Merz: The Distribution of Income of Self-employed, Entrepreneurs and Professions
18
Thus, in absolute DM-values the main redistributive impacts of the German tax law is
given for professions with -15.557 DM followed by the entrepreneurs with
-12.424 DM to be paid to every person below the median to show the before tax
distribution. This is more than 6 times respective 5 times than the redistributional
amount for employees, a remarkable difference.
6.4 Decomposition of Inequality of Employees and Self-
Employed (Entrepreneurs and Professions*)
To answer the question how much of the overall inequality can be 'explained' by the
specific groups a decomposition of the overall inequality into the inequality within
groups and the inequality between these groups is required. Such a decompostion is
available via a classs of additively decomposable inequality measures (Shorrocks 1980,
1984) with
(2) Itotal,c = Iw + Ib = ? g IWg + Ib = ? g (ng/n) (? g/? )c Ic(yg) + Ib
where IW is within and IB is between group inequality, g is the group index, ? is the
overall respective group mean, n is the number of observations, Ic(yg) is the group
inequality index dependend on group's incomes yg; the group weights
wg = (ng/n) (? g/? )c only sums to unity when c = 0 or c = 1. The only class of inequality
measures that satisfies the principle of scale invariance when comparing distributions
with different means, and that ensure that the decomposition procedure is valid for
arbitrary specifications of the partition, belongs to the generalised entropy class with
(3) Ic = (1/n) 1/[c-(c-1)] ? i [(yi/? )c - 1] c ? 0 or 1.
We further use the Theil index as the overall and group inequality index which is given
for c = 1 and applying the rule of de l’hopital by
(4) I1 = 1/n ? i (yi/? ) log(yi/? ).
Thus, the Theil inequality index decomposition by equations (2) and (4) provides
additive group specific inequality contributions. We finally use group specific
inequality shares (%) as a group specific percentage of Iw, the overall within group
inequality part. The between group inequality share (%) is calculated as IB as a
percentage of the overall inequality index Itotal,c.
Table 5 now presents the decompostion of net income inequality by the Theil inequality
index. We see a very dominant within ('intra') group inequality (IW= 93,5% = 100 - 6,5)
compared to the between ('inter') group inequality of IB = 6,5% and a remarkable high
inequality for the self-employed compared to the overall inequality. This very striking
result of a low between group inequality is somewhat surprising, since the occupational
status is often related to a certain income range. This obviously is far less important to
‘explain’ income inequality in Germany. This is in line with results of Becker and
Hauser (1995, p. 330) for a quite different data base, the Income and Consumption
Survey of 1990 and even for the two decades ago.