Monday, July 16, 2007

Review of Laffer Curve

Don Luskin has an interesting discussion on the Laffer Curve. Rather famously, Arthur Laffer drew it on a napkin for Gerald Ford, to explain how a tax rate cut could increase government revenue from that tax. Just a review. Government revenue is expected to be zero if the tax rate is zero. Government revenue is expected to be zero if the tax rate is 100%, because noone would do the job. (If there are other non-cash benefits to the job, then the tax rate is not 100%). If tax rates are low enough, there is less incentive to cheat/ or modify behavior, which leads to very high expected revenue from very low tax rates.

Government revenue from a given tax rate is expected to be positive when the tax rate is between 0 and 100%. This suggests you can increase government revenue from a high tax rate by lowering it, and can increase government revenue from a low tax rate by increasing it. Increasing revenue from a tax rate cut is refered to as "The tax cuts paid for themselves..."

One example in recent years was the luxury boat market. A high tax rate was placed on luxury boats, and revenue from the tax was nearly zero: noone wanted to buy a luxury boat when they were going to buy their boat, and essentially buy another boat for Uncle Sam. The luxury boat industry was essentially destroyed. When the tax rate was reduced, the luxury boat industry came back.

I took the data under discussion, and fit the data using Excel. It fit best to a 4th order polynomial, that is with 0 income associated with 0% tax rate and two positive government revenue humps. (I can not refrain from calling it a camel curve!) I submit that the hump at the very low 10 to 15% level is the tax rate where it begins to make more sense to hire accountants and lawyers rather than to pay the tax. The maximum government revenue point is about 25%, where the rational manager pays for accountants and lawyers, but still has to pay. Higher than 25% the rational investor begins to stop producing. Tax rates above 15% tend to be welfare for accountants and lawyers, but produce very little added revenue for the Government. Tax rates above 25 percent seem to reduce revenue for the government, showing that accountants and lawyers in government who advise government tax rate policy makers are obeying Director's Law: They are optimizing their personal life, not that of their government client.

If the countries which are not identified are removed (using Excel "hide" command) the R value shoots up to .43 for the 4th order curve. Not too shabby for a single parameter to have that much influence on a very complex data set with literally thousands of input parameters from many different countries.

Because I can, I append my comments to Brad Delong's blog, since he will soon delete them.

Grasping Reality with Both Hands: Brad DeLong's Semi-Daily Journal

That there is a tax rate where human behavoir is changed can not really honestly questioned. Even the most liberal economist will advocate vice taxes on alcohol and tobacco as a means to reduce drinking or smoking. What is a criminal statue but an attempt to increase the cost of unacceptable behavior?

I took the data estimates provided in your comments, and used Excel to find the best fit. The best fit was a 4th order "Camel Curve". I found it didn't make any difference if I forced a fit to (0,0) or not. The exclusion of Norway, Luxemburg, or UAE didn't seem to make a difference.
I didn't know some of the countries, so used excel to hide the countries that were not identified. The R value for this "identified country data only" data was .43, rather high for one input parameter in a system that should literally have thousands of input parameters.

Why a 4th order curve? I think there are two Laffer curves. One where people (who can) start hiring accountants and lawyers rather than just paying their 10% to 15% tax rate, and another where people begin to not produce rather than pay the 25% to 30% tax rate after already hiring the accountants and lawyers. The revenue increase from increased tax rates from 15% to 25% is minimal but the demand for accountants and lawyers will greatly increase.

This would indicate that accountants and lawyers who recommend tax increases beyond 15% in their policy advice to government are being more loyal to their personal self interest, than they are to the well being of their government clients.

Hope this helps.

Update: As expected Brad DeLong deleted my comments. Big surprise! Don Luskin included my letter, complete with the camel curve. Thanks Mr. Luskin!

I impatiently await the sure arrival of a mass of heavy red gold for my wonderful writing.


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