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3. The Rational Expectations Revolution
Index:
3. The Rational Expectations Revolution ......................................................................1
3.1
3.2
Introduction........................................................................................3
The worker misperception model ......................................................4
3.2.1 Main assumptions ......................................................................................4
3.2.2 Labour market equilibrium ........................................................................4
3.2.3 Aggregate supply .......................................................................................5
3.2.4 Equilibrium in the output market...............................................................6
3.2.5 Inflation surprise ........................................................................................6
3.2.6 Short run and long run ...............................................................................7
3.3
The model with adaptive expectations...............................................8
3.3.1 Adaptive expectations................................................................................9
3.3.2 Monetary surprise ......................................................................................9
3.3.3 The accelerationist hypothesis .................................................................10
3.4
Rational expectations .......................................................................11
3.4.1 Solving the model with rational expectations..........................................11
3.4.2 Only surprises matter ...............................................................................12
3.4.3 Rational expectations versus perfect foresight ........................................13
3.4.4 Learning ...................................................................................................13
3.4.5 The slope of the Phillips curve.................................................................15
3.4.6 The Lucas critique....................................................................................16
3.4.7 The call for a Real Business Cycles Theory ............................................16
3.5
Rules versus discretion ....................................................................17
3.5.1 The central banker’ preferences...............................................................17
3.5.2 Central bank’ optimum under discretion .................................................18
3.5.3 Inconsistency (under discretion) ..............................................................18
3.5.4 Consistency (under discretion) ................................................................19
3.5.5 Rule ..........................................................................................................20
3.5.6 The role of policy.....................................................................................20
3.6
The new Keynesian model...............................................................21
3.6.1 Staggered wages.......................................................................................21
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3.6.2 Rational expectations and wage stickiness ..............................................22
3.6.3 Policy implications...................................................................................23
3.7
Further reading.................................................................................24
Review questions and exercises...................................................................................25
Review questions .........................................................................................25
Problems ......................................................................................................25
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3.1
Introduction
After World War II, the conventional wisdom was that policymakers have a role in
smoothing the business cycles. Economists and practitioners believed on a reliable trade-off
between inflation and unemployment, as suggested by the Phillips curve. Hence, an aggregate
demand impulse, either using fiscal policy or monetary policy, should have the potential to
expand output and employment, at the cost of some moderate inflation. Since the decades that
followed were characterized by rapid economic expansion across the world, nothing really
serious questioned this wisdom.
In 1970s, however, the Western economies faced two supply shocks, and a new
phenomenon of high inflation and high unemployment, which was coined as “stagflation”.
The Keynesian doctrine, by assuming price stickiness and demand driven business cycles
could not explain such phenomenon. In plus, policies to expand aggregate demand in some
countries resulted in even higher inflation, without impacting significantly on unemployment.
This was not in accordance to the idea of a stable inflation-unemployment relationship, as
described by the Phillips curve.
The failure of expansionary policies in stabilizing the economy paved the way for the
resurrection of the pre-Keynesian view that market economies are inherently stable. The first
wave of this movement was the “monetarist school”, lead by Milton Friedman and his
colleagues at the University of Chicago. Friedman contented that most business cycles are
accounted for monetary shocks. These shocks give rise to inflation uncertainty and
undesirable departures of output from its natural level. Advocate of free markets, Friedman
claimed that policymakers should abstain from manipulating the aggregate demand,
committing instead with simple rules, such as steady money growth.
The second wave was launched by Robert Lucas, with the rational expectations
revolution. Under rational expectations, agents are assumed to make the best possible
forecasts about the future, given the information available at the time of the forecast. Since
information lags regarding the behaviour of prices do not last for long, it will be impossible
for policymakers to achieve long lasting reductions in unemployment by creating inflation
surprises. Under rational expectations, monetary shocks cannot be a good candidate to
explain the business cycles. This conclusion set the agenda for the third wave of the classical
revival, the Real Business Cycles School, led by Finn Kydland and Edward Prescott.
Meanwhile, economists aligned with the Keynesian tradition were launching
macroeconomic models with different types of market failures, to argue that the price
mechanism is too slow, even under rational expectations. Under this reasoning, the neoKeynesian school has claimed that monetary policy is still a powerful stabilization tool.
This note briefly reviews these ideas, focusing on the key assumption of Rational
Expectations. In Section 2, we introduce the workers’ misperception model, which will be
used to explain how information failures may give rise to departures of output away from its
natural level. In Section 3, we describe the case with backward looking expectations. In
Section 4 we solve the same model assuming instead that agents are rational. In Section 5, we
briefly explain how the New Keynesian approach, by coupling rational expectations and
wage stickiness, re-establishes the case for the stabilization role of the central bank.
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3.2
3.2.1
The worker misperception model
Main assumptions
Consider a closed economy with perfect competition and where prices and wages are
flexible. In this economy, production takes place using two factors of production, labour and
capital. The capital stock is pre-determined and equal to 1.
For simplicity, let’s consider a production function with a particular functional form:
Q  zN 0.5
(3.1)
Firms take productivity (z), the output price (P), and the nominal wage rate (W) as
given and choose the number of workers so as to maximize profits. Assuming perfect
competition, this problem delivers the well know optimality condition stating that the demand
for labour is such that the marginal product of labour is equal to the real wage. Solving for N,
this gives:
 z  P
N   
 2  W
d



2
(3.2)
The novelty in this model is that workers do not observe the price level at the time
they make their decisions: workers set their nominal wages taking into account the real wage
they want to receive for each level of employment, and their expectation regarding the price
level, P e .
For simplicity, let’s assume that the supply of labour is infinitely elastic at the desired
real wage,  . Formally, our labour supply function will be as follows:
W  P e
(3.3)
In this model, firms have an information advantage over workers, because they
always observe the price at which they are selling their own output. Workers, in turn, are
concerned with the consumer price index. The consumer price index is an average of all
consumer prices, and hence not readily available. Thus, workers will not immediately notice
when the price level changes.
