Wealth inequality is Misunderstood but Real

[muon2]

I'm glad to see the recognition that income inequality is different than wealth inequality, and perhaps addressing the issue needs different solutions, too. Let me start with a post I made in 2011 about wealth. Unfortunately wormyguy's image that I initially reference no longer displays in Photobucket.

The underlying issue is one of human perspectives of economic distributions. Distributions for population, income, and wealth are different. Moreover, they are related so that each item in that preceding sentence represents an integral of the previous item. If one isn't aware of that difference, the effects can appear quite distorted.

Let me start with the distribution of population by annual household income. Using 2007 data this distribution is roughly flat up to 70K. In other words there are roughly the same number of households earning between 10 and 20K as there are between 30 and 40K or between 60 and 70K. Beyond 70K the distribution falls off exponentially with a drop off such that for every increase by 50K there are half as many households above that number. If you plotted this on a graph you'd see a fairly horizontal line from 0 to 70K and then a curve dropping downward, sort of like this graph, if the 0 line were at about 100K. I'd guess that wouldn't generate a lot of controversy.


This is a different graph than the original which is no longer on the web. Something starting like the purple and ending more like the red is the curve I'm describing. In the next paragraph I'm describing the blue line that cuts off abruptly at 100K$

The income distribution weights each point for the income at that point, and sums the total by means of an integral. To show how this skews the data, lets assume that the population distribution by income were completely flat, and no household made more than 100K. If we divide up the population into 5 equal groups (quintiles), the bottom 20% would get 4% of the total income and the top 20% would get 36% of the total income. That's just the math saying that the integral of a linear function goes as the square of the function.

For a flat distribution the formula would predict that if the lowest share was 1 the next 3 quintiles up would have shares of 3, 5 and 7. Compare that to the actual first four quintiles in the US that have relative shares of 1, 2.6, 4.5, and 7.2 of the total income. Though the match is quite good, it's starting to look unfair since that effect of the square is now factored in.

Of course, the real population distribution is not flat, but has that long tail over 100K like the graph above. Since it is at the high end its effect is magnified by the income integral. It reduces the bottom 20% from a 4% income share to a 3% income share, with the same relative shares quoted above. That leaves 53% in the top 20% instead of 36% from the flat distribution. It's still just due to the income factor squared by the integral.

Wealth is not income, but can be approximated as an accumulated income, which in turn is another integral. Integrating a linear function twice gives a distribution that goes as the cube, or the third power. If I applied this to the flat population distribution described above, then the bottom 20% would have 1% of the wealth and the top 20% would have 49% of the wealth. Even with this absolutely even population distribution many might find this quite unfair - but it's just the nature of the distribution.

Now if one factors in that high income tail, small as it is, the power of the cube, both reduces the bottom and increases the top fractions. The numbers in the thread title are very much in line with the math.

So, I think the question for those who are concerned about wealth or income distribution is to go to the population distribution (something like the graph above) and describe what one would like it to be.

The short form is that the math of wealth vs income dominates the result. Even a uniform income distribution from 0 to 100K$ will produce a skewed wealth distribution due to the way income accumulates (by integration) to become wealth. The only way to have a flat wealth distribution is for everyone to have the same income (or more accurately the same disposable income).

[muon2]

Part 2 is about income and how it has given rise to the discussions about the rich being richer. This is from 2015 with apologies for my homemade chart based on Census data.

I'm cross posting this from US General Politics since it seems relevant here, too. This chart should help guide one's attempts at a solution. The drift of the upper three quintiles away from the lower two quintiles has been generally slow and steady over the last 35 years. The decade before Reagan isn't appreciably different than the decade after, despite considerable differences in national policy.

It seems clear that wealth has migrated towards the skilled professions, even in the middle class, as the global information age has progressed. The greater the skills required, the more rapid the increase in wages. To me that suggests the most effective changes would direct more resources towards education for the skills needed in the current economy, not large scale wealth redistribution or an investment in jobs in less skilled sectors from economies of the past.

Here's a better chart in response to Ernest. This is also from the historical household income data at the US Census. I found that the top of the second quintile (40%) was the most stable in real dollars, only increasing 5% from 1969 to 2014, so I used that to compare the other quintiles. The bottom quintile remained almost unchanged compared to the second quintile during that span of years and is very close to half the second quintile.

The growth is in the upper three quintiles. The middle quintile grew about 17% compared to the bottom two quintiles. Since the bottom two quintiles had little growth in real dollars, that 17% is close to the growth in real dollars since 1967.  The fourth quintile grew at 35% compared to the bottom two quintiles, or about double the rate of the middle. The limit for the upper 5% grew at 54% compared to the bottom two quintiles, or about triple the rate of the middle. My apologies for the year sequence which looked fine until the software rendered it to a bitmap.

The short form here is that it isn't merely about the gains of the top 1%. The entire upper half of household incomes has risen steadily while the lower half has remained stagnant. Within the upper half, the higher the percentile, the more rapid the income rise. But it's been slow and steady over the decades, not something sudden and recent and confined to the 1%.