Week 11 Chapter 16 Determinants of the Money Supply The monetary base is MB R C where R represents the reserves in the banking system and C the currency in the hands of the nonblank public. The money supply is M DC where D is the amount of deposits in the banking system. Suppose that we look at how some the banking system will respond to an increase in reserves if 1. all excess reserves are driven to zero 2. the public does not change its holdings of currency. 3. the proceeds from all loans are put into a deposit. In that case MB R C M D C By assumption (1.) banks will lend out all excess reserves and by (3.) all the proceeds will end up in a deposit. For that reason D will change. By assumption (2.) the nonblank public does not change its money holding, so C 0 and MB R M D If excess reserves have been driven to zero, then all reserves will be required reserves so R rD D and MB R rD D rD M MB rD M (1) 1 M MB m MB rD so there should be a relationship between the monetary base and the money supply. We will write that relationship as M m MB where m is called the money multiplier. It is a variable not a constant. The equation indicates how much the money supply will change for a given change in the monetary base. Recall that the Fed has control of the monetary base. Its supply of the money supply would be as complete if the three assumptions mentioned above are true. To the extent they are not true the Feds control of the money supply will not be as complete. That is why m is a variable and not a constant. The expansion of the money supply will not be as great as Equation (1) indicates because banks will not drive excess reserves to zero and because the public may decide to keep some of the proceeds of the borrowing and lending in the form of cash. Assume that the public has some preferred ratio of currency to currency to deposit holdings C D currency ratio and that banks maintain a certain level of excess reserves relative to deposits ER D excess reserve ratio Recall total reserves are made up of required reserves plus excess reserves so R RR ER and required reserves are a multiple of demand deposits RR rD D so R rD D ER Putting this into the equation for MB = R + C MB rD D ER C MB rD D ER D D C D D MB rD ER D C D D This gives us a relationship between MB and D 1 D MB (2) rD ER D C D Now lets play with the money supply equation briefly M D C D C D D (3) M 1 C D D Now take the representation for D in equation (2) and put it into equation (3) M 1 C D D 1 C D 1 MB rD ER D C D M 1 C D MB r ER D C D D Now we have our relationship between MB and M. The money multiplier is m 1 C D r ER D C D D Example in Text on page 415 rD 0.1 C $400 (all money values in billions) D $800 ER $0.8 M C D $1200 C 400 0.5 D 800 0.8 ER D 0.001 800 1 0.5 1.5 m 2.5 0.1 0.001 0.5 0.601 So if the Fed were to increase the monetary base by $10 billion, this would create $25 billion new money in the economy (assuming the ratios do not change in the meantime) Factors that affect the money multiplier Changes in the reserve ratio A change in the reserve ratio affects the money multiplier. Suppose that the Fed increases the reserve ratio. This means that banks will have to increase required reserves and likely excess reserves as well. To do this banks may have to restrict loans. This limits the amount of demand deposit expansion Banks A with a reserve ratio of 0.10 Figure 16.1 Consider bank A in Figure 16.1 This bank has excess reserves of $1000 if the reserve ratio is 0.10. The bank can lend $1000 and this will start the demand deposit expansion. Suppose the Fed raises the reserve ratio to 0.20. Now bank A has $0 in excess reserves and can lend nothing. Bank A with a reserve ratio of 0.20 This banks will also try to build up its excess reserve holdings by calling in loans. This will further reduce demand deposit creation and spending. This is built into the money multiplier by the ER/D ratio. Using the values of the previous example except for the reserve ratio which is changed from 10 percent to 20 percent we have rD 0.2 C $400 (all money values in billions) D $800 ER $0.8 M C D $1200 C 400 0.5 D 800 0.8 ER D 0.001 800 1 0.5 1.5 m 2.14 0.2 0.001 0.5 0.701 So the result of increasing the reserve ratio is to make the money multiplier smaller and lead to a smaller amount of money creation for a given increase in the monetary base. Changes in the publics desire to hold cash. Suppose that the public decides to increase its cash holdings. In this case the [C/D] ratio increases (the public converts some demand deposits to currency). This will initially decrease reserves in the banking system. Bank A before a cash withdrawal Bank A after $1000 has been withdrawn The reduction in excess reserves will inhibit possible demand deposit expansion. The bank may decide to increase its excess reserve holdings. This will further decrease any money creation. Let’s see what the multiplier tells us. If the public decides to increase its cash holdings the [C/D] ratio will increase. Recall initially that C D 0.5 ER D 0.001 rD 0.1 1 C D 1 