12
is 0,626 + 0,004 (data for 1962/63). The regression coefficient
corresponds to our k. That kO can be explained in the first
place by the presumed fact that with increasing wealth earned
income is less and less important; in the second place perhaps
by the fact that income from shares which dominates for the
larger wealth does not contain the undistributed profits.
Since the Pareto coefficient for wealth was 1,38 in 1962/63,
we should expect it to be 2,20 for income on the basis of
the theory. In reality it was 2,08. A better correspondence
is hardly to be expected, since the independence condition holds
only very approximately.
A similar calculation with Swedish data /20/ gives apparently very
bad results, although the regression of income on wealth is linear.
To take an example: For married couples, both taxed, in 1971, the re
gression coefficient of income on wealth is 0,49, the Pareto coeffi
cient for^income ought thus to be 3,4, but it is in reality 2,5.
The explanation is that the standard deviation of income increases
with wealth (from 0,3 to 0,4 in the highest wealth class). This
produced a thinning out of the tail of the income distribution, thus
leading to a smaller Pareto coefficient than would otherwise obtain.
The effect of increasing standard deviation is actually the same
as that of a steepening of the regression line of income on wealth.