The literature on the distribution of income has resulted into a general impression that this distribution can be approximated by a lognormal distribution, see e.g. Pen & Tinbergen (1977). For the purposes of our exposition it is useful to test this impression. [79] Also, since we will discuss long periods of indexation, notably from 1950 till 2002, it is also useful to look at the distribution in 1950 and a recent one. We then take the distribution data in the appendices for Holland 1950 and 1988.
Figure 21 and Figure 22 plot the resuls of a (rough) estimation. It appears that we get the best fit when we transform the data into logarithms (and recompute the frequency densities - i.e. the transformation required to deal with different class sizes). The logarithmic data are approximately normal, as can be seen in the plot of log[income] versus its frequency density. We can transform the estimated distribution for a plot in the income-frequency format.
Figure 21: Dutch income distribution 1950
Figure 22: Dutch income distribution 1988
In the 1988 plot, the estimation has been done with the 1988 ‘parttimers’ dropped, but they are included again in the income-frequency plot so that we can better appreciate that their inclusion would confuse a discussion on fulltimers. But it is nice to see the dromedary shape returning.
We conclude that income can indeed be approximated as a lognormal distribution, and throughout time; at least as a stylized fact that we can use for propositions and illustrations. [80]
Definitions and formulas
There are some useful definitions and formulas for heterogeneous labour markets. These hold for any distribution, not just the lognormal distribution. Let y and w be micro values that have a certain density. First of all, there are the following accounting definitions, for annual and nominal values: