Chapter 6
CONVERGENCE 2: THE FULL DISTRIBUTION OF INCOME

What has been discussed so far concerns the top 10 percent of the income distribution, with no attention paid to the remaining 90 percent (other than the state average income). This incompleteness obviously limits the relevance of the conclusions drawn previously. This chapter presents the endeavor of estimating the full income distribution, including the lower quartiles, the bottom decile, and the Gini coefficient. This is a challenging task to perform because it implies the generalization of the Pareto approximation to the entire distribution, which, undeniably, is a strong assumption. Therefore, the estimates obtained are far from being perfect, probably need some improvement, but are certainly worth further investigation.

The estimation of the full income distribution can be done for each state, but not for the entire time-period 1913-2003. The latter has to be restricted to 1965-2003. This is because prior to 1965, the number of individual tax returns does not approximate the household population well.

What follows provides first a basic understanding on the Lorenz curve, and explains then how the assumption made on the Lorenz curve and its functional form leads to obtain the three quartiles, the lower decile, and the Gini coefficient.