Mailvox: logical or empirical?

691 doesn’t do the math:

What you cite as a logical blunder is not a logical error at all. Maybe an empirical error. It’s entirely logically possible for a $1 decrease in spending to lead to a $3 decrease in revenue, resulting in a $2 increase in the deficit.

The deficit, the change in debt levels, is the difference between two numbers: spending and revenue. Does the extra debt come from (relatively) higher spending or (relatively) reduced revenues? You claim that spending and borrowing have increased, which would imply that each $1 in extra spending is leading to less than $1 of extra revenue.

But citing debt levels alone is not sufficient to prove your case.

Very well, let’s look and see if what he’s saying is, in fact, logically possible. I pointed out that the debt doubled from $5 trillion to $10 trillion in four years. 691 is claiming that “it’s entirely logically possible for a $1 decrease in spending to lead to a $3 decrease in revenue, resulting in a $2 increase in the deficit.”

There are two ways to show 691’s criticism is incorrect. First, his statement can only be true if the multiplier effect on government spending can be 3x or more. But is that the case? No, it is not.

“For U.S. annual data that include WWII, the estimated multiplier for defense spending is 0.6-0.7 at the median unemployment rate. There is some evidence that this multiplier rises with the extent of economic slack and reaches 1.0 when the unemployment rate is around 12%. Multipliers for non-defense purchases cannot be reliably estimated because of the lack of good instruments.”
– Macroeconomic Effects from Government Purchases and Taxes,
Robert J. Barro and Charles J. Redlick, NBER Working Paper No. 15369 (September 2009)

So, because the unemployment rate never reached 12 percent, the G multiplier cannot possibly have reached 1.0, much less the required 3.0, and therefore it was, as I previously wrote, logically impossible for the post-crisis governments to simultaneously produce large deficits and cut spending.

Concerning the second method, even if we plug in his numbers, we can see they don’t work on an empirical basis either. We’re not dealing in hypotheticals here. What X decrease in annual spending could lead to a 3X decrease in revenue to create a $1.25 trillion deficit? There would have to be a $625 billion decrease in spending as well as a $1.875 fall in revenue to produce it. However, there was a $535 billion INCREASE in spending to go with a $419 billion fall in revenue, thereby providing an empirical illustration of the logical absurdity of his position.