LECTURE 9
Limits to stabilization policies
Øystein Børsum
14th March 2006
Overview of forthcoming lectures

Lecture 9: Limits to stabilization policies




Lecture 10: Open economy




Rational expectations and the Policy Ineffectiveness Proposition,
the Ricardian Equivalence Theorem and the Lucas Critique
Real business cycles
Policy rules versus discretion: Credibility of economic policy
Features of a small, open economy with perfect capital mobility
Aggregate demand and aggregate supply in the open economy
Long-term macroeconomic equilibrium in the open economy
Lecture 11 and 12: Fixed and floating exchange rate regimes
(Prof. Nymoen)


Macroeconomic policy under a fixed exchange rate regime
Macroeconomic policy under a floating exchange rate regime
and inflation targeting
Overview of issues limiting stabilization policies

Possible consequences of rational expectations:



Monetary policy may be ineffective (Policy Ineffectiveness
Proposition)
Tax policy may be ineffective (Ricardian Equivalence Theorem)
Past behavior of economic agents can be a poor guide for
assessing the effects of policy changes (Lucas’ critique)

Real business cycle theory demonstrates that business cycle
fluctuations can be reproduced in a model with market
clearing and a context that is consistent with rational
expectations. The new source of fluctuations is shocks to
production technology

If economic policy is not credible and expectations are
rational, you can achieve better outcomes with rules-based
policy than with discretionary (flexible) policy
PART 1
Rational expectations
What is the appropriate assumption about
expectations?

So far: Backwards-looking expectations
o
o
Allows systematic forecasting errors: Economic agents can be
systematically fooled by policy makers
This is hardly a solid foundation for policy analysis
“You can fool all of the people some of the time; you can even fool
some of the people all of the time, but you can’t fool all of the people all
of the time.” (Lincoln)

Rational expectations hypothesis
o
o
o
Use all available information to make forecasts, including
knowledge about the structure of the economy
Agents will be make forecast errors, but over time, forecasts will
be unbiased
Model-consistent expectations
Is there scope for economic policy if agents have
rational expectations?


Suppose the central bank has no information advantage
compared to other agents in the economy.
Monetary policy is based on expected values of y and 
rt = r + h(te - *) + b(yte - y)

Standard model with goods market equilibrium and aggregate
supply
yt - y = vt - (rt - r)
t = te + (yt - y) + st

Assume for simplicity that the shock variables are identically
and independently distributed over time, with zero mean and
constant variances.
Solving a model with rational expectations


Three-step procedure (cf. textbook)
o
Solve for the endogenous variables in terms of the exogenous
variables (as usual) and the expectations of the endogenous variables
o
Calculate the expected value of the expressions in 1. Solve for the
expected values of the endogenous variables
o
Insert the results from 2 into 1
Here: Use the policy rule to substitute for rt - r in the equilibrium
condition for the goods market
yt = y + vt - [h(te - *) + b(yte - y)]

Use the expression above to substitute for yt - y in the equation for
aggregate supply
t = te - [h(te - *) + b(yte - y)] + vt + st
Calculate the expected values of the endogenous
variables
yt = y + vt - [h(te - *) + b(yte - y)]
 yte = y - [h(te - *) + b(yte - y)]
t = te - [h(te - *) + b(yte - y)] + vt + st
 te = te - [h(te - *) + b(yte - y)]
h(te - *) = b(yte - y)


y te = y
 te =  *
The Policy Ineffectiveness Proposition

In the final solution, inflation and output are unaffected by the
parameters of monetary policy
yt = y + v t
t = * + v t + s t

Why?

AS curve: Deviations in output only due to surprise inflation

Agents perfectly anticipate the effect of systematic monetary policy
(the policy rule) on inflation

Surprise inflation cannot originate from systematic monetary policy,
only from shocks to the economy

Note: Monetary policy does not observe the shocks in time to react to
them
Scope for economic policy under rational
expectations given information advantage


Suppose the central bank has an information advantage
compared to other agents in the economy
Monetary policy is based on actual values of y and 
rt = r + h(t - *) + b(yt - y)

Same standard model with goods market equilibrium and
aggregate supply as in the previous example
yt - y = vt - (rt - r)
t = te + (yt - y) + st

And same assumption about the shock variables
The information advantage makes policy effective

Final solutions for output and inflation depend on the parameters of
monetary policy
vt - hst
yt = y +
1 + (b + h)
(1 + b)st +vt
t = * +
1 + (b + h)

Why?

