
.019 |
.005 |
.021 |
.004 |
.003 |
Pakistan |
.018 |
.058 |
.042 |
.192 |
.075 |
.390 |
.189 |
.106 |
.167 |
Panama |
.003 |
.004 |
.003 |
.004 |
.006 |
.005 |
.004 |
.003 |
.039 |
Portugal |
.020 |
.018 |
.029 |
.031 |
.031 |
.024 |
.046 |
.019 |
.018 |
Singapore |
.013 |
.006 |
.010 |
.014 |
.009 |
.001 |
.014 |
.000 |
.000 |
Spain |
.101 |
.072 |
.085 |
.112 |
.094 |
.061 |
.157 |
.107 |
.357 |
Sri Lanka |
.010 |
.016 |
.015 |
.032 |
.019 |
.062 |
.036 |
.011 |
.015 |
Sweden |
.034 |
.068 |
.033 |
.032 |
.039 |
.007 |
.038 |
.016 |
.024 |
Switzerland |
.049 |
.030 |
.036 |
.025 |
.027 |
.007 |
.034 |
.002 |
.054 |
Thailand |
.029 |
.048 |
.024 |
.169 |
.055 |
.579 |
.090 |
.100 |
.010 |
Trinidad |
.004 |
.002 |
.003 |
.003 |
.003 |
.001 |
.005 |
.001 |
.000 |
UK |
.177 |
.268 |
.227 |
.140 |
.235 |
.012 |
.255 |
.037 |
.377 |
US |
1.00 |
1.00 |
1.00 |
1.00 |
1.00 |
.095 |
1.00 |
1.00 |
.792 |
Uruguay |
.005 |
.007 |
.008 |
.012 |
.013 |
.005 |
.011 |
.008 |
.454 |
W. Germ |
.313 |
.171 |
.271 |
.238 |
.197 |
.070 |
.307 |
.039 |
.156 |
Yugoslavia |
.057 |
.060 |
.052 |
.048 |
.041 |
.083 |
.095 |
.041 |
.213 |
mean |
.105 |
.094 |
.102 |
.140 |
.100 |
.103 |
.133. |
.066 |
.198 |
variance |
.014 |
.033 |
.038 |
.058 |
.033 |
.045 |
.043 |
.031 |
.070 |
CV |
.527 |
.520 |
.522 |
.584 |
.550 |
.484 |
.642 |
.377 |
.803 |
skewness |
3.21 |
3.99 |
3.38 |
2.49 |
3.86 |
2.88 |
2.78 |
4.75 |
1.55 |
kurtosis |
13.6 |
19.9 |
14.8 |
8.20 |
18.9 |
11.0 |
11.0 |
25.3 |
4.51 |
|
K |
P |
C |
S |
R |
A |
M |
T |
U |
Austria |
.030 |
.038 |
.031 |
.201 |
.022 |
.071 |
.019 |
.033 |
.982 |
Bangladesh |
.001 |
.018 |
.009 |
.051 |
.026 |
1.00 |
.018 |
.425 |
.098 |
Belgium |
.080 |
.149 |
.089 |
.050 |
.040 |
.068 |
.047 |
.050 |
.998 |
Canada |
.006 |
.010 |
.006 |
.004 |
.004 |
.008 |
.003 |
.080 |
.745 |
Columbia |
.002 |
.003 |
.002 |
.003 |
.003 |
.039 |
.002 |
.008 |
.273 |
Denmark |
.018 |
.039 |
.022 |
.012 |
.020 |
.044 |
.111 |
.435 |
.137 |
Finland |
.022 |
.043 |
.016 |
.012 |
.015 |
.075 |
.013 |
.581 |
.101 |
France |
.025 |
.039 |
.025 |
.015 |
.015 |
.050 |
.013 |
.061 |
.918 |
Greece |
.008 |
.013 |
.007 |
.008 |
.006 |
.093 |
.007 |
.031 |
.950 |
Hong Kong |
.474 |
.604 |
.684 |
.752 |
1.00 |
.511 |
1.00 |
.005 |
.023 |
Indonesia |
.001 |
0.02 |
.011 |
.054 |
.014 |
.830 |
.018 |
.068 |
.847 |
Ireland |
.005 |
.008 |
.004 |
.005 |
.003 |
.025 |
.004 |
.008 |
.289 |
Israel |
.035 |
.085 |
.036 |
.019 |
.021 |
.036 |
