Old monetarism, new monetarism, and moneyness

Stephen Williamson had a good post recently in which he noted:

Central to Old Monetarism - the Quantity Theory of Money - is the idea that we can define some subset of assets to be "money". Money, according to an Old Monetarist, is the stuff that is used as a medium of exchange, and could include public liabilities (currency and bank reserves) as well as private ones (transactions deposits at financial institutions). Further, Friedman in particular argued that one could find a stable, and simple, demand function for this "money," and estimate its parameters. Lucas does that exercise here, and then uses the estimated money demand function parameters to measure the costs of inflation.

What's wrong with that? The key problem, of course, is that the money demand function is not a structural object. Some central bankers, including Charles Goodhart, figured that out. Goodhart's idea is a bit subtle, but there are more straighforward reasons to think that the parameters we estimate as "money demand" parameters are not structural. First, all assets are to some extent useful in exchange, or as collateral. "Moneyness" is a matter of degree, and it is silly to draw a line between some assets that we call money and others which are not-money.

I challenged him on how important moneyness actually is in new monetarist literature. Why, for instance, do so many new monetarist papers include some variable M if money is a matter of degree? You can't represent the idea "as a matter of degree" with a variable called M which by definition excludes all non-M assets. If you do so, you're already drawing lines between assets.

He never really responded to me. Steve, any thoughts? You've got the floor.