This article came about as a result of watching the Democratic Presidential Debate last Thursday. Senator Sanders and others rail about income inequality in the United States. Their chief complaint is that the rich are sucking up all the money in the country while middle class incomes are stagnant. Senator Sanders offers this problem, probably without any understanding of how income is actually distributed or what it costs to live in the US. In this post, I’ll look briefly at these two topics.
To this point, The Moocher is unaware of any specific proposal to curtail wealth accumulation by the upper extreme of the income distribution.
I revised this article to describe the relationship between income density and income distribution and to attribute and describe the social classes used later in the article. I also added the statement that Senator Saunders had not proposed a way to address income inequality.
The Key Points to Take Away
The basic thesis of this article is that the real problem is not that there are statistical tranches of income or that increasing income and inheritance taxes on those earning more than $1,000,000/year will not, by itself, change the fundamental structure of the economy. The problem is that those at the bottom of the economy, about the bottom half of individual incomes are just getting by or struggling. In this structure, the cost of a basic standard of living is out of reach of over 25% of our population, our underclass and our working poor.
If you use the numbers at the end of this post to estimate an income for a 2 adult, 2 child, stay at home mom household, you get a value of $70,000 for a secure income with recommended savings rates. Reference  shows that the 2012 median household income was $62,000 so less than half of our households meet this standard.
Our economy is an emergent phenomenon resulting from literally trillions of decisions occurring each day. Our affordability trap results from the way these choices fit together, it is an emergent property that results from all of the trade flows in our economy, particularly those influencing the cost of housing, health care, transportation, food, and energy.
I think we will be hard-pressed to find one simple lever to move to fix the personal income/cost of living mismatch. These flows are continually changing in response to new means of production, new desirable goods and commodity costs.
Structural changes (increasing manufacturing automation and clerical task automation) are reducing the number of jobs that yield a working class and middle class incomes . This is largely responsible for the erosion in middle class jobs.
Big C Communism’s attempts to have a centrally planned economy, i.e. to control these emergent phenomena, were a miserable failure. Communism created artificial shortages and excesses as a result of the inability to predict the proper flows of goods and services while attempting to control them. I don’t expect that the US Congress will do any better. The problem is just too complex.
This article wouldn’t be pseudo-scholarly without references so here are a couple.
A bit about statistics
Statistics offer one way to make sense of your income. Where are you ranked in the total US population of incomes? There’s you, those who make less, and those who make more. Reference 1 shows the cumulative income distributions and has a calculator that will figure out your place in this spread.
Their figure 1 shows the total US income summed up from zero to $1,000,000. Your doctors and dentists are in the $200,000 to $400,000 range so this figure includes them but it excludes entertainers, paid athletes, and corporate and hedge fund executives. But it does catch about 96% of the country’s population. Those lofty folk not included account for 4% of the population.
Where the data comes from
The US Census has several sources of data. First it conducts annual surveys. Second, the Internal Revenue Service makes anonymous income data sets available to other agencies, researchers, actuaries, and such. The data used in Reference 1 is very reliable.
The standard of living results appearing in Reference 2 are also taken from Bureau of Labor Statistics and Census Bureau compilations of results. These too are reliable. The thresholds I cite at the end are from memory and, look as I might, I’ve not been able to find a source for them. But they do square with Reference 2.
Average and Median
The figure is plotted on a semi-logarithmic scale. Researchers and engineers use this plot when one of the variables has a large range and the other has a small range. In this case the Y-axis is percent of total income. The X-axis is the log of individual income. So the vertical axis is “natural” while the horizontal axis is “compressed” to fit on the page.
Those looking at the reference will see that US individual median income is $27,000. I’ll come back to this.
If you look at the plot, you see two horizontal lines that mark the median income and the average income. The median income is that mythical income that divides the population into two equal parts. Half make less while half make more. The average income is the total income divided by the number of recipients. These two are different with the median lower than the average. This happens when the distribution is skewed with significantly more of the samples being less than the average value than greater than the average.
The lazy-S curve is what statisticians call a cumulative distribution function. The number plotted at each income level is the total percentage of income samples up to that point. In this plot the curve shows the percent of total samples, not the total income. That curve would have a similar shape but would be plotted log-log and is difficult to interpret. To give an example of how the curve works lets consider a couple of ideal cases.
- Everybody makes $10,000. The plot would show zero up to $9999. At $10,000 it would step to 100%.
- In reality, US income distribution has the shape shown that reflects a most common individual income near $25,000. It rises sharply to the peak and trails off more slowly with a long tail at between your dentist and your favorite corporate CEO. The cumulative distribution continues to rise because the total number of incomes is continually increasing from the start of the dataset to the end of the dataset.
- The curve is steep where there are lots of samples and relatively flat where there are few samples, that is at the left and the right ends. The steeper the curve, the more samples in that slice. That gives the S-curve shown. The slope of the curve is the percent of incomes at that level (the value of the slope vs income is the income density curve. The income distribution curve is the integral of the density curve.)
Statisticians often divide groups into subgroups. One of the most common techniques for expressing this division is to talk of percentile levels. Median income is the 50th percentile income, half make more while half make less. 90th percentile income is that amount at which 90% make less and 10% make more. 99th percentile income is that point at which 99% make less and 1% make more.
The funny thing about statistics, is, that no matter what you do, 50th, 90th, and 99th percentile incomes will always exists. That’s simply statistics. Being on one side or the other implies nothing about your character, your hard work, or anything else. That’s just where you are in the 300 million of us.
Class Income Levels
Looking at Dennis Gilbert’s class model in Reference , about half of our population are in our working class, working poor, and underclass. From the tables, our working class are about 25% of the population. They have safe housing, adequate diet, and reliable transportation to work but are unable to save significantly. The working poor and the underclass together are about 25% of the population. About 1/8 of us are working poor living in compromised housing, nursing a failing vehicle for transportation, and daily life is a struggle. About 1/8 of us are under class unable to work regularly or unable to work.
The researchers cited in Reference  use living conditions, not income level to determine the numbers in the working class, working poor, and underclass. In his model, the underclass are not self-supporting, the working poor have high economic insecurity and risk of poverty. The working class are just scraping by with adequate housing, food, and health care but with limited savings It is coincidence that these levels extend up to the $27,000 median individual income level. The real tragedy is that 1/4 are just getting by, 1/8 are struggling financially and 1/8 are living in serious poverty and 1/4 are unable to save for retirement.
A few years ago, I heard an NPR story that gave these income thresholds.
- $30,000 provides basic subsistence
- $40,000 allows some saving for retirement and misfortune
- $10,000 additional is required for each additional dependent sharing a household
The $30,000 provided safe housing, diet, and basic health care and transportation to support travel to and from work. There were no luxuries. The additional $10,000 allows saving for retirement and emergencies. The third amount is the marginal amount needed to add a child or a stay at home adult to the household. It covered the marginal costs associated with the added individual.
A family of 4 with a secure standard of living requires $70,000 in income from one or two wage earners.
The striking fact that stands out in my mind is that half of us earn too little to live independently at a basic standard of living. This is the real problem with income inequality: that 50% of us earn too little to live independently.