MoneyModel SL

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Monetary Model

Econ302, Fall 2004

Professor Lutz Hendricks, August 19, 2004

1 What this chapter is about

Add money to the intertemporal model.

Then we study:

the eects of monetary policy,

business cycles.

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2.1 Measures of Money

The following is a list of commonly used "monetary ag-gregates:"

CurrencyM0 + Bank reserves held with the Fed

M1 + Checkable deposits

+ Money market accountsM2 + Money market mutual funds

M3 + Certain liquid assets held by institutional investors

M0 is also called base money, high powered money, out-

side money.

M0 is directly controlled by the Fed.

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2.2 Real and Nominal Interest Rates

Real interest rate: giving up one unit of C today yields(1 + r) units ofC0.

Nominal interest rate: giving up one unit of money today

yields (1 + R) units tomorrow.

Both are related through the Fischer equation:

1 + R= (1 + r) (1 + i) (1)

where i= P0PP is the rate of ination.

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Why is this true?

Give up one unit ofC today and invest P units of

money.

Tomorrow, receive P(1 + R) units of money.

Purchase P(1 + R) =P0 units ofC0.

The real rate of return is:

1 + r =C0

C =

P (1 + R) =P0

1 =

1 + R

1 + i

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Approximate Fischer equation: For small i and r:

Real interest rate = nominal interest rate - ination rate

r=R i (2)

Example of a good approximation:

R= 0:06; i= 0:02. Exact:

1 + r=1:06

1:02= 1:039 (3)

Approximate:

r= 0:060:02 = 0:04 (4)

Example of a poor approximation:

R= 0:20; i= 0:16.

Exact:1 + r=

1:20

1:16= 1:034 (5)

Approximate:

r= 0:200:16 = 0:04

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3 Model Structure

Start with the real model of the previous chapter.

Add the requirement that all purchases must be paid for

using money.

The initial stock of money is given and held by the house-hold.

The government injects new money by purchasing goods

in the market or by paying bond interest.

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4 The Timing

With the period, this is the sequence of events:

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4.1 The Household

The household enters the period holding:

Bonds B which pay nominal interest R.

Money M.

The household chooses C; l; Bd; Md to maximize utility

max U(C; l)

subject to

a budget constraint a cash-in-advance (CIA) constraint.

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4.1.2 Cash-in-advance constraint

The reason for holding money in this economy is thatpurchases must be paid with money.

At the beginning of the period, the household holds bondsB

and money

M

.

He receives additional money from the government: R B.

Some money is spent on buying bonds: Bd.

When the credit market closes, the household holds

M =M +

1 + R

B Bd (7)

The CIA constraint species that consumption and tax

payments require money:P C+ P T M

= M +

1 + R

B Bd

The CIA constraint binds, if the nominal interest rate is

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4.1.3 Money demand

What are determinants of money demand?

Lifetime wealth, because it aects consumption.

The nominal interest rate: the opportunity cost of

holding money.

For simplicity we assume:

Md =P L(Y+

; R

)

This is not exactly right! Other factors that should matter

include:

Future income (!C).

Taxes (current and future).

The real interest rate (r !C).

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5 Government

The government combines the Treasury and the Fed.

Budget constraint

P G + (1 + R)B =P T+ B+ M M

Enter the period with outstanding liabilities M + B.

Expenditures G and bond repayment

1 + R

B.

Revenues:

Taxes: P T.

New bonds issued: B.

New money issued: M M.

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6 Equilibrium

We simply add the money market to the Real Model stud-ied earlier.

Note: This is again not exactly right. For example:

changes in monetary variables should aect consumption

and leisure choice.


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6.1 Money market

Money supply is directly controlled by the government(M).

Money market clearing:

M =P L (Y; R) (8)

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6.2 The Complete Model

We simply added money market clearing to the equilib-rium conditions for the real model.

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7 Productivity Shocks

What are the eects of a temporary decline in z?

The real eects are the same as in the real model:

Labor demand declines b/c M PN is lower. Labor supply increases (not by much; lets neglect

that).

Output drops for given inputs.

Result: Y # and r ".

Stagation: A bad productivity shocks causes a reces-sion combined with ination.

Example: 1973 oil price shock.

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8 Monetary Neutrality

What are the eects of monetary policy?

The experiment: Holding M unchanged, the gov-

ernment increases M in the current period.

Assume that the new money is simply given to the house-holds (helicopter drops).

Result: Money is neutral.

This means: a one-time increase in M does not aect

the equilibrium allocation (here: C; l; N; Y ).

How do we see that money is neutral?

Monetary variables do not appear in the labor orgoods market clearing conditions.

The model has a classical dichotomy: monetary

variables do not aect real variables.

Monly aects the money market.

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8.1 Eect ofM on the money market

Money demand remains unchanged: Y and r are deter-

mined in the labor and goods markets.

Money demand is linear in the price (real money demand

is independent ofP).

If(Y; r)remain unchanged, anx%increase inM causes

an x% increase in P.

Real money balances (M=P) are unchanged.

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8.2 Why is money neutral?

An experiment:

On a xed date, the government hands out 100 New

Dollars for every Dollar held by any person.

This is perfectly anticipated by all.

Could there be real eects?

No this amounts to using cents instead of dollars to

denote prices.

Sensible models have the property that changing the unitsin which money is denominated has no real eects.

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8.3 Why might money not be neutral in

practice?

The change in M may not be fully anticipated. If some

contracts are written in nominal terms, they cannot adjust

to ination.

Money is not distributed by helicopter drops.

In practice the Fed uses open market operations:

it buys bonds using the new money (B).

The Treasury can use new money to purchase goods

(G).

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8.3.1 Is money neutral in practice?

The answer depends in large part on whether a monetarychange was anticipated.

Example 1 Famous dis-ination episodes.

Tightening the money supply usually reduces aggre-gate demand.

But there are famous counter-examples: Germany af-

ter WW2.

Example 2 The Fed changes the Federal Funds Rate (itsway of manipulating $M$).

Typically the stock market falls.

But sometimes there is no reaction the change was

anticipated.

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A key insight of monetary economics:

Monetary policy changes have real eects, but only tothe extent that they come as surprises.

This raises many policy issues:

Should the Fed follow monetary policyrulesto makeits actions predictable? Or should it use discretion

to be able to manipulate real variables?

Is the Fed responsible for business cycles? Or does

the Fed help stabilize the economy?

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9 Lucas Money Suprise Model

An illustration of how monetary policy can have real ef-fects, if private agents do not anticipate Fed policy.

We use the Monetary Model with one modication:

Households do not observe M; P; w; z in the currentperiod.

The idea:

Households cannot distinguish real shocks (z) from

monetary shocks (M).

When anMshock occurs, households mistake it for

a z shock and respond by changing labor supply.

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9.1 Eect of an M shock

With complete information: M expansion only causesination P " and nominal wages rise (W =wP).

Households observe higher W, but do not know whether

this is due to a z shock or an M shock.

If it is a z shock, then w has gone up and household

should work more: Ns ".

Therefore: Ys curve shifts out.

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9.2 Second round eects ofM "

C increases due to lower r and higher Y.

I increases due to lower r.

Money demand increases due to lower r and higher Y.

Ms also rises. Therefore (?) P ".

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9.3 Policy Implications

Money is not neutral.

Monetary policy can be used asstabilization policy.

Monetary policy only works, if it can surprise the private

sector.

This is a typical feature of models where money is

not neutral.

Consistently surprising the private sector is hard to

do!

Monetary policy itself can be a source of instability.

It might be optimal for monetary policy to follow a xed

rule.

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