Still, in this model, nominal wages are flexible: whenever the expected price level
increases, this will cause an immediate increase in nominal wages, because workers try to
keep their real wages from falling. Wages are said to be flexible with respect to expected
changes in the price level.
3.2.2
Labour market equilibrium
Given (3.2) and (3.3), the equilibrium in the labour market is given by:
 z  P 
N  
 e 
 2  P 
2
(3.3)
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Equation (3.3) reveals that the employment level in this economy depends on the gap
between expected prices and actual prices: when the actual price is higher than expected, the
real wage is lower than workers desire. Workers will however supply labour at the agreed
nominal wage, because they do not perceive that prices are higher than expected. Firms, in
turn, will demand more labour because they observe the real wage declining.
Of course, as long as the expected price does not change, equation (3.3) implies a
positive relationship between employment and prices, which basically accords to the Phillips
curve. The novelty in this model is that expectations may change, destabilizing the
relationship between employment and prices.
In case there are no information frictions ( P  P e ), the economy will operate at full
employment, just like in the classical model:
 z 
N  

 2 
2
*
3.2.3
(3.4)
Aggregate supply
In this model, prices only influence output to the extent that they are different from
expected. Replacing (3.3) in (3.1), the general expression of aggregate supply in this model
is:
 P
Q  Q*  e 
P 
(3.5)
Where Q* refers to “natural output”:
 z2 

Q*  
 2 
(3.6)
Equation (3.5) describes a family of aggregate supply curves, each one corresponding
to a given expected price, P e . In Figure 1, we depict two aggregate supply curves (AS),
corresponding to P e  1 and P e  2 . The frictionless case, (3.6), correspond to LS, where
output is at its natural level.
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Figure 1 – Aggregate supply with and without information failure
3.2.4
Equilibrium in the output market
In line with the classical tradition, let’s assume that the quantitative theory of money
holds, and that money velocity is equal to 1. Hence, aggregate demand is given by the money
market equilibrium:
M  PQ
(3.7)
The two main equations of the model are aggregate supply (3.5) and aggregate
demand, (3.7). Solving these two equations together, one obtains the equilibrium levels of
output and of prices:
 Q* M
Q   e
 P



0.5
 M
P   P e * 
 Q 
(3.8)
0.5
(3.9)
For instance, when M=1 and P e  1 , we have P=1 and Q  Q * . This particular
equilibrium is described by point 0 in Figure 1.
To make the case as simple as possible, in what follows, we will often refer to the
following parameterization of the model: z  1 and   0.5 . This delivers the convenient
benchmark: N *  Q*  1 .
3.2.5
Inflation surprise
Suppose that our economy is initially in a frictionless equilibrium, with M=1 and
P  P  1 , just as described by point 0 in Figure 1. Then, assume that the money supply
unexpectedly shifts, once-and-for-all, to M=4. This increase in the money supply gives rise to
an increase in the price level, but workers are still expecting the price level to be equal to one.
The fact that the price level increases ahead of expectations causes the real wage rate to
decline, employment to increase, and output to expand above full employment.
e
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The equilibrium in the output market following the monetary expansion is described
by point 1 in Figure 2. This point corresponds to the intersection of the new aggregate
demand, 4  PQ , with the aggregate supply with P e  1 , Q  P , implying P  Q  2.
Figure 2 – Equilibrium in the output market following an inflation surprise
The reason underlying the shift in output ahead of full employment is that firms,
observing the fall in real wage, optimally decide to hire more labour. This is illustrated in
Figure 3: because the price level doubled, the real wage halved. Hence, firms increased their
demand for labour, hiring N=4 and therefore expanding production to Q=2.
Figure 3 – Equilibrium in the labour market following the inflation surprise
It is important to note that in point 1 the labour market is not clearing: workers are out
of their labour supply, so they will not be optimizing. However, workers will only perceive
this in a later stage, when the information regarding the price level becomes available. In this
model, the labour market clears “ex ante” - wages are set such that the labour market is
expected to clear - but not necessarily “ex post”. Because of information failures, one can
generate business cycles in a context where prices are flexible.
3.2.6
Short run and long run
The main idea behind this model is that agents may lack all the information they need
to accurately make their economic decisions. In particular, people may not perceive a change
in the price level caused by a monetary shock. Thus, even if prices are flexible, agents may
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fail to adjust their own prices, giving rise to deviations relative to their optimal paths. In the
aggregate, this results in fluctuations of output around its natural rate.
Note that the equilibrium described in point 1 can only occur in the short run.
Information lags do not last forever. Sooner of later, workers will catch on to the fact that
their purchasing power has declined. Their expected price will rise and accordingly they will
demand a higher nominal wage rate. As a result, the aggregate supply curve will shift up. In
the long run, information failures will vanish and the economy will return to its natural level
(point T in Figure 2, Point 0 in Figure 3).
This is why in this model we have a short run aggregate supply (AS) and a long run
aggregate supply (LR): in the long run, there are no information failures and the implied
aggregate supply is vertical, mimicking the classical model.
The critical question is how long it will take for workers to correctly revise their
expectations.
-
If the adjustment in expectations is slow, the business cycle will be long-lasting.
-
If the revision in expectations is fast, the business cycle will be short-lived.
As we will see in a minute, these two cases mark the distinction between the initial
assumption of adaptive expectations made by Milton Friedman and that of rational
expectations, introduced by Robert Lucas. Depending on the framework, the later case may
also deliver a case in which private agents fully anticipate the policy, eroding its effectiveness
even before it is implemented. We will also see that the later conclusion no longer holds once
we replace the assumption of flexible wages by the assumption that wages are sticky. In the
next sections, we will explore these alternative avenues1.
