The standard way to model income distribution and income inequality is the "agent-based" approach. "Agents" are endowed with utility functions and then left to their own devices to gain/lose wealth.
This approach is inspired by statistical mechanics, which was very successful at modelling the behavior of gases by treating each gas molecule as a pool-ball like entity that gains/loses energy during collisions with other molecules. Predictable distributions of molecular energy follow from these assumptions.
The neoclassical approach is to assume that humans are analogous to molecules, and can be treated using the same mathematical formulae. But is this assumption valid?
Agent-based models completely ignore institutions. If such an approach is valid, it must be able to demonstrate that wealth is unrelated to institutional size. So how can we test this proposition? We can do this by sampling the size of firms controlled by billionaires and comparing it to the size distribution of firms for the total population.
Here's a simple example to demonstrate this principle. Suppose someone hypothesizes that human hair color is unrelated to height. To test this hypothesis, we could sample the height of 1000 redheads, and compare this distribution of heights to the distribution of heights for the total population. If the hypothesis is true, the sample distribution of redheads should be nearly identical to the population distribution. If the hypothesis is false, then the two distributions should be different.
Now back to the supposed independence of wealth from institution size. First we need to determine the distribution of institutional size. Here I use United States firms. The figure below shows the histogram of US firms by number of employees. Note that the distribution is extremely bottom heavy. More than 90% of firms employ less than 10 people. (Data is for the year 2007).
If wealth is independent of institutional size, if we sample the size of firms controlled by billionaires, we should get a very similar distribution to that of US firms as a whole. To see whether this is the case, I used the 2014 Forbes 400 list of the wealthiest people in the United States. I was able to find reliable information about the employment of firms controlled by 360 of these 400 people (when an individual controlled more than one firm, I summed the employment of each firm ).
From the sample size of 360 billionaires, I then created a firm size histogram of the corporations controlled by these billionaires. When plotted against the firm size distribution for the US as a whole, we do not need fancy statistical analysis to know the result. The neoclassical assumption fails miserably: firms controlled by billionaires have a completely different size distribution than those for the total population. It is heavily skewed towards larger firms.
These results provide good support for a power approach to political economy. To become rich, you must control the activity of other humans. It would seem that wealth is derived from power.