Monetary economics - Appunti

IMPLICATION OF TR: THE ZERO-LOWER BOUND

The zero-lower bound occurs when the nominal interest rate is close to zero and there is no

more room to decrease it, while the inflation is low. We want to point out that under this

condition there might be some consequences which can be easily showed. Suppose that the

∗

= 2% = 0%.

inflation target is and the current inflation at time zero is equal to If there

0

is a negative shock in the IS function shifts downwards, the long run interest rate to

implement would be lower than zero, but this might not be achieved because whenever the

= −

inflation rate goes below zero, the real interest rate increases above zero since

instead of decreasing. So, the actual real interest rate will never be as low as needed, that is,

it will never be negative, which is what is needed in order to achieve the long run equilibrium.

Looking at the graph, we have an IS down sloping which intercepts the long run aggregate

supply (vertical black line) where the real interest rate is 0% (point A). The IS curve is shifted

downwards in such a way that output gap at the zero interest rate is negative. On the down

graph we can see that if inflation is zero, there will be a negative output gap. The equilibrium

will need a negative inflation rate equal to -1% that at the same time implies e positive

interest rate. With a positive interest rate and a depressed IS function, we move to point B. If

inflation is low, private agents may revise their expectations downwards, which means the

inflation rate is no longer equal to 2% but is negative. And the optimal interest rate should be

as negative as in the corresponding point C, which cannot be achieved with a negative

inflation rate.

We can see a simple TR that is an inflation targeting rule. The CB is not supposed to target the

output gap. Only inflation is the target not the output. Then we have the Fisher equation that

relates nominal rate, real rate and inflation. ∗

( )

: + −

)

: = −( − + ℎ = 1

∗

( )

: = − − +

ℎ : =−

= 0. /

We assume If we draw the TR in the space, it is a positively sloped straight line,

that is the target interest rate grows as inflation grows above the output gap. The slope of TR

depends only on . The actual interest rate () depends on the nominal one and the inflation

rate. The problem is that if the nominal interest rate is at its zero lower bound and if the

inflation rate is sufficiently low, the actual interest rate might be different from the target

∗

interest rate . This divergence between the actual and the target interest rate might cause

problems.

Look what happens when inflation rate goes down below a certain treshold, triggering a

deflation trap: if the nominal interest rate is at the zero-lower bound and the inflation rate

is sufficiently low, the actual real interest rate may be different from the target needed real

interest rate. Initially, if inflation goes down, the target and actual real rate and the nominal

interest rate decrease consequently. The nominal interest rate hits the zero-lower bound

when inflation is 1%. Then, for example, with an inflation at 0.5%, the optimal real interest

rate would be -2% but since the nominal interest rate is bounded at 0%, the real rate will be

-0.5%, which is higher from what is needed to stabilize the economy. And if the inflation rate

is even lower, for example 0% or -1%, with the target rate is -3% or -5% and the nominal rate

bounded at 0%, the actual real rate is going to be 0% or 1%. The actual real rate is even

increasing instead of decreasing! And we can see what happens to the output gap: lowering

the interest rate helps reducing the output gap, but when the inflation rate is sufficiently low

the output gap increases instead of decreasing. /

In the following graph we can see the TR drawn in the space, that is different from the

/

usual space (in this case the TR will not shift as the inflation changes). As the inflation

goes below 1,5% the real interest rate becomes negative in order to support the aggregate

( = − ),

demand and to stabilize the economy but when the inflation rate hits 1% level,

the actual real interest rate diverges from the target needed real interest rate (shown with

the dashed line). Those points on the dash line are not achievable, the only points achievable

are those on the TR curve (the full line), therefore, certain level of the real interest rate cannot

be achieved. The actual real interest rate becomes 0% at a 0% inflation rate and it becomes

even positive when the inflation rate becomes more negative, when instead a negative real

interest rate is needed. The TR is still linear but the actual monetary policy coincides with the

TR up to a certain level of inflation: as becomes lower and lower with close to zero, the

actual policy rule changes its slope and doesn’t follow the TR any longer.

The implications of this can be shown in the following graphs. If we put (a) TR and (b) IS

negatively shocked together we will get the aggregate demand curve. In this case, if the

inflation rate goes below 1%, the slope of the AD curve changes from negative to positive.

