Income Inequality: A Critique of Piketty & Saez
By Rick Kelo

There are lots of economic inequalities that exist in the world around us.  Some include gender inequality, racial inequality, class inequality, educational inequality, and age inequality.  In this paper we will look at one of these that has become a real political hot button: income inequality.

Income inequality is a tricky subject and very few people understand it.  After reading this article you will know more about the subject than almost anyone else you’ll ever discuss it with.  Also, by the end of this article I’ll have armed you with both the sources & theoretical framework of this topic.  With those two tools you will be able to discuss the topic confidently, and will have the tools to examine new points that come up in the future so your opinion evolves as the topic changes.

Income inequality is a poorly understood topic because it is tricky: some of the measures are absolute, while others are relativistic and only have meaning when put in context of the greater whole.  This article will present income inequality from both directions.  You will not find this approach in almost any other writing on the subject because everyone else writes from a normative standpoint trying to prove a point and picks & chooses only the data that supports that end.

There are two general approaches to any topic of economics: positive and normative.  This article is written from the viewpoint of a positive economics.  We’ll discuss the income gap, look at the cause & effect relationships at play in this topic, and share all the actual facts & data you need to go from “somewhat aware” of this topic to “incredibly well versed.”  I leave the normative judgement of how things “should be” up to you, the reader.

Also, toward the conclusion, I will share with you a very interesting idea the income gap data suggests that you won’t hear elsewhere.

As with my other articles on complex, technical subjects, I promise to give this one to you in plain English.  When I use a technical term I’ll translate it into lay-man’s terms so you know what it means.

This article breaks out as follows:

1. Origins of the 1% & Income Gap
1a. History of Income Distribution
1b. History of the 1% = Piketty & Saez
2.  The Record Income Gap
      2a. Piketty & Saez in detail
2b. Criticisms & Errors
3. What Makes the Income Gap “Change”
3a. Factors that change true income inequality
3b. Factors that change tax return-based inequality
3c. Has the income gap ever changed?
4. The Missed Issue of Improving Wages

1. Where Did the 1% & the Income Gap Come From?

     1a. History of Income Distribution


Here we have two parts: the general history of income distribution and the specific history of the “1%” idea.  Both are quick and easy to explain so I’ll start general then get specific.

For as long as humans have lived together there have always been haves and have-nots.  In our shared tribal history there was the tribal chief, and the chief’s friends then everyone else.  In feudal society it was the monarch, their deeded landowners and everyone else.  In Marxist nations it is the Communist Party officials and everyone else.  This pattern is called bi-nodal: at one far end a small part of society enjoys all the wealth, and far down the scale is everyone else.

This wealth distribution has been the norm for all of human history since mankind began behaving modernly 50,000 years ago.  Only in the last 300 years has this finally changed.

Everyone has heard of the Bell Curve knows that populations above a certain size will distribute in different manners.  Some types of data will have a Normal Distribution (the traditional “Bell Curve”), others a Poisson, and others still different things.  Income does not distribute along a Bell Curve because it isn’t median-based.  Averages don’t matter.  Think of it like this: if Bill Gates & I walk into a store together our average spending power is $30 billion, but the average doesn’t tell you anything about the distribution.

Income distributes along what’s known as a Maxwell-Boltzmann distribution, or a Gibb’s Distribution.  Some experts feel one formula is superior in accuracy to the other, but for the purposes of this article its sufficient for me to just tell you they’re each based upon one another and very similar.

For reference to those who are interested some of the other measures that exist to tell you what the income inequality of a population looks like include the Gini coefficient, the Theil coefficient, and a common graphical way to depict income spreads is using a Lorenz curve.

     1b. History of the 1% = Piketty & Saez

For as far back as economists have studied income distribution they have used quintiles.  So we take a group of 100 people, ask them how much they make, then divide them into five groups of 20 people.  The lowest 20 earners are the bottom quintile, the highest 20 earners the top quintile.  This is where the terms “Lower Class” and “Upper Class” originated.  The middle of the 5 quintiles being, of course, the “Middle Class.”

The idea of the 1% comes from two economists, named Piketty & Saez, who decided to disregard quintiles and instead look at what the few Bill Gates types in the country made.  The notion of the “1%” came from their income inequality study here, and most of the articles that describe how the wealthy benefit from tax cuts from the companion tax study here.

This is an important starting point because almost every class warfare article in circulation today is based upon these ideas.

