A Data-Driven Analysis of the Laffer Curve
Looking at the historical US Laffer Curve, a modern and global Laffer, and offering a critique of the theory
Over this past week, I reread Jordan Ellenberg’s How Not to Be Wrong, which looks at simple-to-understand yet profound results from mathematics. One section of this book is devoted to the Laffer curve, named after the American economist Arthur Laffer.
Ellenberg’s explanation of the curve includes the graphic below and reads, “The horizontal axis here is the level of taxation, and the vertical axis represents the amount of revenue the government takes in from taxpayers. On the left edge of the graph, the tax rate is 0% [which means] the government gets no tax revenue. On the right, the tax rate is 100% [which means] whatever income you have …. goes straight into Uncle Sam’s bag. Which is empty. Because if the government vacuums up every cent of the wage you’re paid … why bother doing it? Over on the right edge of the graph, people don’t work at all. Or, if they work, they do so in informal economic niches where the tax collectors hand can’t reach. The government’s revenue is 0 once again.” (How Not to Be Wrong, Page 27).
Now it’s important to note that Laffer didn’t specify the behaviour of the curve between 0% and 100%. He mainly stated there would exist some maximum. And the curve doesn’t necessarily look like an inverse parabola. The behaviour could be wild in between 0% and 100%.
Overview & Tax Rate
So, what does the actual Laffer curve look like? In the US, we have tax rates and tax revenue for the past 100 years or so. In the first section, we generate the actual curve that plots tax rates and tax revenue. In the following section, we look at the global Laffer curve. We do this by considering 140 other nations and plotting their tax rates against their tax revenues.
Throughout this article, the tax rate considered is the highest marginal federal income tax. Most governments use a progressive income tax method, which imposes varying tax rates on incomes. As an example, consider a single person who made $50K in the US in 2019. The first $10K is taxed at a 10% rate. The next $30K is taxed at a 12% rate. And the remaining $10K is taxed at a 22% rate. More money means a higher tax rate for that money. The highest marginal federal income tax is the highest such rate, which in the US in 2019 was 37% for any dollars after $500K. This tax method is illustrated below.
But there are other areas of taxation. In the US alone, there are consumption taxes (e.g. sales tax), corporate taxes, gift taxes, estate taxes, and more. The Laffer curve doesn’t specify which tax rate should be considered, nor does it specify if an aggregate should be used. I chose to use the highest income tax as the Laffer curve tries to relate work with revenue, and work is taxed through income. The reason I chose the highest rate is that there is greater variance than the average income tax rate. Over the last 100 years, the highest income tax rate went as high as 90% and as low as 35%. This wide range should help us generate a Laffer curve.
Domestic Laffer Curve
To generate the domestic Laffer curve, I started with a list of the highest marginal income tax rates here. Next, I pulled the US Federal Tax Revenue history, which can be found here. These data sets provide information from 1934 through 2012. However, we can’t just compare the two and generate the curve. The US federal government took in $420M of tax revenue in 1934, but this is in 1934 dollars. So, we need to consider inflation. I used this table of consumer price indices and wrote some Python code to convert the revenue to 2012 dollars. Now, our revenue for 1934 sits at $7.2B — a more reasonable number.
With the calculations done, we can put tax rates on the horizontal axis and tax revenue on the vertical to see how our actual Laffer curve looks, shown below.
At first glance, it doesn’t look too bad. The points in the 30% to 40% range are much higher than the points in the 70% to 90% range. This looks deceivingly supportive of the Laffer curve. Let’s take a look at the bookends to see what’s going on.
In 1934, the government took in $0.42B in revenue, which is $7.2B in 2012 money. In 2012, the US Federal government had nearly $900B in revenue. This is about 125 times as much as our adjusted value from 1934. In 1934, the tax rate was 63%. In 2012, it was 35%. Was Laffer right? Maybe, but our data doesn’t imply that result.
We failed to normalize for many factors. For example, in 2012 there were roughly 200M more Americans than in 1934 (Source). Also, the GDP of the United States has increased exponentially since 1934 (Source).
This means there are more Americans paying income taxes, more American goods being bought and sold, and more American trade occurring. Taxes exist at every stage here — meaning more government revenue even with a lower income tax rate.
And this doesn’t just apply for the bookends. In fact, all of those dots in that orange box are tax rates for years after 1980.
One could make an argument for the Laffer curve based on the data above. However, this would be unsubstantiated at best and outright wrong at worst. We need to control for population size, government size, economic output, the current state of the economy, the previous state of the economy, the global economy, other tax revenue collection means, the ability of government to track tax evasion, and many more things before we could make such a definite claim.
