Christina Romer and her husband confirm the Laffer Curve

By Randall Hoven

A successful parasite must keep its host alive, finding the point where it can maximize its intake without killing off its source of sustenance. So, too, with governments taxing their citizenry. With taxation, governments can reach the point where higher rates produce less revenue. 

An academic study found that a tax increase of just 1% of GDP causes a recession and then a permanent loss of 1.84% of GDP compared to what it would have been without the tax increase. The results of this study have some really broad and interesting implications.

The punchline is that this study was done by Christina and David Romer. You might remember Christina as President Obama's first chair of his Council of Economic Advisers. David, her husband, is on the recession dating committee of the National Bureau of Economic Research (NBER), the outfit that everyone relies on to say when recessions start and stop. (The date of this study's release was June 2010. Ms. Romer announced her resignation from Obama's administration in August 2010.)

A key result of this study, published in the American Economic Revue, was the chart below. To quote the Romers,

The key result ... is in panel C, which shows the behavior of real GDP following an innovation of one percentage point to our series of exogenous tax changes ... The estimated maximum effect is a decline of 2.93 percent after ten quarters ... the effect falls to -1.84 percent after 15 quarters, and then remains roughly at that level."

Effect on GDP of a Tax Increase of 1% of GDP

Source: Christina and David Romer, American Economic Revue, June 2010.

First, a decline of 2.93% of GDP means recession. And even after the recession is over (two and a half years after the tax increase), GDP remains 1.84% below where it would have been without the tax increase. 

So while the government might collect 1% of GDP more than it used to, GDP becomes smaller. Thus, the government does not really collect as much as it thought it would using "static" scoring of tax changes. In fact, if we put it all together (as I do in Addendum 1), the result is a Laffer Curve, which I will call the Romer-Laffer Curve.

Christina Romer and her husband not only confirmed both the Laffer Curve and the "dynamic" scoring of tax changes, but they effectively specified them for us.

That is pretty big news. (Paging Dr. Krugman.)

The Romer-Laffer Curve is depicted in the chart below. It says that government revenue, in real dollar terms, is maximized at an overall average tax rate of 44.4% of GDP. In 2007, the U.S. was at 34.5% (U.S. Statistical Abstract, Table 1324). So while the Romer analysis leads to a Laffer Curve, it says we are on the left side of it, meaning government can increase revenues by raising tax rates (at least with the right mix of tax rates).

The Romer-Laffer Curve

But that is not the whole story. First, there is a point at which government loses money by raising tax rates, and that point is not far from where we are now. In fact, it is about where most of Europe was in 2007. (More below.) Also, dynamic scoring is real. The government would collect only a fraction (about 36.5%, from a 2007 baseline) of what it thinks it would collect using static scoring.

The effect of dynamic scoring becomes stronger as we approach the peak of the curve. If the government went all-out in maximizing revenue by raising tax rates as much as possible, it could collect only 5.3% more than it did in 2007 in actual dollars, at best. That would not be enough to cure our deficit/debt problem.

(These results jibe with those of a 2009 study of the Laffer Curve by Harold Uhlig and Mathias Trabandt. The 2010 Romer study implies that tax collections could go from 34.5% to a maximum of 44.4%. That is an increase of 29% as a fraction of GDP. The Uhlig study put that figure at 31%. Those are remarkably similar conclusions given such different approaches.)

In fairness, the Romers' data set was for the United States from 1945 to 2007, and they put significant error bounds on their estimates. That means extrapolating results outside the range of about 25% to 35% of GDP, or outside the U.S. economy, is more speculative. It also means we should not treat figures like 1.84 and 44.4 as precise values.

But if we do use the precise Romer-Laffer Curve to speculate, it leads to a pretty remarkable insight: themature, Western democracies seem to be maximizing government revenue. That is, they are not maximizing the percentage of GDP they take; they are maximizing the actual wealth they take. They appear to be seeking the peak of the Romer-Laffer Curve.