2.  The Record Income Gap

 Alot has been written lately about the income gap reaching record levels.  Below is what people refer to when they talk about the income gap.  This graph is taken from the Piketty & Saez study and shows you the amount of the nation’s income that went to the top 1% by year:

Piketty & Saez Table A1

Piketty & Saez Table A1


      2a.  Piketty & Saez in detail

The whole notion of this income gap and the existence of a super-elite top 1% earner group is based upon the Piketty & Saez study.  They consider themselves as continuing the work of famed economist Simon Kuznets who won the Nobel Prize for proving that societies develop income inequality in the shape of an upside down letter “U” over time (technically named an inverse U-pattern).  In economics this is called the Kuznets Curve.  One of the first things to note about the Piketty & Saez study is these guys found a U-Pattern, not the inverse U-Pattern of the Kuznets Curve.  If you look at their graph above you’ll see the “U” pattern I mean.

Out of the gate this is not a good starting point for the correctness of the Piketty & Saez study.  Knowing this they address it immediately in the very first page of the now-famous study all the class warfare, 1%-type articles are based upon.  Piketty & Saez suggest perhaps their findings are still in keeping with known fact because maybe the graph above is the point where two inverse U-curves are meeting.  More like the center point of a letter “M” in other words.  What they say translates to: I know we’re supposed to find an upside down “U” but we found a right-side up one.  Hear us out though, maybe our findings are really the start and end of two upside down “U”s next to each other.

One could indeed argue that what has been happening since the 1970s is just a remake of the previous inverse-U curve: a new industrial revolution has taken place, thereby leading to increasing inequality
~ Piketty & Saez p. 2

So the first red flag is that Piketty & Saez claim to be updating the Nobel Prize winning work of Kuznets, but they produce the exact opposite result.  What accounted for the difference that gives the appearance Piketty & Saez arrived at the wrong conclusion?  They did not measure income, they measured data on tax returns, and in an interesting way.

Our estimations rely on tax returns statistics compiled annually by the Internal Revenue Service since the beginning of the modern U. S. income tax in 1913.
~ Piketty & Saez p. 4

Ok, so remember we are looking at tax return data, which is central to the points about income distribution we’ll come to next.  Before we move off of Piketty & Saez though I’m going to give you some general criticisms of their work.

      2b.  Criticisms & Errors

CRITICISM 1: The Poor Are Getting Poorer AKA Lack of Proportion.  The Piketty & Saez study is used to state that the rich are getting richer and the poor are getting poorer.  This statement is a guess at best and usually wrong.  Even if the income gap expands it does not necessarily mean the poor have gotten poorer.  Think of it this way: is it larger to have 1/4 of a pizza or 1/5 of a pizza?

It depends on the size of each pizza.  1/4 of a personal pan pizza is a bad deal if the other choice is 1/5 of an extra-large family sized pizza.  The lower proportioned choice is sometimes the superior one, but the Piketty & Saez study is misused to imply things it does not mean: the income gap can increase while the poor are getting richer.  In almost all instances this is what actually happens too.

In other words: is Bill Gates hazardous to our health?  Suppose tomorrow that Bill Gates makes some windfall business decision and doubles his net worth to $110 billion.  He has increased his position by 100%.  At the same time suppose that the average wage of everyone from the middle class on down increases by 20%.  In a relativistic sense the income gap has just skyrocketed, and this relative view hides the absolute truth that someone who was making $30,000/year is now doing much better in absolute terms making $36,000/year.  The position of the common man in this example hasn’t eroded, it has improved.

ERROR 1: All Corporate Taxes Assigned To The Rich.  Piketty & Saez take all the taxes paid by corporations and assign them to the rich.  All taxes on a corporation are paid in one of three ways:

  1. The method Piketty & Saez suggest, which is that it passes through to the owners in the form of lower returns.
  2. Paid by the employee in the form of less wages
  3. Paid by the customer in the form of higher prices.

Piketty & Saez assume that all taxes are paid through Method 1 in that list, which is a considerable error.

we compute income earned by each group as the market income used for ranking tax units plus realized capital gains reported on tax returns plus the employer part of federal payroll taxes (which is not included in wages and salaries reported on tax returns) plus imputed corporate taxes.
Piketty & Saez p. 35

ERROR 2: Corporate Profits Ignored.  This one continues from Error 2.  Piketty & Saez use an unbalanced formula to determine income that creates a wrong impression that the rich benefit from tax cuts that, in many instances, grant no benefit at all to them.  Piketty & Saez took all the taxes corporations paid and considered them paid by the rich, but they do not treat corporate profit as going to the rich.  This calculation makes the whole study completely screwy.  You cannot treat the tax on a corporation toward the rich one way and the profits on it another way.