3.3
The model with adaptive expectations
In a seminal paper, developed as part of its Presidential Address to the American
Economic Association in 1967, Friedman offered an explanation for the apparent trade-off
between inflation and unemployment underlying the Phillips curve. He contended that,
because of information failures, a monetary expansion will cause output to expand ahead of
its “natural level”, giving rise to an inflation surge and a business cycle. In the long run,
1
The split of the economy into firms and workers is a matter of expositional convenience. One could
instead think of different agents trading with each other different products. In such setup, each agent would
observe its own price but not the average price level. The advantage of that framework is that it wouldn’t predict
a negative correlation between output and real wages, which is empirically refuted. The aim of this note is not
however to explain the cyclical behaviour of wages, but rather the role of expectations as an explanation for the
businesss cyles. So, we go on with using the worker misperception model accross the alternative theories.
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however, there will be no trade-off between inflation and unemployment2. With this theory,
Friedman re-stated the effectiveness of monetary policy in the short run and the classical
proposition of money neutrality in the long run.
3.3.1
Adaptive expectations
Friedman assumed that workers guess future prices based on the prices they observed
in the past. This assumption is known as “adaptive expectations”.
The simpler model of adaptive expectations is as follows:
P1e  P
(3.10)
That is, workers expect next period’ prices to be equal to the level observed in the
current period.
3.3.2
Monetary surprise
Consider again the monetary surprise in t=1. At that time, workers were
expecting P1e  1 , because this was the price level observed in t=0. Thus, the monetary shock
caused the economy to move to point 1 in Figure 4, just as described above. In moment t=2
workers will expect P2e  2 , because this was the price observed in t=1. In Figure 4, this is
described by the upward shift in the short term aggregate supply. The new short term
equilibrium (t=2) occurs in point 2, with P2  80.5 , and Q2  20.5 (see 3.8 and 3.9). Then, in
period t=3, the worker will expect P2e  80.5 , implying a further upward move in the
aggregate supply, and so on.
Thus, even if aggregate demand remains unchanged after the first period, the
Friedman worker will be fooled and fooled again, until the final point T is reached.
2
The same conclusion was independently discovered by Friedman and the Keynesian economist
Edmund Phelps: Friedman, M., 1968. The role of monetary policy. American Economic Review 58, 1-17.
Phelps, Edmund S. “Phillips Curves, Expectations of Inflation and Optimal Employment over Time.”
Economica, n.s., 34, no. 3 (1967): 254–281
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Figure 4 – Adjustment under adaptive expectations
In sum: the fact that workers gradually adapt their expectations implies that following
a once-and-for-all shift in monetary policy, output will return slowly to its natural level. In
the short run, a business cycle takes place. Friedman contended that the process through
which workers adjust their expectations can be “surprisingly long”3. In the long run, however,
the quantitative theory will show up and output will be independent of the price level.
3.3.3
The accelerationist hypothesis
The previous exercise relies on the assumption that the increase in money was onceand-for all. If money was allowed instead to expand every year, would it be possible to keep
the economy operating above its natural employment level on a permanent basis?
To answer this question, let’s consider again the main equations of our model,
aggregate supply (3.5) and aggregate demand (3.7). Also consider the simple case in which
N *  Q*  1 . Suppose that the monetary authorities were targeting the output level Q=2. How
much should be the amount of money each year? Replacing (3.7) in (3.5), and using the
assumption of adaptive expectations (3.8), one obtains
Q
M Q
M Q

P1
M 1 Q1
Setting Q=2 every year, this gives
M  2 M 1
3
Together with Anna Schwartz, Friedman wrote “A monetary history of the united states, 1867-1960”.
In this volume, the authors concluded that movements in money did explain most of the fluctuation in output in
that country. They also contend that the Great Depression was the result of a “tragic policy mistake”: the decline
in the money supply caused by bank failures could have been avoided by the Federal Reserve, and it wasn’t.
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That is, it would be possible to maintain output systematically above full employment,
if money supply doubled each period. With such rule, prices would be increasing
systematically ahead of wages, fooling the worker continuously. This, in turn, would imply
an ever-accelerating inflation. Figure 5 illustrates the successive equilibria under the
assumption that the monetary authorities are doubling money every period, surprising
workers again and again.
Figure 5 – The acceleracionist hypothesis
3.4
Rational expectations
In his criticism to the Friedman model, Lucas contended that the adaptive
expectations assumption proposed by Friedman was not satisfactory: workers should learn
with the past mistakes, instead of being systematically surprised by changes in money supply.
Lucas assumed instead rational expectations. Under rational expectations, people are
forward-looking and make the best possible forecast given the information they have4.
3.4.1
Solving the model with rational expectations
4
Lucas, R. , 1972. Expectations and the neutrality of money. Journal of Economic Theory, 4, 103-24.
A forward looking component in expectations had already been accounted for in the work of Edmund Phelps,
though without rational expectations. Rational expectations were first proposed by John Muth, in 1962 (Rational
expectations and the theory of price movements, Econometrica 29, 315-35).
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Under rational expectations, forecasts have to be consistent with the economic model.
People do not know exactly how much the central bank will expand the money supply, but
they know the mechanism through which changes in money affect prices.
In the context of our model, people are assumed to know equation (3.9). Hence, they
will know that P=1 when M=1 and P e  1 (point 0 in Figure 4); that P=2 when P e  1 and
M=4, (point 1); that P  80.5 when P e  2 and M=4 (point 2), and so on. With this model in
mind, people will recognize that there is no point in guessing P e  2 when M=4, because that
would be inconsistent.
