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ECON 310 009 Money & Banking J. Scott Sperling Fall 2001 [email protected]
Money Supply †
We will investigate how the money supply is determined. The major players in determining the money supply are the central bank (the Fed, for our purposes), banks, depositors, and borrowers. The Fed plays a major role in the money supply process so we will begin with how the Fed’s actions affect the money supply.
1 The Fed’s Balance Sheet
Assets
- securities — primarily Treasury securities, controlled by open market operations
- discount loans — the loans the Fed makes to banks, affected by the discount rate set by the Fed
- gold and SDR (special drawing rights) certificate accounts
- coin — Treasury currency (mostly coins)
- cash items in process of collection — checks to be cleared
- other federal reserve assets — includes Fed’s foreign currency reserves
Liabilities
- Federal Reserve Notes outstanding — i.e. those dollars in your pocket
- reserves — the reserve accounts of the banks, consists of deposits at the fed and vault cash (this includes required and excess reserves)
- U.S. Treasury deposits
- Foreign and other deposits — deposits owned by foreign governments, foreign central banks, international agencies and U.S. government agencies
- deferred-availability cash items — delay between the time a check is submitted for clearing and when the bank is credited
- other Federal Reserve liabilities and capital accounts — e.g. stock in the Federal Reserve System purchased by member banks †If you find any errors or have any questions about these notes, please email me at [email protected].
2 The Monetary Base
The monetary base is the combination of Federal Reserve notes outstanding plus reserves plus Treasury currency in circulation.
The monetary base is also called high-powered money since when it increases, the money supply increases more than the increase in the monetary base.
If we lump the Treasury currency in circulation with the Federal Reserve notes outstanding, we get a total of the currency in circulation, C. We will use R to represent reserves and we get a mathematical expression for the monetary base, M B:
M B = C + R
This is gives us the uses of the base, now we need to find the sources of the base to see what affects the monetary base. Remember that a banks assets equal its liabilites, so we can use the Fed’s balance sheet to figure this out. Since Federal Reserve notes plus reserves are equal to the sum of Fed assets minus all other Fed liabilities, we get:
M B = securities + discount loans + gold and SDRs + float + other Federal Reserve assets +Treasury currency − Treasury deposits − foreign and other deposits −other Federal Reserve liabilities and capital (1)
To see how a change in any of these factors affects the monetary base, look at the sign in front of the term in the equation. For example, if Treasury currency increases, then the monetary base increases (there is a plus sign in front of Treasury currency); if Treasury deposits increase, then the monetary base will decrease.
2.1 Controlling the Monetary Base
The Fed can control the monetary base by conducting open market operations and making dis- count loans to banks. The Fed can make an open market purchase (i.e. it buys bonds) or open market sales (i.e. it sells bonds). We will investigate what happens to the monetary base when the Fed conducts an open market purchase.^1
2.1.1 Fed Open Market Purchase From A Bank
Suppose the Fed purchases $1000 of bonds from a bank, let’s say the bank is named Bank Eins. The Fed pays the bank $1000 in the form of a check. The bank either deposits the check in its account (^1) You should be able to figure out what happens when the Fed makes an open market sale (hint: pretty much just the opposite).
Fed Assets Liabilities Securities +$1000 Reserves +$
As you can see, we get the same effect. The OMP (open market purchase) of $1000 results in a reserve increase of $1000 and the monetary base increases by $.
On the other hand, if J.Q.Public decides to cash the check from the Fed for currency then:
J.Q.Public Assets Liabilities Securities -$ Currency +$
Fed Assets Liabilities Securities +$1000 Currency in circulation +$
Unlike our previous results, reserves do not change. But, since currency increased by $1000 , the monetary base still increases by $.
Conclusion: Although the effect of a Fed OMO on currency and reserve levels is uncertain, the effect on the monetary base is (relatively) certain.
2.1.3 Does the Fed have complete control over the monetary base?
The short answer is no. Although the Fed is able to control the monetary base fairly easily with OMOs, other factors such as the float and Treasury deposits tend to fluctuate frequently. These fluctuations are somewhat predictable, therfore the Fed can account for them and is able to accu- rately control the moneytary base.
3 Simple Model of Multiple Deposit Creation
multiple deposit creation : The process whereby, when the Fed supplies the banking sys- tem with $1 of additional reserves, deposits increase by a multiple of this amount.
3.1 A Multiple Deposit Creation Story
We will need to make a couple of assumptions for our model. First, assume that banks do not want to hold any excess reserves (remember excess reserves do not earn any interest). Second, assume that people do not want to hold extra currency, i.e. they want to hold and use checkable deposits. Finally, assume that the Fed has set the required reserve ratio at 10%.
