Income Inequality Is The American Way

Includes: AAPL, SHLD, TGT, WMT
by: PLM Investments


The U.S. income distribution arises from the complex statistical process that leads to success.

The resulting distribution of incomes is inherently unequal by nature of its spread.

Freedom and opportunity along with innate differences give rise to our particular income distribution, and it changes with time.

The very highest earners follow a different, increasingly unequal trend relative to the majority of earners.

Changes in the income distribution over decades of time provide opportunities and challenges for businesses.

Income demographics on a national scale are an important factor in determining commercial markets for all large companies, from Apple (NASDAQ:AAPL) to Wal-Mart Stores (NYSE:WMT). In this article, I describe the U.S. income distribution, its origins and changes with time; and discuss its general impact on businesses. More generally, macro trends like this are important to understand because they provide context for current business conditions.

Here is the 2010 estimated data for U.S. household incomes. The distribution is very close to the well-known lognormal form. Lognormal distributions tend to have an abrupt rise followed by a wide peak and tail, especially when it has large values near the origin. The U.S. income distribution is well-represented by this form: it has been estimated to account for 97-98% of the population.

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If we were to fit a lognormal function to this data plot, there would be a couple of notable differences. It turns out that the very lowest two income levels are not quite matched up. The lowest income groups are affected by policies and social safety-nets that protect the poor by providing support or raising their level.

And the very uppermost two levels are not close to lognormal owing to business factors associated with executive pay. The highest income levels follow their own distribution, being better described by an inverse power law. The highest income groups are affected by a multitude of other factors, especially business norms and tax policies pertaining to executive pay.

Origin of the Income Distribution

In general, lognormal distributions arise from a multiplicative series of randomly distributed factors. That is, the elements of the lognormal distribution are obtained from the probabilities, P1, P2, ... associated with all the factors multiplied together: P1*P2*...*Pn, where n is the number of factors. The resulting structure of the distribution, in the limit that the number of factors is infinite, takes the lognormal form by virtue of the statistical mathematics.

The U.S. income distribution has a lognormal-like form that can be generated from a success distribution model. Within an economic system, and for income distributions in particular, the factors that determine the income distribution are related to individual abilities to achieve success. In the model, each of these factors would have a probability, as I just described, assigned to it for each individual.

Success depends on a huge variety of variables based on personal traits, social placement, and political circumstances. One example I've seen includes the following partial list:

  • social background
  • educational level
  • personality
  • technical ability
  • communication skill
  • motivational level
  • coincidence (being in the right place at the right time)
  • risk tolerance.

A success distribution can be developed as the product of the probabilities associated with all of these types of variables. The lognormal success distribution had been modeled in this manner for income distributions by at least the early 1970s.

Note that, since the zero-income point is fixed at zero, small shifts in the mean or mode primarily affect the shape toward the middle and high incomes. For example, if the mode is shifted to lower income level, there will be an increase in lower incomes, middle income counts decrease and spread (larger standard deviation), and higher income counts increase, all else being the same. Of course, the number of factors in the real-world economic system is not infinite so there can be differences with respect to the ideal lognormal model.

This form of the income distribution arises mathematically and describes a range of incomes that are spread out, i.e., there is inherent inequality owing to the complex nature of success. The specific incarnation of the income distribution has a peak height and width that are impacted by population specifics and socio-political factors, which are subject to governmental policy.

The best that can be done from a humanistic governmental standpoint is to provide equal freedom and opportunity for all to ensure everyone has an unencumbered chance at success. Individuals will ultimately be limited by their innate factors, particular circumstances, and the randomness of everyday life.

Historical Changes in the U.S. Income Distribution

Historical perspective can be gleaned from the following plot, which shows the U.S. income distribution and curve fits every 5 years from 1949 to 1974. The U.S. income distribution has been on a continuous march toward a reduced peak and a larger spread. The falling of the lower-income peak translating into a raising of the higher-income tail. We see the characteristic shift to the left and the rise of the tail discussed and shown above.

Early on, significant changes occurred in timeframes less than a decade. The 1950s and early 1960s economics were almost certainly affected by the Civil Rights Movement and this may be reflected here. As the 1960's ended, the curves continued evolving but at a much slower pace.

These changes in the distribution with time establish a trend toward a more wealthy population. This affected business opportunities during the 1960's and 1970's, in part supporting the rise of discount and lower-level department stores: Wal-Mart, Kmart (NASDAQ:SHLD), and Target (NYSE:TGT) all started their chains in 1962.

Influences On The Very-Low And -High Ends

Owing to the smaller populations in the lowest and highest income groups, they are more subject to influence and variation than the majority of earners. By the mid-1990s, there was a clear bottoming in the lowest income group and a sharp rise in the highest income group. Here are some of the influences on these sub-groups that are differentiated from the main lognormally distributed earners.

The Lowest Income Groups

A reduction in the number of the lowest-level earners is an ongoing political challenge. Fighting poverty is a focus of government and it has been effective. The War on Poverty, for example, has led to a large reduction in the lowest earners.

The Highest Income Groups

The highest earners hold a special position in the income distribution, lying outside the lognormal description. Instead they are described by an inverse power-law distribution like this one from 2000.

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And this one, which shows how the exponent changes with time between 1910 and 2010. Here, smaller powers imply greater inequality owing to these special extreme earners: a larger percentage of population at higher very-large incomes. In this sense, equality began to improve into the early 1970s but then deteriorated until the mid-2000s.

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A quick look at the income gains by percentile over the last 30 years shows the huge change in gains of the highest income earners relative to the rest of the population.

The predominant cause is likely the change in CEO pay, as they have similar curves; however, it's no longer at the growth extremes of the early 2000s. CEO pay inflation and the manner in which corporations expense stock options, for example, influence the high end. It has also been affected by tax policies and public criticism's influences on corporate boards.


Around 1970, two related trends started. First, the flattening of the income distribution produced a meaningful rise in the higher income tail. This started a general negative trend of worse income equality by measure of relative wealth (using the Gini coefficient).

Second, the power-law distribution that describes the very highest earners began to change, indicating more high-end earners receiving higher levels of income. Post-1970, growth at the high end of the distribution accelerated, especially after 1990 when CEO pay took off. This is also a sign of increasing inequality relative to the rest of the income distribution.

The U.S. income distribution has evolved with time following a consistent trend: lowering numbers at low incomes, increasing middle incomes, and increasingly high levels for peak incomes. This is a result of the American economy's free market system operating under the laws and culture of the land. The major structure of the income distribution is inherently unequal owing to the basic statistical nature of success and some factors that lead to extremely high levels of wealth for some people.

Could it be that relaxing constraints or providing incentives for the very high-end earners permitted the middle earners to grow along with it as well? I don't know, but it's certainly possible.

Regardless of the origins of the distribution shifts and makeup, there are business implications to the large growth in the numbers of middle- to high-earners. This shift means more disposable income to spend on expensive electronics and services, for example, and an overall increased standard of living that may lead to less discount shopping.

In a follow-on article, I discuss recent and current impacts of these income distribution changes on corporate America, particularly Apple and Wal-Mart.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.