Under rational expectations, people only make consistent forecasts, expecting the
price level to be equal to what can be expected to be, given the structure of the model. In
particular, given (3.9), the best forecast for the price level will be such that:
 Me 
P   P e * 
 Q 
0.5
e
Solving for P e , this gives the rational expectations forecast:
Pe 
Me
Q*
(3.10)
Hence, the best forecast of the price level depends on what people expect money
supply to be. The next step is to guess the central bank intentions.
With this model in mind, one can see why an equilibrium like the one described by
point 2 in Figure 4 should not occur under rational expectations: agents caught by surprise in
t=1, should adjust their expectations to P e  4 once they realized that money supply had
increased to M=4. The monetary surprise would have produced effects in the first period, but
after the new money supply became known, there is no reason for workers to be fooled again:
workers should accurately adjust their expectations, moving the aggregate supply at once to
its final position. The equilibrium described by point T would be reached in moment t=2, and
not after many periods, during which workers are systematically fooled by inconsistent
guesses.
3.4.2
Only surprises matter
To further explore the model with rational expectations, let’s define the forecasting
error,  as the difference between the actual money supply and the expected money supply.
That is:
M  M e 1   
(3.11)
When   0 , this means that money has expanded faster than expected. Substituting
this in (3.10), one obtains the expected price as a function of the forecasting error:
Pe 
M 1
Q* 1  
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Replacing this in the expression for output (3.8), one obtains
Q  Q* 1   
0.5
(3.12)
Equation (3.12) implies that output will differ from its natural level only to the extent
that agents are surprised by unexpected increases in the money supply. When the money
supply is correctly anticipated (   0 ), then output will be at its natural level.
Referring to the example, since in t=2 people exactly know how much money supply
is going to be (M=4), their RE forecast should be P e  P  4 . In t=1, people where expecting
M e  1 , while the government increased money to M=4. This gave rise to a forecasting error
equal to   3 , implying that output expanded ahead of its natural level, to
0.5
Q  Q* 1  3  2 .
Of course, if the central bank announced that it would expand the money supply to
M=4 and people believed, then the rational expectation at t=1 would be P e  4 , and the
economy would move directly from 0 in t=0 to T in t=1. Under rational expectations and
flexible prices, an anticipated monetary expansion cannot produce real effects.
The statement that predicted movements in money have no effect on economic
activity is known and the “policy ineffectiveness proposition” 5.
The policy ineffectiveness proposition states that fully anticipated changes in the
money supply cannot affect real output. The policy ineffectiveness proposition does not rule
out output effects from unexpected policy changes: monetary surprises will, in general, give
rise to real effects. These real effects will be however short-lived, because people will rapidly
adjust their expectations. Hence, in any case, under rational expectations monetary policy
will have little effectiveness.
3.4.3
Rational expectations versus perfect foresight
Often, the concept of rational expectations is confused with that of perfect foresight.
Under perfect foresight there is no information failure, so people will always know the price
level. If, in plus, prices are flexible, then the economy will be continuously in full
employment.
Under rational expectations, people face uncertainty and make their best forecast,
given the information they have. Hence, forecasting errors are possible.
3.4.4
Learning
5
Sargent, Thomas & Wallace, Neil (1975). "'Rational' Expectations, the Optimal Monetary Instrument,
and the Optimal Money Supply Rule". Journal of Political Economy 83 (2): 241–254.
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Under rational expectations, people learn with past mistakes. Hence, if the monetary
authorities insist in expanding output ahead of its natural level, people will become aware of
the central bank intentions, turning the central banks aim increasingly difficult to be
achieved: in order to surprise and keep surprising, the central bank would need to be
“incredibly imaginative”.
To illustrate this, let’s turn to a previous question: will it be possible for a central
banker facing rational agents to keep the economy operating at Q=2?
To answer this question, let’s refer to Figure 6. In the figure, point 0 describes the
initial situation in which M  M e  1 , and point 1 describes the equilibrium after the
monetary authorities unexpectedly expanded money to M=4.
The interesting question is on what happens next period, t=2. Will people trust that the
money expansion was once-and-for all? Of course, we don’t know. Now, the equilibrium will
depend on how people interpret the words and actions of the central bank, and on how the
central bank expects people to react to its words and actions. The result is obviously
uncertain.
For a moment, assume that the central bank, aiming to fool agents again, successfully
convinced the public that money would not change anymore. Assuming that people believed
and conjectured M e  4 , the central bank could try to surprise again, setting M=16. The
implied equilibrium is described by point 2 in Figure 6. Comparing with point 2 in Figure 5,
you see that under rational expectations, a more aggressive monetary policy will be needed to
keep the economy operating at Q=2 for the second year in a row.
Now put yourself in the worker’ shoes at the time t=3. Suppose the central bank
promises that money will stand at M=16. Of course, you will not believe. You would have
learned with the past mistakes. Eventually, you will conjecture that the central bank wants
you to expect P e  16 , to fool you again, setting M=32, achieving Q=2 (this case is
described by point 2’ in Figure 6). But if you anticipate M e  32 , the policy will not produce
any effect (point 3). Of course, the central bank can try to surprise you with M=64. But will
that work? If the central bank already expanded money from M=1 in t=0 to M=4 in t=1 and
M=16 in t=2, wouldn’t be reasonable to assume that the central bank will expand money this
time to M=64..?
Under rational expectations, the central banker would need to be incredibly
imaginative to keep surprising and surprising again. And most probably, the result of such
attempt would be a highly destabilizing monetary policy.
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Figure 6 – Under RE, people learn about the CB intentions
The example above illustrates how difficult it is to guess what the equilibrium under
rational expectations will be. Expectations depend on the central bank policy, and the later
depends on expectations. The result of this game is highly uncertain.
Under rational expectations the outcome of policy actions in uncertain, because we
cannot be sure to what extent the policy is anticipated. Thus, an activist policy will have no
predictable effect on output and cannot be relied on to stabilize economic activity. Instead, it
may create a lot of uncertainty about policy, translating into undesirable output fluctuations
around the natural rate. Such an undesirable effect is exactly the opposite of what the activist
stabilization policy is trying to achieve.
