The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

The conduct of monetary policy Rodolphe Desbordes

http://www.rodolphedesbordes.com/

Analysis

The central bank

The monetary policy reaction function

The IS curve and choice of r

The central bank

2

The monetary policy reaction function

3

The IS curve and choice of r

4

Empirical interlude

5

Analysis

Empirical interlude

Analysis

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

The objectives of a Central Bank A central bank usually cares about a) Inflation b) Output growth/Unemployment. The Bank’s monetary policy objective is to deliver price stability – low inflation – and, subject to that, to support the Government’s economic objectives including those for growth and employment. Price stability is defined by the Government’s inflation target of 2%. http://www.bankofengland.co.uk/monetarypolicy/framework. htm

The Federal Reserve sets the nation’s monetary policy to promote the objectives of maximum employment, stable prices, and moderate long-term interest rates. http://www.federalreserve.gov/pf/pdf/pf_2.pdf

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

Targeting the interest rate: The Taylor rule The economist John Taylor has suggested that his ‘Taylor rule’ provides a good description of the behaviour of the Fed: Real Interest rate target

=

Stabilising real interest rate +0.5(Inflation gap) + 0.5(Output gap)

i0 − π0

=

rs + 0.5(π0 − π T ) + 0.5(

Y0 − Ye ) Ye

This rule tells us that 1

2

3

If the economy is in equilibrium (no inflation or output gaps), the real interest rate (r0 = i0 − π0 ) ought to be equal to the stabilising real rate of interest (r0 = rs ) . the Taylor rule is an activist rule. Positive inflation or output gap, ceteris paribus, leads to setting a higher real interest rate. The presence of both gaps suggest that the behaviour of the central bank is consistent with its two main objectives, to which it gives equal weight (0.5): price stability and minimising business cycle fluctuations of output around its potential.

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Actual U.S. interest rate and the Taylor rule recommendation

http://research.stlouisfed.org/publications/mt/20100901/mt_20100914.pdf

The Taylor rule describes reasonably well the behaviour of the Fed. It seems to be a reasonably good approximation of how a central bank acts. There are nevertheless some +/- divergences, which suggest overly expansionary or restrictive monetary policies.

Analysis

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

The central bank’s loss function I A central bank cares about inflation (π) and the level of output (Y ). More precisely, it wants to minimise 1

fluctuations of π around its target (π T ).

2

fluctuations of Y around its equilibrium level (Ye ).

Both goals are hard to achieve at the same time since there is a trade-off between output and inflation, as shown by the Phillips Curve (PC), which defines the feasible set of inflation and output pairs for a give rate of lagged inflation: πt

=

πt−1 +

Yt − Ye Ye

The central bank will then try to do its best by minimising a loss function under the PC constraint: Yt − Ye 2 ) + β(πt − π T )2 , or L = ( Ye Yt − Ye 2 Yt − Ye L = ( ) + β[πt−1 + − π T ]2 Ye Ye where β is the central bank’s degree of aversion to inflation.

The central bank

The monetary policy reaction function

The IS curve and choice of r

The Phillips curve: πt = πt−1 +

Empirical interlude

Yt −Ye Ye

Inflation

C’

PC_2 PC_1

t+2

C

t+1

B’

PC_0

B

Current

A’

A

Target

Output Equilibrium output

Anchor points (A, B, C): current inflation is equal to past inflation if Current points (A0 , B 0 , C 0 ): if

Yt −Ye Ye

Y −Ye Ye

= 0.

> 0, current inflation exceeds past inflation.

At time t, πt−1 = 2 and Yt Y−Ye = 2. Hence πt = 2 + 2 = 4. The PC curve goes e through A and A0 . Yt −Ye At time t + 1, πt = 4 and Y = 2. Hence πt+1 = 4 + 2 = 6. The PC curve e goes through B and B 0 . An inflationary spiral occurs.

Analysis

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

The central bank’s loss function II The central bank does not directly influence the inflation rate: 1 It raises the real interest rate... 2 ...to reduce aggregate demand and output... 3 ... which leads to higher unemployment... 4 ... which moderates wage demands... 5 ... which allow firms to increase prices by less than last year. Hence the central bank determines an optimal level of output which, in turn, determines the level of inflation. The central bank will choose the value of Y on a given PC curve which minimises its loss function. There is a one period lag between the interest rate decision and the effect on output and inflation. Hence, in its loss function, the central bank is only concerned with output Yt+1 = Y1 and inflation πt+1 = π1 in period 1. L

=

(

Y1 − Ye 2 Y1 − Ye ) + β[π0 + − π T ]2 Ye Ye

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

The monetary policy reaction function It can be shown that minimisation of the loss function with respect to Y1 gives: Y1 − Ye Ye

=

−β(π1 − π T )

Given the PC curve that it faces, and its preferences, this relationship shows the central bank’s chosen combination of output and inflation. The negative sign is directly linked to the PC curve constraint: the only way that a central bank can reduce inflation is by depressing output. β measures the central bank’s aversion inflation: whatever the PC constraint, a very inflation averse (VIA) central bank always choose to depress output much more than a neutral bank in order to tame inflationary pressures more quickly. The central bank will guide the economy along the MRPF curve.

