Monday, November 18, 2019

The Strange Reality of Hauser's Law

While writing last night's piece on Elizabeth Warren's tax plan, my natural inclination was to reference Hauser's Law, because I've referred to it at least a dozen times over the years.  I initially looked up some of my old pieces but didn't want to just go to those, but I really preferred a reference site in case the idea is new to some of you.  I found that most of my old links didn't work.  One thing led to another and I eventually searched for the topic at one of those old links and found a fresh article, from the beginning of this year.  Even better! 

To begin with, economic laws are different from physical laws.  Physical laws simply can't be broken despite what car commercials may say to try to convince us otherwise.  Social science laws are broken all the time; I've said before the only so-called law I've come across that comes close to the character of physical law is Supply and Demand.  “Ironman” at Political Calculations calls Hauser's law "one of the stranger phenomenons in economic data".  When first noted by W. Kurt Hauser in 1993, he observed:
No matter what the tax rates have been, in postwar America tax revenues have remained at about 19.5% of GDP.
It's hard to see how this could flow from quantum physics or electro-weak unification theory, so we're left to take it as simply an observation rather than as rigorous as physical law.  It's more puzzling because of how much the top tax rates have varied.  Political Calculations provides this analysis of the data, with an explanation. 
In 2009, we found total tax collections the U.S. government averaged 16.8% of GDP in the years from 1946 through 2008, with a standard deviation of 1.2% of GDP. Hauser's Law had held up to scrutiny in principal, although the average was less than what Hauser originally documented in 1993 due to the nation's historic GDP having been revised higher during the intervening years. [Bold added: SiG.  Also: note that the original text reads 17.8% in the first sentence.  Every other reference in the article says 16.8, so I changed this one to agree with the rest of his post.]
Since the publication of Hauser's Law in 1993, the only thing that changed the results of Hauser's Law wasn't a change in the tax rate, it was a change in the way Gross Domestic Product was calculated.  That reduced tax revenues to 16.8% of GDP from the original 19.5%. 

The red line indicates the highest tax rate, which you can see peaked at 92% in the early '50s and has been as low as 28%.  The blue curve, embedded in a gray band at the bottom shows the tax revenue as percentage of GDP.  The gray band is familiar to any of you who have worked with statistical quality assurance techniques: it's the + 3 standard deviations band, which ranges from 13.2 to 20.5%

A little diversion on these tax rates is in order, but space is at a premium.  A long description is here; a short version is that while we have seven tax brackets, when the top bracket was 92% there were 24 brackets.  The highest rates were only paid on income over $3.2 Million - adjusted for inflation.  Today, the top tax rate has dropped to an income under $500,000.  The top tax rate dropped from 90% to 40%, a factor of 2.25 while the income that required paying that rate dropped by a factor of 6.4.  That means many more people are paying the top rate than in the '50s. 

It's interesting to see that individual tax collections have only been about half of that revenue.  The mean of individual income tax collection is 7.6% of GDP with a standard deviation of 0.8%. 

What does all this mean?  It means quite a lot.  The first thing is something I harp on all the time: tax rates are not tax revenues - the money collected.  They're different things.  They may be correlated mathematically but if rates go up, revenues don't automatically go up as much.  People change their lives to save paying tax.  (I know, right?  What a surprise!)  It means that the Dems' wealth tax is not going to make much of a difference in collected revenues.  Simple-minded people like Warren, Sanders, or  Pistachio Kotex will believe that tax revenues will go up enormously with a wealth tax.  Data says that if they raised the top rate even to 90% that revenues wouldn't go up as much as they think - they'd stay in the historical range.  



  1. Put another way, If you tax work at a high enough rate, people stop doing it. Bear in mind that in the early 1950s, with men flooding the market after returning from WWII, half the current workforce stayed home and had babies instead of keeping a job, and that was the norm until the late 1960s. When no-fault divorce (economically favoring the ex-wife in 98% of cases) and the Pill became all the rage.

    Wild coincidences, I'm sure.

    1. I like to say we tax behavior we want to discourage, by taxing tobacco, booze, gambling and income.

      Those two you call out are the ones responsible for the birth rate collapse after the so-called WWII baby boom - especially the Pill. Add in legal abortion around '70(?). The birth rate after WWII didn't even get back to the birth rate from 1900 through the 1920s. The birth rate wasn't historically remarkable, but why should it have been? At the most, it would have delayed the children that soldiers who came back from the war would have had in the early 40s until the second half of the decade. Then consider that a pretty big number didn't come back and there might have been a decrease in births. It was the pill, no fault divorce, and then legal abortion that made the later generations smaller.

      If you look at the chart of birth rates for the 20th century on Wikipedia, the part that stands out as unusual is the deep drop in birth rates during the Depression. That is, before the era of the pill, no-fault divorce and widely available abortions.

  2. I tend to envision government regulation like a finger. There's a water balloon sitting in a cushy chair where it won't roll off. Poke the balloon with the government finger, and the volume of the water balloon doesn't change. The water just moves elsewhere within the balloon.

    I've been reading Albert J Nock recently; he's enjoyable but dangerous. Specifically, the essay Anarchist's Progress in State of the Union (here).

    Two quotes about government jumped out at me as helpful to consider:

    "Government is merely a device for taking money out of one person's pocket and putting it into another's."

    "...if in any given circumstances one went on the assumption that they were a professional-criminal class, one could predict with accuracy what they would do and what would happen; while on any other assumption one could predict almost nothing."

    I knew the first, but the second is helpful in prediction.

    1. But of course. Remember what the philosoraptor said in the famous meme: "If we need government to control bad people, wouldn't bad people join the government to control people?" Include robbery and other gang behavior in control.

      For example:

      The important part is how the petty tyrants strive to set up a society in which anything not specifically legalized is illegal. The better to extract "tribute" from the taxpayers.

  3. That "17.8% of GDP" wasn't an error - we really had calculated that figure back in 2009. What changed between 2009 and 2019 was GDP, which went through a major revision to the historic data in 2013! After that comprehensive revision, when we re-ran the calculation in 2019, we came up with the average of "16.8% of GDP" for tax revenues, which is why you see it everywhere else in our post!

    That small point aside, your reading of our analysis is really solid!

    1. Thanks for dropping by and clearing that up!

      I was looking for a way to let you know I enjoy reading your work and that I'd linked back. I would have asked about that one 17.8%.

  4. A long time back I did a seat of the pants calculation for what average tax rate fell on the median US family. It was 25% off the top, and this included US Income Tax which is so progressive that the median family pays essentially none.

    If you then add in off-the-books thinks like higher electricity rates to fund "Green" energy boondoggles, the government share of the economy is much higher than Hauser's Law predicts.

    Quite frankly, this more than anything explains why Donald Trump got elected.

    1. I'm sure you get this, but for readers who come across this, Borepatch's 2010 post was the percentage of the people's income paid off the top as tax, which isn't what Hauser's Law is talking about.

      Hauser's Law is relating the taxes collected by the Federal government to the country's Gross Domestic Product. It's a very different way of looking at taxes, but ultimately what matters most to the Federal government is what they collect. They need revenue and 70 years of records shows that the revenue collected is remarkably constant as a percentage of GDP regardless of tax rates. Tax rates and tax revenues are not the same thing. Raising tax rates doesn't necessarily raise revenue and lowering tax rates doesn't necessarily lower revenue. After many tax cuts, including the '17 cuts, revenue went up when rates went down.