The goal of the Central Bank it's to control the interest rate, not the quantity of money. If there are not enough reserves in the inter-bank market, and the Central Bank refuses to supply them, the interest rate will go up.
So, if the Central Bank want to control the interest rate, it can't control the quantity of money and vice versa.
Modern Central Banks target the interest rate, not the quantity of money. The quantity of money in the economy it's automatically regulated by the level of economic activity.
"The central bank influences interest rates by expanding or contracting the monetary base, which consists of currency in circulation and banks' reserves on deposit at the central bank"
If you don't feel that quote clarifies feel free to read the rest of the section on monetary policy instruments.
In other words, if they target the interest rate they can't control the monetary base, so, Central Banks don't control the quantity of money in the economy.
If they choose to target the quantity of money in the economy, the tool that they have to use is the interest rate. So, they would lost control over the interest rate.
Modern central banks target the interest rate: they sacrifice control over the monetary base. The central bank don't decide the quantity of money in the economy, they decide the interest rate.
The implication is that they have to cover any necessary reserves by the private banks if they want to keep the interest rate in its target. So, yes, private banks create money when they lend and destroy money when the money is returned. And that's OK because that means that the quantity of money adapts to the activity of the economy.
This is correct. (The Fed has other tools beside open market operations, however, including directly manipulating rates on reserves and the discount rate.) But monetary base != money supply. The Fed manipulates rates to effect changes on the money supply.
Yes, if the money created is in the end kept in the system as a deposit it enables new loans (but it is not necessarily so if the money goes to someone that uses it to cancel a loan of their own, for example).
And due to the fractional reserve requirement the quantity of money cannot be increased without limit by commercial banks. That’s just a mathematical reality, notwithstanding the fact that it’s not usually a binding constraint.
>> they don't have the right to print money the way a central bank does.
> Yes, they do.
The feedback loop is the point, and it remains.