Full text: Konvolut The Personal Distribution of Income 2

18 
showing disproportionately increasing output with any increase 
in input ( cost, or employment ). In fact, however, we often 
find that it is not so amd that both regression coefficients 
are smaller than one, decreasing cost and decreasing returns 
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 while 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 fef 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 1q/9 
in the other regression, But, unless 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 among 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 relation 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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