In this assignment, we will attempt to study the effects that difference in Income Ratio (henceforth known as I.R.) between the years 1980 and 1990 have on the Productivity Growth (P.G.) during the same period of time.
The Income Ratio of one specific year can be found if we take the average
income of the richest faction of a country (the richest 20% of the
population) and divide it by that of the poorest faction (the poorest 20%).
In this assignment, the Income Ratios that were used were those of 13
different countries. The I.R.’s on both 1980 and 1990 were taken for all
these countries and, to find the difference between them, the I.R. for 1990
was divided by the I.R. for 1980, for each country. These new numbers
illustrate the change of I.R. between the two years so that we can compare
how the P.G. changes in relation to the changes in the I.R..
On this assignment, we use inductive reasoning to examine the data and
find a theory (a hypothesis) that would combine the data given in a way
that would make sense, based solely on our data. How do we know if the
“theory” that we formulate makes sense? In this case we will plot the
points (derived from the column “I.R. 1990/1980,” going on the x-axis, and
the column “Productivity Growth 79-90,” on the y-axis). According to how
the points are on the graph in relation to the Average Point (0.94,1.45)
(point that is an average of all values and which divides the graph into
four Quadrants), if 80% of these points are where they would be expected to
be to conform to the hypothesis, then there is no reason to reject this
hypothesis. If, on the other hand, the majority of the points does not
conform to our hypothesis (are not where they were predicted to be), then
it is rejected.
Another method of reasoning frequently used by Mainstream economists is
“deductive knowledge,” as opposed to “inductive,” described above. Their
theory is formulated and only then it is applied to the data. Their theory
on this subject suggests that productivity within a country grows when the
population has incentives to work harder (or to work more). When the gap
between rich and poor increases (an increase in I.R. form 1980-90,
resulting in a larger ratio on the column I.R. 1990/1980), so does the
population’s eagerness to work, therefore increasing the Productivity
Growth. Since when one variable goes up the other also goes up, there is a
positive (or direct) correlation between the two. Mainstream economists use
deductive reasoning to deduce that there exists a positive correlation
between the two factors. In short, their hypothesis is that when the Income
Ratio increases, the Productivity Growth also increases, since people are
more motivated. For this to be true, we would expect a line going up and to
the right on the graph, passing by Quadrants II and IV. Most points (80% or
more) would have to be on these two Quadrants. This, however, is not the
case (see graph), since only about 30.77% of the points plotted satisfy
these conditions.
Since the original hypothesis was rejected, we might want to see if there
is a negative correlation between the two variables (that is, as one goes
up, the other goes down). Our new hypothesis would then be “as the Income
Ratio increases, the Productivity Growth decreases.” Then, in the case of a
high I.R., people in lower classes would rationally start to feel insecure
and that their work is not being recognized by society, therefore losing
motivation and producing less. In this case, since there’s a negative
correlation, one would expect the line on the graph to go downwards, from
left to right, passing on Quadrants I and III. If this hypothesis were
valid, 80%+ of the points would have to be on these Quadrants. This is also
not the case, for only 69.32% of the points are on the appropriate
Quadrants. Like the first, this second hypothesis also has to be rejected.
After analyzing these two relationships and seeing that neither is valid,
we conclude that there is no direct relationship between the two variables
tested. That does not mean that one has no effect on the other (it probably
does), only that there may be other factors and influences involved that
have not been accounted for in this assignment and that one is not the only
factor responsible for the changes in the other.
DATA SHEET

Country Income Ratio 1980 Productivity Growth
1979-90 Income Ratio 1990 Income Ratio 1990 / 1980
United States 9.0 0.4 11.0 1.2
Australia 9.6 0.8 9.6 1.0
New Zealand 8.8 1.4 8.8 1.0
Switzerland 8.7 1.0 8.0 0.91
Canada 7.0 1.1 7.0 1.0
Britain 6.8 2.0 7.0 1.03
France 6.5 2.4 6.0 0.92
Italy 6.1 2.0 5.8 0.95
Germany 5.8 1.6 5.0 0.87
Holland 5.6 1.5 5.0 0.89
Belgium 4.7 2.2 3.8 0.81
Sweden 4.7 1.5 3.8 0.81
Japan 4.2 1.0 3.6 0.85

Average Income Ratio 1990 / 1980: 0.941
Average Productivity Growth 1979-90: 1.45
No. of points conforming to first hypothesis: 4/13 = 30.77%
No. of points conforming to second hypothesis: 9/13 = 69.23%

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