Type author
Carlin
& Soskice
names here
Macroeconomics: Institutions,
Instability, and the Financial System
Chapter 4:
Expectations
These slides are authored by Hillary Wee,
UCL, Cambridge
© Wendy Carlin and David Soskice, 2015. All rights reserved.
Objectives:
Chapter 4: Expectations
By the end of this chapter, students should understand
the following:
▪ Why economic agents form expectations
▪ The Rational Expectations Hypothesis
▪ The Role of Expectations in the 3-equation model
▪ The Lucas Critique and Macroeconomic policy
▪ Inflation Bias and Time-inconsistent policy
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Overview:
Chapter 4: Expectations
▪ Expectations are formed by households, firms and the
policy maker. Expectations influence consumption,
investment, wage-setting and policy decisions.
▪ This is broadly reflected in the 3-equation model:
i.
IS Curve
Tobin’s Q: Firms form expectations of future profits;
Permanent Income Hypothesis: Households form
expectations over their future income.
ii.
PC Curve
Wage setters form inflation expectations (𝜋𝑡𝐸 ).
iii. MR Curve
Policy maker forecasts inflation next period.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Overview:
Chapter 4: Expectations
▪ Risk and Uncertainty: Reason why forming expectations is a vital
part of economic life.
▪ Risk: Known probabilities can be attached to future outcomes
▪ Uncertainty: Impossible to assign probabilities; Unknown outcomes.
▪ The need to attach subjective probabilities to different scenarios:
e.g. The Bank of
England Fan Chart
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Overview:
Chapter 4: Expectations
Rational Expectations Hypothesis (REH):
▪ A method to model agent behaviour
▪ Agents in the model use the model and all available information
to forecast and therefore do not make any systematic error
▪ Model-consistent expectations = Rational Expectations
▪ Recall that in Ch. 2 and 3, wage-setters have adaptive inflation
expectations, 𝜋𝑡𝐸 = 𝜋𝑡−1.
▪ They make systematic errors since with a positive output gap,
inflation always ends up being higher than expected (due to pricesetting by firms).
▪ The assumption of adaptive expectations does not allow agents
to learn from their mistakes.
▪ This kind of expectations formation behaviour is not rational.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Phillips curves and Expectations
The PC, Expectations and Inflation:
▪ Expected period t inflation, given the information set at t-1:
▪ Standard PC:
▪ 2 ways to model inflation expectations:
(i)
Adaptive Expectations: Expect inflation be to what it is in the
previous period; Backward-looking.
(ii) Rational Expectations: Agents use the model and all
available information to form forecasts; Forward-looking.
▪
Question: What does UK data say about how expectations are
formed?
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Phillips curves and Expectations
UK inflation in the post-war period:
▪ 1950s-60s: Positive but stable inflation
▪ 1960s-70s: Shift in bargaining power to workers. Continually
rising inflation is consistent with adaptive expectations
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Phillips curves and Expectations
▪ 1960s-70s: Rise in equilibrium unemployment but the
government tries to keep U low → Inflation keeps rising.
▪ Adaptive
Expectations:
Wage-setters update their
expectations each period to correct for the erosion of
expected real wages → PC shifts upwards each period
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Phillips curves and Expectations
Expectations and the Output-Inflation Tradeoff (I):
▪ Adaptive Expectations PC: πt = πt−1 + α(yt −ye )
▪ Rearranging this yields πt − πt−1 = Δ πt = α(yt −ye )
(Inflation continues to increase so long output stays above equilibrium )
▪ No output-inflation trade-off in the long-run: The policy maker
cannot choose a higher level of constant πt to generate yt > ye.
▪ Under adaptive expectations, there is always upward pressure
on inflation if output is above its equilibrium level.
▪ Absence of a long-run output-inflation tradeoff is supported by
the experience of high inflation and high unemployment in
developed economies (aka. the ‘Stagflation’ of the 1970s).
