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Dynare
dynare
Commits
055710c9
Commit
055710c9
authored
Jan 10, 2020
by
Johannes Pfeifer
1
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Change ordering of optimal policy commands
Moves common planner_objective command to front
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055710c9
...
...
@@ 8137,6 +8137,234 @@ commitment with ``ramsey_policy``, for optimal policy under discretion
with
``
discretionary_policy
``
or
for
optimal
simple
rule
with
``
osr
``
(
also
implying
commitment
).
..
command
::
planner_objective
MODEL_EXPRESSION
;

br

This
command
declares
the
policy
maker
objective
,
for
use
with
``
ramsey_policy
``
or
``
discretionary_policy
``.
You
need
to
give
the
one

period
objective
,
not
the
discounted
lifetime
objective
.
The
discount
factor
is
given
by
the
``
planner_discount
``
option
of
``
ramsey_policy
``
and
``
discretionary_policy
``.
The
objective
function
can
only
contain
current
endogenous
variables
and
no
exogenous
ones
.
This
limitation
is
easily
circumvented
by
defining
an
appropriate
auxiliary
variable
in
the
model
.
With
``
ramsey_policy
``,
you
are
not
limited
to
quadratic
objectives
:
you
can
give
any
arbitrary
nonlinear
expression
.
With
``
discretionary_policy
``,
the
objective
function
must
be
quadratic
.
Optimal
policy
under
commitment
(
Ramsey
)

..
command
::
ramsey_model
(
OPTIONS
...);

br

This
command
computes
the
First
Order
Conditions
for
maximizing
the
policy
maker
objective
function
subject
to
the
constraints
provided
by
the
equilibrium
path
of
the
private
economy
.
The
planner
objective
must
be
declared
with
the
:
comm
:`
planner_objective
`
command
.
This
command
only
creates
the
expanded
model
,
it
doesn
’
t
perform
any
computations
.
It
needs
to
be
followed
by
other
instructions
to
actually
perform
desired
computations
.
Examples
are
calls
to
``
steady
``
to
compute
the
steady
state
of
the
Ramsey
economy
,
to
``
stoch_simul
``
with
various
approximation
orders
to
conduct
stochastic
simulations
based
on
perturbation
solutions
,
to
``
estimation
``
in
order
to
estimate
models
under
optimal
policy
with
commitment
,
and
to
perfect
foresight
simulation
routines
.
See
:
ref
:`
aux

variables
`,
for
an
explanation
of
how
Lagrange
multipliers
are
automatically
created
.
*
Options
*
This
command
accepts
the
following
options
:
..
option
::
planner_discount
=
EXPRESSION
Declares
or
reassigns
the
discount
factor
of
the
central
planner
``
optimal_policy_discount_factor
``.
Default
:
``
1.0
``.
..
option
::
planner_discount_latex_name
=
LATEX_NAME
Sets
the
LaTeX
name
of
the
``
optimal_policy_discount_factor
``
parameter
.
..
option
::
instruments
=
(
VARIABLE_NAME
,...)
Declares
instrument
variables
for
the
computation
of
the
steady
state
under
optimal
policy
.
Requires
a
``
steady_state_model
``
block
or
a
``
_steadystate
.
m
``
file
.
See
below
.
*
Steady
state
*
Dynare
takes
advantage
of
the
fact
that
the
Lagrange
multipliers
appear
linearly
in
the
equations
of
the
steady
state
of
the
model
under
optimal
policy
.
Nevertheless
,
it
is
in
general
very
difficult
to
compute
the
steady
state
with
simply
a
numerical
guess
in
``
initval
``
for
the
endogenous
variables
.
It
greatly
facilitates
the
computation
,
if
the
user
provides
an
analytical
solution
for
the
steady
state
(
in
``
steady_state_model
``
block
or
in
a
``
_steadystate
.
m
``
file
).
In
this
case
,
it
is
necessary
to
provide
a
steady
state
solution
CONDITIONAL
on
the
value
of
the
instruments
in
the
optimal
policy
problem
and
declared
with
the
option
``
instruments
``.
The
initial
value
of
the
instrument
for
steady
state
finding
in
this
case
is
set
with
``
initval
``.
Note
that
computing
and
displaying
steady
state
values
using
the
``
steady
``
command
or
calls
to
``
resid
``
must
come
after
the
``
ramsey_model
``
statement
and
the
``
initval
``
block
.
Note
that
choosing
the
instruments
is
partly
a
matter
of
interpretation
and
you
can
choose
instruments
that
are
handy
from
a
mathematical
point
of
view
but
different
from
the
instruments
you
would
refer
to
in
the
analysis
of
the
paper
.
A
typical
example
is
choosing
inflation
or
nominal
interest
rate
as
an
instrument
.
..
block
::
ramsey_constraints
;

