The argument you linked is ignoring the fact that when you provide a bank with dollars (M1 bailout cash), it is lent out by the banks and creates a much bigger sum of M2 money (bonds, liquid assets) because of fractional reserves.
Any bailout that is large enough, and isn't done in tandem with major deflationary events, would certainly impact inflation.
I think 2008 was spectacularly smooth with respect to inflation/deflation because they allowed enough banks to fail.
M1 reserves are not lent out by commercial banks - they are a liability of the central bank and an asset of the commercial banks or anyone else with access to the central bank's balance sheet. Banks only ever lend you their own liabilities. E.g. if you get a loan from HSBC, you borrow HSBC pounds because you have a deposit with HSBC.
When banks lend, they create a deposit (or credit an existing one) in the name of the customer (liability), and create a corresponding loan (asset) on their balance sheet. Banks don't _need_ reserves, like warehoused cash, to lend. They just need a capital buffer to absorb any credit losses on their loan portfolios.
The M2 money supply only increases if banks lend. In theory, they are more ready to lend when they have a better capital and liquidity position, which an injection of reserves is intended to achieve. But if no-one wants loans then M2 money supply doesn't increase as a result of a higher M1 money supply.
Also, "fractional reserve banking" is not a concept that relates to modern banking. Banks can lend as much as they like within reason. They are no different to any other business which can leverage their balance sheet by adding debt to increase return on equity. Loan creation is limited by:
1) Capital requirements - whereby loan creation is a function of how much capital they have, how risky their existing assets/loans are and how risky incremental loans are
2) Demand for loans from customers, which is a function of the macro environment e.g. interest rates
The thing is that a crisis like this is inherently deflationary! Or at least has a strong negative impact on the business cycle.
> they allowed enough banks to fail.
There really were not a lot of "bank fails and depositors lose money" events. Ones I can think of were Kaupthing (for some reason a lot of UK local government were keeping their money in an Icelandic bank), and Cyprus (deemed too dodgy to bailout).
There was a lot of fiscal policy tightening ("austerity"), the other lever which people forget about.
> I think 2008 was spectacularly smooth with respect to inflation/deflation because they allowed enough banks to fail.
They also started paying interest on excess reserves held at the Fed as they printed up a bunch of money to recapitalize the banks so as to not end up creating trillions of dollars of new money.
This time they injected trillions of dollars directly into the economy (hello, Helicopter Ben) and are now dealing with the effects. All that cash caused a huge bubble in Silicon Valley because people had nothing to do for quite a while except buy and consume stuff off the interwebs.
Now we have the correction for the Covid stimulus spending.
Any bailout that is large enough, and isn't done in tandem with major deflationary events, would certainly impact inflation.
I think 2008 was spectacularly smooth with respect to inflation/deflation because they allowed enough banks to fail.