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Phillips curves and Expectations
Stagflation in the US:
▪ 1950s-60s: Stable relationship between output and inflation
▪ 1970 onwards: Output-Inflation relationship breaks down
High Inflation
accompanied by
high unemployment
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Phillips curves and Expectations
Expectations and the Output-Inflation Tradeoff (II):
▪ Rational Expectations PC: πt = π𝐸𝑡 + α(yt −ye ) + ε𝑡
in which
π𝐸𝑡 = πt
and therefore
yt = ye −
ε𝑡
α
,
ε𝑡 is a random shock term with an average of zero.
▪ Only unanticipated shocks (ε𝑡 ) to inflation and the output gap
cause inflation to be different from its expected value.
▪ There is no trade-off at all between inflation and the output gap.
▪ Question: How do these different ways of forming expectations
affect our 3-equation model?
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Expectations and the 3-equation model
Expectations and the 3-equation model:
▪ Adaptive vs Rational Expectations: example of the CB reducing 𝜋 𝑇
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Expectations and the 3-equation model
Adaptive vs Rational Expectations:
▪ Reduction in inflation target (𝜋 𝑇 ): MR curve shifts downwards
▪ Rational Expectations:
- Economy jumps immediately from ‘A’ to ‘Z’, keeping 𝑦𝑡 = 𝑦𝑒
- Disinflation is costless: No rise in unemployment
▪ Adaptive Expectations:
- CB has to tighten monetary policy to move to ‘B’
- Adjustment takes time and is costly: Unemployment is above
equilibrium level for some periods
▪ Why does rational expectations result in costless adjustment?
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Rational Expectations
Rational Expectations:
▪ Proposition: Output must be at equilibrium (yt = ye ) for rational
expectations to be fulfilled (π𝐸𝑡 = πt ).
▪ If yt ≠ ye then inflation must be infinite:
▪ Suppose instead that α(yt −ye) = β ≠ 0 . Rational expectations
hypothesis (REH) dictates that the LHS and RHS of the PC
should be equal in expectations, so πt = π𝐸𝑡 + β (▲)
▪ Then, the only way in which (▲) holds and where inflation
expectations are fulfilled (π𝐸𝑡 = πt ) is if π𝐸𝑡 = πt = ∞ .
▪ Therefore, REH implies that output is always at equilibrium, in
expectations.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Rational Expectations
▪ Under REH, the CB must set the int. rate at the start of period t to
deliver yt = ye in expectations.
▪ This implies that the IS must take the form: yt = 𝐴 − 𝑎𝑟𝑡
(i.e. no policy lag in the IS).
▪ REH: Wage and price setters know that the CB chooses yt where
the MR curve intersects the PC curve.
▪
(PC under REH)
(MR under REH)
▪ MR intersecting the PC implies:
▪ Thus, for REH (πt = π𝐸𝑡 ) to be fulfilled, it must be that π𝐸𝑡 = π𝑇 .
▪ Rational agents know that CB targets π𝑇 , and expect this π level
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Rational Expectations
▪ The CB knows this is the way π𝐸𝑡 is set, so the relevant PC is
πt = π𝑇 + α(yt −ye )
▪ Combining with the Monetary Rule (MR), the output desired by
the CB is simply yt = ye (see Fig. 4.5 a: where MR intersects the PC)
▪ Thus, the CB implements this output gap using the IS (with no
lags) by simply setting the interest rate, rt as follows:
▪ i.e. the CB sets rt at its stabilizing rate.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Rational Expectations
Implications of Rational Expectations:
1. Economy is at equilibrium output, and inflation is at target
(assuming no random shocks)
•
Dynamic behaviour of 𝜋 (as per Ch. 3) disappears
•
Inflation not built into the system, so no costly disinflation.
2. Simpler job for the CB:
•
No policy lags in the AD
•
Also, no role for a stabilizing CB to move the economy to eqbm.
3. The CB can influence expectations directly since wage and price
setters are forward looking:
•
Under adaptive expectations, actual 𝜋 has to fall before it affects 𝜋 𝐸.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Anchoring Inflation Expectations
Anchoring Inflation Expectations:
▪ Central bank communication is used to keep inflation expectations
(𝜋 𝐸 ) anchored at the inflation target (𝜋 𝑇 ).
