Monetary economics - Appunti completi (ENG)

Monetary economics – lecture notes

Whatever policy is based on targets and instruments. The targets and instruments of monetary policy are

different according to different theories (different combinations):

Targets

Instruments Inflation (to contain) Output (to maximize)

Money Monetarism I, II (flex price) IS-LM (fix price, no inflation)

Interest rate New standard approach (flex price) IS-IT (fix price, no inflation)

There are also other targets which are not accounted for in the matrix. In the past, the CB had also an

exchange rate target (when for instance we had a fixed exchange rate regime from the Bretton Woods

agreements in 1944, where the exchange rate between the Italian Lira and the USD was 624 liras for 1$ and

it was kept for over 20 years). Nowadays of course this target is no longer pursued within the Eurozone as

there are no more national currencies, and with respect of external countries we have a flexible exchange

rate between the Euro and other currencies. The Fed has a dual mandate: to control inflation and to reduce

output gap (difference between actual and potential level of output). The economy tends to stay at a level

of employment which is below full. To start refreshing things:

• For monetarism the only risk is inflation;

• In IS-LM: increasing the quantity of money has an effect on LM (increasing supply of money,

lowering interest rates to increase investments and demand so we move along IS). The CB can

increase directly investments (through its central rate paid and without touching money supply);

• The IS-IT is a different version of IS-LM where the instrument is the interest rate and not the

quantity of money.

Our main concern will be the new standard approach that is different because it’s derived from a fully

dynamic model. The IS-LM, IS-IT and monetarism were based on simple aggregated models. Monetarism II

insisted that macroeconomic models should be micro funded (built on optimizing behaviour of individuals).

This led to complicated models. Moreover, this should not be a static model (maximization of utility over an

infinite horizon). This leads to a general intertemporal equilibrium. This was predicated by monetarism II.

The origin of the new standard approach

The new standard approach was derived from DSGE model so it is quite complicated (in the books). We

should present a simplified version which is static. We are going to use the same (similar) model although

in the original literature there are different models.

Rules vs discretion

Should the monetary policy be implemented under discretion or under rules?

• Rules (public recipe): the supporters of rules say that the authority should write down the rules of

the policy (for example, first the target is announced, then say what will happen if the target is not

reached, etc.). If you have an independent CB, since the magnitude of its power, as a price for the

independence it must respect some rules;

• Discretion: the authority doesn’t have to explain and intervenes when it’s needed. For instance, the

authority can lower interest rate without telling it to the public which is the inflation/output target.

This distinction is more formal than actual.

Rules vs discretion (part 2)

Using either rules or discretion, you may have an independent or a politics guided central bank:

Independent central bank Politics guided central bank

Rules X (ECB)

Discretion X

An independent central bank will usually follow rules because it has a fairly large independence (it can

decide) and operates within the boundaries of the law and it’s accountable as there’s a president of the CB

which is appointed by elected politicians (FED president appointed by US Senate and ECB president

appointed by the EU council). The president of the ECB is constrained by the EU parliament, as he/she has

to address to them the CB operate. However, nobody can tell Lagarde what to do. The ECB is mentioned in

the EU constitution, and it’s written that the ECB should only pursue price stability. A politics guided one

(China or Russia) is not independent so it may use discretion. Central banks are not born independent (the

Bank of England is the first central bank and it was born to finance the king and the kingdom). Also the bank

of Italy was not independent (it was obliged to buy government bonds while now the monetarization of

public debts is not allowed). ECB is based on rules and the models we’ll study under the new standard

approach are based on rules. Remark

If the interest rate is zero and the inflation is negative, the real interest rate is positive and there is no way

to lower it anymore. In a fixed-price world, nominal and real interest rate are the same (IS-LM).

Output stability models

We start talking about IS-LM and IS-IT model. The IS-LM was published in 1937 by John Hicks in a situation

of no inflation and high unemployment. Inflation was not there so it was a fix price model. There were

functions like investments, IS and LM. IS-LM model

Investments (I) are equal to: = −

There was an autonomous/exogenous component (meaning that it does not depend on income while

consumption and savings depend on it) plus a negative relationship between investments and interest rates

(the interest rate is the cost of funding an investment). This is a simplification. Investments are crucial in

the IS-LM model. The IS equation is (equilibrium in goods market):

= ( − * = = + +

!

Where is assumed to be totally autonomous and Of course there is

= + + . = = + .

