Chapter 16 Determinants of the Money Supply. Copyright © 2002 Pearson Education Canada Inc. 16- 2 The Simple Deposit Multiplier (from Chapter 15) Simple

chapter 16

Determinants of the Money Supply

Copyright © 2002 Pearson Education Canada Inc. 16- 2

The Simple Deposit Multiplier (from Chapter 15)

Simple Deposit Multiplier

1D = R

rD

Deriving the formula

R = DR = rD D

1D = R

rD

1D = R

rD


Critique of the Simple Model

The simple model of multiple deposit creation shows how the Bank of Canada can control D by setting R. That simple model however, ignores

1. the public’s decisions regarding how much C to hold,

2. the banks’ decisions regarding the amount of R they wish to hold, and

3. borrowers’ decisions on how much to borrow from banks.

Recall also that the Bank of Canada can exert more precise control over MB ( = C + R) than over R.


The Money Supply Model

Because the Bank of Canada can exert more precise control over MB than it can over R, in Chapter 16 we derive a multiplicative relation between M and MB,

M = m MB,

where m is the money multiplier.

m relates the change in M to a given change in MB.


M = m MB

Deriving Money Multiplier

R = DR

DR = rD D

R = (rD D)

Adding C to both sides

R + C = MB = C + (rD D)

1. Tells us amount of MB needed support D and C

2. An extra $1 of MB that arises from an extra $1 of C does not support any additional D. That is, the C component of MB does not lead to a multiple deposit creation as the R component does.

Money Multiplier


To put it differently,

An in MB that goes into C is not multiplied, whereas an that goes into supporting deposits is multiplied.

We have

MB = C + (rD D)To deal with currency drains, we also assume thatC = c Dwhere c is the currency ratio. Hence,

MB = (c D) + (rD D)

= (c + rD ) D

Money Multiplier (continued)


M = (c D) + D = (1 + c) D

m < 1/rD because no multiple expansion for currency and because as D ER

MBrc

DD

1

MBrc

cM

D

1

Drc

cm

1


rD = 5%C = $40 billionD = $160 billionM (= M1+) = C + D = $200 billion

The money multiplier tells us that, given the behaviour of the public as represented by c = 0.25 and that of banks as represented by rD = 5%, a $1 in MB will lead to a $4.2 in M.

If c = 0 (no currency drains), then m = 20.

An Example

2.405.025.0

25.01

m


Also notice that

This is the deposit multiplier when

c = 25% and rD = 5%.

It tells us that, given the behaviour of the public as represented by c = 25% and that of banks as represented by rD = 5%, a $1 in MB will lead to a $3.3 in D.

An Example (continued)

3.305.025.0

1


So far we have been assuming that the Bank has complete control over MB. This is not the case. The Bank lacks complete control over MB because it cannot unilaterally determine the amount of borrowing by banks from the Bank.

Here we split MB into two components:

• nonborrowed monetary base (MBn). This component of the MB is directly under the Bank’s control because it results from open market operations.

• borrowed monetary base (or advances A). This is the less tightly controlled component of the base, because it is influenced by banks’ decisions.

The Full Model


Hence,

MB = MBn + A

To complete the money supply model, we rewrite it as

M = m MB = m (MBn + A)

where m is defined as before.

Thus, in addition to the effects on M of c and rD , the expanded model stipulates that M is also affected by changes in MBn and A. In fact, because m > 0, there is a positive relation between M and each of MBn and A.

The Full Model (continued)


M = m (MBn + A)

Open market purchases MBn and for given c, rD , and A lead to an in M. Open market sales MBn and for given c, rD , and A lead to a in M. Hence M is positively related to MBn.

For given MBn , c, and rD , an in A will MB and lead to a multiple in M. For given MBn , c, and rD , an in A will MB and lead to a multiple in M. Hence M is positively related to A.

Overview of the Money Supply Process

)(1

AMBrc

cM n

D


Factors Determining Money Supply


M2+ Money Supply Model

M2+ = C + D + T + MMF

C = currency in circulation, D = all chequable deposits,T = all time and savings deposits, andMMF = money market mutual funds.

Assume that C = c D, T = t D, and MMF = f D. Hence M2+ = (c D) + D + (t D) + (f D)

where c is the currency ratio, t is the time deposit ratio, and f is the money market fund ratio.


M2+ Money Multiplier

M2+ = (c D) + D + (t D) + (f D)

= (1 + c + t + f ) D

Recall that

MBrc

ftc

D

12M

Drc

ftcm

1

MBrc

DD

1


rD = 5%C = $40 billionD = $160 billionT = $320 billionMMF = $80 billion

M2+ = C + D + T + MMF = $600 billion, c = 0.25, t = 2, f = 0.5.

The money multiplier tells us that, given the behaviour of the public as represented by c = 0.25, t = 2, and f = 0.5 and that of banks as represented by rD = 5%, a $1 in MB will lead to a $12.5 in M2+ .

An Example

5.1205.025.0

5.0225.01

m


Factors Determining M2+


Let’s use the money supply model to explain the collapse in the U.S. during the Great Depression, 1930-1933.

Between October 1930 and March 1933 there were a number of bank failures in the U.S. For example, in the first bank crisis (from October 1930 to January 1931), 256 banks failed in November 1930 with $180 million of deposits, and another 532 banks failed in December 1930 with over $370 million of deposits.

The most dramatic failure was that of the Bank of the United States (with over $200 million in deposits), which many people associated with a central bank.

Application: The Great Depression Bank Panics


Deposits at Failed Banks: 1929–33

Figure 16-1


Because there was no deposit insurance (the FDIC wasn’t established until 1934), worries about bank solvency caused people to hold more money in the form of C rather than D and T, and banks to hold more deposits in the from of ER rather than loans.

These actions reduced the amount of bank lending, and although MB continued to grow, the quantity of money as measured by broader monetary aggregates plunged. For example, M1 by 25% from 1929 to 1933 (the largest in all of U.S. history).

As a result, real GDP by 27% and u to 25% in 1933.

The Great Depression Bank Panics (continued)


ER/D, C: 1929–33


Money Supply and Monetary Base: 1929–33

Figure 16-3


The Great Depression Bank Panics (continued)

If the Fed had been committed to stable growth in M rather than MB, it would have pursued a more expansionary monetary policy than it did, and perhaps the collapse in the Great Depression would have been avoided!

Documents

Chapter 16 Determinants of the Money Supply. Copyright © 2002 Pearson Education Canada Inc. 16- 2 The Simple Deposit Multiplier (from Chapter 15) Simple