w -w w-B
Gini = (1 - κ)(1 - θ) + ls —----- + u (1 - u )----- (17)
yy
where w~ is the average net wage. The Gini coefficient is thus a function of population proportions
(u,l, s), the number of capital owners κ , the capital share, the wage differential, and the unemployment
subsidy. A higher capital share will increase inequality by raising profits and thus the income of the richest
individuals. A greater wage differential between the skilled and the unskilled will raise the Gini coefficient
as it increases inequality between groups of employed individuals, while a larger unemployment benefit
will reduce the Gini coefficient. The effect of the unemployment rate is ambiguous. This is a standard
effect when there is inequality within and between groups. The unemployed have a low income but are all
equal, while the employed have a higher income but there is inequality within this group. More
unemployment, by increasing the number of individuals in the less unequal category, may increase or
reduce overall inequality. The equalising effect will, however, only dominate for unemployment rates over
50%, hence we expect higher unemployment to increase income inequality.
Our framework of analysis makes a number of simplifications, which are worth mentioning. First,
both the distributions of wealth and of wages have been compressed, since we only have two types of
workers (skilled/unskilled) and one type of wealth-owner. Second, two sources of income are missing.
One are the rents on assets such as land or intellectual property rights and patents, which we ignore as
they are a very minor fraction of the total. The other is pensions. Note, however, that pensions can come
from three sources: they can be provided by pension funds, in which case they are capital income; they
can be private pensions paid by a company to its former employees, in which case they are (most often)
counted as labour payments in the company’s balance sheet; and they can be public pensions. It is only the
third component that we have not included. This could in principle be an important source of income
differences;9 however the data are rarely available. Third, we do not distinguish between personal income
distribution and household income distribution.10 Lastly, note that we have focussed on gross income
inequality, with the only tax we have considered being the unemployment insurance contribution. We also
model the tax rate in a naïve way, considering immediate readjustments after a change in unemployment,
thanks to the balanced budget constraint; available alternatives not considered here are the lowering of the
replacement rate and or a reduction in coverage (see Atkinson and Brandolini 2003).
3. Empirical Analysis
3.1. Empirical specification
We saw in equation (17) that the Gini coefficient of personal incomes could be expressed as a function of
the labour share, the wage premium to skill, the replacement rate, and population shares. The model
9 Indeed Bourguignon et al. (2002) show that a major source of differences in distribution between the US and
Mexico is the level of public pensions in those two countries.
10 Kenworthy (2003) and Esping-Andersen (2004) claim that most of the rising trend in household income inequality
is attributable to changing patterns of income distribution within the family, associated with increased labour market
participation of women and young people, a question beyond the scope of this paper.
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