## 4/15/13

### An unusual feature of income distribution in the USA - a Pareto law at very low incomes

There is an invaluable source of quantitative information on personal income distribution (PID) in the USA which is hidden in a set of clumsy photocopies one can find searching the most remote parts of the Census Bureau web site. Today, we are discussing the distribution of personal money incomes in the age group 14 to 15 years. This is an extremely narrow group with data available only between 1967 and 1974. The essence of this short time series consists in the power (Pareto) law distribution of personal incomes starting from zero level. It is a well-known fact that the highest incomes are controlled by the Pareto law as well as many distributions in physics associated with self-organized criticality.  Therefore, we consider the 14 and 15 years PID as an extremely important quantitative feature likely related to the frozen structure of income distribution not to the long-term process. These people just entered the economy and were distributed over the pre-existing structure straight away.

Some words about the data. I am a long-term user of the CB data but it took me couple minutes to get through a broken link to the directory http://www.census.gov/prod/www/population.html, where the original copies sit. They are not digitized. Fortunately, I did my homework in 2003 and spent a month to convert them into a digital format.  These data allowed developing a mechanical model for the evolution of personal incomes since 1947, which is presented in my book “Mechanical model of personal income distribution”. There is much more left in the dataset, however.

Figure 1 below displays four personal income distributions for 1968. We present three age groups: 14 to 15, 16 to 19, and 20 to 24 years as well as the whole population distribution marked “all”.  In the group 14 to 15 years, there exists a power law distribution with an exponent of -2.01 for the whole income range.  In the group between 20 and 24 and in “all” only higher incomes (>\$5000) are distributed according to the Pareto law. The PID for the group 16 to 19 is rather exponential. Hence, the PID evolves over time. It starts from a power law for very young people and then transforms into an exponential distribution for work experience of a few years. After five to seven years of work, two branches are observed: a quasi-exponential PID at lower incomes and a power-law one for higher incomes. It is important to stress that the PID for the Pareto law for higher incomes is characterized by a different exponent of -3.2 (see Figure 2). This is a quite different distribution.

By all means, the PID evolution expresses both the underlying structure of income distribution and the long-term process.  It is highly unfortunate that the Census Bureau reported so short time series for younger people and did not provide reliable estimates of the Pareto distribution for higher incomes – only three to four estimates covering the range of high incomes.

Figure 1. Four PIDs in 1968. Notice the power law distributions for the whole income range in the group 14 to 15 as well as for higher incomes (>\$5000) in the group between 20 and 24 and in “all”. The PID for the group 16 to 19 israther exponential.

Figure 2. The estimation of two exponents for power law PIDs.