Mimsy Were the Borogoves

Editorials: Where I rant to the wall about politics. And sometimes the wall rants back.

The return of voodoo mathematics

Jerry Stratton, May 18, 2006

Sebastian Mallaby writes that “Nobody serious believes that tax cuts pay for themselves” and then goes on to give an example of tax cuts that come awfully close to paying for themselves. There are other benefits besides tax revenues to look at.

First, when Mallaby says that tax cuts don’t pay for themselves, he means that cutting taxes today doesn’t increase tax revenue. Tax cuts can increase tax revenue. It’s literally a mathematical certainty. Imagine the two ends of the tax equation: 0% tax and 100% tax. If the tax rate is 0%, obviously there will be no tax revenue. But the same holds true on the 100% rate end. Obviously, if the government were to take 100% of everyone’s income, there would be no income to tax. No one is going to work for free.

As the rate moves up from 0%, tax revenues increase. As the rate moves down from 100%, tax revenues increase. At some point in the middle, those two curves meet. That’s the optimal tax rate. If the tax rate is to the left of that optimal rate, increasing taxes will increase tax revenues. If the tax rate is to the right of that optimal point, decreasing taxes will increase tax revenues.

The most well-known example is the Laffer curve. Nowadays, economists tend to posit more dynamic forms of the curve, involving, basically, several different curves for several different kinds of taxes and economies. Nobody serious questions the curve’s existence, however. They can’t: to question it would mean they’re not serious and don’t know math. At best, they’d have to be using some kind of voodoo mathematics that posits magical incentives for workers to continue digging ditches when they aren’t receiving any tangible rewards. The only question mathematically is whether we are left or right of that curve today, how elastic that curve is, and how bumpy it is.

So, Mallaby says that we’re on the left side of one of those curves. Others say we’re on the right. I’m not going to argue either way, because I see a more interesting side to this argument. There are other things we can ask about tax increases and tax cuts. The discussion about tax effectiveness currently seems to assume that as long as a tax increase raises revenue, it’s a good tax increase, and that if a tax cut drops revenue, it’s a bad tax cut. The left/right argument about the Laffer curve mirrors the left/right divide in the United States: it doesn’t really allow for looking beyond the superficial.

There are other things we can ask about that curve, such as how effective tax increases ought to be. As we rise towards the top of a curve, tax increases become very inefficient: taxes need to be raised by large amounts in order to gain small increases in revenue. Even if we’re on the left side of a curve, as we move closer and closer to the right side small tax increases decrease economic growth—or actually decrease the subeconomy being taxed—more and more.

Mallaby quotes N. Gregory Mankiw about how the capital gains tax cuts reduced tax revenue. The tax cuts generated some growth:

How large, exactly? Mankiw reckons that over the long run (the long run being generous to his argument), cuts on capital taxes generate enough extra growth to pay for half of the lost revenue. Hello, Mr. President, that means that the other half of the lost revenue translates into bigger deficits.

That is, dropping the capital gains tax by 5% caused tax revenues to drop 2.5%, because the economy grew enough to cover the other 2.5%. However, this also means that the opposite is true: raising the capital gains tax by 5% will increase tax revenue but at the cost of inhibiting or reversing growth.

Semi-real numbers

I’m going to pull out some easy numbers from 2003 and 2004, averaging and rounding to make the math easy. It’s the idea here that matters. Remember that some people argue less growth than Mallaby quoted, and some people argue more. I’m using the numbers in Mallaby’s column.

We’re talking about the capital gains tax cut, which went from 20% to 15% in most cases. At 20% the tax revenue was about $50 billion per year; that’s on $250 billion dollars worth of capital gains: 20% of 250 is 50.

If all other things were to remain equal, a 5% tax cut is a loss of $12.5 billion in tax revenue, because 15% of $250 billion is $37.5 billion. But Mallaby’s quote says that tax revenue really only dropped by $6.25 billion, because half of that $12.5 billion loss was made up for by economic growth. So instead of $37.5 billion, tax revenue under that scenario would be $43.75 billion.

How do you get $43.75 billion in taxes out of a 15% tax? The total tax base has to be $290 billion. That’s $40 billion dollars more in the economy because of that tax cut. That’s a lot of extra money.

That tax cut may not have paid for itself in tax revenue, but it sure as hell paid for itself in growth. There are a lot of jobs in $40 billion dollars. Dropping taxes 5% increased growth by 16%. A loss of $6.25 billion to the government was a gain of over $40 billion to the general economy (or at least this sector of it).

Taxes are not self-evident. They don’t justify themselves. They require justification. Whether or not this growth is worth this loss of revenue is a question of philosophy, not mathematics. It’s a question of which is more important and at what point: economic growth or taxes.

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