“We use a gross income deŽfinition including all income items reported on tax returns and before all deductions: salaries and wages, small business and farm income, partnership and Žfiduciary income, dividends, interest, rents, royalties, and other small items reported as other income. …. Income, according to our definition, is computed before individual income taxes and individual payroll taxes but after employers’ payroll taxes and corporate income taxes.”
~ Piketty & Saez pp. 5-6

“Computing top shares for incomes before corporate taxes by imputing corporate profits corresponding to dividends received is an important task left for future research”
~ Piketty & Saez p. 13

ERROR 3: Households & Individuals Represented the Same.  Piketty & Saez looks at tax units, not households.  So every high school student working a summer job just skewed the bottom 20% quintile in their study.  That is because Piketty & Saez treat all tax returns as individuals, not as family units.  A two income family with both parents earning $50,000 counts the same as a one income family with one parent earning $100,000 for Piketty & Saez’s purposes.  This error sends the whole study sideways just like the corporate profit thing.  The group Piketty & Saez calls “The 1%” isn’t actually the 1%.  It may be the 2 & 1/2% or the 0.5%, we’re not sure.  But its not the wealthiest 1% of Americans.  Its the top 1% of income tax returns, and that point is important to note because we’ll return to it momentarily.

ERROR 4: Cohabitation Ignored.  According to a census study conducted last year about 11% of American couples living together are unwed (Source).  This amount is increasing each year.  This means that in the Piketty & Saez study 11% of households are under-represented because they do not file a joint married tax return.  This effects the size of the group treated as “The 1%” by making it larger than 1%.  When cohabitation is factored in Piketty & Saez are really looking at the top 1.13% and calling that group the top 1%.

ERROR 5: Failure to Account for Transfers. This is the big one, and we’ll build on the implications of this one for the rest of the article.  Piketty & Saez look at income, but they do not look at transfers.  Economists identify two kinds of transfers, and they are called in-kind transfers and in-cash.  Here are some in-kind benefits that do not reflect on the Piketty & Saez study:

  • Vacation & Sick Days
  • 401K Matching
  • The percent of your total health insurance premium your employer pays
  • Employer provided dental insurance
  • Employer provided vision insurance
  • Employer provided life insurance
  • Flex Spending Account contributions
  • Company cars
  • Employer tuition reimbursement
  • Employee stock ownership plans

Our income measure also excludes non-taxable benefits such as employer provided health care.
Piketty & Saez, p. 5

The inability of Piketty & Saez to see these things causes a great many errors in their conclusions.  We will look at the error it causes in the movement of the overall income gap, which has not gotten any attention yet.  Dr. Richard Burkhauser from Cornell looked recently at what happened to the Piketty & Saez data on the middle class if this error was corrected.  If you used the Piketty & Saez methodology you will find that the income of middle class from 1979 – 2007 grew by 3.2%.  Burkhauser, by fixing errors 4 & 5 I cited above found an income growth of 36.7%!  (Source) You can see from Burkhauser’s study just what a huge distortion this creates.

3. What Makes the Income Gap “Change”

      3a. Factors that change true income inequality

We are going to go deeper starting with an important distinction.  There is real income inequality, then there is the inequality of the incomes that get reported on a tax return.

I’ll give you an example.  Economists have studied the periods before we had tax returns to base income on, and studies that look at the 1800s generally use real estate values from the census.  They have found that income inequality is very high in young adults and gets lower later in life.  An economist named Lee Soltow did one such study and found inequality was very high for people aged 20-29, but got much lower in the cohort group of 30-39 year olds and remained low into older groups.  Now think about income inequality in terms of immigration patterns.  The implication from Soltow’s study is that if the share of 20-somethings increases in a society then inequality will appear to rise even though no true inequality trend exists. (Source: Men and Wealth in the United States, 1850-1870 by Lee Soltow, p. 108).

The factors that change true income distribution include:

  • Expanding education
  • Economic shifts from agrarian to manufacturing to service
  • Demographic changes like population growth & immigration
  • Government redistribution of income
  • The marginal rates of skill growth per member of the labor force (marginal product of labor)
  • Bias conferred by technological changes
  • Labor distortions caused by factors like unions

So let’s think about a few of those.  Suppose that population grows slowly and skills grow quickly.  Under those conditions income inequality will fall because the overall marginal productivity of labor is increasing.  The reverse would be true in different circumstances.  Suppose America adopted totally open immigration again like the days of Ellis Island.  Under those circumstances the ratio of unskilled (therefore low paid) to skilled labor would cause income inequality to rise.  Those are a few thoughts for you.

