Monetary Economics - Appunti completi

R ECAP OF PREVIOUS CONCEPTS

Monetary Policies can be divided in 4 categories with respect to their TARGETS and their

INSTRUMENTS. TARGETS

Inflation Output

Money Monetary Keynesian

Growth

INSTRUMENTS Interest Standard Inflation Keynesian

Rate Targeting

There are several Transmission Channels of Monetary Policy:

1) P C

ORTFOLIO HANNEL Þ

Central bank raises overnight rates Commercial banks raise credit cost and also rate on bonds

and other securities will pay a higher interest rate. So, people will change the balance in its

portfolio between Money and Investments (Financial Assets), for the advantage of the latter.

­ Þ ­, ¯)

(Interest Rate Financial Investments Real Investments

2) C C ( )

Strictly linked to 1)

REDIT HANNEL

Same initial scenario of 1) discourage credit demand and that will cover investments.

à

3) E R C

XCHANGE ATE HANNEL

An example is the Quantitative Easing.

Þ Þ Þ

ECB buys bonds Prices of bonds will go up yields of bonds will go down more liquidity in

the system, that can be spent to buy foreign bonds (with a higher wield) but that will cause a

Þ

deficit in the balance and a devaluation of the € commodities of EU country become more

competitive.

The E R C (3) works better than the C C (2) because the latter is

XCHANGE ATE HANNEL REDIT HANNEL

influenced by the soundness of the bank system. Moreover, is useless to have a high credit supply

if the firms don’t want it (Low Credit Demand). Moreover, commercial banks don’t want to lend

because of the risk to incur in a non-performing loan.

There is another issue:

I CB D CB

NDEPENDENT EPENDENT

R

ULES

D ISCRETION 2

R : If the ECB announces that the money growth rate is that’s a rule.

= + ,

ULES " "$%

The Taylor Rule is another rule: ∗

= + + − + −

" * " " " *

R vs D issue is linked to the T vs I or the I vs D of

ULES ISCRETION ARGET NSTRUMENT NDEPENDENCE EPENDENCE

the Central Bank.

D /I of the Central Bank: a Dependent CB works under the control of the

EPENDENCE NDEPENDENCE

treasury, that can borrow freely or make debt with it. The Central Bank is the Lender of Last Resort

(: if nobody buys the bonds, the government asks the CB to buy them.

An independent CB cannot be obliged to buy sovereign bonds. It decides the money growth rate,

in some cases also the inflation rate (

ECB sets it at a lower but close to 2%. Bank of England is Dependent and

so inflation target is decided by the English Government; it can only decide the instruments to reach the targets. FED

instead is Semi-Dependent by the USA Government; it is quite free but if the government asks it to buy stressed banks

).

or treasury bonds, the FED cannot refuse. The less independent is the Bank of Japan. 3

Why people demand for money?

Let’s start from this equation: (Quantity Equation Fisher Equation)

= or

where: = Money Supply

= Velocity of Circulation

= Nominal GDP

3

and another equation is: (Cambridge Equation)

=

%

4 3

suppose that and

= = = 5

the Cambridge and Fisher formulas so are very linked. A theory says that depends on the

payment habits; for example, electronic payment influences in a positive way.

%

Þ

So, if because we said that .

­ ¯ = 5

For this reason, in more developed countries there is a higher velocity of circulation.

Another theory says that is a function of interest rate, so also is a function of

, .

3

So that = .

3 is due to the fact that if people prefer to hold Financial Instruments more than Liquidity.

­

That is because is like the Opportunity Cost of Cash.

4

Standard Macroeconomic Theory based on utility

ℎ

= +

ln ln

1+ 1+

where: = Utility

= Real Output (GDP)

; = Real Money

<

;

and form the Purchasing Power; we put them under only for an instrumental reason.

ln

< is always concave so it has a unique maximum point and no

log

minimum point. In this way we can be sure that the stationary

st

point (1 derivative = 0) is a maximum.

@

Income from Employment: = ⋅ Wages

=

? < = Number of Employed

; E

Financial Wealth: = +

< < E

= + ⋅

;FG ? <

H ; H ;

Actual/Effective Income: = + ⋅ − ⋅ = + −

? ?

< < < <

H ;

To maximize the utility function under the constraint we solve the Lagrangian:

= + −

? < <

ℎ

= + + − + −

max ln ln ?

1+ 1+

;

, < ℎ

Þ

=0 = −

1+

Þ

=0 = −

1+

ℎ

− 1

1+

Þ

= = = =

− ℎ

1+

5

3

=

ℎ

∗

Where is exogenously determined by the Central Bank.

The other case is the one in which the CB fixes the interest rate .

