Q. Overnight interest rates targets and money supply?

There are many ways to explain the significant connection between overnight interest rate target and money supply. We will use an illustration to demonstrate why a decrease in the overnight rate target increases the money supply. 

Imagine that central bank changes the target from 6% to 4%. Before lowering their target, overnight interest rates were at around 6%, let's say between 5.6% and 6.4%. When central bank cuts the target to 4%, it signals that it wants to see an overnight rate around 4%. 

Remember that central banks generally have standing facilities allowing banks to borrow from the central bank at a rate slightly above the target rate (and to lend at a rate somewhat below). If central bank does nothing but to change the target rate, banks would immediately use the standing facilities and borrow from the central bank. They were used to borrowing at rates around 6% overnight however can now borrow from the central bank at slightly above 4%. Though the central bank doesn't want the standing facilities to be used - it wants overnight rate to be close to the target such that banks lend and borrow from each other in the market. The question then is, how can they influence the overnight market so that banks would want to borrow lend at around 4%? The answer is by increasing the monetary base and so the money supply. 

When central bank buys government securities, it purchases from many companies, individuals and institutions. Deposits and reserves in most banks would increase.So most banks will want to lend overnight and it will drive down the overnight interest rate.  

To summarize: When Central Bank cuts the target rate, they should concurrently increase the monetary base by buying government securities. Growth of the monetary base creates a surplus in the banks, supply of funds overnight increases, demand falls and overnight rate falls. Though the monetary base signifies a small portion of the money supply, a change in monetary base is magnified by the multiplier effect.