Full text: The Personal Distribution of Income

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 
efficient plant will tend to be counted as small plant 
in the input dimension while the unusually inefficient ones 
?;ill be counted as large. In c nsequence there will be 
a bias in fav ur of decreasing returns as measured in the 
input dimension ( regression of output on cost or employment ), 
The inversi n bf the regression corresponds 
t the fact that the rati % of the two standard deviations 
is recipr cal in the two regress! n c efficients If it 
is 9/11 in the regression f input n >utput, it is to/9 
in the other re ressi n But unless the correl ti n c efficient 
is sufficiently high, the regression coefficients 
will both have values be law unity. 
The same mechanism must also be at work ir.tfc 
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 we 1th among small incomes, 
which tends to counteract the natural tendency of wealth to 
increase with income. ;'his may have contributed to the 
flatness of the wealth-income regression in the lower income 
rage, 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 t e sec nd regress! n 
will be m re or less distorted by the dispersi n of values 
round the first regression line. 
If we have two underlying relati-ns then each f 
the regress! n lines will be influenced by b th f them, 
either directly r indirectly, because each will be t sme
	        

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