Discretionary Policy & Time Inconsistency

Question 1

what is a time consistent policy?

Answer 1

where the policy maker takes its optimal action in each period

this period by period optimisation is referred to as discretionary policy making

Question 2

what is discretionary policy making?

Answer 2

period by period policy optimization

Question 3

what is a time inconsistent policy?

Answer 3

where a policy maker may plan or announce a policy to be followed in the future but once at that time finds that it is no longer optimal to implement the policy

Question 4

what is delegation?

Answer 4

where control of policy is given to an independent central bank with a loss function which differs from that of society

Question 5

what is constrained discretion? and give an example.

Answer 5

where standard discretion is constrained

e.g. an announced inflation target

Question 6

what is a bias?

Answer 6

when there is a difference between the time consistent and time inconsistent policies

therefore there are gains from commitment or appropriate delegation

Question 7

give an example of policy.

Answer 7

commitment to future lower interest rates with the current interest rate at the ZLB

if the Phillips curve contains a forward looking inflation expectation such as Et[πt+1] (which iterates forward beyond t+1) higher inflation in the future will imply higher inflation now and a lower real interest rate

however, time inconsistent as once recovery occurs it is sensible to raise interest rates rather than keep them low

Question 8

what are some issues with solutions to time inconsistency and bias?

Answer 8

delegation may make communicating policy (transparency and accountability) more difficult

both commitment (if feasible) and delegation, while initially superior by design, both involve inflexibility (required to make them credible) and hence may no longer be superior if unusual shocks hit the economy and/or our understanding of how it works changes over time

Question 9

what is inflation bias? and what is it crucially dependent on?

Answer 9

time inconsistency problem by which the average inflation rate is too high relative to the social optimum and what could be achieved if commitment was feasible

crucially dependent on the policy maker’s output target being above the natural rate of output

Question 10

what does inflation bias occur?

Answer 10

(i) micro distortions / “economic fundamentals”

• e.g. tax distortions, imperfect competitions, excessive minimum wages, trade unions

(ii) political motivations

• politicians constantly trying to expand economy

Question 11

explain the Barro and Gordon model.

Answer 11

1. AS is a Lucas supply function: y = yn + a(π - πe) + e

• where y is output, yn is natural output, π is inflation, πe is expected inflation and e is a random, zero mean supply shock

2. assumptions:
   (i) expectations formed prior to the monetary policy decision and the realisation of the supply shock (sequencing)

(ii) supply shock realised and monetary policy determined ( ⇒ scope for stabilisation policy)

(iii) output and inflation determined

3. CB aims to min expected value of following loss function:
   V = 1/2 λ (y - yn - k)^2 + 1/2 π^2
4. expected inflation under discretion is positive and exceeds the socially optimal rate, which is zero - there is an inflation bias that is detrimental to welfare
5. if inflation expectations are set at 0 the lower PC in the diagram below applied and there is an incentive for the CB to raise inflation to increase output to A. Hence the socially optimal inflation rate is time inconsistent
6. incentive for CB to confound private expectations is eliminated only when expected inflation is high enough that the marginal cost of inflation offsets the benefit derived from extra output at D

Question 12

what are the assumptions of the Barro and Gordon model?

Answer 12

(i) expectations formed prior to the monetary policy decision and the realisation of the supply shock (sequencing)

(ii) supply shock realised and monetary policy determined ( ⇒ scope for stabilisation policy)

(iii) output and inflation determined

Question 13

what are the implications of the Barro and Gordon model?

Answer 13

a fixed rule, e.g. π = a constant will be preferable to discretionary policy, setting aside the issue of stabilisation policy if there are shocks

although the excess output ambition lies behind the inflation bias, output in excess of the natural rate will never actually be realised, at least on average

Question 14

are interactions between a CB and the private sector best thought of as a repeated game or a one shot game?

Answer 14

interactions between CB and private sector best thought of as a repeated game, not a one shot game

Question 15

what is the benefit of interactions between CB and private sector being thought of as a repeated game, not a one shot game?

Answer 15

repetition won’t solve bias, but opens up possibility of reputation building

marginal cost of inflation in t is not simply higher inflation in t, but also a reputation for setting high inflation in future, which will raise expected inflation and actual inflation in future periods

Question 16

what are the two types of independent central bank?

Answer 16

(i) instrument independence (UK)

(ii) goal independence (NZ)

Question 17

explain Rogoff’s conservative central banker solution to inflation bias.

Answer 17

Rogoff’s loss function:
VR = 1/2λ (y - yn - k)^2 + 1/2 (1 + δ) π^2

inflation weighted by (1+δ) where δ is the conservativeness (extra dislike of inflation) of the appointed CB

minimising VR will give the same results as minimising (1/1+δ)VR (a positive monotonic transformation)

⇒ ↑ in marginal cost of cheating, ↓ time consistent inflation (point R not point D)

but weight conservatism reduces the propensity for CB to dampen output shocks using counter-cyclical policy

the original MR line, “MR(dis)”, slope, -aλ, was optimal but now it will be -aλ/(1+δ) along “MR(Rog)” so output will be too variable and inflation not variable enough in response to shocks

by distorting gradient of MR (flatter), changes how CB respond to shocks (will be more extreme in response to managing inflation in terms of output)

only partial success as deals with inflation bias but at cost of changing how policy maker responds to shocks

Question 18

give an example of the Rogoff solution in practice.