Below is a chart of that same Romer-Laffer Curve with a few representative countries plotted at their 2007 tax rates. The U.S. and Switzerland were the "low tax" countries at 34.5% and 34.2% of GDP, respectively. Norway took the prize for the high end at 58.4%, with Sweden and Denmark not far behind at 54.9% each. Germany was closest to that optimum level at 43.9%. The average for the 22 countries I call the "mature, Western democracies" (see Addendum 2) was 44.0%, or so close to that Romer-Laffer peak of 44.4% that one would have to think that something is going on here.

Where Mature, Western Democracies Lie on the Romer-Laffer Curve

But overall, the mature, Western democracies were clustered in a fairly small range of about +10% of the "optimum" level (from government's point of view) of about 45%. Recall that these countries did not start out there. The U.S., in fact, was at a tax rate of about 5%-10% at the beginning of the 20^th century. The others were way to the left side of the curve as well. Throughout the 20^th century, they all drifted up the Romer-Laffer Curve. Some even surpassed the peak, going down the curve to the right.

And here is what is more interesting. Countries did not simply keep going toward the right.  Most countries that passed the peak went back to the left. Of 22 countries, nine had tax rates above 50% of GDP at some point over 1980-2006. By 2007, all those countries had moved to the left of their maximum tax rates. The average move leftward was 4.5% of GDP. Five of the nine were below 50% of GDP in 2007.

On the other hand, twelve of those 22 countries were taxed below 40% of GDP at some point over that 1980-2007 period. By 2007, all of those countries had moved to the right of their minimum tax rates. The average move rightward was 7.4% of GDP. Six of the twelve were above 40% of GDP in 2007.

We in the U.S. are not familiar with real cuts to government. Then again, we have not passed the Romer-Laffer peak.  But several other countries have taken some genuine action. The Netherlands and Sweden reduced taxes by 8.5% and 8.3% of GDP -- significant moves to the left along the Romer-Laffer Curve. New Zealand moved 7.5% of GDP to the left.

The Peterson-Pew Commission on Budget Reform documents several examples of debt-cutting countries. It lists ten countries that cut government debt by 21% to 77% of GDP just since 1986. (Our federal debt held by the public is about 63% of GDP right now and heading to 90%.) Those countries took meaningful actions such as removing regulations including wage and price controls, downsizing through spending cuts and privatizations, reducing the number of public employees and public employee pay freezes, and reducing subsidies. You might notice that those actions do not include tax increases.

Here is where it gets tough: we do not have a dial we can simply set to 44.4%. Taxes are complex. Multiple things are taxed at multiple rates: personal incomes; corporate incomes; wage income; capital gains; interest income; sales taxes and VATs; federal, state, and local taxes; gasoline taxes; excise taxes; phone taxes; ad infinitum. I would say that each such tax has its own Laffer Curve, interacting with all the others.

Governments constantly tinker with such taxes. What the above implies, however, is that all that tinkering is an evolutionary trial-and-error process to march us up the Romer-Laffer Curve. Government is an organism that tries to maximize its energy intake. It is, in effect, like all other organisms.

An obvious point of contention is that most of us don't want to maximize government wealth. We want to maximize our own wealth. I know of two other studies that looked at optimizing overall GDP growth; one done in 1998 by the Joint Economic Committee of Congress and the other done in 2009 by the Institute for Market Economics. Both studies concluded about the same thing: the growth rate of GDP is maximized at an overall tax rate of no more than 25% of GDP. (As a libertarian kind of guy, I would push for under 10%, a tithe. But people call me an extremist.)

So overall wealth is maximized at a 25% rate, but government wealth is maximized at 45%. Guess which one the U.S. is approaching and Europe has already arrived at.

Here then, is my summary of what all this tax talk means, what economists call "policy implications."