3.4.5
The slope of the Phillips curve
The example in Figure 6 also illustrates a key proposition of the rational expectations
model: the slope of the Phillips curve changes when policymakers try to explore it.
To see this, consider again moment t=1. At this stage, the past history had been of
monetary stability: people trusted M to be stable, because M had been stable before. The trust
in monetary authorities creates the potential for the central bank to explore the positive
relation between prices and output implied by the short term aggregate supply surve: if
money unexpectedly expanded to M=4, then output would increase from Q=1 to Q=2, at the
cost of a price change from P=1 to P=2. In other words, an output gap amounting to
Q  Q*  1 can be achieved with a price increase of P  1 (the relationship between Q  Q*
and P can be interpreted as the slope of a Phillips curve).
After this first move, however, achieving the same output gap will require much
higher inflation rates: because people learn with past mistakes, part of the monetary
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expansion will be anticipated and will impact directly on prices without any real effect. Thus,
a much higher inflation rate will be needed to achieve the same output gap. In other words,
the Phillips curve will become steeper.
With this reasoning, one may guess that an inflation surprise will produce more real
effects in the US than in Zimbabwe:
-
In Zimbabwe, where inflation has been extremely volatile and high, a monetary
expansion will hardly surprise agents, implying that the Phillips curve there is
almost vertical.
-
In contrast, in the United States, where the past experience has been of monetary
stability, the slope of the Phillips curve is moderate. This means that the Federal
Reserve has the potential to expand output by creating an inflation surprise. The
problem however is that once the monetary authorities try to explore the trade-off
between inflation and unemployment, the trade-off dissipates: the Phillips curve
will become steeper and steeper, approaching the limiting case of Zimbabwe.
All in all, although there is a potentially negative trade-off between inflation and
unemployment, this trade-off will rapidly disappear once the monetary authorities try to
explore it.
3.4.6
The Lucas critique
The changing slope of the Phillips curve is an illustration of a key implication of
rational expectations: the statistical relationship between two variables may change when the
policy changes. This poses a serious limitation to the use of large scale econometric models
for policy formulation and forecasting.
The argument, known as the Lucas Critique runs as follows6: Econometric estimates
describe relationships between economic variables as they held in the past, under past
policies. Whenever policy (the rules of the game) changes, the way people form expectations
will also change. Hence, the parameters and elasticities estimated using past data will be a
poor guide to what will happen in response to a policy change.
3.4.7
The call for a Real Business Cycles Theory
In our days, information lags regarding the true inflation in the economy are quite
short-lived. Hence any eventual departure of actual output from its natural rate because of a
6
Lucas, Robert (1976). "Econometric Policy Evaluation: A Critique". In Brunner, K.; Meltzer, A. The
Phillips Curve and Labor Markets. Carnegie-Rochester Conference Series on Public Policy 1. New York:
American Elsevier. pp. 19–46.
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monetary disturbance should necessarily be short lived. With rational expectations and
flexible prices, monetary policy can no longer be a good candidate to explain business cycles.
With such a conclusion, Lucas contended that economists should turn to explanations
for the business cycles not relying on information failures and nominal shocks. This was the
agenda of the real business cycles theory7.
Proponents of the Real Business Cycles theory shifted the analysis away from
information failures and monetary surprises, to focus on productivity shocks and other
frictions that cause fluctuations of the natural rate of output, rather than fluctuations of output
around its natural level. The real business cycles theory abstracts from information failures,
implying that the economy is always at its natural level (the aggregate supply is vertical, even
in the short run). Since productivity shocks tend to be persistent over time, the theory
accounts for multiyear business cycles, without the need to rely on information lags
3.5
Rules versus discretion
Under rational expectations, policymakers cannot presume that economic agents are
passive in regard to policy changes. Changes in policy alter people’ expectations and this in
turn will impact on the effectiveness of policy. Conventional macroeconomic models hardly
account for these interactions. Game theory, in contrast, provides a powerful tool to think
economic policy under rational expectations. Indeed, the conduct of policy can be viewed as
a game, in which the public tries to learn about the policymaker’ intentions and policymakers
try to guess the public expectations.
A famous application of Game Theory to Rational Expectations is the timeinconsistency argument, put forward by Kydland and Prescott in 19778. This argument is
analysed below.
3.5.1
The central banker’ preferences
Assume that the central banker’ preferences are as follows:


U   Q  Q*  P  P   4Q  1  P  1
2
2
(3.13)
7
Kydland, Finn; E. C. Prescott (1982). "Time to Build and Aggregate Fluctuations". Econometrica 50
(6): 1345–1370. King, R. , Plosser, C., 1984. "Money, Credit, and Prices in a Real Business Cycle," American
Economic Review, 74(3), 363-380.
8
Kydland, F, and E. Prescott, C. (1977). "Rules Rather than Discretion: The Inconsistency of Optimal
Plans". Journal of Political Economy: 473–492.
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That is, the central bank values a positive output gap, but it doesn’t like the price level
to deviate from its target P  1 9.
The central banker’ preferences are described in Figure 7. Point 1 implies a higher
price level than point 0, but a higher level of output as well. On balance, given the utility
function (3.13), the central banker’ welfare level will be higher in 1 than in 0.
Figure 7 – The central banker’ preferences
3.5.2
Central bank’ optimum under discretion
Under discretion, the central has the power to choose the price level, P (or,
equivalently, the money supply, M) so as to maximize (3.13) taking people’ expectations as
given. Substituting (3.5) in the objective function (3.13), one may solve the central banker
optimization problem:
P
2


P

2
MaxU   Q * e  Q*   P  P   4  e  1  P  1
P
 P

P

The solution is:
P  1
2
Pe
(3.14)
Thus, the optimal policy from the central bank point of view depends on people’s
expectations.
