Money and Banking Chapter 15 The Money Supply and the Money Multiplier

Chapter 15 The Money Supply and the Money Multiplier CHAPTER OBJECTIVES By the end of this chapter , students should be able to . Compare and contrast the simple money multiplier developed in and the , and , developed in this chapter . Write the equation that helps us to understand how changes in the monetary base affect the money supply . Explain why the multiplier is almost always larger than the , Explain why the required reserve ratio , the excess reserve ratio , and the currency ratio are in the denominator of the , and money . Explain why the currency , time deposit , and money market mutual fund ratios are in the numerator of the money multiplier . Describe how central banks influence the money supply . Describe how banks , borrowers , and depositors influence the money supply . URL books 323

A More Sophisticated Money Multiplier for LEARNING OBJECTIVES . How do the simple money multiplier and the more sophisticated one developed here contrast and compare ?

What equation helps us to understand how changes in the monetary base affect the money supply ?

In Chapter 14 The Money Supply Process , you learned that an increase ( decrease ) in the monetary base ( which ) leads to an even greater increase ( decrease ) in the money supply ( such as or ) due to the multiple deposit creation process . You also learned a simple but unrealistic formula for estimating the change that assumed that banks hold no excess reserves and that the public holds no currency . Stop and Think Box You are a research associate for Moody subsidiary , High Frequency Economics , in West Chester , Pennsylvania . A client wants you to project changes in given likely increases in the monetary base . Because of a glitch in the Federal Reserve computer systems , currency , deposit , and excess reserve will not be available for at least one week . A private , however , can provide you with good estimates of changes in banking system reserves , and of course the required reserve ratio is well known . What equation can you use to help your client ?

What are the equations assumptions and limitations ?

You can not use the more complex money multiplier this week because of the Feds computer glitch , so you should use the simple deposit multiplier from Chapter 14 The Money Supply Process AD ( AR . The equation provides an estimate for changes in deposits . It assumes that the public will hold no more currency and that banks will hold no increased excess reserves . To get a more realistic estimate , well have to do a little more work . We start with the observation that we can consider the money supply to be ofthe monetary base times some money multiplier ( AMS URL books 324

This is basically a less version of the formula you learned in Chapter 14 The Money Supply Process , except that instead of calculating the change in deposits ( AD ) brought about by the change in reserves ( AR ) we will now calculate the change in the money supply ( AMS ) brought about by the change in the monetary base ( Furthermore , instead of using the reciprocal of the required reserve ratio ( as the multiplier , we will use a more sophisticated one ( 711 , and later ) that doesn assume away cash and excess reserves . We can add currency and excess reserves to the equation by algebraically describing their relationship to checkable deposits in the form of a ratio currency ratio excess reserves ratio Recall that required reserves are equal to checkable deposits ( times the required reserve ratio ( Total reserves equal required reserves plus excess reserves So we can render as ER . Note that we have successfully removed and ER from the multiple deposit expansion process by separating them from . After further algebraic manipulations of the above equation and the reciprocal of the reserve ratio ( concept embedded in the simple deposit multiplier , we re left with a more sophisticated , more realistic money multiplier ( So if Required reserve ratio ( Currency in circulation 100 billion Deposits 400 billion Excess reserves 10 billion URL books ' 325

( mI ( mI Practice calculating the money multiplier in Exercise . EXERCISES . Given the following , calculate the money multiplier using the formula , I ' I ' nu 100 100 10 100 100 10 100 10 100 10 100 50 100 50 100 . Once you have , plug it into the formula AMS . So if , and the monetary base increases by , the money supply will increase by . If , and decreases by million , the money supply will decrease by million , and so forth . Practice this in Exercise . Calculate the change in the money supply given the following Stop and Think Box URL ( in in , in 100 200 100 400 400 books 326

Explain Figure and , Figure , US . currency and checkable deposits , Figure . and , 1600 1400 Billions 400 200 . yew , 13 , Date MI Figure . URL books 327 as I , Dill Figure . currency and checkable deposits , If ?

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ea . ChI Figure . currency ratio , URL books 328 I ! 06 03 02 . a In Figure and , has increased because has increased , likely due to net open market purchases by the Fed . Apparently , has changed rather markedly since the early . US . the money multiplier has indeed dropped considerably since about 1995 . That could be caused by an increase in , or Figure currency and checkable deposits , shows that decreased primarily because increased . It also shows that the increase in was due largely to the stagnation in coupled with the continued growth of The stagnation in is likely due to the advent of sweep accounts . Figure US . currency ratio , 2007 isolates for closer study . KEY TAKEAWAYS The money are the same because they equate changes in the money supply to changes in the monetary base times some multiplier . The money differ because the simple multiplier is merely the reciprocal of the required reserve ratio , while the other account for cash and excess reserve . Therefore , and are always smaller than ( except in the rare case where and ER both ) AMS , where AMS change in the money supply the money multiplier change in the monetary base . A positive sign means an increase in the a negative sign means a decrease . URL books 329

The Money Multiplier LEARNING OBJECTIVES . Why is the multiplier almost always larger than the multiplier ?

Why are the required reserve ratio , the excess reserve ratio , and the currency ratio in the denominator of the , and money ?

Why are the currency , time deposit , and money market mutual fund ratios in the numerator of the money multiplier ?

