There is an inverse relationship between the required reserve ratio and the money supply.

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Economics 330

Spring 2002

Lecture 11

Multiple Deposit Creation

Let�s look at the distinction between required reserves and excess reserves:

Consider some examples:

Consider a situation where the required reserve ratio is 10% of checkable deposits

Initial situation:

Now, suppose the Fed makes an open market purchase of $10:� what happens to the bank�s t-account?

Let�s follow the adjustments as they work their way through the banking system:

If we look at what has happened here we find that there is a relationship between the change in the demand deposits and the change in reserves introduced by the Fed into the banking system.� Let�s consider that relationship in general terms:

In our last example,

To recap, when the Fed makes an open market purchase of $10 the monetary base changes by $10 (in other words, the high powered money in the banking system increases by $10) and then through the money multiplier this causes a series of adjustments so that the final total change in deposits is equal to the money multiplier times the change in reserves initially.� In this case, the money multiplier is 10 and the change in reserves initially is 10, so the total change in deposits from this open market purchase is equal to $100.

This simple model of multiple deposit creation ignores

�        Currency drains which can significantly alter the size of the money multiplier

�        Possibility that banks might choose to hold excess reserves

�        Fed behavior with regard to other policy tools other than open market operations

�        Bank behavior

�        Depositor behavior

We�ve been looking at the simple money multiplier, but the control of the money supply is more complicated than this model suggests.� It would be nice to build a model that incorporates

• The possibility of currency drains as a way to model depositor behavior
• The possibility of excess reserves as a way to model bank behavior

So, how do we do this?

Let�s start with looking at the Fed:� the Fed has greater control over the monetary base than it does over the level of reserves.� So, can we build a model that links the change in the monetary base to the change in the money supply?

One way to think about this link is to look at the connection between the change in the monetary base and the change in the money supply:

Money multiplier = the change in the money supply___

����������������������������������� The change in the monetary base

But, what is the money supply?

Let�s define the money supply as M1.� M1 can be written as

M1 = currency + checkable deposits

What�s missing from this definition of M1? Travelers checks:� a very small component of M1.

We could rearrange what we have as follows:

M = m(MB)

Where m =

����������� M =

����������� MB =

How does Fed control the monetary base?� The Fed can control the monetary base through

1.

2.

3.

We can think about the money multiplier being a function of the variables that affect the money multiplier:

Money multiplier = f(depositors� decisions about their holdings of currency and��������������� checkable deposits, the reserve requirements of the Fed, and banks� decisions about excess reserves)

Let�s look at the above statement a little more closely:� What are we trying to model with this statement?

To do something with this, we will need some simplifying assumptions:

1.� The desired level of currency, C, is assumed to grow proportionately with the level of checkable deposits, D.

2.� Excess reserves, ER, are assumed to grow proportionately with the level of checkable deposits, D.

So, this implies that

So, on to building our model:

We know

Reserves = required reserves and excess reserves

Note:� this is no longer assuming that the level of excess reserves is zero.

We can write this symbolically as

We also know

So,

We also know that the

MB = C + R

So,

Let�s consider this equation:� it tells us the amount of the monetary base we need in order to support the existing amount of checkable deposits, currency and excess reserves.

A closer examination of this equation reveals that

• Any increase in the monetary base that goes into currency or excess reserves does not get multiplier or expanded
• Any increase in the monetary base that goes into checkable deposits does get multiplied and therefore altered in its impact

Let�s consider this equation again:

This equation could be altered by noting that

So,

Rewriting this as

At this point it might be helpful to remember the goal:� recall that initially there was a relationship posited between the money supply as measured by M1 and the level of checkable deposits and currency in the banking system.�

Revisiting that relationship

Yet, we also know

So,

Recall that we are looking for a relationship that looks something like

M = m(MB)

And what our equation tells us is that the money multiplier, m, is a function of the currency to checkable deposit ratio, the excess reserves to checkable deposit ratio, and the required reserve ratio.

That is,

Which of the above symbols represent a constant?

We find that the money multiplier is therefore a constant.

Thinking about this multiplier we can note that

• It models the Fed, banks, and depositor behavior:� this is a more complicated money multiplier model than our original model
• This money multiplier has a smaller value than the original simple model because it allows for currency drains and excess reserves

Let�s consider what happens to the money multiplier when one of the following variables is allowed to change while holding the other variables constant (this is the familiar ceteris paribus assumption of economics)

• A change in the required reserve ratio
• A change in the currency to checkable deposit ratio
• A change in the excess reserve to checkable deposit ratio

1.� A change in the required reserve ratio:

A change in the required reserve ratio changes the level of checkable deposits a given level of reserves can support

If the required reserve ratio increases, holding everything else constant:

If the required reserve ratio decreases, holding everything else constant:

So, the relationship between the money multiplier, the money supply and the required reserve ratio can be summarized as follows:

An increase in the required reserve ratio, holding everything else constant, makes the denominator of the money multiplier bigger and therefore the money multiplier gets smaller.

A decrease in the required reserve ratio, holding everything else constant, makes the denominator of the money multiplier smaller and therefore the money multiplier gets larger.

2.� A change in the currency to checkable deposit ratio

When the currency to checkable deposit ratio increases this implies that depositors are converting some of their checkable deposits into currency and this implies that less multiple expansion occurs

The money multiplier and therefore the Money Supply are inversely related to the currency to checkable deposit ratio.