3.5.3
Inconsistency (under discretion)
9
You may interpret P as inflation, if you want.
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Assume that the central bank, under discretion, commits with the target P  1 . Will
this be credible? The answer is no.
The problem is that, once people believed in that target, there would be an incentive
for the central bank to renegate its commitment, creating surprise inflation in an attempt to
achieve a higher social welfare. Indeed, from (3.14), we see that the central bank’ optimal
policy when P e  1 is to set P=3 (with M=9) achieving Q=3. The implied utility will be
2
U  4(3  1)  3  1  4 .
The central bank’ problem under discretion is illustrated in Figure 8: when people
expect P e  1 , the central bank will be maximizing its utility in point I, where the
indifference curve is tangent to the aggregate supply curve.
Figure 8: Inconsistency under discretion
The problem with point I is that it is not consistent: the expected price P e  1 does not
correspond to the actual price. Rational agents will never believe in P=1, because they would
know that the central bank could be tempted to surprise them with P=3.
The conclusion is that the announcement of a policy of low inflation is by itself not
credible under discretion. Once expectations are formed, the monetary authorities have an
incentive to renege on its announcement in order to reduce unemployment. Private agents
understand the incentive to renege and therefore will not believe the announcement in the
first place.
3.5.4
Consistency (under discretion)
Under rational expectations, the public is aware of the central banker’ preferences,
and will form the expectations accordingly. The consistent equilibrium under discretion is
obtained when people formulate their expectations taking (3.14) into account, that is:
P e  1
2
Pe
Thus, the rational expectation under discretion will be
Pe  M e  2 .
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When P e  2 , the optimal policy for the central bank (2.14) is exactly P=2, resulting
in Q  Q *  1 . The consistent equilibrium is described by point C in Figure 9.
Figure 9: Consistent equilibrium under discretion
The consistent case in when the central bank exactly validates the public’ believes.
For this to be an equilibrium, the inflation rate has to be sufficiently high to deprive the
central bank from any incentive to spring an inflation surprise.
In sum, the problem with the consistent equilibrium, is that it delivers the same level
of output as in point 0, but with higher prices. The society will pay the cost of inflation with
no benefit at all. Note that the utility level in point C is U=-1, lower than in point 0, U=0.
3.5.5
Rule
The surprising result of this model is that policymakers may better achieve their goals
by having their discretionary power taken away from them.
The only way the central bank can credibly commit with P=1 is setting it as a rule. If
the central bank abdicates from its discretionary power, adopting a legal rule from which it
cannot deviate, then people will trust the announcement, P=1.
In that case, the economy will lie in point 0. Of course, at point 0 the central banker
will not be optimizing. But since the central bank is constrained in its choices, citizens will
not be exposed to the risk of “temptation”, enjoying a higher welfare than in the consistent
equilibrium under discretion.
3.5.6
The role of policy
How to minimize social losses when policy actions have to be taken frequently is a
question that always concerned economists. Should policymakers act according to rules
which dictate the choices to be made at any moment in time? Or should policymakers have
instead the discretionary power to decide the best policy each moment in time, without being
bounded by any constraint?
The case against activism had been already made by Milton Friedman. Friedman
believed that market economies are inherently stable in the absence of unexpected
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fluctuations in the money supply. Even though monetary policy is a powerful tool, he argued,
governments may lack the knowledge and the will to effectively stabilize the economy10.
Distrusting policymakers and the political process, Friedman defended that central banks
should commit with steady money growth (hence, the label “monetarism”), rather than to
follow discretionary policies.
It was however with the rational expectations revolution that the role of policy was
seriously questioned. First, the monetary policy ineffectiveness proposition states that central
banks may not be successful in influencing output. Second, the time inconsistency argument
states a policymaker entrusted with discretionary power may face a credibility problem. The
reason is that the incentives of policymakers to stick with the announced policy change once
private agents adjust their expectations to the announced policy. Thus, economic performance
may improve if private decision makers know for sure that the central bank will follow a rigid
rule.
3.6
The new Keynesian model
The policy ineffectiveness proposition was challenged by the New Keynesian School.
The New Keynesian School is rooted on the Keynesian postulate that markets are imperfect
and do not always clear. It goes however beyond the Keynesian model, in trying to explain
why prices and wages adjust slowly.
The old Keynesian model had been discredited, because it was based on
macroeconomic aggregates and ad-hoc assumptions, without taking into account individual
optimization. The New Keynesians responded to this challenge, coming up with new models,
grounded on microeconomics and incorporating rational expectations, trying to identify
sources of frictions that prevent wages and prices from fully adjust to change in the price
level, even when fully expected. The aim was to prove that price stickiness was not
incompatible with microeconomic foundations and rationality. The appeal of the new school
was to show how optimizing firms and workers make choices that may have adverse
consequences to macroeconomics.
3.6.1
Staggered wages
10
First, governments may lack the relevant information, such on the true value of multipliers and of the
natural level of output. If, for instance, the natural output is overestimated, there is a risk of policymakers
engaging in expansionary policies which only result is inflation, as it likely to have happened in the early 1970s.
Second, policy actions are effected by different types of lags, such as in the decision-making process, in
implementation, and in the transmission to the real economy. Hence, the risk exist that, once the government
starts to act and the effects of the policy are transmitted to the economy, the later is already on its way to full
employment, risking more instability. Third, policy makers are influenced by lobbies, election calendars and
other pressures. Hence, their actions may deviate too much from the public interest.
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The first wave of the new Keynesian school focused on labour contracts to explain the
sluggish adjustment of nominal wages11. Wages are set by multi-period contracts. Thus, even
if new information appears making desirable a change in nominal wages, workers may find
themselves locked into the wage agreement. Later, when the contract is renegotiated, both
workers and firms may incorporate the new information in their agreement, but they cannot
do so immediately.