      3b. Factors that change tax return-based inequality
Let’s start by putting income taxes in some historical perspective.  In 1928 someone making $106,000/year (in today’s dollars) was only paying 3% in federal income tax.  At that time you had to make $1.4 million/year (in today’s dollars) to be in the 25% federal income tax bracket.  Today you hit the 25% income tax bracket at $72,000 / year.  (Source)  Now compare that to the low point in the Piketty & Saez income inequality study: 1960.  By 1960 if you made an income of over $8,000 (in today’s dollars) then you were paying a 26% federal income tax.  The federal income tax became such a powerful force in the hiding of taxable income that it made income inequality appear to decrease, but as we are about to discuss appearances can be deceiving.

Piketty & Saez looked at income as reported on tax returns going back to 1913.  Below is the same chart of their data from above, but this time the red call-outs identify some of the notable peaks & troughs in the top federal income tax bracket those years.

Piketty & Saez with Top Statutory Tax Rates

Piketty & Saez with Top Statutory Tax Rates

You’ll notice a trend: in periods of high income tax the 1% report less income.  The appearance to the untrained eye is that the income gap is improving, and the 99% are taking home more of the nation’s income…. Except that’s not the case.  Almost all the variation in the Income Gap is attributable to tax avoidance behaviors.  Said differently the 1% hides or takes less income in high tax periods.

Here’s an example: World War 1.  When the federal income tax came out in 1913 the top rate was 7%.  Once World War 1 hit federal government spending went through the roof and the top tax rate was raised to 77%.  However, there was still a budget shortfall so the government issued tax-free bonds to cover the difference.  Immediately the rich started putting their money into tax-free liberty bonds.  Look at the sudden change in the Income Gap around WW1.  The 1% went from having 18.6% of the nation’s income in 1916 to 14.5% in 1920.

It seemed like income equality is approaching!!! Except it wasn’t.

The only thing approaching was one of the worst depressions in American history.  Once the rich began hiding money to avoid the 77% income tax they stopped putting it into railroads, factories, and all the things that stimulated jobs & economic output.  Unemployment went from 2.3% in 1919 to 11.9% by 1921.  (Source). The economy plummeted, and the Depression of 1920 had begun.  (For those interested in learning more historian Dr. Tom Woods provides an excellent summary of the Depression of 1920 hyper-linked here).  And this is the counter-factual to the wrong-headed belief that the income tax somehow decreases income inequality.

Then, as time marched on, Hoover initiated huge tax increases.  Once FDR came into office he mirrored Hoover’s economic policies in almost every way, but just did many more of them.  We’ll just suffice it to say FDR raised the income tax quite a bit as well.  By this point the wealthy had it and had all together devised ways to avoid the income tax.  This became such a problem that FDR conspired and fought to enact an “undistributed profits tax” so he could get his hands on all the corporate earnings that were not being paid out as salaries to the owners of the companies. (Source)

Here is FDR’s Treasury Department describing the problem in an internal memo:

The primary purpose of the undistributed profits tax was to obtain some $600 millions of additional annual revenues by making effective the Federal Government’s prevailing progressive taxation of individual incomes.

[N]ew taxes or the raising of rates on old taxes could hardly be considered at a time when the removal of an outstanding source of tax avoidance under the existing laws would provide all the new revenues needed.  Our high individual surtax rates were obviously ineffective in large part when their application could be postponed for long periods or avoided altogether through corporate retention of earnings.

Between 1923 and 1929, inclusive, more than 45 percent of the compiled net profits, after income and excess-profits taxes, of all corporations reporting net income was not distributed by the corporations and was therefore not subject to the individual income taxes, or their approximate equivalent, applicable to their stockholders. Very large proportions of the incomes accruing for the benefit of members of the upper income groups in the United States had previously escaped the individual income surtaxes for long periods of forever in this fashion.

This tax was very short-lived.  Congress passed it in 1936 and immediately the business world went nuts and abandoned all economic activity of every kind.  They stopped buying equipment and abandoned all plans of expansion.  The Recession of 1937 had begun.  Shocked at the immediate economic damage the law was repealed in 1938.

