2.2. The Gini coefficient in a model economy
Having established that labour market institutions affect labour shares, the relative wage, and the
unemployment rate, we turn to their impact on the distribution of personal incomes. Our empirical
measure of income inequality will be the Gini coefficient. We hence decompose this measure of inequality
into its various components for a model economy with four types of agents.
The labour force (or population) is normalised to one, that is, L + H = 1 . Following our set-up
in the previous section, workers can be either employed and receive the skilled or unskilled wage,
w~s =(1-τ)ws and w~u =(1-τ)wu, or unemployed, in which case they receive the unemployment
benefit B .7 Some individuals also own capital and receive profits. We assume that the owners of capital
are always skilled workers, and that they are never unemployed. Furthermore, we assume that the revenue
raised from employer/employee contributions, τ , is used to finance the unemployment benefit, so that
B = τθy /u .8 This implies that the payment of net wages, capital income, and unemployment benefit
exhaust output, and average income is equal to output per capita, y .
We then have four types of agents characterised as follows:
(i) A fraction u of the labour force are unemployed, and receive the unemployment benefit B ;
(ii) A fraction l of the labour force are unskilled workers earning a net wage w~u ;
(iii) A fraction s of the labour force are skilled workers. Of those s - κ own no capital and have an
income equal to the net skilled wage w~s ;
(iv) There are κ worker-capitalists, each of whom earns profits π as well as the wage w~s .
Our assumptions imply that s + l +u = 1 . We further suppose that w~s > w~u > B , while the profits of
each worker-capitalist depend on the capital share, π = (1 — θ)y / κ .
The degree of income inequality is measured by the Gini concentration index computed across
subgroups of population. With N subgroups, the definition of the Gini concentration index is:
1NN
Gini ~ ∑∑ У> - yj I ∙ n ∙ n1 (16)
2 y i =1j =1
where yi is the income in subgroup i , which has relative weight ni , and y is the average income.
Given our assumptions about the population and their incomes, the Gini coefficient can be expressed as
7 B can also be interpreted as a subsistence wage earned in the informal sector, if an unemployment benefit does
not exists.
8 We are implicitly assuming that profits go untaxed. The implication of this assumption is that the tax rate does not
affect the Gini index directly. The alternative assumption (taxing capital income) will make τ appear in the Gini
index reported in equation (17). In our dataset, the tax wedge is highly collinear with the unemployment benefit and
the unemployment rate, which proved a problem when we introduced it in estimations of the Gini index.
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