Another characteristic of wage revisions is that they are staggered over time: while
some months are more popular than others for adjusting wage contracts, these adjustment
decisions are generally staggered throughout the year. Thus, when new information arises,
instead of a sudden synchronized adjustment of wages - like in the neo-classical model - the
model with staggered wages predicts a slow adjustment process, whereby some fraction of
the labour contracts is revised each year, leapfrogging those that are still locked in their
contract periods.
The central result of this theory is that wages will not respond fully to changes in the
expected price level. Hence, output will return slowly to its natural rate, even under rational
expectations.
3.6.2
Rational expectations and wage stickiness
To see how staggered wage contracts and rational expectations play together in our
model economy, let’s consider again the case with a monetary expansion from M=1 to M=4.
This case is re-examined in Figure 10.
As before, the initial equilibrium is described by point 0, where M=1 and P=1. Then,
the monetary authorities expand the money supply, driving the aggregate demand to the
position depicted in the 4=PQ. In the figure, three equilibria with rational expectations are
considered:
-
Point 1 describes the equilibrium in which the monetary expansion was
unexpected: irrespectively of how staggered contracts are, if the move was not
expected, there will be no adjustment in the AS curve. The equilibrium following
a monetary surprise is the same as in the case with flexible prices.
11
Phelps, Edmund S. (1968). "Money-Wage Dynamics and Labor Market Equilibrium". Journal of
Political Economy 76 (S4): 678–711. Stanley Fischer (1977) Long-Term Contracts, Rational Expectations, and
the Optimal Money Supply Rule Journal of Political Economy. Phelps, Edmund S. and John B. Taylor (1977).
"Stabilizing Powers of Monetary Policy under Rational Expectations". Journal of Political Economy 85 (1):
163–190. John B Taylor (1979), 'Staggered wage setting in a macro model'. American Economic Review,
Papers and Proceedings 69 (2), pp. 108–13. John B Taylor (1980). "Aggregate Dynamics and Staggered
Contracts," Journal of Political Economy, 88(1), pages 1-23, February.
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-
Point 1’ corresponds to the case in which the monetary policy is anticipated, and
wages are flexible. As we already saw, in this case there are no real effects and all
money expansion is fully reflected in increasing prices.
-
Point 1’’ describes the case in which the monetary policy is anticipated, but some
positive fraction of the labour contracts is locked into last-year wage agreements.
Although all workers are aware of the monetary shift, some will face a real wage
loss, allowing output to expand ahead of its natural level. Thus, the short term
aggregate supply adjusts only half-way.
Figure 10: Monetary shock under rational expectations and staggered wage contracts
In sum, just like in the new-classical model, an unanticipated monetary shift has a
larger effect on output than anticipated policy. The novelty is that the ineffective proposition
does not hold: in the model with wage-stickiness, an anticipated monetary disturbance
produces real effects, even under rational expectations. This theory is grounded in empirical
evidence, that anticipated monetary changes do have real effects12 .
3.6.3
Policy implications
The main implication of rational expectations is that economists are no longer as
confident in the success of activist stabilization policies as they once were. Since expectations
change with the policy, the success of a particular policy will depend critically on the public's
expectations about that policy. If the policy becomes unpredictable, the game between
policymakers and the public may become highly destabilizing. To eliminate undesirable
fluctuations of output around its natural rate, the monetary authorities should thus generate as
12
Mishkin, Frederic S. 198a. ''Does Anticipated Monetary Policy Matter? An Econometric
Investigation.'' Journal of Political Economy 90 (February 1982): 21– 51.
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few policy surprises as possible. Central bankers should follow clear and transparent rules.
This includes a strong commitment with low inflation.
The finding that monetary policy produces real effects challenges however the view
that central banks should act strongly in response to an inflation surge13. Since a monetary
contraction produces real losses even when fully anticipated, the best policy may be instead a
gradual adjustment, so that agents have time to revise their contracts. Such policy should be
smooth and communicated as much in advance as possible, so as to avoid agents to be taken
by surprise. The new wisdom is that central banks can implement stabilization, but following
clear rules, being transparent in their forecasts and intentions.
3.7
Further reading
Robert Gordon, Macroeconomics, 9th edition: Chapter 17.
13
Under flexible prices, the society could benefit if the central bank followed a shock therapy (“cold
turkey”) when inflation raised above target. The reason is that this will be credibility-enhancing, allowing agents
to align faster their expectations with the policymaker intentions, reducing the real costs of disinflation.
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Review questions and exercises
Review questions
1. Comment: “When policymakers try to explore the trade-off between inflation and
unemployment, the trade-off disappears”.
Problems
2. In a given economy, the labour supply is given by W P e  8 . The output market
operates under perfect competition, with the representative firm having the following
production function: Q  zN .
0 .5
a) Explain the labour supply function.
b) Find out the demand for labour when Z=4.
c) Describe the supply side of this economy, identifying the short-run (SS) and the long
run (LS) supply curve. Represent graphically the case in which P  P e  1 .
d) (Classical dichotomy) Suppose that the real money demand in this economy was
given by m=Q. Find out the equilibrium in this economy, assuming that M has been
constant at M=1.
e) (Long term neutrality) Now suppose that at t=1 the money supply increased to M=4.
