Tuesday, February 14, 2012

The CBO and potential output

Jim Bullard from the St. Louis Fed has been pilloried for his comments about what affects potential output.

Noah Smith accuses him of being a Solow Model denialist (saints preserve us)!

Tim Duy says that can't be right because Bullard is too dense to even realize that Potential GDP is calculated using the Solow model.

People, I'm not here to defend Jim Bullard. But I am here to say that according to the link provided by Duy to the CBO's description of how they calculate potential output, the statistic is a mess. Making sausage is a much cleaner enterprise.

First off, it's based on an accounting identity! God I love the government:

Qnfb = ALaK1-a

(this is my crudely typed version of equation 3 in the CBO document)

Sadly they forgot the third bar in the equal sign. This is an accounting identity! A is TFP which is defined as what's left over in output after we impute the effects of labor and capital (the CBO freely admits this by the way). a is assumed to be 0.30 and constant over time.

So, forecasting potential output means forecasting potential TFP, potential labor, and actual capital (read the document if you doubt me) and plugging those values into the equation.

People, they ain't using the Solow model to accomplish those tasks!

Potential labor and potential TFP are forecasted by piecewise linear regressions where the breakpoints ARE NOT DETERMINED BY ANY SORT OF STATISTICAL CRITERION (again, read the document if you doubt me).

The CBO method is arbitrary and weak. Defending it via appeal to authority by saying "it's based on the Solow model" is pathetic.

First of all, the Solow model stinks! It cannot come close to describing the evolution of the world income distribution since 1950.

Second, the measure of potential output is crucially dependent on all the forecasting assumptions used to produce potential Labor and potential TFP, which are not based on any real economic theory or optimal statistical algorithm.

Finally, the CBO itself says things that are remarkably Bullard-like right in the document Duy links to:

"CBO's framework explicitly models the factors that determine the accumulation of capital, so the projection for the capital stock is fully consistent with CBO's projections for private saving and the federal budget. Specifically, a higher projected rate of saving will lead to faster accumulation of capital and faster growth of potential output. Therefore, a higher projected federal surplus, which generally raises
the rate of national saving, will speed up the growth of the capital stock and potential output in the model. Conversely, a recession or other event that depresses the saving rate will temporarily slow the accumulation of capital and the growth of potential output."

That's right, according to the CBO, federal deficits lower the path of potential output! It must be true, after all, it's based on the Solow model.

Give me a break.


Anonymous said...

I can't see the identity equation. The URL looks wrong. Can you check it out, please?

Angus said...

Tried to enlarge what I cut and pasted from CBO. URL is to a long document. It works fine on my computer.

Hope this helps.

Noah Smith said...

Here's the follow-up:

Hey, if you chuck the Solow model, you chuck the Solow model! You might be right and you might be wrong...