Transcript Inflation Bias

The Inflation Bias and
what to do about it
Professor Anne Sibert
Spring 2012
Bad monetary policy in the 1970s and 1980s led to a revolution
in central bank design in the 1990s
Inflation in 1981
(percent change in average consumer prices)
25
20
15
10
5
0
Canada
France
Germany
Source: IMF, World Economic Outlook database
Italy
UK
US
Examples of Changes in bank
legislation
• Reserve Bank of New Zealand Act of 1989
binds the Reserve Bank to price stability
• Bank of England Act of 1997 imposes an
inflation target on the Bank of England
• Bank of Japan Act of 1997 orders the pursuit
of low inflation
This lecture:
• Why was monetary policy so bad in the 1970s
and 1980s? Why do monetary policy makers
cause too much inflation?
• The classic model of an inflation bias: the
time-inconsistency problem
• How can we do to solve the timeinconsistency problem
The Phillips Curve
Suppose we have the following sequence of events: (1) wage setters choose a
fixed nominal wage W; (2) the price level P is observed; (3) firms decide how
many workers L to hire.
Real wage
Labour demand
curve
W/P
L
Labour
The Phillips Curve
Suppose that P1 < P2 < P3. It is seen that higher prices lead to higher
employment.
Real wage
Labour demand
curve
W/P1
W/P2
W/P3
L1
L2
L3
Labour
The Phillips Curve
• There is a positive relationship between inflation and employment.
• The Phillips Curve’s name comes from a 1958 article by William Phillips:
Phillips, William (1958), The Relationship between Employment and the
Rate of Change of Money Wage Rages in the United Kingdom, 1861-2957,
Economica, 25, 283-299.
• In 1960 Paul Samuelson and Robert Solow showed a similar correlation
between inflation and employment in the United States. They called this
relationship a Phillip's Curve. Samuelson, P. and R. Solow (1960),
"Analytical Aspects of Anti-Inflation Policy," American Economic Review 50,
177 - 194.
• The idea that there is a relationship between inflation and output dates
back at least as far as the 1920s when Irving Fisher wrote a paper on the
subject.
• For many years many economists and policy makers believed that there
was a stable relationship between inflation and employment. This led to
the Keynesian idea that policy makers could increase employment if they
were willing to tolerate higher inflation.
Challenges to this View
• In the late 1960s Milton Friedman and Edmund Phelps challenged the idea
of a stable long-run relationship between employment and inflation.
• They argued that workers and firms cared about real wages and that if
they believed policy makers were increasing inflation with the intent of
increasing employment then they would demand higher nominal wages.
• Thus, policy makers could not systematically increase employment by
increasing inflation
• Stagflation (the simultaneous occurrence of high inflation and high
unemployment) in the 1970s lent empirical support to Friedman's and
Phelps's criticism.
• Today few economists believe that there is a stable long-run Phillip's
curve.
• See: Phelps, E. (1967), "Phillips Curves, Expectations of Inflation and
Optimal Employment over Time," Economica 34, 254--281 and Friedman,
M. (1968), "The Role of Monetary Policy," American Economic Review 58,
1-17.
The Rational Expectations Revolution
• The advent of the rational expectations revolution in the late 1960
and early 1970s led to a new approach to modelling the labour
market.
• Suppose that wage setters have a preferred employment rate L*.
They dislike deviations from this rate. Suppose further that they
expect the price level to be Pe and they choose the fixed contractual
wage so that L = L* when P = Pe.
• When the price is equal to wage setters' expected price,
employment is equal to their preferred employment rate L*.
However, if the price level is higher than expected, then the real
wage is lower than expected and employment is higher than L*.
This gives us the expectations-augmented Phillips curve: there is a
positive relationship between employment and unexpected
inflation. A policy maker can increase employment above L* if and
only if he produces inflation that is higher than expected.
Why does the policy maker want to
increase employment?
• One might wonder why a policy maker would want to
increase employment above that preferred by wage
setters.