∗ ∗

is the Fixed rate which makes be equal to .

(Note: Inflation Target is a fixed price world is useless) 6

IS – LM M ODEL This was written to reconcile the Keynesian view

(which was not modelled) with Neoclassical view

= Investment Savings

(Loanable Funds). In the Keynesian theory,

= Liquidity Money

Savings are dependent on Income.

was written by Hicks (1937).

IS-LM Model

He wrote: =

,

but the popular equation is: =

If savings depend on Income () and Investment depend on Interest Rate () the model is

undetermined (this equation cannot be solved, as it has two unknowns).

So, we need another equation to solve the model: that is why we bring in the .

= ,

(Supply of Money) is equal to (Liquidity) which is a function of and

.

= Supply of Money

= Demand for Money

Now with two equations we can determine the two unknowns and given the exogenous

,

variable (which is the Supply of Money).

IS-LM Model

Now we shall use a simple linear formulation of the :

: = − ℎ

= = Transaction Demand for Money

.

( ) ( )

+

Demand for money must be equal

%

% ^ \

a

to the Supply of money to have an equilibrium in = = Speculative Demand for Money

−ℎ .

^

$

the money market.

: we have a negative relation between the Demand for Money, , and the

+

^ % ^

$ interest rate, .

nd a positive relation between the Demand for Money, , and Income,

+ .

: a

% % ^

\

If you have a given quantity of money which is the Supply by the Central Bank, you have a part of

this which is devoted to the Transactions motive and another part which is devoted to the

Speculation motive; and, given the Supply, if one part increases, the other must go down.

If we represent on the graph, the quantity of money can go

either or to or to , so we will have a straight line

% ^

with a 45° slope which represents the M S , and we

ONEY UPPLY

can see that if many amount goes to , very little goes to

%

and vice versa.

^

And if the Supply of Money increases (­) the line moves

upward, and if the Supply of Money decreases (¯) the line

moves downward. 7

This equation can be derived from a

simple Income-Expenditure model

(studied in macroeconomics)

A simple way to represent the is to write:

: = − = Real Income

The higher is the more elastic is the investment

= Exogenous Demand

with respect to the interest rate (and the lower is = Sensibility of Investment to interest rate

the less elastic is the investment with respect to the

interest rate).

− Negative relation between investment and 1

à =

= Money Multiplier

1− 1−

interest rate = marginal propensity to consume

1 − 1 − = marginal propensity to save out of Disposable Income

(where Disposable Income is “income net of tax”)

and

= =

In this model , so consumption = Tax rate (or tax pressure)

in the basically depends on the

−

current income ( ) and current income only (so

there is no intertemporal optimization)

You solve the model by substituting one equation into the other and finally you get:

1

= +

ℎ

1− 1− + ℎ

This is the reduced form of the model (which is the solution

of the model) in which you have one variable as a function

of the parameters and exogenous variables such as and

(where stands for the Transaction demand for money and

stands for the Speculative demand for money).

ℎ

The feature of this is that once you have you can

substitute this equation into either the or the and get

so, this is precisely what you get from the graphical

;

representation, in which you have and

.

These two straight lines represent the equilibrium interest rate and the equilibrium income.

When the two lines cross, we have a given level of and of which are compatible with

equilibrium in both the Money and the Goods Markets.

(NB: This is not a supply and demand model)

These two straight lines ( and represent Equilibrium Loci.

)

= Locus of equilibria on the Goods Market, that gives you a schedule on the interest rate and

income which are compatible with each other in equilibrium.

= Locus of equilibria on the money Market, that gives you a schedule on the interest rate and

income which are compatible with each other in equilibrium. 8

The point where two loci cross belongs to both loci so it must be the General Equilibrium of the

Economy as the quantities of and are compatible with both the equilibrium in the Money and

in the Goods Market.

Money Supply () enters the equation determining Real Output () so there is N M

O ONEY

N , and is quite evident that if Money Supply increases, the level of Output increases

EUTRALITY

Þ

(­ the multiplier is positive so if the Money Supply increases, the Real Income will

­);

increase. (This model well represents the Keynesian view in which a change in the Money Supply will imply a

change in the level of Output)

The Multiplier of the Money Supply is :

(this comes from the above reduced form of the IS − LM Model)

ℎ

Money Supply Multiplier =

1− 1− + ℎ

s

• if The Money Multiplier would be greater than the Public Expenditure (or exogenous

> 1

t demand, multiplier.

)

s

• If The Money Multiplier would be lower than the Public Expenditure (or exogenous

< 1

t demand, multiplier.