br

This
block
lets
you
define
constraints
on
the
variables
in
the
Ramsey
problem
.
The
constraints
take
the
form
of
a
variable
,
an
inequality
operator
(>
or
<)
and
a
constant
.
*
Example
*
::
ramsey_constraints
;
i
>
0
;
end
;
..
command
::
evaluate_planner_objective
;
This
command
computes
,
displays
,
and
stores
the
value
of
the
planner
objective
function
under
Ramsey
policy
in
``
oo_
.
planner_objective_value
``,
given
the
initial
values
of
the
endogenous
state
variables
.
If
not
specified
with
``
histval
``,
they
are
taken
to
be
at
their
steady
state
values
.
The
result
is
a
1
by
2
vector
,
where
the
first
entry
stores
the
value
of
the
planner
objective
when
the
initial
Lagrange
multipliers
associated
with
the
planner
’
s
problem
are
set
to
their
steady
state
values
(
see
:
comm
:`
ramsey_policy
`).
In
contrast
,
the
second
entry
stores
the
value
of
the
planner
objective
with
initial
Lagrange
multipliers
of
the
planner
’
s
problem
set
to
0
,
i
.
e
.
it
is
assumed
that
the
planner
exploits
its
ability
to
surprise
private
agents
in
the
first
period
of
implementing
Ramsey
policy
.
This
is
the
value
of
implementating
optimal
policy
for
the
first
time
and
committing
not
to
re

optimize
in
the
future
.
Because
it
entails
computing
at
least
a
second
order
approximation
,
the
computation
of
the
planner
objective
value
is
skipped
with
a
message
when
the
model
is
too
large
(
more
than
180
state
variables
,
including
lagged
Lagrange
multipliers
).
..
command
::
ramsey_policy
[
VARIABLE_NAME
...];
ramsey_policy
(
OPTIONS
...)
[
VARIABLE_NAME
...];

br

This
command
is
formally
equivalent
to
the
calling
sequence
::
ramsey_model
;
stoch_simul
(
order
=
1
);
evaluate_planner_objective
;
It
computes
the
first
order
approximation
of
the
policy
that
maximizes
the
policy
maker
’
s
objective
function
subject
to
the
constraints
provided
by
the
equilibrium
path
of
the
private
economy
and
under
commitment
to
this
optimal
policy
.
The
Ramsey
policy
is
computed
by
approximating
the
equilibrium
system
around
the
perturbation
point
where
the
Lagrange
multipliers
are
at
their
steady
state
,
i
.
e
.
where
the
Ramsey
planner
acts
as
if
the
initial
multipliers
had
been
set
to
0
in
the
distant
past
,
giving
them
time
to
converge
to
their
steady
state
value
.
Consequently
,
the
optimal
decision
rules
are
computed
around
this
steady
state
of
the
endogenous
variables
and
the
Lagrange
multipliers
.
This
first
order
approximation
to
the
optimal
policy
conducted
by
Dynare
is
not
to
be
confused
with
a
naive
linear
quadratic
approach
to
optimal
policy
that
can
lead
to
spurious
welfare
rankings
(
see
*
Kim
and
Kim
(
2003
)*).
In
the
latter
,
the
optimal
policy
would
be
computed
subject
to
the
first
order
approximated
FOCs
of
the
private
economy
.
In
contrast
,
Dynare
first
computes
the
FOCs
of
the
Ramsey
planner
’
s
problem
subject
to
the
nonlinear
constraints
that
are
the
FOCs
of
the
private
economy
and
only
then
approximates
these
FOCs
of
planner
’
s
problem
to
first
order
.
Thereby
,
the
second
order
terms
that
are
required
for
a
second

order
correct
welfare
evaluation
are
preserved
.
Note
that
the
variables
in
the
list
after
the
``
ramsey_policy
``
command
can
also
contain
multiplier
names
.
In
that
case
,
Dynare
will
for
example
display
the
IRFs
of
the
respective
multipliers
when
``
irf
>
0
``.
The
planner
objective
must
be
declared
with
the
:
comm
:`
planner_objective
`
command
.
*
Options
*
This
command
accepts
all
options
of
``
stoch_simul
``,
plus
:
..
option
::
planner_discount
=
EXPRESSION
See
:
opt
:`
planner_discount
<
planner_discount
=
EXPRESSION
>`.
..
option
::
instruments
=
(
VARIABLE_NAME
,...)
Declares
instrument
variables
for
the
computation
of
the
steady
state
under
optimal
policy
.
Requires
a
``
steady_state_model
``
block
or
a
``
_steadystate
.
m
``
file
.
See
below
.
Note
that
only
a
first
order
approximation
of
the
optimal
Ramsey
policy
is
available
,
leading
to
a
second

order
accurate
welfare
ranking
(
i
.
e
.
``
order
=
1
``
must
be
specified
).
*
Output
*
This
command
generates
all
the
output
variables
of
``
stoch_simul
``.
For
specifying
the
initial
values
for
the
endogenous
state
variables
(
except
for
the
Lagrange
multipliers
),
see
:
bck
:`
histval
`.
*
Steady
state
*
See
:
comm
:`
Ramsey
steady
state
<
ramsey_model
>`.
Optimal
policy
under
discretion