Answer 18

In the UK MPC members drawn from academia, industry, financial services, trade unions, etc - some members are naturally more averse to inflation and each member should value extra output less around election time

Question 19

does evidence support the idea of Rogoff’s conservative central banker?

Answer 19

extent to which conservative CB model can explain trends towards increased CBI is unclear

Question 20

what is Lohmann’s (1992) adaptation of Rogoff’s conservative central banker?

Answer 20

Lohmann (1992) shows that it is welfare improving to appoint a weight conservative CB but limit independence

in normal times CB sets policy ⇒ low time consistent inflation

in times in which the supply shock is large the government overrides CB and implements aggressive stabilisation policy

by design better than straight Rogoff but harder to implement ideas, communicate and build credibility around it

Question 21

explain Walsh’s contracts for central bankers as a solution to inflation bias.

Answer 21

offer head of CB state-contingent payments contract

requires that government makes a transfer to CB (t) = t0 - akπ so the loss function becomes:
V = 1/2λ (y - yn - k)^2 + 1/2π^2 - t0 + aλkπ

last two terms are perfomance-related pay terms

adding linear term doesn’t change MR gradient

double success as solves both inflation bias and also the MR line is not distorted in removing it

Question 22

what are the limitations of Walsh’s contracts for central bankers?

Answer 22

(i) what practical mechanisms can be used to implement the contract transfer in practice?

(ii) contract ensures optimal stabilisation policy after a supply shock assuming shocks do not change other model parameters

(iii) displacement problem remains

Question 23

what does the evidence on the link between CBI and inflation suggest for the solutions to inflation bias?

Question 24

what are some common cause explanations for the CBI/inflation relationship?

Answer 24

public distaste for inflation may lead to the election of anti-inflation governments who then create independent central banks in order to lock in low inflation conditions ⇒ no causal effect

Posen (1993) argues that financial sector opposition to inflation is the key driver of both inflation and CBI

Question 25

is the evidence on the time inconsistency problem and the inflation bias convincing?

Answer 25

despite the vast theoretical literature on the time inconsistency problem and the inflation bias, it has been hard to find convincing evidence that these phenomena are important in practice

establishing causal links is difficult

Question 26

fill in the blank: a ________ cross-country correlation is found between inflation performance and measures of CBI.

Answer 26

a NEGATIVE cross-country correlation is found between inflation performance and measures of CBI

Question 27

what are the objections to evidence on CBI and inflation?

Answer 27

Alessina & Summers (1993) show that low inflation achieved by virtue of CBI is apparently a ‘free lunch’ (no additional volatility in real variables), but this is inconsistent with the conservative central banker hypothesis

this suggests not Rogoff as would expect a relationship between output and CBI, more consistent with Walsh as wouldn’t expect a relationship here

Question 28

what are the common cause explanations for the CBI/inflation relationship?

Answer 28

public distaste for inflation may lead to the election of anti-inflation governments who then create independent central banks in order to lock in low inflation conditions ⇒ no causal effect

Posen (1993) argues that financial sector opposition to inflation is the key driver of both inflation and CBI

Question 29

when does stabilisation bias occur? check this

Answer 29

occurs when the CB is forced to over-compensate for a change in the economy through raising interest rates more than the optimal amount

occurs due to an inability to commit to future interest rates

• this can happen for many reasons: e.g. limitations placed on the CB by a government, or through a loss of credibility

Question 30

what loss function is used with stabilisation bias?

Answer 30

Assume the same loss function as before but with k = 0:
V = 1/2λ (y - yn)^2 + 1/2π^2

it is quadratic so the marginal cost of output and inflation deviations from their target values is increasing in the size of the deviation

• makes large deviations disproportionately costly

Question 31

what is crucial to the existence of stabilisation bias?

Answer 31

crucial to the existence of stabilisation bias is the presence of a forward looking expected inflation term in the Phillips curve/AS relationship

Question 32

what is the NKPC form for stabilisation bias?

Answer 32

NKPC form:
πT = βEt[πt+1] + γ(yt - yn) + εt

Question 33

under NKPC how does expected inflation react to a shock?

Answer 33

under NKPC, expected inflation can react contemporaneously to the cost push shock (not the case with adaptive expectations)

Question 34

what is a key insight with stabilisation bias under NKPC?

Answer 34

key insight is that, under discretion, Et[πt+1] is not under the control of the policy maker, it is a given, so the best that they can do if there is a cost push shock t>0 is to “share” its impact on and y according to the optimal MR line

Question 35

what does credibility have to do with stabilisation bias under the NKPC?

Answer 35

if commitment is feasible the “spikes” when the shock hits can be made smaller by manipulating Et[πt+1]

if a credible commitment is made at time t to make inflation at t+1 negative this effectively offsets part of the impact of t>0 so the combined contemporaneous impact on and y can be smaller

Question 36

how do commitment and discretion differ to generate stabilisation bias?

Answer 36

under commitment Et[πt+1] effectively becomes an additional policy instrument for dealing with the time t shock

this is not possible under discretion because once time t+1 arrives no earlier promise is binding (it is time inconsistent) and the policy maker will simply react to the time t+1 shock ignoring the past

thus commitment and discretion differ so there is a bias and it’s called stabilisation bias as it relates to stabilising the economy when shocks occur