Full text: The Personal Distribution of Income

9 
minimum of assessed wealth,while all the income receivers 
with lower wealth are not included in the data.If we try 
to fill in these missing data in our imagination,assuming 
fairly low levels of wealth for these people, we could 
easily conceive that also the regression of wealth on 
income would become linear.The inclusion of wealth below 
the tax limit which is presumably the lower and the more 
frequent the lower the income would reduce the mean wealth 
in all income classes but it would reduce it the more the 
lower the income. In other words the mean wealth in the 
lower income classes as shown by the data very strongly 
overstates the real mean wealth,and this the more the 
lower the wealth. 
There is no proof,of course,that some curvilinearity would 
not remain even if full wealth data were 
available,although it would be surprising that the two 
regression lines should be so different in character. 
The cross classification of wealth and income,available 
for the Netherlands and Sweden, will now be discussed in 
the light of the theory contained in equation (8). It 
would be too much to expect a verification: For one thing 
the estimate of the Pareto coefficient for income is 
always more or less arbitrary because it depends on the 
range of income classes included when fitting a straight 
line to it. But any attempt to illustrate an abstract 
argument by concrete data is better than speculating in 
the void. 
The most impressive feature of the data is the linear and 
very regular character of the regression of income on 
wealth. The regression coefficient is in most cases around 
2/3 but it may be as low as 1/2. A considerable defect of 
the data is the unequal size of the wealth (as well as the 
income ) classes. The range of the classes increases with 
the wealth.The last but one wealth class has a range about 
four times as great as the lower wealth classes. This 
makes it very difficult to decide whether the variance and 
higher moments of income are independent of the size of 
wealth. In the Swedish data the variance increases in the 
higher wealth classes. This may,however, be plausibly 
explained by the increase in the range of these classes. 
The same defect marrs the comparison of the conditional 
distributions of income in the various wealth classes. 
They all have a Pareto tail,but the Pareto coefficient is 
markedly lower in the last two or three wealth classes 
than in the others.This,again,may be plausibly explained 
by the greater range of these high wealth size classes.
	        

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