> I doubt that we have a huge paper notes mass being hoarded in the US, most of it should be circulating pretty constantly.
I suspect most of the seigniorage these days ain't in the paper notes, but in database entries. Ie reserves that banks hold at the central bank. (Though Interest on Excess Reserves makes this topic more complicated than it used to be in the past.)
The rest of your comment seems to be about what is logical for an individual or perhaps for society. And that's useful, but not at all where I wanted to go with my comment. I was purely speculating on how to get the maximum seigniorage for the central bank.
> Pension funds, 401k are all tight to various investments, indices, etc. that are all reflection of the total economy. And I see it as my participation in the broader economy as I spend money that creates jobs and creates new economic exchanges further, and as a shareholder I capture that value back anyway. People should keep their spending at their social level if they want to keep the economy going smoothly.
People keeping their money as cash under the mattress implicitly also lend it out to the economy. An inflation targeting central bank will notice that (statistically) less spending is going on when the money is under the mattress, and print more money to compensate. When you start spending the mattress money, the central bank will remove money from circulation to compensate.
The net effect on the economy is pretty much the same as if you had stuck it directly into a bank account. (The main practical difference is in who's doing the asset allocation. But the amount of total spending is about the same: it's whatever the central banks decides it should be. No need for you to help smooth it out.)
You are right that with an inflationary currency, keeping money under the mattress is a losing proposition for the individual. But with eg a deflating currency, cash might be a decent investment. (And you can get into these kinds of regimes without crashing the economy, by eg central bank that targets a constant nominal GDP, or with the historic gold standard.)
That's why I was bringing up the example of Japan: when they had deflation, people were keeping lots of cash around.
Just for clarity: I wasn't even thinking so much about money under the mattress, but mostly about 'cash in your wallet'.