In the long run, what would be the price level and the level of output? What about
wages? Represent in a graph.
f) (Adaptive expectations). Assume that workers form their expectations according to
P e  P1 . Describe the short term equilibrium at the time of the monetary expansion
(t=1). Namely: find out the price level and the level of output and describe this in the
SS/AD space. Find out the real wages and the level of employment and describe this
in the W/P, N space. In the following period (t=2) will workers meet their labour
supply curve? Explain.
g) According to this model, real wages react pro-cyclically or counter-cyclically?
h) (Accelerationist hypothesis) Now assume that the government wanted the economy
to operate continuously at Q=2. Given the law that governs expectations, would that
be possible? How? How reasonable would that case be?
i) (Rational expectations). Instead of postulating adaptive expectations, consider the
case in which workers were rational. Describe the short term adjustment to a change
in the money supply from M=1 to M=4, distinguishing the cases in which the policy
was anticipated and not anticipated.
j) (RBC) Finally, assume that P e  P each moment in time (perfect foresight). Which
macroeconomic models are consistent with this assumption? Examine, in this case,
the implications of changes in the parameters Z and M. Which one will produce an
output change?
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3. Consider an economy where the aggregate demand and the aggregate supply are given
by the following expressions q td   t  p t and q ts  p t  pˆ t , where q refers to output,
p refers to the price level, p̂ stands for the “expected” price level and  is the money
supply. Assume that the monetary policy takes place after public expectations are
formed.
a) (Aggregate demand) Explain the equation describing the aggregate demand: what is
the implied theory? Plot the aggregate demand in the (q,p) space, for the cases in
which   0 and   1 .
b) (Aggregate supply) Explain the equation describing the aggregate supply.
Distinguish the “short term” and the “long term”. Plot the aggregate supply in the
(q,p) space, for the cases in which pˆ  0 and pˆ  1 2 .
c) (Rule governing the price level) Find out the equilibrium levels of q and p as
functions of p̂ and  .
d) (Adaptive expectations): Suppose that economic agents formulate their expectations
according to the following rule: pˆ t  p t 1 . Suppose that initially p t 1   t 1  0 . If the
central bank surprised economic agents with a and once-and-for-all increase in the
money supply to  t  1 , how much will be p t and q t ? And p t 1 and q t 1 ? Describe
the adjustment process in graph. Explain why these economic agents cannot be
rational.
e) (Rational expectations): Now assume that economic agents know the rule that
governs the price level. In that case, what will be their best forecast for p̂ t ?
f) (Perfect foresight): If economic agents knew for sure that the central bank would
increase the money supply once-and-for-all to  t  1 , how much should be p t and
qt ?
g) (Central bank preferences): From now on, assume that the central bank has
following utility function: U  q  p 2 . Explain this utility function and represent
corresponding indifference curves in the space (q,p). In particular, plot
indifference curves corresponding to U  0 , U  1 4 and U  1 4 . Find out
slope of these curves when p  1 2 .
the
the
the
the
h) (Discretion): Assume that the central bank is totally unconstrained in its monetary
decisions. Show that in this case is optimal monetary rule will be  t  1  p̂ t . What is
the implied price target?
i) (Temptation): Suppose that the central bank announces a zero inflation target for
moment t and economic agents believe, i.e, pˆ  0 . Will it be optimal for the central
bank to stick with this promise? Explain the central bank optimal policy, with the help
of a graph. Compute the corresponding utility level. (A: U  1 4 ).
j) (Inconsistency): Explain why the above equilibrium is inconsistent. Could this
central bank credibly commit with the zero-inflation target under discretion?
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k) (Consistency): If the public was aware of the central bank preferences, how much
would be p̂ t ? In that case, what would be the central bank optimal choice for  ?
Explain why such equilibrium would be consistent. Compute the central bank utility
level in this case. (A: U  1 4 ).
l) (Rule) Finally, assume that the central bank is forced to follow the rule   0 .
Assuming that this rule is fully enforced by law and that the public is aware of this,
what would be the equilibrium? Compare the central bank utility level in this case to
the case with discretion. (A: U  0 ).
m) What does this exercise suggest regarding the optimal institutional design of a central
bank?
4. Consider an economy where the aggregate demand and the aggregate supply are
given, respectively, by M=PY and Y  P P e . In this economy, M has been constant
at M=1
a) (Theory) Explain the two equations.
b) (Adaptive expectations). Assume that workers formed their expectations according to
Pe  P1 . Assuming that in the period before P=1, describe the short term equilibrium
at the time of the monetary expansion (t=1), as well as the subsequent adjustment of
the economy to the long run.
c) (Anticipated change) Suppose that, at t=1, the money supply changed from M=1 to
M=9. If the policy was announced and it was credible, how much should output and
prices be?
d) (Discretion): Suppose that the central bank’ preferences were given by
2
U  4 Y  1  P  1 and well known by the public. Could the central bank under
discretion credibly commit with P=1? And with P=2?
5. Consider an economy where the mandate of the central bank includes ensuring price
stability and an adequate level of employment in the economy. In this economy,
agents are rational and perceive the central bank objective function to take the
following form: U   p  p e   5 p  0 .05 2 , where p refers to inflation and p e refers
to expected inflation.
a) Explain the central bank objective function.
b) Suppose the central bank announced the inflation rate to be 5%. Will this
announcement be credible?
c) Sticking to the case with discretion, which inflation target would be fully credible?
Explain, with the help of a graph.
d) Suppose the parliament in this country was considering restricting the mandate of the
central bank to pursue the objective of price stability only (inflation 5%). Would such
change be welfare improving in this context?
e) Explain the policy implications of this model.
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6. Consider the following Central Bank problem:
1
max B  2u  u    2
2
s.t. u  u  0.02   e  where u  0.05 .
a) Suppose the central bank announces an inflation rate of zero percent, but it has
discretionary power to change the policy after expectations are formed. If the public
believed in the central bank target, would it still be optimal for the central bank?
b) What will be the equilibrium rate of inflation and unemployment if the public has
rational expectations?
c) Explain, in light of this framework, why tying the central bank hands may improve
the macroeconomic performance.
d) Discuss the pros and cons of using rules to restrict the policy options of the central
bank.
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http://sweet.ua.pt/afreitas/aulas/notas%20apoio/notasmacro.htm