▪ If the inflation target is perfectly credible and 𝜋 𝐸 is anchored, then
an inflation shock will only last for one period.
▪ There is costless disinflation (unemployment does not rise): The
PC reverts back to the one indexed by 𝜋 𝑇 in the next period.
Modelling CB credibility (χ):
• PC:
where
• Expected Inflation is a weighted average of the inflation target and
lagged inflation.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Anchoring Inflation Expectations
CB Credibility (χ) and the adjustment to an inflation shock:
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Anchoring Inflation Expectations
CB Credibility (χ) and the adjustment to an inflation shock :
χ = 0 : Fully Backward-looking
• After a π shock, CB needs to raise r → some periods with yt < ye.
χ = 1 : Firmly anchored at 𝜋 𝑇
• Only 1 period effect of π shock → PC reverts to PC (𝜋0𝐸 = 𝜋 𝑇) →
CB does not need to change r → yt = ye (Disinflation is costless)
χ = 0.5 : Partially anchored at 𝜋 𝑇
• After a π shock, CB needs to raise r, but to a lesser extent than
χ = 0 → fall in output is lower, adjustment to equilibrium quicker
• PC shifts down to PC (𝜋0𝐸 = π’) instead, economy moves to point C
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Anchoring Inflation Expectations
▪  Credible inflation targeting → Lower cost of disinflation
▪
Drivers of CB credibility:
1. Independence
CB is free from political pressure, it can stick to its policy objective
2. Transparency
Transparent decision-making process; CB communicates their
views and actions → assists in forming inflation expectations.
▪ Question: Do credibility and transparency matter?
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Modelling:
Anchoring Inflation Expectations
Late 1990s: The developed world central banks have realized
the importance of credibility and transparency:
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (I):
The Lucas Critique
The Lucas Critique:
▪ Models that rely on relationships found in historical data are
problematic.
▪ Relationships in historical data are conditional on past policy
regimes, and will break down if the policy regime changes.
▪ Economic agents change their behaviour in response to the
new policy regime
▪ Problematic if agents use rational expectations, but policy
maker interprets data as though they are not REH agents.
▪ Applications in the 3-equation model under REH:
Government spending effects & revoking CB independence.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (I):
The Lucas Critique
The Lucas Critique and the model (I):
▪ The Government raises spending (𝐺) after the CB sets rt , and
after wage and price setting is already done.
▪ Autonomous demand (𝐴) increases, so yt > ye.
▪ In the current period, the CB and agents cannot react.
▪ Under REH, agents assume π𝐸𝑡 = πt and believe that yt = ye ,
therefore inflation stays on target.
▪ In the next period, the CB reacts by increasing rt+1 so that yt+1 =
𝐴 − 𝑎rt+1 = ye
▪ Inflation is now at target and output falls back to equilibrium.
▪ If wage and price setters have rational expectations, the best a
fiscal stimulus can do is a 1 period increase in 𝑦.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (I):
The Lucas Critique
The Lucas Critique and the model (II):
▪ *Evidence from (I) suggests that govt. expenditure (𝐺) boosts 𝑦
without increasing π*.
▪ So the govt. takes away CB independence and bars it from
increasing 𝑟 in response to increasing 𝐺.
▪ Increasing 𝐺 causes next period inflation to increase, since the
CB cannot react by increasing 𝑟.
▪ Under REH, agents can only be ‘fooled’ once by the govt, they
will build the higher 𝑦 level into their wage bargaining.
▪ Thus the boost in 𝐺 results in a rise in π.
▪ As before, REH implies that π is expected to be infinite.
*Lesson: Forecasting policy outcomes using historical relationships
such as in (I) can produce poor economic outcomes.*
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (II):
Expectations and Inflation Bias
Expectations and Inflation Bias
▪ What happens if the govt. has both an inflation and an
output target (which targets a below-equilibrium level of
unemployment)?
▪ This gives rise to Inflation Bias: Output stays at equilibrium
but inflation is above target
▪  This outcome is unambiguously worse than if a CB
simply targets 𝜋 𝑇 and a zero output gap.