• Total wealth is maximized when total government taxes are 25% of GDP or less.
• The U.S. was at 35% in 2007 and heading higher. Not only does this give a bigger piece of pie to the government, but it also shrinks the pie.
• There seems to be a limit on government growth, at least in mature, Western democracies. In such countries, government seeks to maximize its own wealth, and it does so at an overall tax rate of about 45% of GDP.
• Most mature, Western democracies cannot raise more real revenue by raising taxes. About half of them are on the "wrong side" of the Laffer Curve. Even the "low tax" countries like the U.S. can raise only about 5% more, in real wealth, than they did in 2007. And that assumes they do it "right." All such countries are near the peak of the Romer-Laffer Curve.
• Therefore, deficits and debts must be reduced by cutting government spending, not raising taxes.
• Furthermore, such cutting does not mean "austerity." It means a government that both taxes and spends about 45% of its economy. That is not what I would call austerity.
• Finding such an "optimum" point is not a matter of turning a dial. The political-economic system achieves such a point by evolutionary trial and error over decades to achieve the mix of taxes, tax rates, and public services and benefits that the market can stand and the electorate can abide by.

There is both good news and bad news here. The bad news is, of course, that we would all be richer, on average, if government shrank significantly. The good news is that the pain seems to be limited. Germany is the current example of where we all seem to be headed. (Maybe not your first choice, but it beats Zimbabwe and Venezuela.)

I expect Norway, Sweden, Denmark, and France to shrink their governments a bit, and for the U.S., Switzerland, Australia, and Ireland to grow theirs. We'll all meet at 45%. Hello, Germany and New Zealand

(I don't expect the 2010 Tea Party election to march us back down to 25%. I think it is just a reaction to Obama's lurch to reach Norway's 60% in a single bound. I expect our fickle electorate to seek the Romer-Laffer peak over time, just like Europe's.)

Thank you, Christina Romer. You cleared up a lot of confusion for us.

All this, of course, assumes the "mature, Western democracies" can keep a lid on Iran and all the crazies everywhere seeking WMD and a new caliphate. It also assumes George Soros doesn't run the world. But if we can't make such assumptions, we've got bigger problems than taxes. Remember, there are only two things certain in life, and only one of them is taxes.

Randall Hoven is the creator of Graph of the Day.  He can be contacted at randall.hoven@gmail.com or via his website,randallhoven.com.

Addendum 1. Math insert for those who care. Developing the Romer-Laffer Curve.

R₀ = federal revenues, as fraction of GDP, without a tax change.

T = tax change, as a fraction of GDP, in addition to R₀.

R = federal revenues, as a fraction of GDP, with a tax change:  R = R₀ + T.

G₀ = GDP without the tax change.

G = GDP with the tax change.

G = (1 + ST)G₀, where S = sensitivity to the tax change.

The Romer study said GDP is sensitive to tax changes. In fact, a 1%-of-GDP increase in taxes would cause the long-term GDP to be 1.84% lower than it otherwise would have been. That is a sensitivity, S, of -1.84.

In 2007, government in the U.S. collected 34.5% of GDP, or R₀ = 0.345.

So the actual revenues collected once the tax increase settles in is as follows.

Revenues = RG = (R₀ + T)(1+ST)G₀ = (0.345 + T)(1 - 1.84T)G₀.  Or

Revenues as fraction of G₀ = 0.345 +0.365T -1.84T².  (This is the Romer-Laffer Curve, with T as a decimal, e.g. 0.1 for 10%.)

Revenues, in real dollar terms, would be maximized at T = 0.099, meaning total revenues at 44.4% of GDP (34.5% + 9.9%).

Addendum 2. The 22 "mature, Western democracies." These are the OECD countries without Asia (Japan and South Korea), without the lesser developed countries of Mexico and Turkey, and without the recently liberated former Soviet satellites of the Czech Republic, Hungary, Poland, and Slovakia.

Australia

Austria

Belgium

Canada

Denmark

Finland

France

Germany

Greece

Iceland

Ireland

Italy

Luxembourg

Netherlands

New Zealand

Norway

Portugal

Spain

Sweden

Switzerland

United Kingdom

United States

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