..
command
::
discretionary_policy
[
VARIABLE_NAME
...];
discretionary_policy
(
OPTIONS
...)
[
VARIABLE_NAME
...];

br

This
command
computes
an
approximation
of
the
optimal
policy
under
discretion
.
The
algorithm
implemented
is
essentially
an
LQ
solver
,
and
is
described
by
*
Dennis
(
2007
)*.
You
should
ensure
that
your
model
is
linear
and
your
objective
is
quadratic
.
Also
,
you
should
set
the
``
linear
``
option
of
the
``
model
``
block
.
*
Options
*
This
command
accepts
the
same
options
than
``
ramsey_policy
``,
plus
:
..
option
::
discretionary_tol
=
NON

NEGATIVE
DOUBLE
Sets
the
tolerance
level
used
to
assess
convergence
of
the
solution
algorithm
.
Default
:
``
1e7
``.
..
option
::
maxit
=
INTEGER
Maximum
number
of
iterations
.
Default
:
``
3000
``.
Optimal
Simple
Rules
(
OSR
)

...
...
@@ 8390,236 +8618,6 @@ Optimal Simple Rules (OSR)
``M_.endo_names``.
Optimal policy under commitment (Ramsey)

.. command:: ramsey_model (OPTIONS...);
br This command computes the First Order Conditions for maximizing
the policy maker objective function subject to the constraints
provided by the equilibrium path of the private economy.
The planner objective must be declared with the :comm:`planner_objective` command.
This command only creates the expanded model, it doesn’t perform
any computations. It needs to be followed by other instructions to
actually perform desired computations. Examples are calls to ``steady``
to compute the steady state of the Ramsey economy, to ``stoch_simul``
with various approximation orders to conduct stochastic simulations based on
perturbation solutions, to ``estimation`` in order to estimate models
under optimal policy with commitment, and to perfect foresight simulation
routines.
See :ref:`auxvariables`, for an explanation of how Lagrange
multipliers are automatically created.
*Options*
This command accepts the following options:
.. option:: planner_discount = EXPRESSION
Declares or reassigns the discount factor of the central
planner ``optimal_policy_discount_factor``. Default: ``1.0``.
.. option:: planner_discount_latex_name = LATEX_NAME
Sets the LaTeX name of the ``optimal_policy_discount_factor``
parameter.
.. option:: instruments = (VARIABLE_NAME,...)
Declares instrument variables for the computation of the
steady state under optimal policy. Requires a
``steady_state_model`` block or a ``_steadystate.m`` file. See
below.
*Steady state*
Dynare takes advantage of the fact that the Lagrange multipliers
appear linearly in the equations of the steady state of the model
under optimal policy. Nevertheless, it is in general very
difficult to compute the steady state with simply a numerical
guess in ``initval`` for the endogenous variables.
It greatly facilitates the computation, if the user provides an
analytical solution for the steady state (in
``steady_state_model`` block or in a ``_steadystate.m`` file). In
this case, it is necessary to provide a steady state solution
CONDITIONAL on the value of the instruments in the optimal policy
problem and declared with the option ``instruments``. The initial value
of the instrument for steady state finding in this case is set with
``initval``. Note that computing and displaying steady state values
using the ``steady``command or calls to ``resid`` must come after
the ``ramsey_model`` statement and the ``initval``block.
Note that choosing the instruments is partly a matter of interpretation and
you can choose instruments that are handy from a mathematical
point of view but different from the instruments you would refer
to in the analysis of the paper. A typical example is choosing
inflation or nominal interest rate as an instrument.
.. block:: ramsey_constraints ;
br This block lets you define constraints on the variables in
the Ramsey problem. The constraints take the form of a variable,
an inequality operator (> or <) and a constant.
*Example*
::
ramsey_constraints;
i > 0;
end;
.. command:: evaluate_planner_objective ;
This command computes, displays, and stores the value of the
planner objective function
under Ramsey policy in ``oo_.planner_objective_value``, given the
initial values of the endogenous state variables. If not specified
with ``histval``, they are taken to be at their steady state
values. The result is a 1 by 2 vector, where the first entry
stores the value of the planner objective when the initial
Lagrange multipliers associated with the planner’s problem are set
to their steady state values (see :comm:`ramsey_policy`).
In contrast, the second entry stores the value of the planner
objective with initial Lagrange multipliers of the planner’s
problem set to 0, i.e. it is assumed that the planner exploits its
ability to surprise private agents in the first period of
implementing Ramsey policy. This is the value of implementating
optimal policy for the first time and committing not to
