Chapter 22. The limits to stabilization policy:

Credibility and uncertainty

ECON320Prof Mike Kennedy

Overview

• So far we have assumed that policy is effective at stabilizing output and inflation fluctuations based on the assumptions that:– Policymakers have perfect information on the current state of the

economy– Policy actions have predictable and known quantitative effects– All announced policy actions are credible (the public believes that the

central bank will do what it says it will do)

• These are strong assumptions that may not be valid in a real world setting setting

• In what follows, the model will be adjusted to take account of these features

Credibility:The time-inconsistency of optimal monetary policy

• What happens when policymakers can undertake discretionary policy actions, after agents have formed their expectations?

• Start by assuming that all shocks are zero• The aggregate supply curve when γ = 1:

• Goods market equilibrium simplifies to:

• The central bank can control the current output gap and thus the rate of inflation for any given

• The loss function is written in terms of y*, the desired level of y

• Because of distortions we assume that:

Credibility con’t• From the above we have

• Which means that we can write the loss function as

• If the inflation target, π*, is zero, then the Taylor rule would be:

• Assuming that the central bank sticks to the above Taylor rule, then equilibrium under rational expectations becomes

• The question investigated here is: Does the central bank have an incentive to cheat?

Determining the incentive to cheat• We can calculate the change in SL at the point where

• This says that the social loss can be reduced if the central bank induces some surprise inflation which moves y closer to y*

• The outcome is that a central bank that can engage in discretionary policy will not want to stick to the Taylor rule

• Minimizing SL (2nd equation, slide 4) wrt π:

‘Cheating outcome’ with surprise inflation

• The difference between the social loss with the Taylor rule (SLR) and that with cheating (SLC) measures the temptation to cheat:

Temptation to cheat

Time-consistent monetary policy

• From the final equation we see that the greater is ω, the greater the temptation to cheat

• The important point emerging from the previous slide is that the policy maker has no incentive to deliver price stability; that is to follow a Taylor rule

• The problem here is that rational agents will know this or at least they will figure it out as time passes

• In this case, the time consistent rational expectations equilibrium is one where inflation is higher and output is back at potential

• This is now time consistent in that the central bank delivers the rationally expected inflation rate, which unfortunately is now greater than zero

Time-consistent monetary policy and credibility• The equation on the previous slide illustrates the problem of

building credibility when the central bank has discretion• The final outcome is one where inflation is permanently

higher but there are no output gains• The outcome is worse than one under a Taylor rule where

expectations would equal π* = 0 and output would be at potential

• The social loss when the policy maker has discretion is now

• The first term represents the loss due to inefficiently low output while the second term is the loss due to higher inflation – how can the second be eliminated?

Building a reputation• The above assumed that policymakers were short sighted• If they care about their reputations then the outcome will be

different• If the central bank pursues a rules-based policy then

• If under discretion, if the bank cheats, then the optimal π is:

• Knowing that this is the public’s expectation of π, the best thing the central bank can do is deliver it

• In this way, it gains credibility

Building a reputation con’t• The temptation to cheat when reputation matters can be

written as:

• The first term is the same as derived in slide 5 (final equation) and shows the gain from using discretion

• The second shows the cost to the policymaker’s reputation which occurs in the second period

• The term 1 + ρ shows that the policymakers discounts the future loss – the higher is the discount rate (ρ) the less reputation is valued and the greater the incentive to cheat

Building a reputation con’t• The condition can be evaluated based on previous equations

• The policymaker will stick to the policy rule as long as the short-run gains are less than the next period costs

• The policymaker will not want to cheat if:– The discount rate (ρ) is low; that is reputation is valued highly, and– The value of the inflation aversion parameter (κ) is low

• Note that the value of ω, the measure of market distortions, does not affect the sign of the expression – a higher value of ω increases the current period gain but also the next period loss

Delegating monetary policy

• The issue here is the government and whether they would place sufficient weight on the future outcomes of their actions

• For this reason many economist advocate delegating monetary policy to an independent central bank

• There are varying degrees of independence as shown in Table 22.1, with Canada, along with Japan and the UK, occupying a middle ground

• Suppose that the bank considers the loss from instability to be given by

• The parameter ε measures the degree to which the inflation aversion of the central bank exceeds that of the government – a measure of the bank’s conservatism

Delegating monetary policy con’t

• Define 0 ≤ β ≤ 1 as a measure of the degree in independence that the government has given the central bank

• Optimal monetary policy is determined by minimizing the modified loss function

• The time consistent rational expectations equilibrium with policy delegated to a conservative central banker is:

• Compared to the last equation in slide 8 (the equilibrium with cheating) we see that we get lower inflation – it would go to zero as ε approaches infinity, which would be complete inflation aversion

Delegating monetary policy con’t • Recall again the government’s loss function

• Subbing in the outcome for inflation from the previous slide we get

• The higher is the term βε, the lower will be the loss• Two conditions give this result:

– The central bank must have some independence (β > 0)– The central bank must have a greater aversion to risk than the

government (ε > 0)

• We should expect to see a better inflation outcomes in countries that have more independent central bank, which we do observe (Fig 22.2 in the text)

An example of delegating monetary policy:The case of the Bank of England

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10 year interest rate

An example of delegating monetary policy:The case of the Bank of England

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5 year interst rate

Credibility versus flexibility

• There is a trade-off between flexibility and credibility which arises (not surprisingly) in the case of supply shocks with high variances

• With a conservative central bank, the reaction to the rise in inflation will exacerbate the variance in output to such an extent that social welfare falls

• In the end some flexibility may be desirable • In such cases, communicating with the public and markets will

be very important

The implication of measurement error

• In real time, when policymakers have to make decisions, current estimates of the state of the economy are likely not providing an accurate picture

• A particular dramatic illustration of this is shown in Fig 22. 5 in the text

• Policymakers significantly overestimated the degree of slack in the economy

• This reflected both errors in measuring actual output but as well the level of potential, which we now know was weakening

• The result was a long period of inflation during which inflation expectations rose and became difficult to bring down

The implication of measurement error• To study the implications we first start by defining the following and• Now suppose that each gap deviates from its true values as

follows

• The variables μ and ε are random with zero means and constant variances and they reflect the degree of uncertainty about the output and inflation gaps

• The Taylor rule now becomes

The implication of measurement error

• Assume that expected inflation equals the bank’s target π*, then the SRAS becomes

• Allowing for only demand shocks AD becomes

• The Taylor rule along with the SRAS and AD curve are a complete model, which yields the following output gap expression

• From this expression it follows that the variance of output is

The implication of measurement error

• The final equation on the previous slide, the variance of the output gap, is reproduced here

• In the absence of errors, the variance of the output gap would be

• Thus the errors contribute to output instability by inducing policymakers to put in place the wrong interest rates

The implication of measurement error• From the SRAS equation (first equation, Slide 17), it follows

that, if the variance of the output gap can be minimised, then so will the variance of the inflation gap

• Deriving the first order conditions for minimising the variance wrt h and b we get

The implication of measurement error• From the above two equations it can be shown that

• The greater is the uncertainty regarding the output gap relative to the inflation gap, the larger is the central bank’s response to the inflation gap

• The above equation and the final equation on the previous slide yield

and

The implication of measurement error• Suppose now that the measurement errors are expected to

persist in the following way

• We can expand these back to get

• Then the variance will equal

The implication of measurement error

• This will modify the final two expressions on slide 20 to

and

• The message here is that the more persistent are the shocks the smaller are the optimal levels of b and h

• In this case, go slow