Some conclusions

How much control does the central bank have over money supply?

The central bank’s control of the money supply is not precise. It
has in fact to wrestle with two problems that arises due to the
fractional reserve banking system. For one, the central bank does
not control the amount of money that households choose to hold as
deposits in banks (cr). Secondly, the central bank also does not
control the amount of money that banks choose to lend or to put it
another way it does not control the amount of reserves banks
choose to hold (rr). From the above equation, we can see that the
central bank controls the money supply indirectly through its
direct control of the monetary base and by influencing the size of
m by changing the reserve requirement. The central bank however,
cannot control cr nor the entire rr (or more specifically ER/D)
While the simple multiplier (1/RRR) is stable because the central
bank almost never changes the RRR, the real-world multiplier m
can vary quite a bit from year to year.

From the equation, it is clear that m changes when there is a change
in cr and rr. What therefore determines cr and rr?