Rivalry and are 4 brothers alike?

Mon, 25 Mar 1996 17:51:13 -0500 (EST)
INTT000 (INTT@MUSICB.MCGILL.CA)

On March 21, Bruce McFarling wrote:

" I have used Tieting Su's paper in JWSR as the basis for a
discussion of trade blocs in International Trade and Finance.
Tieting provides a figure (Figure 5) that illustrates his results
regarding the degree of overlap between the German, Japanese,
and US trade blocs that he detected. The three dimensions of the
figure are: Intensity of rivalry; structural rivalry, and consistency
of rivalry. I was wondering whether anyone on the list would be
able to translate the three dimensions into terms that would be
sensible to third year economics students?

Virtually,

Bruce R. McFarling, Newcastle, NSW
ecbm@cc.newcastle.edu.au "

The following is the brief response and I hope it can be useful for
Bruce and others on the net.

THREE DIMENSIONS OF RIVALRY AND ARE ALL FOUR
BROTHERS ARE ALIKE?

Technically the method I used in the article is based on
decomposition of the Euclidean Distance measure of similarity,
which I believe, is better than correlation measure or any method
which is based on correlation (such as factor analysis).

I understand it is challenging to teach undergraduates
"decomposition of the Euclidean Distance" and prove vigorously
that it is better than correlation methods. I will try to put the ideas
in simple terms.

To systematically study the US-Japanese commercial rivalry
in the Asia-Pacific region, a correlation analysis based on their
respective profiles of market shares in different industries in the
region can be used. While high positive correlation between their
profiles suggests a competitive structure, a high negative
correlation a complementary structure. However the correlation
method, as used in Q-type analysis (to explore similarity between
units of analysis) has serious limitations. To understand why, I
would like to use the following example, which is in line with the
logic used by the inventors (F. Galton and K. Pearson) of the
correlation method in studying the law of inheritance of human
physical and psychic (intellectual and moral) characters.
The following table shows the hypothetical IQ scores of
four brothers in the same family from four different types of IQ
tests.

--------------------------------------------------------------------------
IQ Tests Brothers in the Same Family
-------- ----------------------------
Brother A Brother B Brother C Brother D
--------- --------- --------- ---------

IQ testA 80 20 60 70
IQ testB 100 40 70 90
IQ testC 80 20 60 70
IQ testD 100 40 70 90

--------------------------------------------------------------------------

The hypothesis is that if intelligence stays in the family, the
brothers should perform similarly. How is similarity usually
measured? By correlation coefficients. If you correlate the IQ
profiles of all the four brothers, you will find that all the
correlation coefficients are positive 1s, indicating perfect
correlation which tends to support the hypothesis. But are all the
four brothers alike in their performance on IQ tests?
A closer look at the original data (rather than the perfect
correlation coefficients) will reveal that not all of them have
similar performance. At this juncture, I suggest that you plot the
data and draw their IQ profiles (with the IQ scores as the vertical
coordinate and the four IQ tests as the horizontal one). The plot
will easily reveal the limitation of the correlation analysis.
A comparison of the IQ profile of Brother A with that of
Brother B reveals that the Shape (correlation) of their profiles are
the same, their levels of performance (called Distance) are far
apart. The result shows at best they share similar interests but not
similar performance.
A comparison of the IQ profile of Brother A with that of
Brother C reveals that although their shapes are similar, they differ
in the degree to which their profiles fluctuate (called Scatter) as
well as in Distance. In other words, Brother C's performance is
more consistent that of Brother A.
While correlation technique can detect the similarity in
Shape, it fails to capture the other two aspects of similarity,
namely, Distance and Scatter, the Euclidean Distance incorporates
all the three aspects.
According to correlation, all the four brothers in the above
example are alike in intelligence. According to Euclidean Distance
only Brother A and Brother D are alike.

How is this relevant to my study of the structure of rivalry?
To start with, if one relies on the literature of competitiveness in
the US, one wonders if it is necessary to conduct such study. A
glance at that literature (HOW WE ALLOWED JAPAN TO
TAKE THE LEAD; IN THE SHADOW OF THE RISING SUN;
SILENT WAR are just a few examples) may suggest that there are
intensive rivalry between the two. However, given the ability of
the US in shaping the economic order of the region during the
Cold War period and its strong political, economic and military
presence and powerful tools (such as the "trade deficit") the US
has used in the region in the post-Cold War period, doubts can be
and are raised whether the complementary structure in the Cold
War period has been fundamentally changed. Hence it is
necessary to conduct a systematic analysis.

In the following I would like to discuss the three concepts
in Euclidean Distance which are systematically implemented in the
study.

As I mentioned before, to systematically study the US-
Japanese commercial rivalry in the Asia-Pacific region, a
correlation analysis (to detect "structural rivalry") based on their
respective profiles of market shares in different industries in the
region can be used. While high positive correlation between their
profiles suggests a competitive structure, a high negative
correlation a complementary structure. However their market
profiles may be very similar in shape but they are so far apart that
they are only potential rivals.

Consider the following comparison:

----------------------------------------------------------
Industries The hypothetical market profiles

The US profile The Japanese profile

ind. 1 60% 15%
ind. 2 40% 10%
ind. 3 70% 20%
ind. 4 80% 22%
....

----------------------------------------------------------

In this scenario, Japan is at best a POTENTIAL rival of the US.
Correlation coefficient will fail to capture such difference, which
can only be detected by Distance (to find the "intensity of
rivalry").

Furthermore, consider the following scenario:

---------------------------------------------------------
Industries The hypothetical market profiles

The US profile The Japanese profile

ind. 1 80% 15%
ind. 2 30% 10%
ind. 3 60% 12%
ind. 4 40% 11%
....

--------------------------------------------------------

In addition to the difference in Distance, a comparison of
the two profiles shows that they also differ in Scatter (design to
detect "consistency of rivalry"). The Japanese profile is more
consistent than that of the US. This difference may result in
different "collective behaviour" of the US and Japanese business.
For example, the US firms in the industry with relatively
small share of the market (as in the case of ind. 1 and 3) may be
very anxious in expanding their market share while those in the
industries with large share may be more interested in maintaining
the status quo. As a result sectoral conflict may rise with regard
to strategies to be used and the concerted collected action of the
business community would not be easy to coordinate. And the
opposite should be true for the Japanese business.

It is based on the reasoning described above, I employed
the three concepts in Euclidean Distance in analyzing the structural
rivalry between the US and Japan. I should stress again that the
findings are only preliminary and comments will be greatly
appreciated.

Tieting Su
Department of Sociology
McGill University, Montreal, Canada