Download Chapter 11: Modeling Money

Chapter Eleven
Modeling Money
Why Do We Need a Model?
• To show how the functions of money
affect the demand for money
• To learn how money interacts with other
variable in the economy, such as income,
prices, and interest rates
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The ATM Model of Demand for Cash
• How do we decide how often to go to the
ATM?
– The costs (both in time and money) of using the
ATM increase as we go more often
– The amount we want to spend
– The risk of loss or theft
– Opportunity of holding cash in lieu of earning
money in the bank (dependent upon nominal
interest rates)
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The ATM Model (cont’d)
• ATM visits often follow a saw-tooth pattern
• Cash balances decline as Tracy nears a visit
to the ATM
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The ATM Model (cont’d)
• Tracy needs to minimize her total cost of holding cash
• Her average cash balance over time is considered to
represent her demand for money
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The ATM Model (cont’d)
• Tracy’s ATM visits can be affected by a number of factors
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Weaknesses of the ATM Model
• The variables above only apply to a single person
• Building a more complete model necessitates the
consideration of exogenous and endogenous variables
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Exogenous & Endogenous Variables
• Exogenous variables occur outside a model
– In the ATM model, four variable are exogenous
•
•
•
•
Nominal interest rate
Tracy’s daily spending
Costs of a visit to the ATM
Possibility of loss or theft
• Endogenous variables are determined within
the model itself
– In the ATM model, three variable are exogenous
• Number of days between visits to the ATM
• Amount withdrawn at each visit
• Average cash balances
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Model Conclusions
• General-equilibrium models are ones in which
all variables are endogenous
• Partial-equilibrium models are ones in which
at least some variables are exogenous
– The ATM model is a partial-equilibrium model
• Economists generally prefer to work with
general-equilibrium models because they are
more broadly applicable and believable
• Partial-equilibrium models, however, are often
useful building blocks for general-equilibrium
models
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The Liquidity Preference Model
• The liquidity-preference model illustrates how
money demand and supply determine the
nominal interest rate
• The model assumes that people choose between
either holding cash (a preference for liquidity) or
investing it at the nominal interest rate
• The model assumes a fixed money supply, as
controlled by the Fed
• In general, people will prefer to invest more
money when the nominal interest rate (the price
of money) is higher
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The Liquidity Preference Model (cont’d)
• The slope of the
demand curve
depends on how
sensitive demand is
to the level of i. The
location of the
demand curve
depends on other
variables, such as
incomes
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The Liquidity Preference Model (cont’d)
• The equilibrium point represents the nominal
interest rate I
• What happens when the nominal interest rate
is above equilibrium?
– The quantity of money demanded would be less
than the quantity of money supplied
– Because rates are higher, people would use their
income to invest (buy bonds) instead of holding
cash, thereby raising the price of bonds
– A rise in the price of bonds implies a fall in the
nominal interest rate
– This process would continue until equilibrium was
restored
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The Liquidity Preference Model (cont’d)
• The liquidity-preference model is still not a generalequilibrium model because the prices of goods and
services, the money supply, and people’s incomes
remain exogenous
• The endogenous variables are the quantity of money
demanded, the nominal interest rate, the equilibrium
quantity of money, and people’s spending
• The model can be used to illustrate how changes in
the exogenous variables affect the endogenous
variables
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The Liquidity Preference Model (cont’d)
• When the money supply (exogenous) increases,
the nominal interest rate (endogenous) declines
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The Liquidity Effect
• This model demonstrates the liquidity effect,
the inverse relationship between the money
supply and the nominal interest rate
• This is widely believed to be the primary
short-run effect of expansionary monetary
policy
• This also correlates to business cycles- when
people’s incomes rise and/or as the prices of
goods and services increase, they increase
their demand for money, and vice versa
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Income and the Liquidity Effect
• As people’s incomes rise and the money supply is held
constant, upward pressure is brought to bear on nominal
interest rates
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The Price Level and the Liquidity Effect
• The demand for money is proportional to the price
level
• Prices can also be considered in terms of real
money demand, which shows that demand for
money is dependent on income and the nominal
interest rate
M / P  m(Y , i)
D
• As the real money demand function is not affected
by changes in the money supply or the price level, it
is helpful for analyzing the demand for money over
time
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The Dynamic Model of Money
• The liquidity-preference model is a static
model, or one which does not allow for
changes in variables over time
• A dynamic model does allow for such changes
• Time is important to include in a model of
money because, like financial investments,
money can also serve as a store of value
• Further, both the inflation rate and the nominal
interest rate are both dependent on time
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The Dynamic Model of Money (cont’d)
• The dynamic model of money starts with the
economy in a steady state, or long-run
equilibrium
• This enables us to describe what the
endogenous variables will do if not disturbed.
• Shocks can affect variables in both the shortand long-run
• The dynamic model is interested in how these
shocks affect the model
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Effects of an
Increase in
the Money Supply
• The economy is in a
static state until time 1,
when the Fed increases
the money supply,
causing nominal
interest rates to decline,
and incomes and the
price level to rise
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Price Level & Income Effects
• The increase in the money supply causes a
decline in interest rates, causing a subsequent
increase in the demand for money
• This situation is described by the price-level
effect, as an increase in the price level
increases the demand for money
• Increases in income also raise the demand for
money, pushing up nominal interest rates, also
known as the income effect
• Both effects move interest rates in the
opposite direction as the liquidity effect, which
dominated at first (between time 1 and time 2)
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Effects of an Increase in the Growth Rate
of the Money Supply
• The economy is in a static state until time 1, when the
Fed increases the money supply, causing nominal
interest rates to decline, and incomes and the price
level to rise
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Effects of a Well-Anticipated Increase in
the Growth Rate of the Money Supply
• When people expect inflation to rise quickly, the nominal
interest rate is also likely to rise quickly, possibly
eradicating the liquidity effect
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Using Money Models in Practice
• The Fed must know how much money people want to
hold so that it can supply the appropriate amount
• A problem with money models is that in fact there is
more than one kind of money; economists do not
necessarily know which one a model specifies
– They may use a measure of money most closely related to
the theoretical model
– They may make the model more complicated so that it
matches actual data more closely
• It is easier to account for changes over time by using
logarithms of demand for money and income
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