This PDF is a selection from an out-of-print volume from the National
Bureau of Economic Research
Volume Title: NBER Macroeconomics Annual 1997, Volume 12
Volume Author/Editor: Ben S. Bernanke and Julio Rotemberg
Volume Publisher: MIT Press
Volume ISBN: 0-262-02435-7
Volume URL: http://www.nber.org/books/bern97-1
Publication Date: January 1997
Chapter Title: An Optimization-Based Econometric Framework for
the Evaluation of Monetary Policy
Chapter Author: Julio Rotemberg, Michael Woodford
Chapter URL: http://www.nber.org/chapters/c11041
Chapter pages in book: (p. 297 - 361)
Julio J.
Rotemberg
and Michael
Woodford
MASSACHUSETTS
INSTITUTE OF
TECHNOLOGY;
AND
PRINCETON
UNIVERSITY
An
Optimization-Based
Econometric
Framework
for
the
Evaluation
of
Monetary
Policy
1.
Introduction
In
this
paper,
we
develop
a
small,
structural
econometric model
to
be
used
in the
quantitative
evaluation of
proposed
rules for
monetary
pol-
icy.
The
quantitative
evaluation of
monetary
policy
rules
has
gained
increased attention
in
recent
years
(see,
e.g.,
McCallum,
1988,
1997;
Taylor,
1993a;
Bryant,
Hooper,
and
Mann, 1993;
Henderson and Mc-
Kibbin, 1993;
Feldstein and
Stock,
1994;
Leeper
and
Sims,
1994; Levin,
1996;
and Fuhrer
1997a).
Our
approach
differs from these
studies
in
that
we
derive our econometric
specification
from
an
explicit
model of in-
tertemporal optimization
on
the
part
of both the
suppliers
and the
pur-
chasers of
goods
and
services.1
Rigorously grounding
our
structural relations
in
optimizing
individual
behavior
has
two
important advantages.
The
first is
that we
are
able to
respond
to the well-known Lucas
(1976)
critique
of econometric
policy
evaluation.
Our
analysis
of
hypothetical
policy
rules takes full
account
of
the
way
that an
understanding
of
the
change
in
policy regime
ought
to
affect the
decision rules of
private agents,
and
make them
different than
those that
underlie the
statistical correlations observed in
past
data.
We
wish
to
thank Eduardo
Loyo
for
superb
research
assistance,
Ben
Bernanke,
Frank
Diebold,
Jeff
Fuhrer,
Bennett
McCallum,
and Chris Sims for
helpful
comments,
and
the
NSF
for research
support.
1.
Leeper
and Sims
(1994)
made
an
ambitious effort
of this
kind,
although,
unlike
us,
they
do not derive
their
price dynamics
from
producer optimization.
Ireland
(1997)
is
another
recent
study
with an aim
similar to
ours,
although
our
approaches
differ
considerably
in
their
details.
298
-
ROTEMBERG
&
WOODFORD
Much of the
recent work cited above does
respond
to the
Lucas
critique
to at least some
extent,
by incorporating
forward-looking specifications
of at
least some of
the
models' structural
relations,
and
assuming
ra-
tional
(or model-consistent)
expectations
in
analyzing
alternative
poli-
cies.
But
because no
attempt
is made to derive the
complete
structural
model
from
internally
consistent
foundations
in
terms of
individual
opti-
mization,
doubts
must remain as to
whether
the
posited
structural rela-
tions should
genuinely
be
invariant
to
changes
in
the
policy
regime.
Demanding
that one's structural relations be
derived from individual
optimization
also
has
the
advantage
that evidence from other
sources
about
the
nature of
the
problems
that individuals
face can be used to
corroborate the
quantitative
specifications
that are
used to
explain
the
relations
among aggregate
time
series.
Ultimately,
this is the
only way
in
which the "observational
equivalence"
of a
multitude of alternative
possi-
ble structural
interpretations
of the
comovements
of
aggregate
series can
be resolved.
We make little
attempt
here
at
such
validation
of our
pro-
posed specification.
But because our model
parameters
refer to
con-
cepts,
such
as
the
elasticity
of firms' demand
curves,
or
the
average
length
of
time that
prices
remain
fixed,
that
have
clear referents
apart
from
the role of these
parameters
in
our structural relations
linking
inter-
est
rates,
inflation,
and
output
in
the
economy
as a
whole,
it
becomes
possible
to consider
the
reasonableness of our
specification
on
grounds
other
than
simple
statistical measures of
goodness
of fit.
The second
advantage
of
an
optimization-based approach
is that
the
specification
of individuals'
decision
problems
that is
used
to
explain
the
effects of
monetary policy
can also be used for
purposes
of
welfare
analysis.
Of
course,
the
analysis
of
the
deadweight
losses associated
with alternative
policies
in
terms of
the individual
preferences
that ac-
count for
the
predicted
responses
to
a
policy change
is
by
now the
standard
method of the
public-finance
literature.
But this method has
been little
applied
to
problems
of
monetary
policy,
the main
exception
being
analyses
of
the
special
issue
of
the
costs
of
steady
inflation
(e.g.,
Lucas,
1993).
Analyses
of
optimal
monetary
policy-or
at
least those
that
are
based
upon
econometric models-consider
instead
the
problem
of
minimizing
one
ad hoc
loss
function or another.
Here we
show,
instead,
how
a
utility-based
measure
of the
deadweight
loss associated
with
price-level
instability
can be
derived,
and how most
of its
parameters
can
be determined
from our
estimated
structural
equations.
We can use this
measure to
address
questions
such
as Summers's
(1991)
suggestion
that
a
positive
average
rate of
inflation is
desirable
in
order
to make it
possi-
ble for nominal interest
rates to
be
lowered
as
necessary
for
stabilization
purposes.
