Monetary Economics - Appunti completi

AS

in the expected inflation.

So, we see that the dynamics under an announced shock is just a jump (there is no path). 61

Surprise (Non Announced) Expansionary Monetary Policy

Whereas, if we have surprise ( Note that you are not surprising people if you change the money supply

).

growth rate by this year, next year, in two years and so on

2% 2% 2%

Suppose that this change is made every 3 months (like the decision of the FED). Maybe in 2

quarters economic agents learn that the Central Bank will increase the Money Supply growth rate

by (that is the new rule), so is not a surprise in a couple of quarters. And, even if the money

2%

growth rate is increased by this quarter, next quarter, ... then, once again this is a

1% 2% 3%

pattern, and this pattern can be recognised by people, can be learned and incorporated in

expectations, so there will be no surprise; in a short while this pattern will be discovered and there

will be no surprise.

So, a “surprise” is if the Central Bank decides the money growth rate randomly (so you draw your

balls and decide the money growth rate as and then and then and then

−10%, +5%, 0% +10%

just random). But we will not rely on a Central Bank which is drawing its decision from random

choice (this is not a policy).

Indeed, if you use such a surprise rule, the only result we have is just to increase the Variance of

output: output fluctuates from to to … and the Variance of it will just go up, so we are

+ − =

going to add instability to the economy instead of stabilizing the economy.

An increase in “surprises”, i.e. a more active monetary policy, adds to the instability of GDP:

ã^ ã^

^ ^

where , and are the variances of shocks. Only might be under the control of the CB.

ä ä

å æ

ã^

By increasing , would also increase and output would be de-stabilised.

Var

"

The foreseen component of monetary policy is entirely effective on prices:

that after substituting from

(15):

Even without surprise, determines Monetary policy should exclusively be targeted to price

· .

stability.

The result of this is something which is, in a sense, not surprising, but quite interesting.

The question we should ask after this is: Why should the Central Bank attempt at destabilizing an

economy which is stable? Why should the Central Bank change its money supply rule if the

economy is stable?

But this is the consequence of the assumption that the economy is stable, so policy can just

destabilize it. The consequence of this is that the Central Bank should have just one target: Price

Stability. This because the money supply growth rule does affect inflation (surprise or not

surprise); output is not affected, except for a blip, if the monetary policy is not announced and

people are surprised. So, Monetary Policy is Output Neutral but is Not Inflation Neutral, it is

perfectly able to affect inflation; which also means that monetary policy should be used to take

inflation under check (and this is precisely the duty that the European treaty gives to the Central

62

Bank; so in a sense, the statue of ECB and European Treaty may be thought as written as under

this model: that is, that the Rational Expectations Monetarist Model of the 1980s was embodied in

the European Treaty, Maastricht Treaty of 1992, in which the duties of the ECB were set and the

ECB only pursue price stability, because that’s the only thing a Central Bank is able to do, if this

model is true). 63

implemented at zero costs, as agents would immediately revi

expectations downward. Inflation would jump downward and

gap would be created.

The Cost of Disinflation

Another consequence of the Rational Expectation assumption is that Disinflation may be costless if

people have Rational Expectations. ASL

Suppose that the initial inflation rate is π

too high, as in this case is . Suppose

~

that the Central Bank announces a

Contractionary Monetary Policy in order e0

AS ( )

π

to disinflate the economy (this is

something that, for instance, Paul e1

AS ( )

π

Volker, the President of FED did in π 0

1982; he said “the inflation rate post oil

shocks and oil crisis in the early 1980s is AD

π 0

too high and I want to bring it down to a 1

more healthy level” and he said “the AD 1

model tells me that this can be done y

y

without costs, that is that 0 L

unemployment will not increase and output will not go below its long run level. Therefore, if I

announce the change in the monetary policy (that is, I announce the disinflation target) people will

believe me and they will behave accordingly”).

Andrea Boitani () Money

I announce a lower money growth rate so the curve shifts down. People will believe that my

AD

new inflation target is lower ( ) and they will believe that money growth will be lowered

%

accordingly and they will change their expectations rationally downwards: that is, the will shift

AS

down and the economy will jump from the old steady state ( to the new steady state

, ),

* ~

( ) at no cost in terms of Unemployment or Output.

,

* %

The conclusion is,

«If expectations are rational, an announced disinflation programme may be implemented

at zero costs, as agents would immediately revise their price expectations downward.

