Tuesday, September 25, 2012

Laffer vs. Poisson

Laffer (on the left) versus Poisson (on the right)
I’m still thinking about the current controversy on where the “hump” in the Laffer curve should be placed.

Maybe it’s time to do a little “thinking outside the box.”  What if the Laffer curve is not the proper representation for the economic situation we wish to model?

If you check out Wikipedia, you see that the Laffer curve is presented as a parabola, typically skewed to the right so that the peak in the curve is after the midpoint. Why is that? Why should the Laffer curve be based on a geometric shape?

Maybe it’s because a parabola implies a scientific basis.  We use a parabola to approximate the path of a fly ball in baseball.  It is based on scientific phenomena (drag and gravity) and allows us to predict where the ball will be at any given time if we know the velocity of the ball when it leaves the bat.

Does that sound like something that should be applied to economics?  Wouldn’t a statistical tool be better?

The Poisson distribution (see image above on the right) deserves a closer look.  It is meant to model the probability of actions, not to predict a specific action.  Furthermore, in contrast to the Laffer curve, it provides a better model of behavior near the 100% tax rate.  The Laffer parabola shows the tax collected will be zero, whereas the Poisson distribution has it tapering down toward zero.  It indicates that even though nobody should want to pay all their income in taxes, some idiot will do it.  That is a better model of reality.

And that’s important!  We should be using tools that represent actual data.  The model should reflect our reality, not a vision of what we want our reality to be.

The acceptance of the Laffer curve in our culture is based on the idea that the hump in the curve is skewed toward the right.  That implies higher tax rates will generate increasing tax revenue, even at tax rates over 50%.  The Poisson distribution skews the curve the other way.  It implies that if you set tax rates too high, you will see diminishing returns.

Do you see why the Poisson distribution is not being applied in our current political environment?

If our cultural narrative is to promote more federal government activity in our lives, then we need to be shown how greater government is good for us and makes us feel better.  One way to do that is to emphasize that increased taxes don’t hurt.

If the Poisson distribution shows the opposite, our culture will make sure it never sees the light of day.

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