• One answer is labour market distortions. An example is
a tax on wages.
• If workers work more than they gain from the extra
wages and the economy gains from the extra tax
revenue. However each worker views his contribution
to aggregate tax revenue to be so relatively tiny that he
does not take this into consideration.
• Thus, the socially optimal level of employment is
higher than rate most preferred by wage setters.
Other ways to get an ExpectationsAugmented Phillips Curve
• In the 1970s academic economists split. One camp was willing to
assume that there were nominal rigidities, even though they could
not explain why such rigidities arose. These economists were
sometimes called salt water economists as they tended to be
associated with universities on the east and west coasts of the
United States. (MIT, Harvard, Princeton, Stanford)
• The other camp insisted that everything in a model be consistent
with rational optimising behaviour. These economists were
sometimes called fresh water economists because they tended to
be associated with universities in the interior of the United States.
(Chicago, Carnegie-Mellon, Minnesota, Rochester)
• The leading fresh water economist Robert Lucas constructed a
model that produced an expectations-augmented Phillips curve
even though all prices are perfectly flexible. His result was based on
informational asymmetries.
The Lucas (1972) Model
• Lucas argued that firms learn the price of their own good
before they learn the aggregate price level. Thus, if they
see that their price has gone up, they do not know if it is
because demand for their good has gone up, causing an
increase in the relative price of their good which would call
for an increase in their output, or if it is because there is
inflation and all prices have gone up. To the extent that
they do not expect inflation they increase their output.
Thus, there is a negative relationship between inflation and
output.
• See Lucas, R. (1972), "Expectations and the Neutrality of
Money," Journal of Economic Theory, 4, 103--124. This
paper is beautiful, but some find the informational
assumptions unappealing
Why is Inflation Costly?
•
•
•
•
•
•
•
Shoe-leather costs: The opportunity cost of holding non-interest bearing money is
the nominal interest rate. The higher is inflation, the higher is the nominal interest
rate and the more resources households and firms expend to avoid holding money.
Menu costs: If prices change, then menus and other price lists must be updated.
Firms often set prices in advance and keep them unchanged for some time. If not
all prices are set simultaneously, then inflation causes relative prices to be
distorted.
Inflation makes the currency an inconvenient unit of account; a yardstick is not as
useful if its size keeps changing.
Inflation can interact with the tax system in a way that produces distorted or unfair
outcomes. For example, in years of high inflation, people may pay capital gains
taxes on real capital losses.
Inflation can redistribute income in a way that is regarded as unfair: the
sophisticated and relatively wealthy gain at the expense of the poor and the badly
educated.
Disinflation is also costly, for most of the same reasons.
The Time-Inconsistency Problem
Suppose that the monetary policy maker is benevolent and has the same
preferences as society.
Suppose that society dislikes deviations from the socially optimal level of
employment Lo and that it also dislike deviations form zero inflation.
Let the society's welfare function be:
𝑊 = −𝜑 𝐿 − 𝐿𝑜
2
− 𝜋 2,
where φ > 0 is a parameter that measures the weight that society puts on
losses due to deviations of actual employment from their socially optimal
level relative to losses due to deviations of inflation from zero.
In the above equation it is assumed that optimal inflation is zero. This may
seem at odds with real-world central banks that typically aim for low but
positive inflation. This, however, is because measured inflation is believed to
be significantly higher than actual inflation.
Suppose there is an expectations-augmented
Phillips curve:
𝐿 = 𝐿∗ + 𝜋 − 𝜋 𝑒 ,
where πe is wage setters’ expectation of
inflation.
Suppose that socially optimal employment is
higher than wage setters’ preferred
employment:
𝐿𝑜 = 𝐿∗ + 𝑑,
where d > 0 arises from a distortion in the
labour market.
Society’s Objective Function
Putting this together yields
𝑊 = −𝜑 𝜋 − 𝜋 𝑒 − 𝑑
2
− 𝜋 2.
The key feature: Society likes unexpected
inflation and dislikes actual inflation.