AS curve: Deviations in output only due to surprise inflation

Agents know the policy rule and can anticipate the monetary policy
response to various shocks, but they do not observe the shocks

Monetary policy observes the shocks and can react to them

Monetary policy will create surprise inflation if that is the appropriate
response to the shocks that hit the economy
Ricardian equivalence: Ineffectiveness of tax policy

Related to the ideas behind the Policy Ineffectiveness
Proposition is the Ricardian Equivalence Theorem (sect. 16.3)

Consumers have rational (forward-looking) expectations about
taxes:



They realize that a government tax cut today will necessitate a
tax increase in the future (through the intertemporal government
budget constraint given no changes in government expenditure)
Consumers experience increased income through the tax cut,
but they decide to save it in order to pay the increased taxes in
the future
Conclusion: No effect on today’s consumption from a tax cut
The Lucas’ critique: Be cautious about historical
econometric relationships

The Lucas’ critique is about the stability of econometric
relationships: After a policy change, historical econometric
relationships may no longer be valid because economic
agents change their behavior

Implication for policy makers: Past behavior of economic
agents can be a poor guide for assessing the effects of policy
changes

Lucas: Should estimate parameters that are invariant to
changes in government policy rules (so-called “deep”
parameters) such as tastes or technology
PART 2
Real business cycles
Overview of real business cycles theory


Our AS-AD model of the business cycle:

Expectational errors and sluggish price adjustment played key roles

The model assigned an important role to demand shocks

Business fluctuations were associated with fluctuations in involuntary
unemployment (cf. microfoundations of the SRAS curve)
Real business cycle theory (basic version):

To explain business cycles, there is no need to postulate nominal
and/or real rigidities, backwards-looking expectations or sluggish
adjustment

The business cycle could be driven mainly by fluctuations in the rate
of productivity growth (a form of supply shock)

The employment fluctuations observed during business cycles reflect
voluntary movements in individual labor supply (intertemporal
substitution in labor supply, no involuntary unemployment)
In the simple RBC model, the production-side
resembles a basic growth model

Assume that the production-side of the economy can be
described as:

Production function:
Production
function: Yt  Kt  At Lt 
1
,
0   1

Labor
productivity:
Actual
productivity:
lnAt  gt ln
stA
, t  gt  st ,
Actual productivity:
where
s
st 1
t
2 ~ N 0 , 2
s


s

c
,
0


<1,
c
 c
t <1,
1
 ct 1 ,
0t  
c
N 0 , t
t 1
t

c

In other words: Stochastic, autoregressive shocks to labor productivity

Trend productivity:
Trend
productivity: lnAt  gt
Capital
accumulation: K  1    K  S
Capital
accumulation:
t
t 1
t 1

In the simple RBC model, there is market clearing
in every period (including the labor market)

Arbitrage
Saving: St  s  Yt ,
o Saving (= investments):
0  s 1

 wt 
o Labor
supply: supply: L 
Labour
  ,
 wt 
s
t
o Profit maximization:
Profit
maximization:
o Trend
real wage:
Trend
real wage:
0
 Kt 
Yt
wt 
 1    

Lt
A
L
 t t
wt  1    cAt ,
o Labor market
clearing:
Labour market
clearing:
Lt  Lst

 
c k
*

The solution to the simple RBC model is a ADL
model

As shown in the textbook (pages 585-86) the solution to this
model is:


 1  

ˆyt  
 ˆyt 1  
 st ,
 1   1    
 1   1    


1
1 

Source of impulse in the model: A positive productivity shock
raises wages, labor supply and output (income)

Propagation mechanism in the model: Higher output raises
savings (investments), thereby increasing the capital stock in
the next period. Higher capital stock raises next period’s output
(income), thereby raising savings, and so on…

Labor supply in the model:
ˆ  ˆy
L
t
t
The simple RBC model fits the U.S. economy quite
well, except it generates too high persistence
Source of data: Economic Outlook Database (OECD)
1. α = 0.33, η = 0.83, ω = 0.1, σc = 0.015
2. Annual data for the business sector
Note: The cyclical components of output and employment have been estimated via linear OLS
detrending of annual data
Some problems with the basic RBC theory

Is technological progress really so time-varying as postulated
in the RBC model?