Indeed the periods with the highest income tax rates have also been the periods with the most stagnant economic performance, and the periods where wealth inequality was at its lowest.  This point goes right back to Criticism 1: because income inequality appears low does not mean things are good for the lower 99%.  The 1920s was a highly prosperous decade, the 1960s was a highly prosperous decade, and the 1980s was a highly prosperous decade.  In all cases income inequality got “worse” by the method Piketty & Saez viewed things.  As I’m about to suggest though, there is good reason to believe how they viewed things was not how they really were.  And the answer was right in front of their faces, but they failed to connect the dots:

Top tax rates were very high from the end of World War I to the early 1920s, and then continuously from 1932 to the mid-1980s
Piketty & Saez, p. 23

Our results suggest that the decline in income tax progressivity since the 1980s and the projected repeal of the estate tax might again produce in a few decades levels of wealth concentration similar to those at the beginning of the century.
~ Piketty & Saez, p. 24 

      3c. Has the income gap ever changed?

The income gap between the 1% and everyone else stayed at a very stable plateau all the way through the Gilded Age of the 1870s until the onset of World War 1.  As I described in the couple examples above there is a very strong reason to conclude that changes in tax policy caused the wealthy to defer their income in hopes of a lower taxed future.  Some kept that money in their businesses as retained earnings.  Some moved it into tax exempt areas like the “Liberty Bonds” we learned about.  However, there was a third route we have not discussed yet which was far more prevalent than the other two.

It has to do with Error 5 identified above.  Piketty & Saez do not measure untaxed benefits but this is precisely the income source that became popular under the high tax regimes in the mid-20th century.  C-Corporations have nearly no limitations on the fringe benefits.  So for the owners of businesses, which the super-majority of the 1% are, from the 1940s through early 1980s it was profitable, legal and logical to disguise your income in fringe benefits.  Owners of a business can use the company to pay for their car, gas, car insurance, life insurance, country club dues, school tuition, cars for their family members and so on.  The list is of possibilities is literally nearly endless, and those things taken as fringe benefits instead of income are not only not declared on one’s personal tax return but are actually a deduction on the corporate tax return.  Companies only pay taxes on the money they have not spent at the end of the year.

Most of the entire change in the “income gap” during the super-high tax regime that appears less unequal is not because the income distribution to the 1% actually changed at all.  That income was simply distributed in the form of a tax deduction instead of taken as income to be taxed at 91% or 71%.

There are countless other ways that became fashionable to distribute income to yourself without putting it on the tax return form that Piketty & Saez measured.  To give just one last example another trick was to keep unrealized capital gains, then use the underlying asset as collateral on a loan.  On your tax return your income was reduced by the loan deduction.  This was even true if the item you took the loan on (say a stock purchase or a commodity or a piece of real estate) went up in value.

The powerful force of tax avoidance cannot be emphasized enough in the appearance of income inequality changes.  In 1931 someone who made $120,000/year (in today’s dollars) paid a 3% federal income tax.  By 1941 it had risen to 21%!  By 1951: 43%!  In just 20 years time the income tax grew by over 1400%!  (Source)


4. The Missed Issue of Improving Wages

The Piketty & Saez study is used to imply that the rich are getting richer and “something” must be done about it!  The “something” is always suggested by a politician, and always involves creating a bigger bureaucracy.  That is because for generations now politicians have been running for office by promising to get to Washington and “do” things.  Except when a politician says “do” it doesn’t mean what it means to you and me.  “Do” describes some type of productive activity when we get to work.  When a politician gets to work “do” actually means “spend.”

Spend doesn’t really mean “spend” though because the federal government runs a deficit.  It really means tax and borrow; the trading of future economic growth for consumption today.  That action will make the income gap only worse.  Well the actual income gap won’t change, but the income gap as it appears using the flawed Piketty & Saez methodology would appear to increase the further that trend is continued out into the future.  Why?  Its simple crowding out: the more hampered America’s economy becomes the less economic growth it will experience.  The wealthy 1% are not harmed by this because they are not the recipients of the majority of the growth in either absolute or relativistic terms, the 99% are the ones harmed.

Ludwig von Mises said it best this way:

What constitutes the greater wealth of a capitalistic society as against the smaller wealth of a noncapitalistic society is the fact that the available supply of capital goods is greater in the former than in the latter. What has improved the wage earners’ standard of living is the fact that the capital equipment per head of the men eager to earn wages has increased. It is a consequence of this fact that an ever increasing portion of the total amount of usable goods produced goes to the wage earners.

None of the passionate tirades of Marx, Keynes and a host of less well-known authors could show a weak point in the statement that there is only one means to raise wage rates permanently and for the benefit of all those eager to earn wages—namely, to accelerate the increase in capital available as against population. If this be “unjust,”then the blame rests with nature and not with man. (Source)

The greater portion of our economy passes into the hands of government, even in the name of “redistribution” against this perceived income inequality, then the lesser the amount of capital remaining to fund the economic growth that rising wages depends upon.