Another story due to Guillermo Calvo
• Increasing the money supply produces direct revenue called seigniorage.
It also decreases the real value of the government's outstanding debt. This
is called an inflation tax.
• Both seigniorage and the inflation tax are increasing in unexpected
inflation. (Optimal inflation may not be zero because there may be some
seigniorage revenue even when inflation is expected.)
• It is believed that for most advanced economies (at least in normal times)
that (direct) taxation is less distortionary than inflation. But, there is a
significant cost associated with administering and complying with the tax
code.
• For countries with inefficient tax systems or for countries with
extraordinary revenue needs it may be optimal to collect some
seigniorage or inflation tax. Thus policy makers may like unexpected
inflation.
• Calvo, G. (1978), "On the Time Inconsistency of Optimal Policy in a
Monetary Economy," Econometrica 46, 1411-1428.
Optimal Monetary Policy
• The timing of events is that wage setters choose a
fixed contractual nominal wage based on their
expectation of inflation and then the monetary
policy maker choose their monetary policy. Thus,
monetary policy makers take expected inflation
as given and choose actual inflation to maximise
social welfare.
• It is assumed that the monetary policy maker can
perfectly choose inflation. This is untrue but
unimportant here.
Optimisation:
Set the derivative of the objective function with
respect to inflation equal to zero:
𝑑𝑊
𝑑𝜋
= −2 𝜋 − 𝜋 𝑒 − 𝑑 − 2𝜋 = 0.
Note that the second derivative is negative, so
the solution is a maximum.
Rational Expectations
Solving yields
𝜋=
𝜑 𝜋𝑒 +𝑑
1+𝜑
.
There is no uncertainty in this model and is
assumed that wage setters know the monetary
policy maker’s objective function. They, too can
maximise it. It is assumed that their expectations
are rational and that π = πe. Substituting into the
above equation yields
𝜋 = 𝜑𝑑.
Inflation Bias
This is unfortunate. The monetary policy maker chooses π > 0
even though society dislikes inflation and even though it does
not increase employment (because it its expected).
Society would be better off if the monetary policy maker
could commit himself to zero inflation. In this case there
would be no increase in employment because the zero
inflation is expected, but at least there would be not costly
inflation.
The problem with this is that if the policy maker announces
that he is going to choose π = 0 and this is believed then he
should reneg and set
𝜋=
𝜑 𝜋𝑒 +𝑑
1+𝜑
=
𝜑𝑑
.
1+𝜑
Game in extensive form
Expect inflation
inflate
Time-consistent
ourcome
Don’t expect
inflation
don’t
inflate
inflate
Best outcome for
society
don’t
inflate
2nd best outcome is
not subgame perfect
Inflation Game
• No matter whether wage setters choose a contract based
on zero inflation or on strictly positive inflation, the
monetary policy maker will choose strictly positive
inflation.
• Knowing this, wage setters should choose a contractual
wage based on an expectation of strictly positive inflation.
• No promise by the monetary policy maker that it will
choose zero inflation is credible.
• In game theory jargon the outcome where the monetary
policy maker announces that he will set zero inflation, this
is believed and the policy maker does indeed choose zero
inflation is not subgame perfect. It is based on an incredible
announcement.
Time-Inconsistency Problem
•
The monetary policy maker's optimisation problem can be contrasted with that of
an engineer trying to control a missile. The following quote is from the Wikipedia
article "Trajectory Optimization" and the italics are mine.
– For tactical missiles, the flight profiles are determined by the thrust and load factor (lift)
histories. These histories can be controlled by a number of means including such techniques
as using an angle of attack command history or an altitude/downrange schedule that the
missile must follow. Each combination of missile design factors, desired missile performance,
and system constraints results in a new set of optimal control parameters.
•
•
•
The flight profile depends on what happened in past. The engineer can use
standard control theory techniques to solve his problem. In contrast, the state of
the economy depends on what the economic policy maker is expected to do in the
future and standard optimisation techniques do not work.