3.� A change in the excess reserve to checkable deposit ratio

An increase in the excess reserve to checkable deposit ratio means that the banking system is effectively using more of its reserves to support a given level of checkable deposits. In other words, when the bank chooses to hold excess reserves it will reduce the number of loans that it can make for a given level of checkable deposits.

The money multiplier and the Money Supply are inversely related to the excess reserve to checkable deposit ratio.

What determines the excess reserve to checkable deposit ratio?

1.      The market interest rate

2.      Expected deposit outflows

Let�s consider each of these in turn:

a.� The market interest rate

What happens to the opportunity cost of holding excess reserves with changes in the interest rate?

Thus, the interest rate and the excess reserves to checkable deposit ratio are inversely related to each other.

b.� Expected deposit outflows

The excess reserve to checkable deposit ratio is positively related to expected deposit outflows.

Intuition:

Our model is not quite complete!� Let�s turn our attention to discount loans and build them into the money multiplier model we are creating.

What do we know?

• First, a discount loan is a loan from the Fed to a bank and the discount rate is the interest rate that the Fed charges the bank for the loan.
• The Fed cannot predict the amount of borrowing banks will want to do from the Fed and so the Fed can only set the discount rate

Consider the monetary base again:

The monetary base could be broken into two distinct parts:

1.� The part controlled by the Fed

2. The part less tightly controlled by the Fed

This idea can be written as

Thus, the nonborrowed monetary base is under the Fed�s control primarily through open market operations.

Let�s add this new component to our model of the money multiplier process:

So, the money supply is a function of

�        The required reserve ratio

�        The currency to checkable deposit ratio

�        The excess reserve to checkable deposit ratio

�        The nonborrowed monetary base

�        The level of discount loans

What determines the level of discount loans?

1.� The market interest rate

�As the market interest rate rises holding everything else constant, the level of discount loans increases since it is relatively cheaper to borrow from the Fed.

2.� The discount rate

As the discount rate increases holding everything else constant, the level of discount loans decreases since it is relatively more expensive to borrow from the Fed.

3.� The spread between the market interest rate and the discount rate:

As the spread increases holding everything else constant, the level of discount loans increases.

So, summarizing our money multiplier model we have

Let�s consider a numerical example:

Suppose that

The required reserve ratio = .10

Currency = $1000 B

Checkable Deposits = $ 1500 B

Excess Reserves = 0

M1 = $2500 B

Calculate the currency to checkable deposit ratio and the money multiplier:

Interpretation of the money multiplier:� for a given value of the money multiplier, an increase in the monetary base will lead to an increase in the money supply equal to the product of the money multiplier times the change in the monetary base. (This assumes that everything else is held constant.)

What happens to the money multiplier if excess reserves equal $500 B?

An increase in the excess reserve level reduces the size of the money multiplier:� there is an inverse relationship between the level of excess reserves and the money multiplier.

Suppose that the required reserve ratio increased to .2, what happens to the money multiplier?� We know

The required reserve ratio = .2

Currency = $ 1000 B

Checkable Deposits = $1500 B

Excess Reserves = $500 B

Money Supply = $2500 B

As the required reserve ratio increases holding everything else constant, the money multiplier decreases:� there is an inverse relationship between these two variables.

We can summarize our findings in a table:

����������� �

Historical perspective:� Money Supply Movements from 1980 to 1996

Question:� does our model of the money supply process help us understand movements of the money supply?

In the period 1980 to 1996 we see high variability in the money supply growth rate:

How is this variability explained?� The model we have worked on suggests that there is a relationship between the money supply and the monetary base.

So, the variability in the money supply growth rate has two potential sources:

1.      the money multiplier or

2.      changes in the monetary base (the nonborrowed monetary base and/or the level of discount loans)

So, during this period what is the money multiplier doing and what is happening to the monetary base?

Observations:

�        Over the entire period, the average growth rate of the money supply is fairly well explained by the average growth rate of the nonborrowed monetary base

�        Discount loans are not much of a player with regard to the growth rate of the money supply EXCEPT in 1984.� What happened then?� The Fed increased the level of discount loans dramatically to bail out Continental Illinois National Bank. (see graph)

***Over long periods of time, the primary determinant of movements in the money supply is the nonborrowed monetary base.� The nonborrowed monetary base is controlled by the Fed through open market operations.

Empirical evidence suggests that 75% of the fluctuations in the money supply can be attributed to Fed Reserve Open Market Operations which determine the nonborrowed monetary base.

What about in the short run?

The money multiplier fluctuates a lot in the short run�what lies behind this?

The currency to checkable deposit ratio fluctuates a lot in the short run and this causes the money multiplier to fluctuate

Let�s turn our attention to the historical period from 1930-1933:� the Great Depression

• Lots of bank panics

• Bank panics imply a reduction in the money supply

• What happened to the currency to checkable deposit ratio in the period (see graph)

• What happened to the excess reserve to checkable deposit ratio in the period (see graph)

• What was the effect on the money supply? (see graph)

• The money supply during the Great Depression fell by over 25% despite a 20% increase in the level of the monetary base
• This underlines the importance of the currency to checkable deposit ratio and the excess reserve to checkable deposit ratio during bank panics
• It also underlines how the Fed�s job of conducting monetary policy is complicated by depositor and bank behavior

What is the relationship between reserve ratio and money supply?

What is the inverse of the required reserve ratio?

What is the relationship between the reserve ratio and the money multiplier inverse or direct?

What happens to money supply when required reserve ratio increases?