.016 |
.021 |
.718 |
Italy |
.038 |
.050 |
.033 |
.022 |
.021 |
.101 |
.024 |
.100 |
.603 |
Japan |
.230 |
.252 |
.257 |
.292 |
.125 |
.765 |
.167 |
.137 |
.177 |
Netherlands |
.085 |
.180 |
.091 |
.064 |
.053 |
.120 |
.042 |
.031 |
.951 |
New Zland |
.002 |
.003 |
.002 |
.002 |
.001 |
.006 |
.001 |
.001 |
.045 |
Norway |
.067 |
.114 |
.032 |
.004 |
.039 |
.108 |
.031 |
.311 |
.178 |
Pakistan |
.002 |
.011 |
.005 |
.016 |
.006 |
.357 |
.011 |
.168 |
.366 |
Panama |
.005 |
.011 |
.006 |
.005 |
.009 |
.071 |
.004 |
.021 |
.704 |
Portugal |
.012 |
.020 |
.020 |
.015 |
.015 |
.129 |
.016 |
.275 |
.222 |
Singapore |
1.00 |
1.00 |
1.00 |
1.00 |
.633 |
.505 |
.782 |
.010 |
.055 |
Spain |
.009 |
.013 |
.009 |
.009 |
.007 |
.050 |
.009 |
.080 |
.748 |
Sri Lanka |
.009 |
.030 |
.016 |
.026 |
.015 |
.535 |
.020 |
.301 |
.298 |
Sweden |
.023 |
.089 |
.026 |
.019 |
.022 |
.046 |
.016 |
.172 |
.354 |
Switzerland |
.061 |
.072 |
.051 |
.026 |
.028 |
.074 |
.026 |
.011 |
.368 |
Thailand |
.003 |
.010 |
.003 |
.016 |
.005 |
.584 |
.006 |
1.00 |
.024 |
Trinidad |
.055 |
.061 |
.044 |
.031 |
.035 |
.116 |
.040 |
.478 |
.103 |
UK |
.027 |
.080 |
.040 |
.018 |
.030 |
.016 |
.002 |
.026 |
.836 |
US |
.007 |
.013 |
.008 |
.006 |
.006 |
.006 |
.004 |
.033 |
.983 |
Uruguay |
.001 |
.002 |
.001 |
.002 |
.002 |
.007 |
.001 |
.004 |
.154 |
W. Germany |
.074 |
.077 |
.072 |
.047 |
.039 |
.151 |
.044 |
.066 |
.858 |
Yugoslavia |
.012 |
.024 |
.012 |
.008 |
.007 |
.157 |
.012 |
.051 |
1.00 |
mean |
.074 |
.096 |
.081 |
.085 |
.069 |
.205 |
.077 |
.154 |
.488 |
variance |
.035 |
.039 |
.042 |
.046 |
.038 |
.072 |
.046 |
.017 |
.131 |
CV |
.393 |
.488 |
.393 |
.396 |
.346 |
.759 |
.359 |
.702 |
1.35 |
skewness |
4.00 |
3.54 |
3.57 |
3.37 |
3.86 |
1.58 |
3.59 |
2.15 |
0.17 |
kurtosis |
18.9 |
15.3 |
14.8 |
13.3 |
16.8 |
4.25 |
14.4 |
7.78 |
1.34 |
|
K |
P |
C |
S |
R |
A |
M |
T |
U |
SW |
.999 |
-.708 |
.323 |
.087 |
-.942 |
.548 |
.959 |
-.900 |
-.404 |
DS |
-.028 |
-.091 |
.029 |
.061 |
.057 |
.453 |
-.084 |
.154 |
-.312 |
DW |
-.030 |
-.088 |
-.033 |
-.012 |
-.089 |
.726 |
-.084 |
-.065 |
.264 |
|
K |
P |
C |
S |
R |
A |
M |
T |
U |
|
Content |
- |
- |
- |
- |
- |
+ |
- |
+ |
+ |
|
S |
+ |
- |
- |
- |
- |
- |
+ |
- |
- |
|
W |
+ |
+ |
+ |
+ |
+ |
- |
+ |
+ |
+ |
|
D |
- |
- |
- |
- |
- |
- |
- |
- |
+ |
v2n/v1n v2k n
m v2m/v1m v1k 1
Figure 1. Factor abundance distance
v2m/v1m M m v3m/v1m 1 M v3m v2m 1 v3k v1k v2k
Figure 2. Factor abundance with 3 factors