Arthur Laffer’s Curve: Does Increasing Tax Rates Increase Revenues?

When the United States and the individual states find themselves in turbulent financial times, they tend to claim taxes need to be increased in order to shore up revenues.  When states and countries find themselves with budget gaps, instead of trimming programs  they tend to attempt to keep the same level of programs by increasing the tax rate.  The Laffer Curve is the idea that cutting taxes can spur economic activity over time, so lower taxes take a smaller slice of a much bigger pie increasing revenues overall.

Taxation vs. Work

The main form of tax one thinks of when thinking of tax in America is the income tax.

America taxes production in the form of income taxes.  This tax can be looked upon as a tax on working, or a disincentive to work.  In this framework we will view marginal tax rates- high taxes will discourage work while low taxes will encourage work.  Work we will consider productive… the more work that one has incentive to do, the more economic production will result.

In this theoretical framework, we will say that you are your most productive when all of the fruits of your labor come back to you.  This 0% tax bracket also guarantees no government revenues will be collected.  On the other end of the spectrum is the maximum tax bracket, the 100% bracket.  I hope you will agree, (again, theoretically– one article in the New Republic claims Russia had a 100% effective tax rate) that in a country or state where your labor is taxed at 100% you will refuse to work.

Let’s go ahead and make the claim that there is a linear reduction in the amount of work you will do for a given tax rate.  The graph therefore looks like this:

I know, it’s not very interesting… but you probably envisioned an image like this in your head.

This isn’t the image we are looking for… we need a relationship between the tax rate and government revenues… yes we want to maximize government revenues using this chart.  Let’s graph the amount of economic productivity taxes capture in a new data series:

In our theoretical economy we just sketched up, the most economic units can be collected with a tax rate of 50%.  If this image seems familiar, you’re absolutely correct.  You’re looking at a crude Laffer Curve.  In our invented fantasy economy, a 50% tax rate means 50 economic units are produced, and the government takes 25 of them.

The Laffer Curve is Not a Law

The Laffer Curve isn’t a law of economics, it’s merely a theoretical framework for understanding why, as President John F. Kennedy said in 1962:

“It is a paradoxical truth that tax rates are too high and tax revenues are too low and the soundest way to raise the revenues in the long run is to cut the rates now”.

Our fantasy economy and revenue graph is centered at 50%, but that doesn’t mean 50% is the ideal tax rate in a real world economy.

Many factors will increase or decrease the incentives to work… the United States has a very good infrastructure and law system, for example.  On the negative side, states also impose taxes making our math harder, and there are taxes on consumption and other things which Americans also pay (sales taxes, car registration fees, property taxes, etc.).

It’s also important to note that even if you accept the Laffer Curve and the sole goal of a tax program is to increase tax revenues, tax rates may currently be too low and could be increased.  While economic incentives for production will decrease with any tax tweaks to the upside, more revenue would come into the government’s coffers in that scenario.  The Laffer curve is best used as an illustration of the theoretical effects of tax law changes – but note that it doesn’t argue that we should always cut taxes.

More Theory: Increasing Potential GDP

GDP, or gross domestic product, is one way measure of all the goods and services produced in a country in a given period; in essence it’s a country’s overall productivity.

You can find the United States’s GDP simply on FRED.

In the example economy in our previous article, a tax rate of 50% lead us to a GDP of 50 economic productivity units.  Remember, the government takes 25 of these units from our fantasy economy.  Some of the 25 unit remainder may actually be used to increase productivity.

We’ll have to make a new graph… this one assumes maximum theoretical economic productivity increases at a rate of 20% of the units which are not taken by the government.  Let’s look at some constant tax rates when held over a 5 year span in this new scenario:

How to reproduce this graph?  Determine the growth rate of the theoretical maximum GDP for each bracket.  I’m using 20% growth on the amount not taken by taxes.  Compound the difference to find the theoretical maximum GDP for the year you want.  Multiply the tax rate by the theoretical max scaled by the amount of productivity you determine will be lost in each tax bracket. For year 5, I came up with 5% growth a year in the 50% bracket, meaning a theoretical GDP maximum of 163.81.  Half of that incentive is gone, so you should calculate the tax on what’s left to be 40.95 economic units.

In our wonderfully simple fantasy model, it’s better over the 5 year period to tax in the 30% to 40% range because an increasing GDP means the government can draw revenues from a larger tax base, especially in later years.  You can change the numbers as you see fit… different assumptions lead to different numbers.  Still, it’s time to turn to the real world results.

The Laffer Curve and Hauser’s “Law”

Kurt Hauser discovered an interesting fact about tax revenues collected as a percentage of GDP going back a long time in the United States.  Spanning a vast amount of administrations and tax brackets, tax receipts as a proportion of Gross Domestic Product strangely are limited to around 19.5% of GDP.  The Wall Street Journal took a look at Hauser’s law in the period from 1950 to 2007 in the United States.  Sure enough, even with the massive changes in the United States over that 57 year period, the law holds true.  There is seemingly a maximum limit on the amount government can extract from an economy.  Check out the article here.

Furthermore, the (awesomely) interesting economics and investing site Political Calculations ran a similar study on personal income tax collections as a proportion of GDP from 1946 to 2006.  Again, the results are astonishing… the average percent collection as a percentage of GDP is 8%, ranging from 7.2% to 8.8%.  They took a look at 1954’s steeply progressive tax rate structure versus the structure in 2006 and found that even with the new tax structure, 2006 saw more government revenues even adjusted for inflation.

Where Does the Excess Economic Activity ‘Go’?

When it comes to tax rate differences between the states, it’s easy to imagine that capital and productivity can move into other states.  That’s why it’s disingenuous for states like California to increase tax rates too high, companies can either migrate or never start in California, but in Arizona or Nevada instead.

On the other hand, country defections are much harder to pull off, but not impossible.

People and companies stay in the United States for more than just taxes.  Our affluent consumer base, law system, infrastructure, education system, and security all contribute to attracting people and companies to set up shop and stay in the country.  However, with more onerous tax laws, entities may concentrate more of their energy to avoiding taxes than being productive in the first place.  Workers can also decide to work less hours overall, reducing total output – an interplay with the so called substitution and income effects.  Some combination of factors leads to the fall off in productivity, and only a moderate tax system can collect the proper amount of revenues while encouraging growth.

So the answer to the question above:  In many cases, increasing tax rates does not increase revenues… or it increases them slower than leaving tax rates alone or reducing them would have done.  It’s important than countries (and in the United States, the states) keep this in mind when designing their tax brackets.  Because growth is encouraged with lower tax rates, it’s better to err on the lower side of taxes.

(A reader sent in an interesting video series from the Center for Freedom and Prosperity on the Laffer Curve.  Check out Part I, Part II, and Part III; it’s an enjoyable series)