Wednesday, August 11, 2010

Visualizing the Laffer Curve

From Greg Mankiw's blog, this article asks economists "Where does the Laffer Curve peak?". I thought I'd graph some of the answers.

The following is the typical Laffer curve. At a 0% tax rate, revenue is zero. At 100% tax rate, revenue is again zero, because nobody will work if they give all their income to the government. The peak revenue is somewhere in between.

This graph assumes some sort of linear elasticity: if you tax me at 10%, then I work 10% less. This elasticity can be seen in the following graph:

Nobody believes this is what the elasticity looks like. Instead, people believe it looks at bit more like the following graph, where workers are relatively insensitive to changes in tax rates when they are low.

This leads to a Laffer curve that is shifted to the right:

The more you believe workers are insensitive to tax rates, the more the peak shifts to the right. In this case, the peak has moved from 50% to 65%.


Saez, Slemrod, and Giertz have a paper that tries to analyze elasticity. They claim that workers are insensitive to tax rates until they become very high. Their Laffer curve looks like the following:

In this case, they assume a peak around 73%.

Their paper discusses a lot of other things about the curve. For example, if tax rates where 100%, then income would not actually drop to 0%. Instead, people would find ways of sheltering income from the tax man. For example, they might instead change to corporate taxes, where a corporation would pay the corporate tax rate and purchase everything for the worker. Or, they would move income offshore. Or, they would move into the black market economy and not report income. So, there is a difference in "income" and "taxable income".

They also point to other policy choices that affect elasticity. Deductions for charitable contributions increase the elasticity on the high end, as rich people would rather give money to charities than to the government. If charities are more efficient at increasing social welfare than the government, then this would be a good thing, despite the fact it reduces government revenue.

I haven't digested the paper yet, but it's pretty interesting.

ANSWER: Ludlow and Mankiw

Both Larry Ludlow and Greg Mankiw claim that income tax not only reduces output from workers, but also growth. In other words, if tax rates cause workers to produce 1% less, then they also reduce growth by (let's say) 1%. Thus, instead of growing at 3.00% GDP this year, we'd grow at only 2.97%. This compounds year after year. (Stephen Moore also implies this, but not as strongly).

Note that they don't say exactly how much it will impact growth -- I'm just making the raw assumption (declines in GDP equivalent to decline in growth) to have something to play with. In the graph below, I start with my "Traditional Laffer #2" graph that peaks at 65%, then assume 3% growth over 10 years, with taxes reducing that growth 1-to-1.

This shifts the peak down to about 58% from 65%.

Of course, this compounds out to infinity. Assuming you keep a tax policy constant for a century, you get something like the following:

This brings the optimal tax rate down to 45%. In the long run, of course, "we'll all be dead". This analysis suggests that what we are really doing is taxing our grandchildren in order to pay for things today.

ANSWER: Martin Feldstein

Martin Feldstein points out that before we reach the peak, we reach a point where marginal deadweight loss exceeds the marginal revenue.

In other words, lets say we are 1% from the peak. If we increase taxes to reach the peak, we'll get $100-million additional revenue. On the other hand, the additional deadweight losses could be $1-billion.

So I've graphed this (based on my Laffer #2 above, that peaks at 65%).

Whereas this Laffer curve would peak at 65%, the point at which marginal deadweight losses start to exceed marginal revenue gains is at 48%. In other words, at this point, a $100-million increase in revenue will reduce GDP by more than $100-million.


I can see the information better as graphs than equations. These graphs make gross and certainly inaccurate assumptions, so they can't be used for any real purpose (such as predicting the Laffer peak). Moreover, I've probably made some egregious mistake in equations, invalidating the guesswork even further.

...and I'm not an economist, so have probably made obvious errors they can point out.

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