Theme 5: Macroeconomic policy.
Part 2: Monetary policy (III)
1
Issues in monetary policy
1. Time-consistent policy. Reading: B&W ch. 16.3
2. Lucas’ critique. Reading: B&W ch. 15
3. If time (cursory): Real business cycles. Reading: B&W ch. 14.5-6
Øystein Børsum
Temporary lecturer, University of Oslo
April 29, 2005
2
1
2.1
2
Model setup
Time-consistent policy
Seminal article: Kydland and Prescott (1977) “Rules rather than discretion:
The inconsistency of optimal plans”
Model adopted from the book Foundations of international macroeconomics by
Obstfeld and Rogoff (1996). Often referred to as the ”Barro-Gordon model”.
Conclusion: Under plausible conditions, the government may be better off
commiting to an ex ante rule of monetary policy. Provides a rationale for
explicit inflation targets.
Workers commit to nominal wage contracts for period t at time t − 1. They
care about real wages, and must forecast inflation.
Aggregate supply curve:
yt = ȳ − (wt − pt) − zt
(8.4)
where ȳ is the flexible price equilibrium output (or trend level of output) and zt
is a supply shock with expected value zero and uncorrelated over time. Output
is decreasing in the log real wage wt − pt thus increasing in the price level.
Workers are committed to setting Et−1yt = ȳ will negotiate Et−1wt = pt at
time t − 1.
3
4
Monetary policy is set after wt and zt are observed. Monetary policy sets
inflation πt
πt = pt − pt−1
(8.4)
Et−1πt = Et−1pt − pt−1 = πte
(8.4)
For notation we use:
The monetary authorities try to minimise a loss function including both output
and inflation:
Lt = (yt − ỹ)2 − λπt2
where ỹ is the desirable level of output from the monetary authorities’ perspective. The desirable level of inflation is zero. λ represents the emphasis given
to inflation stabilisation relative to output stabilisation.
ỹ > ȳ means that the authorities have a desire to drive output above its
equilibrium level (presumably, in order to drive down unemployment).
Use the supply curve and the definition of πte to obtain:
Lt = (πt − πte − k − zt)2 − λπt2
Question: Will the fact that the monetary authorities always set πt after workers
have decided wages, lead to yt = ỹ > ȳ ? Surprisingly, no!
We presume that
ỹ > ȳ
with
ỹ − ȳ = k
5
2.2
6
Solution and implications of optimal discretionary policy
Step 1: Determine the monetary authorities’ reaction function (optimal policy
response) given πte
Step 2: Impose rational expectations
Suppose wages are set according to a promise by the monetary authorities that
actual inflation will be zero. This determines expectations to πte = 0. The
optimal response of the central bank is to chose πt∗ so that Lt is minimised.
dLt/dπt = 2(πt − πte − k − zt) − 2λπt
For how long will workers put up with inflation always being higher than
promised? Impose rational expectations:
πte = Et−1πt∗ = Et−1
πte + k + zt
1+λ
Using Et−1zt = 0 and solving for πte :
πte =
k
>0
λ
π e + k + zt
πt∗ = t
1+λ
t
If πte = 0 then Et−1( k+z
1+λ ) > 0 so workers get fooled! Workers are promised
low inflation, but then monetary authorities drive up inflaiton because of their
desire to reduce unemployment.
7
"
8
#
Optimal monetary policy response is then:
k +k+z
zt
k
zt
t
πt∗ = λ
= +
= πte +
1+λ
λ 1+λ
1+λ
2.3
Outcome with a monetary policy rule
The equilibrium is obviously sub-optimal: Higher inflation at no average gain
in output.
Inflation varies around πte due to shocks zt , but there is no systematic deviation. Hence Et−1yt = ȳ and not ỹ ! Discretionary monetary policy fails to
systematically increase output above ȳ (thereby failing to systematically reduce
unemployment).
Suppose instead a monetary policy rule requiring the authorities to set:
k.
Moreover, there is a positive, undesired inflation in every period equal to λ
This inflation is decreasing in the weight that monetary authorities put on
inflation relative to output (λ), and increasing in what the authorities perceive
as the desirable level of output (k = ỹ − ȳ).
in every period (instead of optimising Lt). This implies πte = Et−1πtrule = 0.
Ealuate the loss function, take expectations and compare:
πtrule =
zt
1+λ
Et−1L∗t > Et−1Lrule
t
Intuition: πte must be driven up to a point where the marginal loss from increasing inflation exactly outweight the marginal utility from increasing output.
Graph.
zt
In fact, πtrule = 1+λ
is the solution to the minimisation problem min Et−1Lt
i.e. it is the optimal policy rule.
9
10
3
Conclusion: By committing to an optimal ex ante rule of monetary policy, the
monetary authorities may achieve lower inflation at no average loss in output.
Provides a rationale for explicit targets of monetary policy, e.g. inflation targets.
The Lucas’ critique and rational expectations
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 behaviour.
Most famous application: A.W.Philips plotted wage inflation against unemployment and found a robust negative correlation for the period 1861-1957.
Once governments tried to exploit it to reduce unemployment, the relationship
broke down. Suppose the historical correlations were based on a policy regime
that ensured no systematic increases in inflation. After the policy change, economic agents no longer have any reason to believe that inflation will be stable
(but rather increasing or high). As a result, the historical correlations break
down.
Implication for policy makers: Past behaviour of economic agents can be a
poor guide for assessing the effects of policy changes. Lucas: Should estimate
deep parameters.
11
12
The Lucas’ critique is closely linked to how agents form expectations about the
new policy. If agents have rational expectations, a number of activist policies
will have no real effects in the economy.
Example: The effect of a tax reduction will depend on whether it is perceived
to be temporary or permanent. A permanent reduction will increase permanent
income, and may therefore have a large impact on consumption. A temporary
reduction will only have a small impact if consumption is smoothed. If the
temporary reduction is expected to lead to a temporary increase at a later
time, there might be no effect on consumption! Ricardian equivalence.
The tradition following Lucas often takes the view that rational expectations
dominate the economic decisions of households and firms. Empirical tests show
that the empirical relevance of the Lucas’ critique is overstated.
Nevertheless, rational expectations have become a common modelling assumption in macroeconomic theory.
13