## Thursday, December 06, 2007

### Taxes and GDP

Depending on how you measure it, the United States the governments' (fed, state, and local) share of the annual Gross Domestic Product (GDP) is a bit less than 1/3. The governments' take is, therefore, around \$4 trillion.

Let's quickly define what "share" and "take" mean. Consider a pie. The "share" (S) is simply a fraction of the pie. The "take" (T) is the weight of the given piece of pie. Given a pie that weighs W, the equation is T = S⋅W. Simple enough.

Clearly, for T to increase, either S or W need to increase (or both). However, in the case of the American pie called GDP, there is also a relationship between S and W. As the governments' share (S) of GDP increases, the pie makers (the private sector) make a relatively smaller pie, so W decreases. Therefore it's not clear if the governments' take will go up our down if they choose to increase their share. If GDP decreases faster than S increases, the take would decrease. If GDP (W) decreases slower than S increase, the take T would increase.

Let's say for a moment that the governments wanted to exactly maximize its take. To do so they would pick the share that maximizes the equation T = S⋅W and therefore the change in W would exactly offset the change in S if S increases or decreases. Let's say the governments have successfully done so and that the current share of 1/3 maximizes their take. If so, we would predict that for each percent increase (or decrease) of the governments' share of GDP, GDP would decrease (or increase) by approximately 3%.

Sure enough, according to a recent paper by Christina and David Romer of the University of California, Berkeley, tax revenue increases are a significant negative for the economy and the relationship between share of GDP and size of GDP happens to exactly maximize the governments' take:
Our baseline specification suggests that an exogenous tax increase of one percent of GDP lowers real GDP by roughly three percent.
Governments exist only to exert and extend their power via a parasitic relationship with their economic host. One-third GDP maximizes our governments' take so that's what they take. No more, no less.

Howard said...

One-third GDP maximizes our governments' take so that's what they take. No more, no less.

So our "stationary bandits" are smarter and more efficient than most other places. What happens if some critical mass of the electorate becomes aware of this...?

Howard said...

Looking at this post, it might be worth letting the private sector outstrip the growth of government until the take is a few percentage points lower.

Bret said...

howard wrote: "So our "stationary bandits" are smarter and more efficient than most other places."

My guess is that the stationary bandits are smart and efficient most places. Other places have higher taxes because the private sector is not as efficient so the government won't get a bigger take from reducing their share. In other words, it makes sense for higher taxes in France because reducing taxes 1% of GDP there might only increase GDP by 2% (instead of 3% here).

"What happens if some critical mass of the electorate becomes aware of this...?"

Probably nothing. The government is probably more powerful than the people.

"...it might be worth letting the private sector outstrip the growth of government until the take is a few percentage points lower."

Maybe. What was surprising about the Romers' study was that they didn't see any effect on growth - the effect was only on the absolute size of GDP and it reached the new size in about 3 years.

If, instead, it was actually 1% per year forever, that'd make quite a difference. Perhaps it's some mix of the two.