L1, and L2. How have changes in these components contributed to the changes in
national inequality? This section will develop a sense of the quantitative contribution
of each of these forces to the actual changes in national inequality between
the early 1990s and late 2000s for the four countries under study.
Using equation (13.2), we can write the change in national inequality as
dL = Axdx + Akdk + AL1dL1 + AL2dL2 (13.3)
where
Ax =(L1 − L2)+[(k −1)/(x(k −1)+1)]−log(k) (13.4a)
Ak = x/(1− x + xk)− x/k (13.4b)
AL1 = x (13.4c)
AL2 =(1− x) (13.4d)
The four coefficients, Ax , Ak , AL1,and AL2, can all be calculated from the actual
data. Notably, their numerical values will be different depending on whether the
base-year or end-year data are used, as shown in Table 13.3.
In the following accounting exercise, we use the average of