1. The Determinants of the Money Supply
The money multiplier, reserve and currency ratios, and borrowed reserves

2. M1 and the Monetary Base
Recall our definition of M1 as currency in circulation plus checkable deposits
Recall our definition of MB as currency in circulation plus reserves
The Fed has greater control over MB than it does over M1
Checkable deposits are influenced by a number of factors that the Fed does not have direct control over.
We link MB and M1 together through the money multiplier
M1 = m*MB
For every $1 increase in the MB, the money supply (M1) increases by m*$1
m is almost always greater than 1.

3. The Currency Ratio
How much currency does the public hold relative to their checkable deposits?
We assume that the desired level of currency (C) is a constant fraction of checkable deposits
The currency ratio is a constant (in equilibrium) defined as:
c = C/D
C can change, but only in constant proportion to D

4. Reserve Ratios
What fraction of checkable deposits do banks hold in reserve?
Banks are required by the Fed to hold a minimum fraction in reserve defined as the reserve requirement ratio (rr)
Banks may choose to hold excess reserves (i.e. a fraction of deposits held in reserve above and beyond the minimum required by the fed).
Let RR be the required reserves held by banks
RR = rr*D, where rr is a parameter set by the Fed
Let ER be the excess reserves held by banks
ER = e*D, where e is assumed to be a constant proportion set by banks
Total reserves (R) = RR + ER = rr*D + e*D = (rr+e)*D
Note that we have been assuming so far that ER=0 (i.e. the reserve requirement is binding).

5. Deriving the Money Multiplier
We define MB as currency (C) plus reserves (R)
Using our definitions:
MB = C + R
MB = c*D + rr*D + e*D
MB = (rr + e + c)*D
The monetary base is equal to the fraction of deposits allocated to required reserves, excess reserves, and currency in circulation

6. Deriving the Money Multiplier
MB = (rr + e + c)*D
Rearranging gives:
Recall M1 = C + D = (c*D) + D = (1+c)*D
Plugging in our definition of D:
Since M1 = m*MB:

7. The Money Multiplier The money multiplier is defined as:
m = (1+c)/(rr+e+c)
If no currency is held and banks hold no excess reserves, then the money multiplier is simply the inverse reserve ratio
A 10% rr will produce a multiplier of 10
A 20% rr will produce a multiplier of 5
In reality, people do hold currency and banks do hold excess reserves.
As a result, the banking system is limited in the amount of money it creates through fractional reserve banking (i.e. multiple deposit creation)
Money held as currency or in reserve is not being loaned out.

8. Example 1
Suppose the desired currency ratio is 40%, the reserve requirement is 10% and the excess reserve ratio is 0.5%
The money multiplier is
m = (1+0.4)/( ) = 2.77
A one dollar increase in the monetary base will lead to a $2.77 increase in the money supply
Note that if c = e = 0, then the money multiplier would have been 10.
Accounting for currency and excess reserves is clearly important.

9. Example 2
Let c = 0.25, e = 0.001, and rr = Compute the money multiplier
m = (1+0.25)/( ) = 3.56
The Fed decides to increase rr to 20%. What happens to the money multiplier (and the money supply as a result?)
m = 1.25/0.456 = 2.74
A smaller multiplier means that banks create less money through lending and therefore the money supply will fall.

10. Example 3
What happens to the money multiplier when the desired currency ratio rises?
Let c = 0.2, rr = 0.25, and e = 0.05
m = (1+0.2)/( ) = 1.2/0.5 = 2.4
Now suppose c rises to 0.3, while all other variables remain constant
m = (1+0.3)/( ) = 1.3/0.6 = 2.17
Increasing the fraction of deposits held as currency causes the money supply to fall
Money is being taken out of the banking system where it could have been used to make loans.

11. Factors that Determine the Money Multiplier
Changes in the required reserve ratio r
The money multiplier and the money supply are negatively related to r
Changes in the currency ratio c
The money multiplier and the money supply are negatively related to c
Changes in the excess reserves ratio e
The money multiplier and the money supply are negatively related to the excess reserves ratio e

12. Changes in the Currency Ratio
We have assumed that the constant currency ratio is an independent parameter for simplicity.
A more complete analysis would examine the factors that cause c to change.
Changes in income/wealth
Larger proportions of currency are held by people with low income/wealth
As income/wealth rises, the ratio of currency to deposits falls
Changes in expected returns
As the interest rate on deposits rises, c falls
As the cost of acquiring currency falls, c rises
Fears of bank insolvency (i.e. bank panics) cause c to rise sharply
Increases in illegal activity cause c to rise

13. The Currency Ratio Over Time
Series of bank panics
ATM’s lower the cost of acquiring currency
Big tax increases
Increased illegal drug trade

14. Changes in the Excess Reserve Ratio
What are the costs and benefits to banks of holding excess reserves?
Market Interest Rates (-)
Every dollar held as an excess reserve has an opportunity cost equal to the interest rate it could have earned as a bank loan
As market interest rates rise, this opportunity costs increases and banks hold fewer excess reserves
e is negatively related to market interest rates
Expected Deposit Outflows (+)
The main benefit of holding excess reserves is that they insulate the bank (somewhat) from sudden deposit outflows
With excess reserves, banks do not have to call in loans, sell off other assets, or borrow from the Fed to cover deposits being withdrawn
If banks think that deposit outflows will increase, they would be wise to increase their excess reserve ratio
e is positively related to expected deposit outflows.

15. Excess Reserves and Market Interest Rates

16. The Decline of the Reserve Ratio as a Policy Tool
The preceding analysis suggests that the Fed can increase/decrease the money supply by lowering/raising the reserve ratio.
While the Fed used this policy tool in the past, it has become ineffective in the past decade or so.
The Fed allows banks to classify some of their membership deposits at the Fed as required reserves
Banks have found that they need to keep extra currency in ATM’s over weekends and holidays. This currency is classified as vault cash and counts toward required reserves
With these two developments, banks actually hold more reserves than the minimum required by the Fed
If rr is not binding, then any change in rr will have little to no effect. (only works if you significantly increase rr!)

17. Borrowed Reserves
Open market operations are controlled by the Fed, but the Fed does not directly control the amount of borrowing by banks from the Fed
We split the monetary base into two components, the non-borrowed monetary base (MBn) and borrowed reserves by banks (BR)
MBn= MB – BR  MB = MBn + BR
M1 = m*MB = m*(MBn + BR)
The money supply increases with both the non-borrowed base and with borrowed reserves
An increase in BR frees up more bank deposits for loans
BR tends to be very small since the Fed keeps the discount rate above the market interest rate.

18. Factors that Change the Money Supply

19. Changes in the Money Supply, 1980-2006

20. Explains long run movements
Explains short run fluctuations

21. The Bank Panics of the Great Depression
The model we have developed here can be used to explain the sharp reduction in the money supply during the Great Depression
Prior to FDIC, there was no publicly provided insurance for bank deposits
With the Great Depression, many bank loans failed
People worried (rightfully) that their bank did not have enough in reserves to cover all deposits
They rushed to their bank to withdraw their money while their was still something left in reserve
This sparked a series of bank panics where even financially stable banks were affected
These bank panics directly led to a reduction in the money supply, even though the Fed would have actually preferred an increase in M1 at this time
Fears of bank insolvency caused c to rise
Increases in expected deposit outflows caused e to rise
The multiplier declined sharply

22. Currency and Excess Reserve Ratios During the Great Depression

23. M1 and MB during the Great Depression