This is because the AD curve is derived jointly from the TR and the IS curve, so when gets

low enough with close to zero, a change in the slope of the TR will cause a change also in

the slope of AD. The new shape of the AD implies that there is no inflation rate that is low

enough to reach the long-run level of output (d). The real interest rate increases instead

of decreasing and the negative output gap becomes even larger! Therefore, the monetary

policy, which consists of changing the interest rate, doesn’t work any longer and

unconventional monetary policy instruments shall be used.

(LESSON 12) In a context of zero-lower bound, the aggregate demand curve might be upward

sloping in a range of values where the nominal interest rate is zero and the inflation rate is

low. In the Friedman model, after a demand shock, the shift of AS downwards, because of

expectations revision, is a stabilizing process. As expectations are revised downwards the AS

shifts downward. This will produce a lower output gap. The economy ends up in a point where

the output gap is filled and the inflation rate has gone down.

′

But this is not the case when the AD is upward sloping, as the process is not stabilizing. If the

AS crosses the AD in its upward sloping range, expectations revision leads to a more negative

output gap. The zero-lower bound occurs at an inflation rate that is not zero. In a ZLB context,

the downward shift of the AS function leads to a larger and larger output gap. There is a

downward spiral of inflation and GDP together. There is no stability: the market cannot fill

the output gap itself and a policy intervention is needed. Which kind of intervention?

(1) A possible intervention is an expansionary fiscal policy: it shifts the AD curve to the right

and even if the zero-lower bound is not changed, the new aggregate demand function

crosses the AS function precisely at . The fiscal policy is able, under ZLB condition, to lead

the economy back to the long run level of output, that is, to fill the output gap. The inflation

will go up but it is what is needed as it was too low before and now has to be set to a higher

level. The fiscal policy is effective. When the policy maker uses fiscal policy, there might be

budget problems. An expansionary fiscal policy might entail a deficit leading to higher debt.

How deficit is financed also matter: bond or printing money. This second method usually takes

the form of helicopter drop.

(2) Another possible intervention is an expansionary policy based on the Quantitative

Easing: the CB is targeting the quantity of money. The QE works thought an enlargement of

the actual budged of the balance sheet of the CB. Formally, the actual quantity of money is

on the debt side of the CB balance sheet. When the CB buys bonds or private securities on

the open market, the CB is enlarging its assets side and at the same time the debt side

increases as well. The balance sheet is always balanced but its amount is getting bigger when

a QE policy is implemented.

The basic idea is that, increasing the quantity of money, the CB acts indirectly on the interest

rate. Suppose the long run interest rate is given by the sum of the policy rate plus risk

.

premium = +

Suppose that you are in a situation where the short run interest rate is equal to zero (we are

talking about real rate but we can also talk about nominal rate). Suppose that the yield curve

is represented by the black line. Given that the CB is not able to influence the part of the yield

curve that is below zero (remember the zero-lower bound problem), what the CB wants to do

is to affect the yield curve that is above zero by reducing the risk premium in order to get a

,

yield curve like the red one. Lowering the risk premium the CB will lower the long run

= + .

interest rate, given by This can be achieved through a QE policy: if the CB buys

long-term bonds, the price of those long-term bonds will go up whereas their yields will go

down. The strategy is to buy long-term bonds in order to flatten the yield curve and reduce

the long-run interest rate.

Another type of open market operations aimed to reduce long-rung interest rate. The CB is

fixing the short-term interest rate and announced purchases program targeted to long-term

securities. The CB is lending long term to commercial banks and accepts long-term bonds as

collateral. It is not properly a purchase. Long Term Refinancing Operation (LTRO) are semi-

unconventional monetary policy but it is always aimed at lowering the risk premium α, which

makes long run yields higher than short term.

(3) These were some unconventional monetary policies the CB could implement when facing

the zero-lower bound. Another instrument is based on the revision of expectation thought

targeting a higher inflation rate. In the next graph we have an expectations management

pursued by the CB which says that the inflation target is being increased and so, if the inflation

target does so and if the CB is credible, the AS curve will shift upwards from AS1 to AS2. If we

combine expectation management and QE, there will be a convergence to the long run level

of output in a quicker way respect to a QE policy alone.

The actual management of expectation can be very useful. The difficulty of this policy is that

if the CB is not able to achieve a low inflation target, it