Is it really plausible that recessions are periods of
technological regress?

Do the observed fluctuations in employment really reflect
intertemporal substitution in labor supply? More generally:
Is all recorded unemployment really voluntary?

The RBC model predicts that the real wage is procyclical. This
is in line with U.S. data, but not consistent with European data.

Response: Real business cycle theorists have tried to make
their models more realistic by allowing for various frictions and
rigidities, including (in some cases) nominal rigidities.
The most influential contribution of real business
cycle theory is methodological


At the methodological level, RBC theorists have made a
lasting contribution by pointing out that:

Supply shocks may play an important part in the explanation of
business cycles

A satisfactory theory of the business cycle should consist of a
dynamic stochastic general equilibrium model which is able to
reproduce the most important stylized facts of the business cycle
The Nobel committee on Kydland and Prescott’s business
cycle models:

“The Laureates laid the groundwork for more robust models by
regarding business cycles as the collective outcome of countless
forward-looking decisions made by individual households and
firms regarding consumption, investments, labor supply, etc.
Kydland and Prescott's methods have been widely adopted in
modern macroeconomics.”
PART 3
Rules versus discretion
Policy rules versus discretion: a credibility problem

Discretionary policy: Policy makers react in an ad-hoc manner
to the specific circumstances of the situation, using all relevant
available information

Intuitive advantage of discretionary policy: Flexibility to adopt
the optimal policy at all times

Seminal article: Kydland and Prescott (1977) “Rules rather
than discretion: The inconsistency of optimal plans”

Conclusion: Under plausible conditions, the government may
achieve better results by committing to follow a rule for
monetary policy

Provides a rationale for explicit inflation targets
The setup is a standard AS-AD model where the
government wishes to increase y above y

Assume a simplified standard AS-AD model setup without shocks
yt - y = - (rt - r)
t = te + (yt - y)

Monetary policy tries to minimize a social loss function
SLt = (yt - y*)2 + t2

Assume that the socially optimal level of output is above the trend
level of output
y* = y + 

SLt = (t - te - )2 + t2
The Taylor rule is a benchmark for the performance
of discretionary policy

Suppose the central bank follows a Taylor rule with an inflation
target equal to zero and no attempt to increase output above
its trend value
rt = r + ht + b(yt - y)

The solution to this model is
t = te = * = 0

and
yt = y
The social loss under the Taylor rule is only due to 
SLR = 2
Incentives for discretionary monetary policy to
disregard the inflation target

Suppose the central bank announces that it will stick to an
inflation target * = 0 (as in the benchmark case with the
Taylor rule) and the public believes it (te = 0)

What is optimal policy given these inflation expectations?

At zero inflation, output is at y. A small increase in inflation
would:



Give a small increase in the social loss from inflation (small
because inflation is at its optimal level)
Give a large decrease in the social loss from output (large
because output is far – the distance is  – from its optimal level
Conclusion: A small increase in inflation would be desirable.
The discretionary central bank will not want to stick to its promise
( = * = 0)
Optimal monetary policy with given inflation
expectations

Minimize the social loss function in order to find the optimal
level of inflation for the central bank (with given inflation
expectations te)
dSLt / dt = 0

2(t - te - ) + 2t = 0

If te = 0 then the solution would be
t =


1+
The social loss is
>0
and
SLC = 2 -
yt = y +

1+

1+
< SLR
In the time-consistent rational expectations
equilibrium, the social loss is higher

Rational expectations about inflation must be consistent with
the central bank’s optimality condition for monetary policy:
2(t - te - ) + 2t = 0

Rational expectations:
te

-
te
-+
te
=0

 te

=

Given this expected inflation, the solution and the social loss
are

e
t = t =
and yt = y

SLD = 2 +

1+
> SLR
Illustration of the different model equilibriums
Central bank independence coupled with rules
and/or reputation cures the inflation bias

Delegating monetary policy to the central bank keeps it at a
distance from political incentives



Instrument independence is common (operational indep.)
Goal independence is more rare
Building reputation


Repeated games: If the central bank can only brake its promise
once, the incentive to stick to the inflation target is increased
Choose a “hawkish” central bank governor (tough on inflation)