No, the GDP isn't shrinking ex-deficit

This is a common claim:
As shown below, when one strips out the change in government debt (the actual increase in U.S. Treasury debt outstanding) from the change in GDP growth, the organic economy has shrunk for the better part of the last 20 years.

Data St. Louis Federal Reserve

The argument is that since deficits flow directly into GDP via

GDP = C + I + G + X

(an increase in Government spending mathematically creates an equal increase in GDP), and deficits (~5% of GDP) are greater than GDP growth (~2% real growth), then GDP (i.e. the economy) is actually shrinking if you back out the contribution from deficit spending.

The argument has been made by others, including Karl Denninger, and forwarded approvingly by John Mauldin. I've even made the claim myself on Twitter.

Seems legit, right?

The problem with the argument is that it confuses the level of the deficit with the change in the deficit.

The deficit affects the level of GDP. The change in the deficit affects the change in GDP (that is, GDP growth).

To illustrate, assume we have been running somewhat constant 5% GDP deficits, similar to the current situation. Now assume we immediately stopped deficit spending and ran a balanced budget. GDP would immediately decline by 5% for that year. But what would happen next year with another balanced budget? The GDP would not experience another 5% contraction from austerity. It's the change in deficit, not the level that moves GDP growth. The chart above gets this exactly wrong, showing that somewhat steady 4-5% deficits create continuing declines in the "ex-deficit" economy.

None of this, of course, is to say that our current path of perpetual deficits greater than GDP growth is in any way sustainable or a good idea. It's not! But we're not shrinking, and we wouldn't perpetually shrink in the absence of deficits.

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