The seminal work of Kydland and Prescott (1977) discusses this problem, called
time inconsistency, and its implications for monetary policy. The model here is due
to Barro and Gordon (1983), who popularised the idea of Kydland and Prescott.
See Kydland, F. and E. Prescott (1977), "Rules Rather than Discretion: The
Inconsistency of Optimal Plans," Journal of Political Economy 85, 473-491 and
Barro, R. and Gordon D. (1983), "A Positive Theory of Monetary Policy in a Natural
Rate Model," Journal of Political Economy 91, 589-610.
Taxing Capital
• The notion of time inconsistency, or the inability of policy makers or
others to commit themselves to the optimal plan, appears else where in
economics.
• It is a standard result in public finance that is less distortionary to tax
capital than to tax labour. Even workers should prefer capital taxes to
labour taxes. In either case workers bear the burden (either because they
pay the tax or because the burden is passed onto them in the form of
lower real wages) and capital taxes additionally distort capital formation.
• However, once capital is already put into place it is better to tax capital.
There are no distortions in this case because capital, unlike labour, cannot
be instantly adjusted.
• Consider a model where capital is put into place and then the taxes on
capital and labour are decided. The optimal outcome requires a
government to commit itself to not taxing capital. But owners of capital
know that once the capital is in place it will be taxed. So, in making their
investment decision they believe capital will be taxed and they invest too
little.
Commitment
•
Another example of a time inconsistency problem is that of a firm that
would like to borrow. This firm is confronted with two projects: one is risky
and one is safe. It would be willing to do either investment if it were able
to borrow the necessary funds, but it prefers the risky investment. A bank
is willing to lend to the firm if and only if it undertakes the safe project.
The optimal outcome if for the firm to commit itself to undertaking the
safe project and for the bank to make a loan. But, if the bank cannot itself
to undertake the safe project then it will not be able to borrow. The bank
will know that once the firm has the money it will undertake the risky
project.
• The firm and the bank can enter into a legally enforceable contract that
requires the firm to invest in the safe project. This commitment device
makes the firm and the bank better off.
• Unfortunately, it is more difficult for the government to commit itself to a
course of action. How does a government bind itself to follow a law,
particularly when not following it can make everyone better off?
Conservative Central Bankers
• One solution to the time-inconsistency problem is to
appoint a central banker who does not share society’s
preferences.
• If you appoint a central banker who cares solely about
inflation then he will sets inflation equal to zero and this
will be expected.
• One problem with this is that it is not always easy to
ascertain someone’s preferences. President Eisenhower
nominated Earl Warren for Chief Justice of the US Supreme
Court in the greatly mistaken belief he would be
conservative. Likewise, Pres. George H. W. Bush nominated
David Souter in the mistaken belief that he would be
conservative.
Central Bank Independence
• Making the bank operationally independent does not
necessarily solve the time-inconsistency problem. If the
central bank shares the government’s preferences, it
will have a time-inconsistency problem as well.
• However, Bernanke et al (1999, p. 25) argue that
central bankers are apt to be more inflation averse
than the government, saying that this, “… may be the
result of ‘tough’ central bankers … or it may just be that
their professional backgrounds and socialization make
central bankers relatively hawkish on inflation.”
Inflation Targets
• Either appointing conservative central bankers or
imposing a legally binding inflation target on the
central bank has the problem that it will cause the
central bank not to react to or not react enough to
stochastic shocks that are realised after nominal wages
are set but before monetary policy is made.
• Such shocks provide a stabilisation role for a central
bank. Any commitment device that removes the
inflation bias may be at the expense of the central bank
being able to respond to these shocks.
What if the central bank has a
stabilisation role?
• Suppose that the timing of events is
1. Wage setters chose the fixed nominal wage
2. A shock shifts the labour demand curve
3. The monetary policy maker chooses inflation
• The monetary policy maker has better
information than the private sector (because
he chooses his action later) and he can use
this information to offset the shock: the
central bank has a stabilisation role.
