I’d say that Cochrane’s pure quantity theory of money argument against the stimulus is not nonsense like Fama’s effort to learn about the world from an accounting identity. This means I disagree with Krugman who focuses on the word “accounting” in Cochrane’s post.
I’d note that there have been many attempts to define and measure money and all show variable velocity which increases when nominal interest rates are high.
Sitting on money is not pathological. In the real world we can’t spend money instantly (in which case the velocity would be infinite).
Also he is wrong about “printing money”. Liquid assets of the US gov are not included in any estimate of the stock of money- If M1, M2 etc stay the same and they increase then, according to Cochrane’s unique personal definition, the money supply will have been increased.
I wonder what Friedman would think of the fact that a prominent prof at U Chicago doesn’t know the definition of M1.
More importantly money holdings by firms (and the gov if you count them) are insignificant compared to money holdings by households. The correct quantity variable for money demand estimates is consumption not GNP, because almost no money is used to lubricate investment or government consumption. This was proven by Mankiw and Summers in 1987. Here is a link to SSRN where you have to pay. Don’t pay for it, but if you do get the WP or the published version in the Journal of Money Credit and Banking, please read the acknowledgments.