Not
only
does
our econometric
model
allow us to
discuss
Optimization-Based
Econometric Framework
*
299
quantitatively
how
much
variability
of nominal
interest rates would
be
necessary
for full
stabilization,
but our
welfare measure in
principle
allows a direct
comparison,
in
comparable
units,
of the
deadweight
losses
associated
with
incomplete
stabilization
on
the
one hand and
higher average
inflation
on the
other.
Our
analysis proceeds
in five distinct
steps.
In the
first
step,
we
esti-
mate
a
vector
autoregression
(VAR)
model
of the
joint
process
of
interest
rates, inflation,
and
output.
We
use
this
VAR
for two
purposes.
The
first
is
to
identify
the actual
monetary policy
rule
employed
by
the
Fed.
Following
Taylor
(1993b),
we
suppose
that this rule
is a
reaction
function
that
sets
interest rates as
a function of current
and
past
values of
output
and inflation. The second
purpose
of
this
VAR
is
to
estimate the
way
output,
inflation,
and interest
rates
respond
to a stochastic
disturbance
to
the
monetary policy
rule. Thus
we learn how
the
economy responds
to a
monetary
shock
under the current
monetary
policy
rule,
using fairly
standard "structural
VAR"
methodology (e.g.,
Cochrane, 1994;
Leeper,
Sims,
and
Zha,
1996).
In
the
second
step,
we
postulate
a
simple
theoretical model
that
can
account for the estimated
response
of
output
and
inflation
to
monetary
policy
shocks.
In
this
model,
we assume
that
there
are
impediments
to
the
free
adjustment
of
prices.
In
particular,
we
consider
a variant
of
the
Calvo
(1983)
model
in
which
a
firm's
opportunity
to
change
its
price
arrives
stochastically
and
where,
if
this
opportunity
does
not
arise,
the
firm
must
keep
its
price
constant.
We choose the
parameters
of
this
extremely
stylized
model
so
that the model's
predicted responses
to
monetary policy
shocks match
as
closely
as
possible
the
estimated re-
sponses
from the VAR.
In
the third
step,
we combine the
quantitative specification
of the struc-
tural
model
(with
the
parameters
obtained
in
step
two)
with the
vector
autoregression
model
to
identify
the
shocks
to the
structural
equations.
The
failure of the
VAR
to contain
any
stochastic
singularities implies
that
the
model's structural
equations
have residuals
as
well,
which
we
can
interpret
in
the context
of
the model as
indicating
stochastic
variation
in
preferences
and
technology.
We
compute
what
these
disturbances
have
been
over
our
sample period,
and
use
the
VAR
representation
to deter-
mine
the stochastic
process
followed
by
the real
disturbances. One
impor-
tant
advantage
of
our method of
analyses
is
that,
once we
take into
account these
constructed
disturbances,
our model fits the data
nearly
as
well
as an unrestricted
vector
autoregression.
This
good
fit
provides
an
additional
rationale for
being
interested
in the
model's
implications
con-
cerning monetary policy.
In
the fourth
step,
we use the
quantitative
model with
parameters
300
*
ROTEMBERG &
WOODFORD
estimated
in
step
two and
shock
processes
estimated
in
step
three to
simulate the
consequences
of
hypothetical
monetary
policy
rules.
Using
the
estimated
historical shock
series,
we can
simulate alternative histori-
cal
paths
for
the
U.S.
economy.
In
particular,
we can
compute
the realiza-
tions of
output,
inflation,
and
interest rates
under counterfactual rules.
What is
particularly
attractive about this exercise
is
that,
under the actual
monetary
rule
estimated
in
step
one,
the
simulated
paths
of
output,
inflation,
and interest rates
are
identical
to
the actual
paths.
Thus,
the
simulations
with
counterfactual rules
provide
alternative
historical
paths
for
the U.S.
economy.
In the fifth and final
step,
we
use
the
parameters
estimated
in
step
two
to
compute
the welfare
consequences
of
different
monetary
rules. More-
over,
we
derive
the rule that
would
have
maximized
the
utility
of
our
representative
households
given
the shock
processes
obtained
in
step
three.
2.
The
Effects
of
Monetary Policy
Shocks
under the
Current
Policy
Regime
In
this
section,
we describe our econometric characterization of
the cur-
rent
monetary
policy
regime,
and our
estimates
of the effects of mone-
tary policy
shocks under
that
regime.
By monetary
shocks
we mean
exogenous
stochastic
shifts in the
feedback
rule used
by
the Fed to set
the
Federal funds
rate.
Our interest
in
the effects
of
such shifts
does not
derive
from
a
belief
that
they
have
played
an
important
role
in
the
generation
of
fluctuations
in
either
output
or inflation
in the
period
with
which
we are concerned.
Rather,
we
are interested
in
them
because
they
can
be
econometrically
identified
without
our
having
to commit
our-
selves
to
detailed
assumptions
about
the true structural relations
that
determine
output
and
inflation.
The
monetary policy
shocks
and their effects
cannot,
of
course,
be
identified
without
at
least
some weak
a
priori assumptions.
In
particular,
we assume
that
recent U.S.
monetary
policy
may
be
described
by
a
feedback
rule
for the federal
funds rate
of the form
nr
n.r
ny
rt
=
r*
+
E
u'k(rt-
-
r*)
+
k(rt-k
)
+
OYt-k
+
et,
(2.1)
k=l
k=O
k=O
where
rt
is
the
Federal
funds rate
in
period
t,
and
ir,
is the
rate of inflation
between
periods
t
-
1
and
t,
yt
is
the
percentage
deviation of real GDP
from
trend,
and
r*
and
Ti*
are
long-run
"target"
values for the funds rate