Global Laffer Curve
I spent a decent part of my afternoon compiling data sets, cleaning them, writing code, and generating outputs. And as I went to write this, I realized I am no more certain about the nature of the Laffer curve than when I began. So, I tried a different approach. What if instead of looking backwards, we looked outward? The UN lists about 200 sovereign nations, and each has a different tax rate and varying government revenues.
I pulled two lists from Wikipedia. The first had various countries and their highest marginal income tax rate. The second had a list of countries by tax revenue to GDP ratio. This ratio allows us to meaningfully compare the tax revenue of nations whose GDPs vary substantially. I cross-referenced these lists and generated the chart below.
Here we see that government revenue increases as the tax rate increases. Is this a Laffer curve? Maybe. For example, the maximum tax revenue could occur for income tax rates at 60%, and any higher tax rate could cause revenue to dip. In this case, we would be seeing only the left half of the curve.
What about those three points in the middle of the graph? Those are Afghanistan, Norway, and Algeria. Each country has a very high proportion of tax revenue to GDP even with much smaller tax rates. And those three dots in the top right? Finland, Denmark, and Sweden. These are countries with a high tax rate and high tax revenue.
As mentioned previously, the Laffer curve doesn’t specify behaviour at 60%. It really doesn’t specify behaviour at all. It says at 0% and 100% tax rate, revenue is 0. Perhaps revenue and rate both increase to 90% at which point revenue declines. Perhaps there are multiple peaks. Perhaps the curve depends on other unknown factors. Or perhaps most likely, the graph looks like the one below, which stems from American mathematician Martin Gardner.
A Critique of Laffer
While the behaviour of the Laffer curve isn’t specified in the middle, it is specified at the endpoints. Laffer’s contention is that a tax rate of 100% would generate no government revenue. The idea is that no one would work or spend any money since the government takes every penny. I understand the reasoning behind this, but I’d like to point out an interesting result from our data. We’ll look in the 60% — 90% range since the US has never had a 100% income tax. (Although President Roosevelt tried doing this with Executive Order 9250!)
I realize I’m cherry-picking a few data points, but they’ll help highlight my thoughts. From 1935–1939, the tax rate was: 63%, 79%, 79%, 79%, and 79%. From 1941–1945, the tax rate was: 81%, 88%, 88%, 94%, and 94%. However, if we plot the corresponding government revenue and apply a linear trend line, we see a slope of 54 for 1935–1938 and a slope of 534 for 1941–1949. The units on this slope are trillions of dollars per percent increase in the tax rate. This is shown in the graph below.
As a note, I do realize these two time periods are very different. The Great Depression went through 1933, and the war effort certainly increased manufacturing and production, which likely boosted GDP.
We see more government revenue generated even as we get closer and closer to 100%, which doesn’t seem very Lafferian. However, the US entered World War II on December 7, 1941. As mentioned, wars can boost GDP as a whole, and this may be the reason for the jump in tax revenue.
But also there was great support for entering the war, with 91% of Americans supporting Roosevelt's decision (Source). I would argue that Americans saw a higher tax rate as their way to support the war effort and that this did not deter them from earning more income. This could help explain the dramatic increase in revenue from 1941–1945, even with much higher taxes.
In a broader sense, taxpayers are content with higher taxes if the taxpayer believes their taxes are being put to good use, like winning World War 2. The Laffer curve relies on a key belief — the government cannot spend money as effectively or as appropriately as I, the taxpayer, can.
This makes taxpayers less inclined to contribute to the federal government. And this is my critique of Laffer. When taxpayers believe their taxes are being used most appropriately, higher tax rates do not discourage taxpayers to work. When this happens, taxpayers adopt a more selfless attitude. They believe their work efforts and earnings are still contributing to important societal good. I realized I don’t have much concrete evidence to support this theory. I offer it as a general idea with a bit of backing from data.
Closing Note
My background in Economics is limited, so I’m standing on shaky ground here with some of my analysis. With the massive amounts of financial data out there, I imagine we could generate a fairly appropriate Laffer curve, once we’ve included some of the additional factors mentored above. But I’ll leave that to the professionals. As for the original question — what does the curve actually look like? I really have no idea. But if you’d like to read more, see here, here, and here.
In the meantime, I plan to stick with mathematics, where √2 is irrational, no matter GDP, tax rate, economic productivity, or anything else.
Thank You for Reading.
Questions? Comments? Email me at andrew.oliver.medium@gmail.com. I’d love to hear from you!
