Mind the Gap

A lot of noise is being made about the widening income gap.  There are various reasons that the income gap is growing and we will discuss these another time but let’s first take a look at what has happened to incomes by quintile over time so that we can discuss facts rather than innuendo.  The data is available from the Census Bureau.


(In real terms) lowest 2nd 3rd 4th highest Total
1967 Income  $9,615  $26,633  $42,543  $59,534  $107,129  $245,454
% of total income 3.9% 10.9% 17.3% 24.3% 43.6% 100%
2012 Income  $11,490  $29,696  $51,179  $82,098  $181,905  $356,368
% Total Income 3.2% 8.3% 14.4% 23.0% 51.0% 100%
growth ’12 vs ’67 19.5% 11.5% 20.3% 37.9% 69.8% 159%
Growth in $$  $1,875  $3,063  $8,636  $22,564  $74,776  $110,914
% of total growth 1.7% 2.8% 7.8% 20.3% 67.4% 100%

So one of the most widely touted arguments defending a widening income gap (including by Milton Freidman) is that there has been growth at all levels of income over time (our data stretches from 1967 to 2012).  This does happen to be the case.  All incomes have gone up in real terms since ’67.  So then what’s the problem?  Well let’s think about why incomes are important.  What does income represent?  Income is money that can be used to transact goods and services or invested to create more income/wealth.  The goods and services we have directly impact our quality of life (albeit these are not the only parametres of life quality but here in America they are likely the largest drivers outside of perhaps health and some would debate even that in the US).  Bottom line is that income highly correlates to quality of life.  However, I suggest there is not a linear relationship between income growth and increase to quality of life but that the rate at which one’s quality of life improves is dependent upon their quintile.  Let’s see what we can find out.

If everyone’s income is growing can we assume their quality of life is also growing?  I would claim it is not that simple.  Think about the bottom quintile.  In 1967 they were making on average just under $10K.  Forty-five years later they added $1.9K to their income (all figures are in real dollars so apples to apples).  So then we need to ask ourselves how much does that growth in income add to their quality of life.  Most would agree that earning $10K a year probably leads to essentially negative disposable income meaning that you are literally barely surviving.  At $12K they are in effectively the same spot.  Barely surviving and so despite a 20% increase in income we see that quality of life really doesn’t change here. Some will say that these folks are generally not putting much effort into quality of life.  Granted perhaps there is some of that (although I’m sure many folks would have a lot to say about that topic) but we are not making value judgments.  We only want to find out if income growth equates to improvement in the quality of one’s life because prevalent arguments use income as a proxy for quality of life.

The second quintile had average income in 1967 of $26.6K.  By 2012 they added $3K to that figure.  So let’s again reconcile this increase to change in quality of life.  At $26K you are much better off than the lowest quintile.  You are likely able to survive and may or may not have some disposable income but certainly very little savings and as such no safety net meaning any deviations in income results in significant reduction in quality of life.  Adding $3K to this may or may not provide a slight safety net but does not really change ones disposable income in a meaningful way as any deviation in income here too will lead to a significant reduction in quality of life.  So you are still living in a state of perpetual risk.   Now let’s compare and contrast to the upper middle 4th quintile.

The fourth quintile in 1967 was earning $59K and had increased that to $82K by 2012.  We could assume at almost $60K people are now moving into an area where they are not just surviving but are managing to both save and have some discretionary spending.  These folks could have some deviation in income and likely not fall apart economically at least in the short term.  So the additional $23K in income is for the most part all disposable income to be split between additional savings and additional discretionary spending (a second car, dinners out, etc).  And so here we do see a considerable increase to quality of life.  That’s great but so let’s move on to the top quintile since we did look at the lowest.

The fifth quintile was generating $107K back in 1967.  Today that has grown to $181K.  Not spending too much time thinking about this we know that these folks were very comfortable in ’67 and have added $75K to that by 2012.  Let’s compare to the lowest two quintiles to get a feel for what this means.  The top quintile in 1967 had a very comfortable standard of living and added to that $75K which is 41x and 25x larger than the lowest and second quintile increases, respectively.  In fact, the $75K additional income is 6x and 2.5x the lowest and second quintile total incomes, respectively.  So again the argument that the lowest quintile had income growth of almost 20% between 1967 and 2012 is not indicative that quality of life increased by 20%.  Whereas the highest quintile had 70% growth and income and much of that does directly increase quality of life.  I would suggest that quality of life as a function of income growth has a sigmoid shape (see example below).  Meaning there are low to modest increases in quality of life relative to income growth in the lowest quintiles.  As we move through the middle and upper quintiles quality of life improves faster relative to income growth.  Moving through the highest 1% quality increases will have diminishing marginal returns relative to income growth.  If I have $100M and increase that to $150M I don’t see much difference in quality of life.  I am a rock star at both levels.  The growth in income per quintile relative to total increase in income across all quintiles seems to work as a better proxy for quality of life improvements (I’m just eyeballing this).  Refer to the last line item of the above chart.  We see that it would look something like the sigmoid chart example below (although we don’t have the top 1% in our data we should logically assume diminishing returns).  The significance is that it takes a far greater increase in income growth in the lowest quintiles to result in any quality of life improvement than is required in the upper quintiles.  Maybe the way to think about it is from a breakeven standpoint.  Surviving has a set of fixed costs and not until our income is beyond a breakeven point do we see any noticeable improvement in profits or quality of life.

Example of a Sigmoid Function:

To wrap this up let’s go over what we’ve done here.  We looked at the prevalent argument suggesting a widening income gap is not a problem because incomes grew at all levels.  We deciphered that the argument is based on the idea that income represents quality of life, which is the crux of the issue.  What we found is that while quality of life improved for the upper half the lower half has seen very little or no improvement despite material income growth at all levels.  Please remember we were not interested in making judgments regarding fairness.  We only set out to see if the prevalent argument based on income growth as a proxy for quality of life is a valid argument and I believe we highlighted serious flaws in its validity.  As to whether or not everyone deserves an improving quality of life, well it is a very subjective and extremely complicated issue made more so be the highly charged nature of the debate.  I would argue (and will another day) there is blame attributable to both ends of the income continuum.  Individuals must accept a great deal of blame for lacking the integrity to withstand policies designed to destroy individualism among entire communities.  Policy makers should be ashamed for turning entire demographics into essentially children who rely on the state for their survival to ensure their votes.  Corporations should realize that frightening entire herds of mammoths off a cliff in one hunt might seem like a big success in the moment but eventually you are left with a barren landscape where just survival becomes difficult.  Each of these are in part responsible for the growing income gap.  The real discussion regarding the gap will explore the devastating consequences of what’s driving it.  For now, however, I’ve talked enough and so for the moment I will leave it to you to mind the gap.