11
Income and health* Ggpjrical Fatteras
The foil wing renakrs refer to the cross-classifications
of wealth and income published in Holland and Sweden. These data
show certain characteristics which are found ajso in other
cross-section data concerned with size distributions, especially
data from official publications like censuses etc.
The first feature is that the groat bulk of the observations
is concentrated in the corner of the first ( the north-east ) quadrant.
In other words these distributions are very skew. A great many of the
units are small in either dimension.
The second feature is that the wealth distribution is
heavily truncated ( in Sweden for example at 150.0C crowns)
while the inc me distribution is given down to rather lw levels.
If the mean income in the vari>us wealth classes is
calculated aalinear regressim of a very regular pattern is btained.
( This "regression of the first kind" as we may call it differs
fr >m the usual least squares regressin in that it d ees not
assume a or!rl a certain mothem tiwal functifor the re .ression;
see Gerald CramAr, Mathematical etheds f Statistics,Pro neeton 1946jfo tjc>
m
if the regression of the means turns out to be inear as is the case
here, then it sh lid be the same as the result of a linear least
squares regress! n; this may be not quite true only in so far as
we fail to use weights for the means corresponding to the various
fre uencies in the different wealth classes ).
The same regression of the first kind in the other dimension «
wealth on income — gives a completely different picture* he mean
wealth in the lower income classes does not indrease with income
at all; for higher incomes it increases very strongly, so that
a strongly ourved regression line results.
At least one, and probably the most important reason for
the curvi.linearity of this regression line lies in the truncation
of the wealth data. If we try to fill in the missing wealth data
in o r imagination, according to plausible and common ses.se prior
knowledge, we find that the regression of wealth on incot e might
well be quite linear and rather steep} at least it w >u d be very
much nearer to linearity than it is n w The inclusion of cases
with wealth below the tax li it, which is rrbably he lower and
the more frequent the 1 wer the inc me, w uld reduce the mean wealih
in all inc sae c asses but it w u d reduce it the more the 1 wer the