0.5 m 2.5 rD C D ER D 0.1 0.5 0.001 Suppose now the public decides to hold more cash so that C D 0.8 . In that case C D 0.8 ER D 0.001 rD 0.1 1 C D 1 0.8 m 2.0 rD C D ER D 0.1 0.8 0.001 Banks decide to increase excess reserves. Suppose that the banks decide to increase excess reserves. As we have seen earlier this will tend to reduce lending which, in turn, will reduce increases in the money supply. Suppose that we look at the multiplier with our original data where rD 0.1, C D 0.5, and ER D 0.001 . In that case the multiplier was m 2.5 . Suppose that the excess reserve ratio increases to 0.01 C D 0.5 ER D 0.01 1 C D 1 0.5 m 2.46 rD C D ER D 0.1 0.5 0.01 As expected the multiplier becomes smaller if banks increase excess reserves. If the costs of holding excess reserves increases banks will hold less excess reserves. If the benefits of holding excess reserves increase, then banks will hold more of them. Market interest rates If interest rates on loans increase banks will find it more costly to hold excess reserves rather than lending the funds. So one would expect to find the multiplier to increase when interest rates increase. See the graph on the next page The relationship between interest rates and [ER/D] Expected deposit outflows. Another factor that affects a banks decision of whether to increase holdings of excess reserves is whether it thinks deposits will increase or decrease. If the bank feels that deposits are likely to flow out of the bank, then it may try to build up its supply of excess reserves (perhaps by not making new loans). If the bank feels that deposits are likely to increase, it may be willing to make more loans. Other factors that determine the money supply We have been assuming that the Fed has complete control of the monetary base. The Fed can restrict discount loans to banks but cannot force banks to borrow. Thus the Fed does not have complete control over reserves. It can influence banks decisions of whether to borrow, but cant control the decision. We will break the monetary base into two parts, the borrowed and nonborrowed monetary base. MBn MB DL MBn the nonborrowed monetary base MB the monetary base DL discount loans. where it is presumed that the Fed has greater control of the nonborrowed base. Then the multiplier relation can be written as M m MBn DL Effect of changing MBn There is nothing new here. If the Fed buys securities then nonborrowed reserves will increase. An increase in MBn then supports an expansion of the money supply. A sale of securities by the Fed will decrease nonborrowed reserves and hence the money supply. Effect of changing DL If banks borrow from the Fed this will increase reserves and hence increase the monetary base. There is nothing new here either. Market interest rates and the discount rate There is something new here. When banks borrow from the Fed they can make loans or buy securities with the funds they borrow. Suppose that the interest rate that a bank can earn from a loan or security (pretend the interest rate is the same on each, it just makes life easier) is i and that the interest rate the bank pays for a discount loan is id . Now consider i id . A bank may be willing to lose money and borrow if id i in certain circumstances. Suppose a very good customer needs a quick loan. The larger id gets relative to i the less likely this will occur, however. If i increases the banks may be tempted to make loans even though their ER position is weak and then borrow from the Fed as a means of building up ER. If banks do lend more because of the increase in market interest rates, then the money supply will expand. The whole point here is that the money supply is not absolutely independent of interest rates as we pretended in earlier chapters. In earlier chapters we assumed that the money supply could be set absolutely without regard to the interest rate. This assumption is not quite true. The money supply is also affected to some extent by interest rates. Note also the Fed can affect the money supply by manipulating the discount rate. Money supply growth since 1980 It has varied a lot, from –0.11% to 13.1% MB was mostly nonborrowed reserves save for the period in 1984 when the Fed made massive loans to the Continental Illinois National Bank. Note the change in m means it will be difficult for the Fed to control the money supply. Note particularly the sharp decline in the multiplier after about 1994. This suggest that we might expect a sharp decline in M1. The Great Depression Bank Panics. During the Great Depression a large number of banks failed and bank panics ensued. One would expect to find that the [C/D] ratio to increase as people converted D into C. One would also expect that banks would tend to increase the [ER/D] ratio in anticipation of runs on deposits. If [C/D] and [ER/D] decline we would expect to see a decline in m and hence in the money supply. The money supply declined about 25%. This is true even though there was a20% increase in MB. Now since M m MB this decline in M must be the result of the decline in m.