Suppose that the expectations-augmented Phillips curve is:
𝐿 = 𝐿∗ + 𝜋 − 𝜋 𝑒 + θ,
where θ is a shock to labour demand that has mean zero and variance σ2.
Then society’s objective function becomes
𝑊 = −𝜑 𝜋 − 𝜋 𝑒 − 𝑑 − θ 2 − 𝜋 2 .
The central bank takes expected inflation as given and it knows the shock.
Maximising with respect to inflation yields
𝜋=
𝜑 𝜋𝑒 +𝑑+θ
1+𝜑
.
The wage setters do not know the shock. They have rational expectations and their
expectation of inflation is the statistical expectation. Thus, 𝜋 𝑒 = φ𝑑 and
𝜑𝜃
𝜋 = 𝜑𝑑 + 1+𝜑.
Society’s expected welfare is
𝜎2
𝐸 𝑊 = −φ
+ 1 + 𝜑 𝑑2
1+𝜑
If instead, society appointed a conservative central banker who always chose zero
inflation, then expected welfare would be
𝐸 𝑊 = −𝜑 𝜎 2 + 𝑑 2 .
Society is better off with a conservative central bank if and only if
𝜎 2 < 1 + 𝜑 𝑑.
Rogoff (1985) showed that if the government could precisely pick the preferences φ*
of the central banker then it should pick one who was more conservative than
society (that is φ*< φ), but not one who cares solely about inflation.
See Rogoff, K. (1985), “The Optimal Degree of Commitment to an Intermediate
Monetary Target,” Quarterly Journal of Economics 100, 1169-1189.
It is hard to believe that the government can precisely gauge someone’s preferences.
Rogoff’s model led to a sizable academic literature on the trade-off between central
bank credibility and the ability of the central bank to stabilise. This literature
probably puts too much emphasis on the central bank’s stabilisation role.
In reality, uncertainty is not captured in one readily observable variable. The state of
the economy is extremely difficult to observe, describe and interpret. Moreover,
making monetary policy is difficult.
Milton Friedman and the monetarist school, however, famously questioned even a
short-run stabilisation role for monetary policy, claiming that there are long, variable
and uncertain lags between the implementation of monetary policy and when its
effects occur and that these lags cannot be easily predicted.
Central banks cannot “fine tune” the economy. At most, they can offset some large
and observable shocks.
Walsh Contracts
• Walsh (1995) proposes that the government should
enter into a contract with the monetary policy maker
who has a stabilisation role.
• The contract imposes a linear penalty on a central bank
in excess of its target and pays a reward for inflation
below target.
• If the contract is written properly, society gets the
optimal outcome. There is no inflation bias and the
central bank stabilises the shock to the labour demand
curve.
• See Walsh, C. (1995), “Optimal Contracts for Central
Bankers,” American Economic Review 85, 150-67.
Problems
• This only works if it is credible that the government will
enforce the contract. But the time-inconsistency
problem arises precisely because policy makers are not
credible. Giving the government the responsibility for
monitoring the central bank and punishing deviations
merely shifts the time-inconsistency problem from the
central bank to the government.
• This solution requires the unrealistic assumption that
the government knows the exact preferences of the
central banker.
• Probably for these reasons, real-world examples of
Walsh contracts are hard to find.
Escape Clauses
• Lohmann (1992) suggests that in normal times
monetary policy should be made by an independent
central banker who is more conservative than society.
• If a large shock occurs the government should threaten
to override the central bank if it does not stabilise.
• Requires that the government knows the preferences
of the central banker. It must be believed that the
government will intervene in extraordinary times but
refrain from intervention in normal times.
Real World Examples
• The New Zealand government is allowed to
override the central bank and the central bank
is allowed to accommodate the first-round
effect of a shock on prices in “extreme
economic circumstances”.
• The UK Treasury is allowed to instruct the
Bank of England on monetary policy for a
limited time.
