Saturday, November 12, 2011

US Income Inequality And Pareto Distributions

My comment to The Wall Street Journal article, "Income Ladder's Sticky Steps" by Carl Bialiki:
Income and wealth follow mathematical rules known as power law distributions, as noticed by the economist Vilfredo Pareto over 100 years ago. More familiarly, people know these rules as the 80-20 rule. For example, twenty percent of customers produce 80 percent of sales, etc.

These types of income distributions have several characteristics. They are scale free -- meaning that sub-parts have the same characteristics. For example in the top 10 percent of wealth or income, the top 20 percent of that group will have 80 percent of the income or wealth. The same is true for the top 1 percent or the bottom 10 percent.

While the exact break down can vary and need not be exactly 80-20 (can be 80-30 or 70-10 for example), all economies, at all times, have unequal concentrations of wealth and income. For example, 20 percent of countries produce about 82 percent of GDP.

The US Income Pareto distribution changes over time. The inequality levels, as measured by a Pareto distribution were high around 1920 and are about the same level as now. Pareto inequality declined from 1920 until around the 1970's and started to increase again until the beginning of the recession. No one has a good answer as to why income level distributions have been cyclical over the last 100 years, or whether it will continue its trend towards more income and wealth concentration or reverse as it did in the 1970s.

Power law distributions are a fundamental rule of nature, just like the binomial distribution.

Networks and Internet sites also follow power law rules and 20 percent of sites get 80 percent of traffic. So do many other natural, sociological and economic phenomena.


As an example, think of all the aspiring singers and rock groups, or high school and college football and basketball players. Only a few will get professional contracts and of those, only a few will become stars with multi-million dollar salaries. Think of mom and pop stores. How many will become a Wal-Mart?

Should governments ban us from shopping at the large national chains because of their concentration of sales and forced us to shop at stores with higher prices, older merchandise, and tougher return policies? Should we have to buy music from groups we do not like because their song sales are low? Should we have to use doctors that are not the ones recommended by our friends and families because too many people use those doctors and ignore the others? Should we have to watch professional sports teams that use players that otherwise would not be selected?

Our daily consumption choices create much of the wealth and income concentration.

Should someone who can take a mom and pop store, turn it into a Wal-Mart and expand its sales a million or more fold get paid the same amount as someone whose local store never expands its locations, items it carries or goes out of business? Should a quarterback, who loses most of his games and throws lots of interceptions, get paid the same amount as a quarterback who can consistently win and take his team to the Superbowl?

Pareto distributions (power laws) have another characteristic. If the leaders are eliminated, other leaders form. If you eliminate the top income earners, top internet sites, top musical groups, top doctors, etc., other earners, sites, groups and doctors will become the top 20 percent garnering 80 percent.

It is our natural tendency to be social animals; herded like sheep, into the same music, clothes, movies, cars, etc. that creates wealth and income concentration. It is also the entrepreneurial spirit of the US to reward success, while inwardly we harbor jealously and beliefs that under the right circumstances, we too could have achieved that level of success.


  1. "No one has a good answer as to why income level distributions have been cyclical over the last 100 years, or whether it will continue its trend towards more income and wealth concentration or reverse as it did in the 1970s."

    My jaw hit the floor when I read that. It would seem that even some very well read people have no idea that the economy grew more than twice as much under 12 years of FDR as under the last 48 years of Republican presidents combined.

    It would seem that the idea that you need a strong middle class in which capital owners and labor have relatively balanced power and influence in society in order to simultaneously provide both the capital growth and demand growth that must come hand in hand to have a strong society.

  2. sf_jeff

    First, correlation does not prove causality - a key concept you need to know before looking at any form of statistic.

    Second, you seem to discount the impact of WWII. This was the main kick start for economic growth in the U.S. and continued long after as much of the world was stuck rebuilding while we were not. We were the suppliers of that rebuild and benefitted greatly during the subsequent few decades.

    There is still zero proof that without WWII, FDR's socialist programs would have gotten the US out of the economic cycle it was in any sooner than any other form of policy.

    In fact, looking at Japan and how they have been trying to do the same thing for that last 20 years from their lost decade and they are still lost, the reality is that any program, either democratic or republican would have failed to produce much if not for the war.