Income Change Calculation
The income change is calculated by measuring the relative change in income for a specific percentile group compared to the
base year (1980). The formula for this calculation is given by :-
\( \begin{aligned}
\Delta_{c,p,t} = \left( \frac{s_{c,p,t} - s_{c,p,1980}}{s_{c,p,1980}} \right) \times 100
\end{aligned} \)
Where :-
\( \begin{aligned}
s_{c,p,t} =
\end{aligned} \)
income share of country c, percentile group p, in year t.
\( \begin{aligned}
s_{c,p,1980} =
\end{aligned} \)
income share of the same group in 1980.
This formula computes how much the income share for a given percentile group has increased or decreased, expressed as a
percentage relative to its income in the base year. A positive result indicates an increase in income relative to 1980,
while a negative result indicates a decrease.
Gini Calculation
The Gini coefficient measures income inequality within a population. It is calculated using the Lorenz curve, which plots
the cumulative income share against the cumulative population share. The Gini coefficient is calculated using the following
formula :-
\( \begin{aligned}
G = 1 - \frac{2 \sum_{i=1}^{99} ( \frac{p_i + p_{i+1}}{2} ) \cdot ( \frac{q_i + q_{i+1}}{2} ) }{ \sum_{i=1}^{99} p_i}
\end{aligned} \)
Where :-
\( \begin{aligned}
p_{i} =
\end{aligned} \)
is the income share for the i-th percentile group.
\( \begin{aligned}
q_{i} =
\end{aligned} \)
is the cumulative population share for the i-th percentile group.
This formula calculates the area between the Lorenz curve and the line of perfect equality, where a lower Gini coefficient
(closer to 0) indicates greater equality and a higher Gini coefficient (closer to 1) indicates greater inequality.
The Gini coefficient provides a snapshot of the income distribution across the entire population, with larger values
suggesting a more unequal society.