Note that , is the money multiplier . With a little bit more work , one can also calculate the money multiplier ( Recall from Chapter Money that , where time and savings deposits and money market funds , money market deposit accounts , and overnight loans . We account for the extra types of deposits in the same way as we accounted for currency and excess reserves , by expressing them as ratios against checkable deposits ( time deposit ratio ( money market ratio which leads to the following equation ( ER ) Once you calculate , multiply it by the change in to calculate the change in the , in , just as you did in Exercise . Notice that the denominator of the ma equation is the same as the In , equation but that we have added the time and money market ratios to the numerator . So is always , which makes sense when you recall is composed plus other forms of money . To verify this , recall that we calculated In , as when Required reserves ( Currency in circulation 100 million Deposits 400 million URL books 330

Excess reserves 10 million We now add time deposits of 900 million and money market funds of 800 million and calculate ( ER ) 100 ) 400 ) 400 ) This is quite a bit higher than because time deposits and money market funds are not subject to reserve requirements , so they can expand more than checkable deposits because there is less drag on them during the multiple expansion process . Practice calculating the money multiplier on your own in the exercise . EXERCISE . Calculate the money multiplier using the following formula ( Excess ' or ( Deposits 100 100 10 100 100 10 100 10 100 100 10 100 10 100 10 100 50 100 50 100 100 10 KEY TAKEAWAYS Because is part of , is always ( except in the rare case where time deposits and money market funds , in which case ) URL books 331

That fact is reflected in the inclusion of the time deposit and money market fund ratios in the numerator of the multiplier equation . Moreover , no reserves are required for time and money market funds , so they will have more multiple expansion than checkable deposits will . The required reserve ratio , the excess reserve ratio , and the currency ratio appear in the denominator of the , and money because all three slow the multiple deposit creation process . The higher the reserve ratios ( required and excess ) the smaller the sum available to make loans from a given deposit . The more cash , the smaller the deposit . The currency , time deposit , and money market mutual fund ratios are in the numerator of the money multiplier because is composed of currency , checkable deposits , time deposits , and money market mutual funds . would equal and , which is highly unlikely . Note iff means if and only if . URL books 332

Summary and Explanation LEARNING OBJECTIVE . How do central banks , banks , depositors , and borrowers influence the money supply ?

By way of summary , Figure Major on explains why each of the major variables , and nu in the ways implied by the equations presented above . Figure Major on and As we saw in Chapter 14 The Money Supply Process , currency holdings , excess reserves , and required reserves slow down the multiple deposit creation process by removing funds from it . The bigger and are , the less each bank lends of the new deposits it receives . The bigger is , the less money is deposited in the place . For those reasons , we place those variables in the denominator . The larger the denominator , holding the numerator constant , the smaller , or will be , of course . The appropriate money supply components compose the , and checkable deposits for , and currency , checkable deposits , time deposits , and money market mutual funds compose the numerator for . This leaves us to consider why , and change over time . Short term , the currency ratio varies directly with the interest rate and the stability of the banking system . As the interest rate increases , the opportunity cost of keeping cash increases , so people are less anxious to hold it . People URL books 333

are also less anxious to hold currency if the banking system is stable because their money is safer in a checking deposit . If interest rates are extremely low or people believe the banks might be shaky , they naturally want to hold more physical cash . Longer term , may be by technology and loophole mining , encouraging bankers and depositors to eschew traditional checkable deposits in favor of sweep accounts . The required reserve ratio is mandated by the central bank but , as noted 10 Innovation and Structure in Banking and Finance , loophole mining and technology have rendered it less important in recent years because sweep accounts allow banks to minimize the de jure level of their checkable many places , is no longer a binding constraint on banks so , as well see , most central banks no longer consider changing it as an monetary policy tool . This in no way affects the money multiplier , which would provide the same figure for , or whether we calculate them as above or replace and with , where total reserves . Stop and Think Box Prove the assertion made above This in no way affects the money multiplier , which would provide the same for In . or whether we calculate them as above or replace and with , where total Suppose that 100 , 200 , and 500 and that is composed of required reserves of 100 and excess reserves of 100 . That means that must equal ( 500 ) Under the formula provided in the text , Under the formula suggested above , Excess reserves ( or just reserves in a system without required reserves ) are inversely related to the interest rate . In the early and early , when the interest rate was well less than percent , was high , at to . In the and , when interest rates were 10 percent and URL books 334

higher , dropped to to . As we learned in Chapter Bank Management , expected deposit directly excess reserve levels as banks stock up on reserves to meet the . When uncertainty is high or a banking crisis is in progress or appears imminent , bankers will increase ER to protect their banks . In summary , the central bank the money supply by controlling the monetary base and , to a far lesser extent , the required reserve ratio . Depositors , banks , and borrowers the money supply by and , specifically by determining the money multiplier , with depositors largely in control of depositors and banks interacting via deposit expectations to determine and borrowers , depositors , banks , and the central bank interacting to determine interest rates and hence to some extent both and . KEY TAKEAWAYS Central banks control and , and affect interest rates , which in turn affect and . Depositors determine by deciding how much cash versus deposits to hold . They also influence interest rates . Banks influence interest rates and determine by deciding how many excess reserves to hold in the face of expected deposit and interest rates . Borrowers influence the interest rate and hence to some extent and . URL books 335

Suggested Reading , George . The Money Supply Process A Comparative Analysis . New York , 1999 . URL books 336