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

e MRPF [ Y1Y−Y = −β(π1 − π T )] curve e Inflation

PC_1

Current

B

PC_0

C Next period Inflation

C’ A

Target

MRPF_VIA

MRPF Next period output

Output

Equilibrium output

If π0 = π T , then Y1 = Ye . Therefore the MRPF curve goes through A. The slope of the curve is −β. Hence, it is downward sloping with respect to output and gets steeper as β becomes large. The target output of the central bank will be at the intersection of the MRPF and PC curves [C or C 0 ].

Analysis

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

The IS curve We can use a simplified IS curve to describe the logarithm of current output Ln(Y1 )

=

A − ar0

And we can define rs as the real rate of interest that equates future output Y1 to equilibrium output Ye : Ln(Ye )

=

A − ars

Finally we can rewrite the IS equation in output gap form Ln(Y1 ) − Ln(Ye ) =

Y1 − Ye Ye

=

−a(r0 − rs )

r0 − rs

=

1 Y1 − Ye a Ye

For the output gap in the next period to be negative, the current interest rate must exceed the stabilising real rate of interest.

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

e The IS curve: r0 − rs = − a1 Y1Y−Y e Real interest rate

Chosen

Greater interest-rate sensitivity

Stabilising

IS

Output

Inflation

PC_1

Current

B

PC_0

Next period Inflation A

Target

MRPF Next period output

Equilibrium output

Output

The slope of the IS curve is − a1 . It is downward sloping with respect to output. rs must be consistent with the equilibrium defined by MRPF /PC. Hence the choice of the real interest rate will depend on the central bank’s aversion to inflation (β) and how sensitive is AD to a rise r (a).

Analysis

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

Implied Taylor rule given the MRPF/PC/IS equations To get an expression with the current inflation gap, replace π1 using PC: Y1 − Ye 1 Y1 − Ye π0 + − πT = − Ye β Ye 1 Y1 − Ye π0 − π T = −(1 + ) β Ye And to get an expression with the real interest rate gap, replace IS: π0 − π T

=

(r0 − rs )

=

Y1 −Ye Ye

using

1 )a(r0 − rs ) β 1 (π0 − π T ) a(1 + β1 )

(1 +

If you assume that a = β = 1, then you get a simple Taylor rule (without the output gap): (r0 − rs )

=

0.5(π0 − π T )

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

Changes in the U.S. inflation rate and the output gap

Source: Cecchetti, Stephen (2008). Money, Banking, and Financial Markets. New York: McGraw-Hill, 2nd edition.

The graph shows that a positive (negative) output gap leads to rise (fall) in inflation over the following 18 months.

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

Does monetary policy influence the business cycle?

Source: Cecchetti, Stephen (2008). Money, Banking, and Financial Markets. New York: McGraw-Hill, 2nd edition.

The graph shows that recessions (shaded bars) are usually preceded by a rise in the interest rate.

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

The initial equilibrium Real interest rate

Stabilising

IS

Output

Inflation

PC_0

Target

A

MRPF

Equilibrium output

Output

The economy is at a stable equilibrium y = ye , r = rs , Ď&#x20AC; = Ď&#x20AC; T . We are on the PC/MRPF curves. We know that an economy is no more at a stable equilibrium if one or several of these conditions are not satisfied.

Analysis

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

A permanent rise in AD Real interest rate

B

Stabilising A

IS0 IS

Output

Inflation

PC_0

Inflation 0

Target

B

A

MRPF

Equilibrium output

Output 0

Output

There is a permanent rise in AD, represented by an upward shift of the IS curve (the component A increases). This rise in AD will trigger a rise in output above its equilibrium level (y0 6= ye ). According to the PC curve, this positive output gap will increase the inflation rate (Ď&#x20AC;0 6= Ď&#x20AC;T ).

Analysis

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

The central bank’s response in the initial period Real interest rate

r_0

C

Stabilising

IS0

A

IS

Output

Inflation

PC_1

PC_0

Inflation 1 C A

Target

MRPF

Output 1

Equilibrium output

Output

Since π0 > πT , the Central Bank will adjust r in order to react to the permanent AD shock. It will choose r0 such as it minimises its loss function given the constraint that the combination of output/inflation must be on PC1 . Unemployment has to increase in period 1 to generate lower inflation in period 1. Note the lag structure of the model: r0 → Y1 → π1 .

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

The central bankâ&#x20AC;&#x2122;s response in the first period Real interest rate

r_0 r_1

D

Stabilising new Stabilising

IS0

A

IS

Output

Inflation

PC_1 PC_2 PC_0

Inflation 1 Inflation 2

D

Target

A

MRPF

Output 1

Output 2

Output

Equilibrium output

The central bank will choose r1 given the forecasted PC2 . Given that a large output gap has been initially created, the central bank e can safely lower the interest rate. As long as Y â&#x2C6;&#x2019;Y < 0, inflation will fall. Ye The central bank guides the economy along the MRPF /IS curves.

The central bank

The monetary policy reaction function

The IS curve and choice of r

Empirical interlude

Analysis

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2

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