)

This makes us able to see if an increase in the Money Supply is more effective than an increase in

s s

the Public Expenditure in increasing the level of Output, if or it is less effective, if

> 1, < 1.

t t

The multiplier of the reduced form of the model tells us that a unitary increase in the value of

has an impact on equal to the value of the multiplier itself (which is usually and

≠ 1 > 1).

An increase in implies an increase in which both implies an increase in Consumption and in

Taxation.

So, an increase in Public Expenditure () causes an increase in Income; this increase in Income (net

of taxes) will give right to an increase in Consumption (which is Expenditure); so the increase in

Consumption will imply a further increase in Income which will give rise to further increase in

Consumption, further increase in Income and so on …

And as and you also have a tax rate (which is≤ this process comes to an end (so this is

< 1 1)

not an infinite multiplication, but it is finite), because the multiplier is finite (not infinite).

The above descripted process can be written in symbols as:

Þ Þ Þ

­ ­ ­ ­ This multiply ignores the Money Market

ß ­ Þ ¯ Þ Þ Þ

­ ¯ ¯

% ^

But we can’t ignore

the Money Market will go up by ℎ

The Transaction Demand

for Money goes up (how

much more depends on ) a

If the Money Supply is given ( )

an increase in must be

% 9

followed by a decrease in

Þ Þ Þ

The multiplier process (­ ignores the Money Market, but we cannot ignore

­ ­ ­ …)

the Money Market in this model. So:

­, Þ

If then that is that the Transaction Demand for Money goes up (more income more

­

%

money is demanded for transactions), how much more depends on now if the Money Supply is

; ¯;

given (that is an increase in must be followed by a decrease in , so but in order to

)

% ^ ^

have a lower demand for Speculative motives the interest rate must be higher (­), how much

higher depends on this will make investments go down (¯) by and if then

ℎ; , ¯ ¯.

This process involves the 3 parameters and which are the 3 parameters in the element that

, ℎ,

reduces the denominator of the Money Multiplier () of the equation to the multiplier of the

reduced form model. 1

= 1− 1− 1

Public Expenditure Multiplier =

1− 1− + ℎ

This element lowers the size of the multiplier:

• and increase the denominator.

• decreases the denominator

ℎ

They represent the influence of the Money Market on the multiplication process (Note: This effect

is ignored by the multiplier of the Goods Market (), but must not be ignored in reality and in the

complete IS − LM Model).

The equation Money Multiplier () ignores this effect as in the simple Income-Expenditure

model the Investment () is an exogenous variable (not depending on while in the

), IS −

Investments depend on so this effect must be considered, as the Money Market here

LM Model ,

has influence on the Real Market, and this link is precisely that the Interest depend on the

quantity of Income. And this is the real reason why Monetary Policy can be effective on Output.

This dependency of real variables output on the monetary variables (Money Supply) goes through

the dependence of the Money Demand on the interest rate and the dependence of the

investment function on the interest rate; that is the link, that is why the Central Bank affects

output! (without such a link money would be neutral. In a Loanable Funds quantity theory model, there is no

real effect of the money supply, money is neutral: investments and savings determine the interest rate

independently of the money market; so, when income is determined on the goods market, enters the quantity

.

equation and the supply of money only determines the price level. That’s the pre-Keynesian model)

So, this is the basic result of and within this model we can represent Monetary

IS − LM Model

Policy. 10

Monetary Policy is represented by a shift in the LM:

• An Expansionary Monetary Policy (­) delivers a lower level of interest rate (¯) and a

higher level of Income (­).

• A Contractionary Monetary Policy is represented by an accrual shift in the LM, lower

money supply (¯) and you will have a higher interest rate (­) and a lower level of

Income (¯).

So, in a Monetary Policy is represented by an increase or decrease of the Money

IS − LM Model

Supply () and you have the interest rate () as an endogenous variable. Of course, Monetary

Policy () can be coupled with Fiscal Policy (), that is a change in in that case you may have

;

that both curves shift and the combination of Monetary Policy and Fiscal Policy is quite typical of

the and was typical of Monetary and Fiscal Policy in 1950s and ‘60s, when Central

IS − LM Model

Banks and Governments were not independent on each other and they were acting together in

order to pursue output stability (and a wide literature was written in order to find the best

combination between Monetary Policy and Fiscal Policy).

This is a very encompassing model (special cases): we have cases in which the is horizontal

(L T ); or cases in which the is vertical (= Investment strictly independent on the

IQUIDITY RAP

interest rate). a ¯)

Decrease in the Money Supply (

ß a ­

Increase in the Money Supply ( )

ß

Notes:

- Money is exogenous

- Interest rate is endogenous

11

Another approach is one in which the policy instrument which is used by the Central Bank is the

interest rate