Prosperity vs. Inequality

Much attention is given to the inequality in income and wealth.  Calls to "tax the rich" and raise the minimum wage are efforts to reduce this inequality and appeal to the moral concept of "fairness".  However, a more careful look at the data begs for an alternate focus.  The goal should not be equality but instead the goal should be to lift people out of poverty.

My hypothesis is that general prosperity is the way to overcome poverty.  By general prosperity, I mean a system of organizations, traditions, processes, laws, behaviors that promotes prosperity.  Prosperity is therefore the correct measure.

I. Common Sense Reasoning 

You have a choice of living in one of two society:

1. A very equal society where the gap between the top and bottom of wages is small
2. A very prosperous society where even the bottom wage earners have all of the basic necessities.

Here is another condition of these two societies:

1. In the equal society, the bottom 50% do not have the basic necessities.
2. In the prosperous society, the top 1% have 90% of the wealth.

The rational choice is the prosperous society.  The problems in the equal society are real resulting in a lack of absolute wealth while in the prosperous society it is more a matter of perception resulting from comparison to the ultra wealthy.  

In the next sections, I attempt to prove that this is not just a thought experiment but a reality.

II. Income Distribution

In a previous post [1], I describe the shape of the income distribution for United States.  It turns out that this shape applies to other countries.  (Note: there are better models for fitting the data [2] but I will stick with the simplicity of my original model).

The original model of income distribution has been simplified to two parameters: "scale" and "shape".

Fitting Parameters for Income Distribution

Parameter	Impact on Equality	Impact on Prosperity
Shape	Lower values improve equality	Lower values reduce poverty.
Scale	Larger values widen the absolute gap, but relative wage gap remains the same	Larger values increase prosperity

In order to decrease poverty, both the shape and scale parameters need to increase.

The following table shows the parameters for the United States and China.

Fitting Parameters for US and China

Country	Shape	Scale	Gini Coefficient
United States	1.0	61,160	~0.4
Australia	0.6	52,776	~0.3
China	0.6	1,920 7,863	~0.4

Note: The China data was bi-modal (two peaks) which implies an overlay of two functions.

While the "Equality" parameter for China (0.6) results in greater equality than the U.S. (1.0), it is the larger "Prosperity" parameter for the U.S. (61,160) that results in fewer people in poverty than in China (1,920 and 7,863).

The data used with fitted log-normal distribution are shown in the next figures.

III. Additional research

Similar results have been published by Max Roxer and associates at ourworldindata.org.  For example, the article "Incomes across the Distribution" [3] includes findings from this research that support my hypothesis:

Australia has also seen an increase in inequality, but ... the incomes of all households increased substantially. This contrast is a good example that makes clear that we cannot rely on aggregate measures – like mean GDP growth and inequality measures – alone. We have to study incomes across the entire distribution to be able to see what is happening.

A last example makes clear that we should not focus on economic inequality alone: Greece has seen substantial reductions in inequality, yet the fall in incomes outweighs this development.

In "Income Inequality" [4], Global income inequality is plotted at three different times showing that the world has transitioned from most in poverty, to  divided by rich and poor, and finally to a richer, more equal world.

References:

[1] http://wrauny.blogspot.com/2013/02/why-are-people-poor-and-what-can-we-do.html
[2] Income Distribution in the United States, A Quantitative Study. http://www.roperld.com/economics/IncomeDistribution.htm
[3] Income across the Distribution, https://ourworldindata.org/incomes-across-the-distribution/
[4] Income Inequality https://ourworldindata.org/income-inequality/