MP - IS-PC-MR model

Question 1

What does closed economy output depend on?

Answer 1

Expenditure (C + I + G) which depends on real interest rate

(C = consumption, I = investment, G = gov. expenditure)

Question 2

What do central banks do with rates?

Answer 2

Set nominal interest rates (r) in period t-1

Question 3

What does CB setting r influence?

Answer 3

Output (via IS curve) in t

Inflation (via PC) in t

Question 4

What are real interest rates?

Answer 4

Nominal interest rates minus expected inflation

Question 5

What assumption do we make regarding consumer inflation expectations & the impact on CB setting r?

Answer 5

Backward-looking & therefore predetermined

Meaning by setting nominal rate at t - 1, CB also sets r that period to influence y, π in t

Question 6

What relationship does the IS curve demonstrate?

Answer 6

Relationship between nominal interest rates (r) (in t - 1) and output (y) (in t)

Question 7

What assumption do we make about the CB and nominal rates?

Answer 7

CB has perfect control over nominal rate

Question 8

What does a lower interest rate do to output & inflation?

Answer 8

Increases short-run output and therefore puts upward pressure on inflation

Question 9

What is CB inflation targeting?

Answer 9

Aiming to reach an optimal outcome of πT and output γe (on VPC)

Minimises the weighted sum of quadratic deviations from (πT, γe)

Question 10

What is the monetary rule (MR)?

Answer 10

The range of output/inflation possibilities define by PC at the prevailing expected inflation rate

Set of best responses for all possible π^e

Question 11

How is CB monetary policy and MR related?

Answer 11

CB sets MP to achieve a point on MR

Question 12

How can we get to MR from the loss function?

Answer 12

Substituting PC in the loss function, taking FOC, and re-arranging yields the MR equation

Question 13

What does the slope of the MR define?

Answer 13

Speed at which CB pursues the inflation target

Question 14

Is the IS curve upward or downward sloping?

Answer 14

Downward

Question 15

What determines the slope of the MR curve?

Answer 15

If α = β MR slope is -1

Larger β (in the loss function) rotates MR anti-clockwise & smaller β rotates it clockwise

Larger α (in the PC curve) rotates MR anti-clockwise & smaller α rotates it clockwise

Question 16

What might lead to a greater β?

Answer 16

Past experience of high inflation (eg Bundesbank)

Openness to trade / finance which makes high inflation more distorting (eg Swiss National Bank)

More inflation averse CB eliminating inflation more quickly

Question 17

What relationship does the MR show on a graph?

Answer 17

Relationship between inflation (π) and output (y)

Negatively sloped

Question 18

What might lead to a greater α?

Answer 18

More positively sloped WS curve, and more negatively sloped PS curve leading to a steeper PC

Steeper PC means inflation can be controlled more efficiently and CB responds to this incentive with rapid inflation reduction

Question 19

What makes up the 3 equation model & each of their relationships?

Answer 19

IS: IS curve, relationship between real interest rate and output
- downward sloping, drawn alone

PC: PC, relationship between inflation and employment (inflation and output)
- upward sloping, drawn with MR curve

MR: MR curve, relationship between inflation and output
- downward sloping, drawn with PC

Question 20

What can the IS-PC-MR model be used to analyse?

Answer 20

Optimal monetary policy and macro adjustment following a shock

Question 21

What is the initial reaction to an unexpected shock?

Answer 21

Since shock is unexpected, monetary policy unch. in current period

Adaptiveness (backward looking) implies inflation expectations do not react to current period shocks

So r = rs in the current period & output rises to y1 on IS1 (IS curve shifts outwards / up & right) = economy moves to B (same rate, higher output)

This raises inflation via PC to π1 = economy moves to B (along the PC curve, output and inflation increased)

Question 22

Dynamics of reaction to unexpected shock after initial move of economy to B?

Answer 22

CB infers that new inflation π1 in current period raises inflation expectations next period, so πe = π1

This intersects the MR at C, and is the preferred point of the CB, so to achieve C in the next period, the CB raises real interest rates today

Current real rates raised to r1 to give output y2 and inflation π2 next period

Question 23

Does a rise in real rates move the economy immediately?