reoptimize in the future.
Because it entails computing at least a second order approximation, the
computation of the planner objective value is skipped with a message when
the model is too large (more than 180 state variables, including lagged
Lagrange multipliers).
.. command:: ramsey_policy [VARIABLE_NAME...];
ramsey_policy (OPTIONS...) [VARIABLE_NAME...];
br This command is formally equivalent to the calling sequence
::
ramsey_model;
stoch_simul(order=1);
evaluate_planner_objective;
It computes the first order approximation of the
policy that maximizes the policy maker’s objective function
subject to the constraints provided by the equilibrium path of the
private economy and under commitment to this optimal policy. The
Ramsey policy is computed by approximating the equilibrium system
around the perturbation point where the Lagrange multipliers are
at their steady state, i.e. where the Ramsey planner acts as if
the initial multipliers had been set to 0 in the distant past,
giving them time to converge to their steady state
value. Consequently, the optimal decision rules are computed
around this steady state of the endogenous variables and the
Lagrange multipliers.
This first order approximation to the optimal policy conducted by
Dynare is not to be confused with a naive linear quadratic
approach to optimal policy that can lead to spurious welfare
rankings (see *Kim and Kim (2003)*). In the latter, the optimal
policy would be computed subject to the first order approximated
FOCs of the private economy. In contrast, Dynare first computes
the FOCs of the Ramsey planner’s problem subject to the nonlinear
constraints that are the FOCs of the private economy and only then
approximates these FOCs of planner’s problem to first
order. Thereby, the second order terms that are required for a
secondorder correct welfare evaluation are preserved.
Note that the variables in the list after the ``ramsey_policy``
command can also contain multiplier names. In that case, Dynare
will for example display the IRFs of the respective multipliers
when ``irf>0``.
The planner objective must be declared with the :comm:`planner_objective` command.
*Options*
This command accepts all options of ``stoch_simul``, plus:
.. option:: planner_discount = EXPRESSION
See :opt:`planner_discount <planner_discount = EXPRESSION>`.
.. option:: instruments = (VARIABLE_NAME,...)
Declares instrument variables for the computation of the
steady state under optimal policy. Requires a
``steady_state_model`` block or a ``_steadystate.m`` file. See
below.
Note that only a first order approximation of the optimal Ramsey
policy is available, leading to a secondorder accurate welfare
ranking (i.e. ``order=1`` must be specified).
*Output*
This command generates all the output variables of
``stoch_simul``. For specifying the initial values for the
endogenous state variables (except for the Lagrange multipliers),
see :bck:`histval`.
*Steady state*
See :comm:`Ramsey steady state <ramsey_model>`.
Optimal policy under discretion

.. command:: discretionary_policy [VARIABLE_NAME...];
discretionary_policy (OPTIONS...) [VARIABLE_NAME...];
br This command computes an approximation of the optimal policy
under discretion. The algorithm implemented is essentially an LQ
solver, and is described by *Dennis (2007)*.
You should ensure that your model is linear and your objective is
quadratic. Also, you should set the ``linear`` option of the
``model`` block.
*Options*
This command accepts the same options than ``ramsey_policy``, plus:
.. option:: discretionary_tol = NONNEGATIVE DOUBLE
Sets the tolerance level used to assess convergence of the
solution algorithm. Default: ``1e7``.
.. option:: maxit = INTEGER
Maximum number of iterations. Default: ``3000``.
.. command:: planner_objective MODEL_EXPRESSION ;
br This command declares the policy maker objective, for use
with ``ramsey_policy`` or ``discretionary_policy``.
You need to give the oneperiod objective, not the discounted
lifetime objective. The discount factor is given by the
``planner_discount`` option of ``ramsey_policy`` and
``discretionary_policy``. The objective function can only contain
current endogenous variables and no exogenous ones. This
limitation is easily circumvented by defining an appropriate
auxiliary variable in the model.
With ``ramsey_policy``, you are not limited to quadratic
objectives: you can give any arbitrary nonlinear expression.
With ``discretionary_policy``, the objective function must be quadratic.
Sensitivity and identification analysis
=======================================
...
...
Johannes Pfeifer
@JohannesPfeifer
mentioned in commit
ae111589
·
Jan 10, 2020
mentioned in commit
ae111589
mentioned in commit ae111589a09836791207a27cc7655c7801be145c
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