How currency withdrawal affects M1

[William Hummel]

An analysis of how a deposit or withdrawal of currency to or from a US bank affects the M1 money supply provides an instructive example of how our monetary system works. On average depositors withdraw more currency than they deposit, so let's consider the withdrawal by an individual depositor. Assume the amount is $100 to keep the arithmetic simple. The bank debits his account, thereby decreasing aggregate transaction deposits by the same amount the currency in circulation increases. That leaves M1 unchanged -- for the moment.

 

Since vault cash is part of a bank's reserves, the bank will have lost $100 in reserves. If the bank had no excess reserves before the withdrawal, it will need to acquire $90 in reserves to cover its remaining transaction deposits. In seeking to borrow that amount in the Fed funds market, its bid will cause the overnight interest rate on Fed funds to increase. The Fed will notice the increase and inject $100 into the banking system to counter the upward pressure on the interest rate. Of course the actual scenario is not as neat and precise as this, but we are only seeking to understand the principle.

 

Why $100 instead of $90? Because the Fed creates a new transaction deposit when in buys securities to inject reserves. Whichever bank ends up with the $100 deposit needs only $10 of new reserves to cover it. Thus it can lend the other $90 in the Fed funds market, which is exactly what the original bank needs. The end result is that aggregate transaction deposits are restored to their prior level.

 

Other things equal, M1 increases due to withdrawal of currency from banks when the Fed acts to maintain control of the short-term interest rate, its normal monetary policy response. The same result applies for a deposit of currency, but with the Fed's response reversed.

 

William

 

 

[Joe Leote]

William,

R = RC + RB

Bank reserves R equal vault cash RC plus reserve balances RB.

As you describe below, banks tend to lose vault cash RC in proportion to currency withdrawals by non-banks. The pressure on levels of reserve balances RB is persistently downward if banks make withdrawals from Fed to replenish vault cash RC. In any event it is clear from the plots below that Fed must defend the small amount of reserves and vault cash held by banks prior to the crisis.  Fed must "isolate" the bank balance sheet from being depleted or engorged by a flow of currency causing changes in reserve levels that interfere with control of the fed funds target rate. Fed can monitor reserve balance levels by inspection on its books, but the exact process of tracking levels of vault cash and currency outside banks appears to be fairly complicated and to my knowledge not explained by Fed.

 

Joe

[William Hummel]

Joe,

 

In the scenario I described, the bank initially loses $100 in RC, and its deposit liabilities decrease by the same amount. It then borrows $90 in the Fed funds market to cover its remaining deposit liabilities. RB is now up by $90. If the bank then swaps $100 of RB at the Fed to restore RC, RB would be $10 short of its original value. In other words, for every $100 of currency withdrawn by depositors, other things equal, RB drops by $10 if the bank chooses to fully replenish RC.

 

I'm not sure that's a problem, but I don't see any way to around it. How would the Fed "isolate" the bank balance sheet from the effect of currency flows in and out of the bank?

 

William

[John Hermann]

Beautifully explained William.
John

[Joe Leote]

William,

Just to clarify:

(1) at the point where a customer withdraws currency 100 from an individual bank, the change for ALL Banks is:
(1a) debit transaction accounts TA [-100]
(1b) credit vault cash RC [-100]
(2) at the point where the individual bank borrows $90 of RB in the fed funds market, the aggregate change in RB for ALL Banks is zero.
(3) at the point where the individual bank orders currency to replenish vault cash, the change for ALL Banks is:
(3a) debit vault cash RC [+100]
(3b) credit reserve balances [-100]
(4) if Fed purchases Treasury securities to offset the currency drain, the change for ALL Banks is:
(4a) debit reserve balances [+100]
(4b) credit transaction accounts [+100]
(5) Fed logs item 4 as follows:
(5a) debit Treasury securities MPA [+100]
(5b) credit reserve balances RB [+100]

Now the original bank still has to fund a $90 reserve deficit but another bank should gain the +90 reserve surplus due to clearing Fed payment on the Treasury security purchase.

I think the aggregate Bank balance sheet levels are isolated by Fed servicing the currency drain but there may be further implications for how Fed manages the fed funds rate anyway.

The three items that may influence the fed funds rate: (A) original bank is -90 reserve deficit; (B) aggregate Bank balance sheet is down -100 reserve balance levels at the point where a bank replenishes its vault cash; and (C) clearing bank after Fed purchases a Treasury is up +90 reserve surplus.

Joe