# Full text: The Personal Distribution of Income

T.S
showing disproportionately increasing output with any increase
in input ( cost, or employment ). In fact, however, we often
find that it is not so and. that hoth. regression coefficients
are smaller than one, decreasing cost and decreasing returns /
A '
apparently coexisting.
How is this possible? It can only occur with
wide dispersion round the regression line. The exceptionally
effieient plant will tend to be counted as small plant
in the input dimension whi?e the unusually inefficient ones
will be counted as large. In consequence there will be
a bias in favour of decreasing returns as measured in the
input dimension ( regression of output on cost or employment ).
The inversion sf the regression corresponds
to the fact that the ration of the two standard deviations
is reciprocal in the two regression coefficients. If it
is 9/10 in the regression of input on output, it is 1o/9
in the other regression. Sut-, mnless the correlation coeffieient
is sufficiently high, the regression coefficients
will both have values■below unity.
The same mechanism must also be at work in - '•
the wealth-income distribution: Those with high return for
a given wealth will be classified nong large incomes, those
with low returns with the same wealth among small incomes,
which tends to counteract the natural tendency of wealth to
increase with income. This may have contributed to the
flatness of the wealth-income regression in the lower income
range, although the chief reason for that is no doubt the
truncation of the wealth distribution.
The preceding example of plant size, in which
only one underlying theoretical relamion is presumed to exist,
shows that while it is logical to expect in this case,
if one regression reflects the underlying relation, that the
other should as it were represent the inverse of it, yet in
reality this will not be true because the second regression
will be more or less distorted by the dispersion of values
round the first regression line.
If we have two underlying relations then each of
the regression lines will be influenced by both of them,
either directly or indirectly, because each will be to some

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