"

taxation and the multiplier captures it: . is the propensity to consume. The IS is an

= =

! "#$("#&)

equilibrium condition that says that investments are equal to savings or aggregate demand is equal to

aggregate supply. The equilibrium income that satisfies this depends on the multiplier and the bracket.

Apparently the higher the interest rate, the lower the equilibrium income and this can be represented in a

graph. All the points in the line can be equilibrium points so we need something that allows us to

understand the true equilibrium point. To do this we need the LM equation.

LM equation

Also this is an equilibrium condition between supply and demand of money (equilibrium in money market):

: = +

" (

is the supply of money (or in real terms controlled by the central bank, remember we are in a

=

model where the tool is money). The demand of money is made of two components:

1. Transaction demand of money : demand/quantity of money for transaction purposes (to buy

things). This is positively correlated with the level of income of course (so it depends on );

2. Liquidity preference demand of money : it depends (negatively) on the interest rate. Here

comes the liquidity preference theory. Keynes said that people want to keep money (except for

transaction purposes) if the interest rate is very low. If it is high, it must be convenient to hold

assets (because they have a yield while money doesn’t). There is a shadow cost in holding money,

the cost of leaving other opportunities outside of the portfolio so it’s the loss in term of returns

that you abandonee. The higher is the interest rate and the higher is this shadow cost.

In conclusion we can say: : = − ℎ

This is a linear formulation that simplify the model. We can solve for obtaining:

= −

ℎ ℎ

So there is a positive correlation between and so the curve will be upward sloping:

depends negative on so if the central bank increases it,

the interest rate goes down (ceteris paribus). This last

equation tells us what monetary policy can do controlling the

quantity of money. Let’s see this other graph. Suppose the

∗

black line is full employment income ( ). What can we do to

, .

place closer to it? The LM equation is the so

= −

- -

increasing we will lower interest rate reaching that

income. The interest rate must be lower to achieve this.

Remember that here there is no concern for inflation because

the assumption is fix price.

The equilibrium level of income (intersection point) can be expressed as (solving simultaneously LM in IS):

1

/

= ∙ E + F

ℎ

1 − (1 − ) + ℎ

This is the so-called reduced form (one unknown variable is function of parameters and exogenous

variables alone). A reduced form must contain just one unknown. There is a monetary feedback effect

0, ∗

which is . Suppose you want to increase the output level to reach so you increase the money supply.

-

This leads to a reduction in the interest rate that increases investments as well. If investments go up, the

whole aggregated demand goes up which implies an increasing income that increase the demand for

money for transaction purposes. An increase in supply for money implies an increase in demand for money

(both in and ). Moreover, increasing investments will also bring an increase in consumption (due to

" (

the increase in income) which will also increase aggregate demand and income.

Consequences and fiscal policy

The increase of money needed to achieve the desired level is quite large. To understand this quantity the

central bank must know and This is why monetary policy was considered less important than fiscal

, ℎ.

one because the desired level could also be reached increasing the government spending (or reducing

taxes) and moving the IS up (which has a big negative effect on the budget, this justifies deficit spending

that want to reach high level of income/employment). This implies a high interest rate. The government

∗

can achieve the same . You can also achieve it through a combination of them.

Introduction to the IS-IT model

Why should we look at the money market equilibrium to find an interest rate compatible with full

employment? Why shouldn’t the central bank just fix it? This is the simplification that the IS-IT model

allows to have. In this model the IS is the same:

= − = ( − )

!

The central bank chooses the interest rate so that

∗ . The central bank supplies as much money

= ∗

as needed to achieve . Then, of course, we have:

∗ ∗

= ( − )

!

The IS-IT is a simplification of the IS-LM. This

corresponds to the practice of central banks since

1990 where they choose the interest rate and define

the quantity of money as needed to achieve it. We

don’t need the equilibrium in the money market, we

∗

just need to fix . This is the fix price world.

∗ ∗

Moreover, if we must lower it to achieve or, if we don’t to change it, we can reach the

>

1

employment increasing government expenditure so through the IS. The fiscal policy is another time an

alternative. Government debt and deficit

A government deficit (, expenditure higher than tax income) increases the government debt. The

increasing government debt is: ̇: −

1

is the initial value of government debt, is growth rate of nominal income (PIL said AI). Remember that

1

if there is no inflation: In this case we can rewrite it as:

= = 0.

1 ̇ ( (

= − ) − = − ) − (

is the real interest rate, is outstanding debt, is primary budget surplus. is the actual

− ) =

deficit which is made by spending on interest payments (interest rate times the debt) minus the primary

surplus (government budget balance excluding interest payments on public debt) which reduces deficit

while expenditure for interest payments increases it. If there is a primary deficit in the brackets you have +.