If the Fed makes an open market purchase of $1000 from Bank Eins, then Bank Eins’ reserves increase by $1000 and since there is no increase in checkable deposits, the bank’s excess reserves are $1000. Since the bank does not want to hold excess reserves, it can make a loan and assume the loan is credited to the borrower’s checking account. The changes on Bank Eins’ balance sheet are:
Bank Eins Assets Liabilities Securities -$1000 Checkable deposits +$ Reserves +$ Loans +$
Bank Eins has just created money!! (Remeber, checkable deposits are part of the money supply (M1).) Note that a bank cannot make a loan(s) for greater than the amount of its excess reserves, because once the borrower writes a check to make purchases, the reserves leave the bank. Now let’s see what happens when J.Q.Public writes a check that gets deposited in another bank. The checkable deposits and reserves decrease by $1000 and Bank Eins’ final balance sheet looks like:
Bank Eins Assets Liabilities Securities -$ Loans +$
J.Q.Publics check gets deposited into an account a Bank Zwei:
Bank Zwei Assets Liabilities Reserves +$1000 Checkable deposits +$
Bank Zwei does not want to hold any excess reserves (which are $900, it has to hold $100 in required reserves to support the $1000 deposit) so it makes a loan for $900. Assume that the loan amount will be deposited into another bank, then:
We know that RR is equal to the required reserve ratio times the total deposits, so:
RR = rdD,
and substituting for RR gives us rdD = R.
Dividing by rD yields:
D =
rD
R.
Taking the change in both sides, gets us the same equation as above:
∆D =
rD
∆R.
3.3 What’s Wrong with our Simple Model?
The simple deposit multiplier is exactly that, simple. There are a couple of problems we can point out right away. First, if any person along the line of deposit creation in our story decides that she wants to hold currency as opposed to deposits, then deposit creation is stopped at that point. Second, if any bank along the chain wanted to hold excess reserves, multiple deposit creation would halt. Therefore, we need to develop a model which addresses these issues.
4 The Money Supply Model
4.1 The Money Multiplier
First, consider the relationship between the monetary base, M B, and the money supply, M.^4
M = mM B (3)
where m is the money multiplier. The money multiplier tells how much the money supply changes when there is a change in the monetary base. We will no derive the equation for m which describes the affect of currency, excess reserves, and the required reserve ratio on the money multiplier.
To address the problems with the simple model, we introduce a couple new terms that relate the ratios of currency and excess reserves to deposits.
C D
= currency ratio ER D
= excess reserve. (^4) We will use the M1 monetary aggregate to build this model, but we can just as easily do the same with M2 with a couple of extensions to the same logic.
The bar above each expression represents that we assume these ratios are constant in equilibrium.
Now, remember that the total reserves in the banking system is equal to required reserves plus excess reserves: R = RR + ER.
Required reserves are equal to the required reserve ration times the amount of deposits:
RR = rDD.
Substituting this expression into the previous equation yields:
R = rDD + ER.
The monetary base is equal to reserves plus currency, substituting our expresson for reserves yields: M B = R + C = rDD + ER + C.
Note that the equation implies that the only thing that multiplies from a change in the monetary base is deposits.
Now with a little bit of algebraic manipulation we get the expression:
M B = rDD +
ER
D
D +
C
D
D = D(rD +
ER
D
C
D
Dividing both sides by D, we get:
D =
rD + ERD + CD
M B (4)
Remembering that the money supply is equal to currency plus checkable deposits (see chapter 3):
M = D +
C
D
D = D(1 +
C
D
Using equation (4) to substitute for D, we get
M =
1 + DC
rD + ERD + (^) DC
M B. (5)
Note the similarity to equation (3). The funky term in the middle is simply m:
m =
1 + DC
rD + ERD + CD
Now let’s try to figure out what all this alphabet soup means. Let’s look at a numerical example to see how it all works out and what it all means. Let rD = 0.10, C = 8000, D = 14000, and ER = 100. Now let’s see what our multiplier is:
m =
In other words, for every $1 increase (decrease) in the monetary base, the money supply increases (decreases) by $2.32.
4.3 The Non-borrowed Monetary Base: Another View of Money Supply
We can also look at the monetary base as consisting of borrowed and nonborrowed funds, i.e. the borrowed monetary base would be discount loans from the Fed. Mathematically:
M B = M Bn + DL.
We can substitute this into our expression for the money supply to get:
M = m(M Bn + DL). (7)
Thus, we can see two more things which affect the money supply: changes in the nonborrowed monetary base and changes in Fed discount lending. The Fed controls the discount rate. Ceteris paribus, and increase in the discount rate decreases the amount of discount loans. Another fac- tor that affects discount lending is the difference between market interest rates (particularly the fed funds rate) and the discount rate, which is called the spread. When the spread increases, the amount of discount loans also increase because bank profits from discount borrowing increase.