▪ Next, we study inflation bias in the cases of adaptive and
rational expectations.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (II):
Expectations and Inflation Bias
Inflation Bias from targeting above-equilibrium output
Inflation Bias
= π𝑋 − π𝑇
= 4% - 2%
= 2%
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (II):
Expectations and Inflation Bias
(i) Adaptive Expectations and Inflation Bias
▪ CB targets 𝑦𝐻 > 𝑦𝑒 : MR shifts rightwards (The ‘bliss point’ is
now 𝐴′)
▪ CB forecasts that the PC stays at 𝑃𝐶 (π𝐸0 = 2), since π𝑡 is
unchanged by targeting 𝑦𝐻 , and since agents form adaptive
expectations (π1𝐸 = π0 = 2)
▪ CB chooses optimal point 𝐵 by lowering 𝑟.
▪ However, 𝑦 > 𝑦𝑒 at 𝐵, so upward pressure increases inflation to
3% and the adaptive expectations PC shifts upwards.
▪ The CB re-optimizes by lowering 𝑟 again in achieving point 𝐶.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (II):
Expectations and Inflation Bias
(i) Adaptive Expectations (contd.):
▪ At 𝐶, 𝑦 > 𝑦𝑒 so inflation increases and the PC shifts up further.
▪ The adjustment process ends when the economy moves to point
𝑍, where output is at equilibrium but inflation is above its target!
▪ Inflation bias highlights the futility in targeting 𝑦𝐻 > 𝑦𝑒 .
Size of the inflation bias is larger:
▪ The higher target output (𝑦𝐻 ) is than equilibrium (𝑦𝑒 ).
▪ The less inflation averse the CB is (steeper MR curve, low 𝛽 )
▪ The lower the output sensitivity of inflation is in the PC (low 𝛼;
Large fall in 𝑦 needed for low 𝜋, so CB just aims for higher 𝜋 ).
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (II):
Expectations and Inflation Bias
(ii) Rational Expectations, Inflation Bias and
Time Inconsistency
▪ 𝑦𝐻 target announced: Instantaneous adjustment from point 𝐴 to 𝑍.
▪ Forward-looking, rational agents know that given the new MR
curve, the medium-run equilibrium is at 𝑍.
▪ This generates the same inflation bias as before.
▪ Ex-post, the CB would have been better off committing to 𝑦𝑒 , but
they cannot do so due to time inconsistency.
▪ A CB that prefers 𝑦𝐻 always has an incentive to boost 𝑦 after
prices are set → Rational wage and price setters preempt this,
and set prices consistent with a 𝑦𝐻 target.
 A CB with a preference for 𝑦𝐻 > 𝑦𝑒 cannot credibly commit to 𝑦𝑒 .
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Application (II):
Mitigating Inflation Bias
(iii) Mitigating Inflation Bias
▪ Delegation
Delegating monetary policy to a CB which has no incentive to
set output above equilibrium
Longer term tenures for policy makers ensure that they take into
account policy impact over a longer period of time
▪
Reputation Building
2 period Game Theory example: The CB builds a ‘tough’
reputation (i.e. sets 𝑦 closer to 𝑦𝑒 ) to keep inflation expectations
low → bigger gain from increasing 𝑦 in the next period
Many periods: The benefits from behaving ‘tough’ increase.
Period 1’s situation is repeated until the last period, since there
are high gains from keeping π𝐸 low.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System
Summary
Chapter 4: Expectations
▪ Risk and uncertainty makes forming expectations necessary
▪ Under rational expectations, the CB can influence π𝐸 directly
▪ REH: Instantaneous and costless adjustment to shocks.
▪ CB transparency & credibility anchors π𝐸 closer to π𝑇
▪ The Lucas Critique highlights the problem in basing policies
on historical relationships between macroeconomic variables
▪ Inflation bias is caused by the CB targeting output above its
equilibrium, irrespective of rational or adaptive expectations;
A solution to this is an independent CB.
Carlin & Soskice: Macroeconomics: Institutions, Instability, and the Financial System