Reputation Models
Consider a simpler objective function for
society:
𝑊 = 𝜑 𝜋 − 𝜋 𝑒 − 𝜋 2 /2.
The central bank chooses
𝜋 = 𝜑.
This is expected and
𝑊 = 𝑊3 ≡
𝜑2
− .
2
Other outcomes
• If actual and expected inflation are zero then
the payoff is 𝑊 = 𝑊 2 ≡ 0.
• If expected inflation is zero and actual
inflation is φ then the payoff is 𝑊 = 𝑊 1 ≡
𝜑2
.
2
• If expected inflation is φ and actual inflation is
zero then the payoff is 𝑊 = 𝑊 4 ≡ −𝜑 2 .
• Note that 𝑊 1 > 𝑊 2 > 𝑊 3 > 𝑊 4 .
Infinite-Horizon Game
• In reality the monetary policy scenario does not
occur just once, it occurs over and over.
• Suppose it is repeated an infinite number of
times. Suppose that society and the monetary
policy maker’s discount factor is φ
• Suppose wage setters expect zero inflation in the
first period and zero inflation thereafter as long
as inflation has always been zero. If they ever
observe inflation of φ then they expect inflation
of φ forever after.
• What would the monetary policy maker do?
Equilibrium with zero inflation
• Either the monetary policy maker chooses zero
inflation forever. Or, there is some period where he
chooses inflation of is φ. After that, inflation of is φ is
expected so he chooses inflation of is φ forever after.
• The monetary policy maker will choose zero inflation
forever if
1 + 𝛽 + 𝛽2 + ⋯ 𝑊 2 ≥ 𝑊 1 + 𝛽 + 𝛽2 + ⋯ 𝑊 3
• This is true if 1 − 𝛽
𝑊1
+
𝛽𝑊 3
≤0⟺𝛽≥
1
.
2
• If society cares enough about the future then there is
an equilibrium with zero inflation.
Problems with this
• This is not the only equilibrium. An obvious equilibrium is
where wage setters expect inflation of φ every period and
the monetary policy maker chooses φ every period.
• There could be an equilibrium where actual and expected
inflation is φ in odd periods. In period zero expected
inflation is zero and expected inflation is zero in even
periods if actual inflation has always been zero in even
periods and is φ if it has ever been φ in an even period.
Actual inflation is zero in even periods.
• Along with too many equilibria, zero inflation forever might
be attained by different threats. It might occur if wage
setters threat to play non-cooperatively forever if they ever
see a deviation. A threat to play non-cooperatively for N>1
periods may also work.
A finite horizon
• Suppose that the game is played a finite number T times.
• In period T the wage setters have no credible threat do
deter the monetary policy maker from inflation is φ and
this is expected.
• In period T-1 the wage setters have no credible threat
because their only credible strategy in T is to expect φ. So
in T-1 actual and expected inflation is φ. Things unravel
backward. The only equilibrium is actual and expected
inflation of φ each period.
• But, people are probably not that rational. If the monetary
policy game were repeated 100 times you might get
cooperation for much of the time.
Hawks and Doves
• Suppose that a fraction 𝜌 ∈ 0,1 of all policy
makers are hawks who only care about inflation
and always choose zero inflation. A fraction 1 − 𝜌
are doves who maximise social welfare.
• Suppose that the monetary policy game is played
twice. If a dove inflates in period zero he is known
to be a dove and expected inflation is 𝜑 in period
one. But, if he chooses zero inflation, then wage
setters are not sure if he is a hawk or a dove. In
period one the dove inflates.