Answer 23

No, as there is a transmission lag, so r1 today is sufficient for y1 tomorrow

Question 24

Dynamics of reaction to unexpected shock after economy moves to C?

Answer 24

Now the CB has moved the economy to C by raising rates to r1, at C inflation is π2, and this will become the expected inflation rate the period after implying now on the PC πe = π2 (π2 < π1)

CB then targets D on this PC constraint & MR line, setting rates to r2 whilst the economy is at C so output falls to y3 at D

Process repeats until economy returns to point A

Question 25

When do real and nominal rates peak?

Answer 25

Real interest rates peak in the period the shock occurs, but nominal rates (real rates plus expected inflation, backward-looking) maximum is one period after shock occurs

Question 26

What happens in period t-1 of an unexpected one period IS shock?

Answer 26

Nothing known, nothing happens, CB has set nominal rate to some r, taking into account inflation expectations

Question 27

What happens in period t of some unexpected one period IS shock?

Answer 27

IS shock happens, the economy would move straight up to A’ on higher IS curve at the same output, but unexpected means CB hasn’t adjusted rates in t-1 So, the economy moves to B (higher output at y1, higher IS curve at IS1). Moves along the PC from A to B as output has increased = inflationary CB sees this happen and so raises rates to some r (r1)

Question 28

What happens in period t+1 of some unexpected one period IS shock that happened in t?

Answer 28

As it is a one period unexpected shock, the IS drops back to IS0, r1 put in place in t now comes into affect due to adaptive expectations With the new rate of r1, the economy moves to C on the higher PC curve of π1 due to the adaptive expectations such that πe = π1 Output drops, and CB sees the negative output gap so drops rate to r2 < r1

Question 29

What happens in period t+2 of some unexpected one period IS shock that happened in t?

Answer 29

Adaptive expectations means new PC2, πe = π2, the CB lowering rates to r2 now impacts the economy and it moves to D with higher output. Process repeats until PC has fallen back to PC0

Question 30

What does the extent to which the CB raises r in response to inflation disequilibrium depend on?

Answer 30

Depends (i) negatively on a (semi-elasticity of expenditure w.r.t r (inverse slope of IS)

Question 31

Will countries with more powerful monetary transmission raise interest rates by more or less?

Answer 31

Less, flatter IS, changing rates impacts a change in the economy more directly

Question 32

What is the α parameter (from real interest rate solution) like in the UK? And why?

Answer 32

Large α parameter in the UK Due to: high fraction of floating rate mortgages, high private sector debt

Question 33

Do CBs receive signals regarding future state of demand? & what does this mean for MP?

Answer 33

Yes, in practice, CBs do receive signals regarding future state of demand, so pre-emptive MP is an option

Question 34

Why do CBs not act on pre-emptive MP despite receiving signals regarding future state of demand?

Answer 34

Signals are uncertain, meaning a future IS shift (demand side) may not occur Acting pre-emptively only for no shock to occur generates inefficient volatility in output and inflation = pre-emptive policy actions muted compared to baseline IS-PC-MR model

Question 35

What does greater uncertainty of signals & greater CB aversion do to policy interventions?

Answer 35

Greater uncertainty and greater CB aversion to making ‘false moves’ = the more gradual policy interventions

Question 36

What is the Brainard principle?

Answer 36

Uncertainty over parameters such as α and a limits policy interventions compared to basic IS-PC-MR case

Question 37

What does the CB need to consider when responding to signals regarding future state of demand?

Answer 37

Weigh up the downsides of responding to false signals vs. upside of stabilising the economy against the forecast demand shock (quicker recover as per graphs)

Question 38

Why do we not get a Taylor rule in this framework?

Answer 38

If α = β = a = 1, then IS-PC-MR solution generates this description of US monetary policy, except output gap term There is no output gap as PC has no lag from y to π: if we know exp. inf. (and hence PC position) and we know inf. gap (position on PC), we also know yt-1 - ye So the output gap does not convey any information over & above inflation gap = reacting to inflation alone is sufficient