Inflation would jump downward and no output gap would be created.».

Which, widely, means that,

«Under Rational Expectations the Central Bank may set the Inflation Target at whatever

level and achieve it without costs».

The Paul Volker experience was not entirely satisfactory because the unemployment rate went up and output

went down (a negative output gap turned up). The explanations for that are two:

1. Rational Expectations are wrong. People don’t have Rational Expectations

2. People didn’t believe that Paul Volker did actually implement the contractionary policy (so they didn’t

believe that was the new target. So, the actual money growth rate was different from the one they

%

expected, because they expected a money growth rate which was higher than the actual money growth

rate Paul Volker implemented; so, there were some real effects. If the curve doesn’t shift down as

AS

much as is needed in order to jump to the new steady state you will have some real effect (that is, the

new and the new will cross at a point at which ). This argument has been a sort of a basis

AD AS <

*

of debate that took place in the early 80s and still takes place about “Credibility”: how and why people

do actually believe what the Central Bank announces. 64

2. Hyperinflation and staggered contracts

C ’ M

AGAN S ODEL

We shall look at a model of Cagan, which was in the proposed in the 1950s. in the 1950s it was

analysed with Adaptive Expectations, but then has been gone through once again in 1970s and

1980s with the Rational Expectations hypothesis.

So, we shall compare the results that can be achieved by the use of both these Expectations

assumptions.

Hyperinflation is something that takes place in a sort of short period of time, even if it can last for

couple of years, and what we mean by saying that it takes place in a short period of time is that

inflation can be very high by today, and in episodes of hyperinflation the most famous was the one

of German Hyperinflation in early 1920s, when prices went up by or per day. So, this

100% 200%

very fast burning of inflation is the reason why models of Hyperinflation assume that output is

given, because output doesn’t change day by day. So, these models are, in a sense, a simplification

of the standard because Output is fixed; only Prices do change day by day. And

AS – AD Model

now when we talk about and they are now meant to be days or weeks (and no

period 1 period 2,

more quarters or years); so that means that the time span of a period is very very short.

So, Output is given in this framework and only prices do change. We shall talk about the Money

Caganís model

Demand Function, and looking at episodes of Hyperinflation, we shall first of all for specify that

most of this lecture talk about deterministic environment, and therefore when we are going to

talk about Rational Expectations, we are referring to perfect foresight, which is just a way we

make things simple. So, we shall look at a deterministic demand function, and we shall see this

In episodes of hyperináation output and the interest rate may be

Money Demand Function is strictly dependent on Inflation, but not only on present inflation but

also future inflation.

regarded as constant.

Notice that, in episodes of hyperinflation output and the interest rate may be regarded as

constant.

The deterministic dynamic money demand function is:

Then the deterministic dynamic Money Demand function is:

et

! = ! ( ! )

p a p p

m̃ (1)

t t t

+ 1

Here what we have is that the term on the left is the real money demand ( ) put in growth

−

" "

log terms (i.e. it is the growth of real money that people want to have).

>

a 0. The higher is expected ináation the lower is current demand

We see that this depends negatively on the expected inflation rate, which is reasonable: as we

for money.

expect inflation is going to be higher tomorrow than it is today, you want less money because

money loses purchasing power over the day. So, the higher the inflation, the more you want to get

p

Solve (1) for to get:

t

rid of the money (money is not a good store of value, when you expect inflation to be higher by

the day, so you want to get rid of it). This is the reason why we have a negative sign here. So, the

a

1

higher is expected inflation the lower is current demand for money.

e

= +

p p

m̃ (2)

t t +

t 1

Whereas we have a positive sign for inflation ( ), because if inflation today is high, then you want

+ +

a a

1 1

"

to have more money, because in order to provide the same amount of goods, you need more

money.

so, the signs are correct.

> 0,

Andrea Boitani () Money March 2014 2 / 15

65

>

a 0. The higher is expected ináation the lower is current demand

for money.

p

Solve (1) for to get:

t

Solve equation for to get:

(1)

" a

1 et

= +

p p

m̃ (2)

t t + 1

+ +

a a

1 1

Here we determine inflation ( ) as a function of money growth rate ( ) and future expected

" "

"”

inflation ( ). So, in this simple model we have that inflation today depends on expected inflation

tomorrow, so that inflation today is higher the higher is the expected in