Bayes Rule
Suppose that wage setters believe that doves choose zero
inflation in period zero with probability p*. Then if the see
zero inflation in period zero, they believe the monetary policy
maker is a dove with probability P = 𝑃𝑟 𝑑𝑜𝑣𝑒 𝜋0 = 0 =
𝑃𝑟 𝜋0 =0,𝑑𝑜𝑣𝑒
𝑃𝑟 𝜋0 =0
=
𝑃𝑟 𝜋0 =0,𝑑𝑜𝑣𝑒
𝑃𝑟 𝜋0 =0,𝑑𝑜𝑣𝑒 +𝑃𝑟 𝜋0 =0,ℎ𝑎𝑤𝑘
𝜋0 = 0 𝑑𝑜𝑣𝑒 𝑃𝑟 𝑑𝑜𝑣𝑒
𝜋0 = 0 𝑑𝑜𝑣𝑒 𝑃𝑟 𝑑𝑜𝑣𝑒 +𝑃𝑟 𝜋0 = 0 ℎ𝑎𝑤𝑘
=
𝑃𝑟
𝑃𝑟
𝑝∗ 1 − 𝜌
𝑝∗ 1 − 𝜌 + 𝜌
𝑃𝑟 ℎ𝑎𝑤𝑘
=
• Let 𝑝 be the probability that a dove chooses
zero inflation in period zero. Ignoring terms
that do not depend on 𝜌, his payoff is
1−𝑝 𝜑2
2
− 𝛽 1 − 𝑝 𝜑 2 − 𝛽𝑝𝑃𝜑 2 .
• The dove takes P as given and maximises this
objective function to find p.
• In equilibrium, the beliefs of wage setters are
consistent: Thus, p* = p.
Equilibrium where doves always inflate
• If doves always inflate and wage setters see that period
zero inflation is zero, they will believe that the policy
maker is a dove with probability zero.
• The doves objective function is
1−𝑝 𝜑2
2
− 𝛽 1 − 𝑝 𝜑2 .
• This is maximised at p = 0 (doves always inflate) if 𝛽 <
1/2.
• So if 𝛽 < 1/2 there is an equilibrium where hawks and
doves separate. Hawks choose zero inflation in period
zero and doves choose strictly positive inflation in
period zero.
Equilibrium were doves
never inflate in period zero
• If doves never inflate (p = 1) and wage setters see
zero inflation they will believe that the policy
maker is a dove with probability 1 – ρ.
• The doves objective function is
𝛽 1 − 𝑝 𝜑2 − 𝛽𝑝 1 − 𝜌 𝜑2 .
1−𝑝 𝜑2
2
• This is maximised at p = 1 if is 𝛽𝜌 >
1
2
−
1
.
2
• If 𝛽𝜌 > there is an equilibrium where hawks
and doves pool. No policy ever inflates in period
zero.
One other outcome
1
2
• If 𝛽 1 − 𝑃 = then doves are indifferent and
randomise.
• This is the case when 𝑝 =
1
2
2𝛽−1 𝜌
1−𝜌
• This occurs when 𝛽 > > 𝛽𝜌.
∈ 0,1 .
Another Solution:
Peg the Exchange Rate
• One strategy for insuring low inflation is for a
government to peg its currency to the currency of
a country that can be counted on to pursue low
inflation.
• It is a central result in the theory of international
finance that if a country is to maintain a fixed
exchange rate, it cannot follow an independent
monetary policy.
• As long as the country maintains its peg, it must
follow the less inflationary country’s monetary
policy.
Why it might work
• As long at it has enough foreign reserves to
buy back its monetary base it is always
possible for a country with a fixed exchange
rate to maintain its peg.
• Policy makers may be able to commit to
pursuing the monetary policy necessary for
maintaining a fixed exchange rate, at least for
a while, because devaluations can cause
severe economic disruption and are not a
career-enhancing move for the policy maker
involved.
Why it might not
• Successfully maintaining a peg does not necessarily
guarantee price stability.
• More importantly, however, in a world with highly
mobile capital, fixed exchange rates are subject to
speculative attacks.
• Few large advanced economies have a pegged
exchange rate: Denmark is a rare exception.
• Some developing, transition and very small economies
still opt to peg their currencies. This is because
developing and transition economies are especially
vulnerable to the time-inconsistency problems
associated with inefficient tax systems and because it is
particularly difficult to make monetary policy in very
small economies