̇

(

The second alternative tells us that is very important. If there is no change in the

− ) = 0

government debt even if you have a primary deficit ( provided that

< 0), > .

Some considerations

The government debt increases if the interest rate is very high but of course it depends also on the growth

rate and on the primary surplus. Moreover, there is a different implication in monetary and fiscal policy:

̇

• An expansionary fiscal policy: turns in a so increases unless you are able to increase

− +

above ; ̇

• An expansionary monetary policy: lowing it can go below so the condition can be met

= 0

more easily. Introduction to other models

Fix price models were substituted by models that accounted for the possibility of inflation. That was a

turning point in the macroeconomic theory. This was made possible thanks to the Phillips curve. There was

a trade off in the increase in money wage and unemployment. The increase in money wages (“salari

nominali”) is higher, the lower is the unemployment rate.

What about inflation and his relationship with money wages and unemployment

There must also be a relationship between changes in money wages and changes in prices (this is a positive

relationship). Suppose that prices are set as markup over costs which are (simplifying) only labour costs. If

productivity is constant and mark-up is constant, prices will go up as much wages go up. This increase can

be cautioned by changes in productivity and mark-up:

• Mark-up: if the markup goes down, prices might increase less than wages;

• Productivity: if productivity goes up, prices might increase less than wages.

We discovered a relationship between money wages and inflation so there is also a relation between

inflation and unemployment. The unemployment goes up when output goes down (firms don’t need

people at work). This makes money wages going down (same direction of the output) and inflation goes

down (also this is a positive relationship with output). and have the same direction of

.

Important conclusion

We have a tendency of prices increasing when the economy is heating up (output is increasing). Prices are

not fixed. The policy maker has to accept the trade-off that the more you get closed to full employment,

the more money wages will go up and the more prices will increase. The government must choose.

Modigliani intuition

Suppose that people bargain over real wages: &2

= + ( − )

&2 is the bargained real wage, is the pavement because it’s the unemployment benefit. are the labour

force and both and are logarithms. If unemployment is low, the contractual power of labourers

increases and so salaries are higher. Of course it must be true that at previous time:

2

= + ( − )

&#"

&#"

The increase in the bargained real wage is simply equal to:

2

2

− = −( − )

&#"

&#"

It only depends on the change in the unemployment rate. If now it is higher than in the past, the real

change in real wage will go down (even if the bargain power is the same).

Non-Accelerating Inflation Rate of Unemployment (NAIRU)

Suppose that (in the previous period the economy was in equilibrium) which is the long

= =

#" &#" 3

run equilibrium level of unemployment (level of unemployment in which the Phillips curve cross the

axes). We can rewrite the variation as: 2

&2

− = ( − )

3 &

&#"

Connecting it to inflation

We must remember that real wages are so the difference between nominal salary and price

= −

& & &

levels, all in logs: 2

&2

− − ( − ) = ( − )

& &#" 3 &

&#"

Reordering we get: 2

&2

( − ) = ( − ) + ( − )

& &#" 3 &

&#"

2 2

Then we assume at time that where is the real wage actually paid and is the

− 1 =

&#" &#"

&#" &#"

real wages accepted by trade unions (bargained real wages) so we can finally obtain:

Z

&2 2

)

− = − + ( − → = + ( − )

&#" & &#" 3 & & 3 &

Z

&2 is which is the percentage change in money wages and it is equal to inflation rate plus

−

&#" In final we have a Phillips curve (linear and not convex as the prior). People want to increase

( − ).

3 &

salary both if the unemployment is below the long run equilibrium and if the inflation is high.

Monetarism and Phillips curve

The actual Phillips curve which is used in monetarist macroeconomic is slightly different. We derived:

Z 2 )

= + ( −

& 3 &

For monetarists the inflation rate should be the expected rate at time wages are bargained (if bargain is in

January, people don’t know the inflation rate for year so they ask for increase in wages based on this:

)

Z 2 &4 )

= + ( −

3 &

In the original version of the Phillips curve, expected inflation was absent, meaning that inflation was solely

linked to the output gap. If the actual inflation rate is different form the expected one, people will be

disappointed because the expectations have gone wrong. Workers will be happier if the inflation rate turns

to be lower than expected because the real wages will be higher. Entrepreneurs are not happy. Both are

happy only if the actual rate is equal to the expected one. This Phillips curve can be translated in

inflation/u