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Document recent changes to evaluate_planner_objective 

Related to https://git.dynare.org/Dynare/dynare/-/issues/1680
pac-components
Johannes Pfeifer 2021-09-16 15:44:08 +02:00
parent 5a21b11d77
commit d5b66ea28a
1 changed files with 124 additions and 44 deletions
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168
doc/manual/source/the-model-file.rst
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@ -1431,6 +1431,10 @@ in this case ``initval`` is used to specify the terminal conditions.
steady state computation will still be triggered by subsequent
commands (``stoch_simul``, ``estimation``...).
As such, ``initval`` allows specifying the initial instrument value for
steady state finding when providing an analytical conditional steady state
file for ``ramsey_model``-computations.
It is not necessary to declare 0 as initial value for exogenous
stochastic variables, since it is the only possible value.
@ -1776,8 +1780,9 @@ in this case ``initval`` is used to specify the terminal conditions.
histval-block nevertheless takes the unlogged starting
values.
* In :comm:`Ramsey policy <ramsey_model>`, where it also
specifies the values of the endogenous states at which the
objective function of the planner is computed. Note that the
specifies the values of the endogenous states (including
lagged exogenous) at which the objective function of the
planner is computed. Note that the
initial values of the Lagrange multipliers associated with
the planner’s problem cannot be set (see
:comm:`evaluate_planner_objective`).
@ -2438,6 +2443,16 @@ blocks.
arbitrary expressions are also allowed, but you have to enclose
them inside parentheses.
The feasible range of ``periods`` is from 0 to the number of ``periods``
specified in ``perfect_foresight_setup``.
.. warning:: Note that the first endogenous simulation period is period 1.
Thus, a shock value specified for the initial period 0 may conflict with
(i.e. may overwrite or be overwritten by) values for the
initial period specified with ``initval`` or ``endval`` (depending on
the exact context). Users should always verify the correct setting
of ``oo_.exo_simul`` after ``perfect_foresight_setup``.
*Example* (with scalar values)
::
@ -2524,6 +2539,27 @@ blocks.
var v, w = 2;
end;
|br| *In stochastic optimal policy context*
When computing conditional welfare in a ``ramsey_model`` or ``discretionary_policy``
context, welfare is conditional on the state values inherited by planner when making
choices in the first period. The information set of the first period includes the
respective exogenous shock realizations. Thus, their known value can be specified
using the perfect foresight syntax. Note that i) all other values specified for
periods than period 1 will be ignored and ii) the value of lagged shocks (e.g.
in the case of news shocks) is specified with ``histval``.
*Example*
::
shocks;
var u; stderr 0.008;
var u;
periods 1;
values 1;
end;
*Mixing deterministic and stochastic shocks*
It is possible to mix deterministic and stochastic shocks to build
@ -10169,6 +10205,84 @@ with ``discretionary_policy`` or for optimal simple rules with ``osr``
With ``discretionary_policy``, the objective function must be quadratic.
.. command:: evaluate_planner_objective ;
This command computes, displays, and stores the value of the
planner objective function under Ramsey policy or discretion in
``oo_.planner_objective_value``. It will provide both unconditional welfare
and welfare conditional on the initial (i.e. period 0) values of the endogenous
and exogenous state variables inherited by the planner. In a deterministic context,
the respective initial values are set using ``initval`` or ``histval`` (depending
on the exact context).
In a stochastic context, if no initial state values have
been specified with ``histval``, their values are taken to be the steady state
values. Because conditional welfare is computed conditional on optimal
policy by the planner in the first endogenous period (period 1), it is conditional
on the information set in the period 1. This information set includes both the
predetermined states inherited from period 0 (specified via ``histval`` for both
endogenous and lagged exogenous states) as well as the period 1 values of
the exogenous shocks. The latter are specified using the perfect foresight syntax
of the shocks-block.
*Example (stochastic context)*
::
var a ...;
varexo u;
model;
a = rho*a(-1)+u+u(-1);
...
end;
histval;
u(0)=1;
a(0)=-1;
end;
shocks;
var u; stderr 0.008;
var u;
periods 1;
values 1;
end;
evaluate_planner_objective;
.. matvar:: oo_.planner_objective_value.unconditional
Scalar storing the value of unconditional welfare. In a perfect foresight context,
it corresponds to welfare in the long-run, approximated as welfare in the terminal
simulation period.
.. matvar:: oo_.planner_objective_value.conditional
In a perfect foresight context, this field will be a scalar storing the value of
welfare conditional on the specified initial condition and zero initial Lagrange
multipliers.
In a stochastic context, it will have two subfields:
.. matvar:: oo_.planner_objective_value.conditional.steady_initial_multiplier
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`).
.. matvar:: oo_.planner_objective_value.conditional.zero_initial_multiplier
Stores the value of the planner objective when the initial
Lagrange multipliers associated with the planner’s problem are 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 value corresponds to the planner
implementating optimal policy for the first time and committing not to
re-optimize in the future.
Optimal policy under commitment (Ramsey)
----------------------------------------
@ -10298,38 +10412,18 @@ conditions in the ``model``-block and a ``planner_objective`` as well as potenti
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.
.. command:: ramsey_policy [VARIABLE_NAME...];
ramsey_policy (OPTIONS...) [VARIABLE_NAME...];
|br| This command is formally equivalent to the calling sequence
|br| This command is deprecated and formally equivalent to the calling sequence
::
ramsey_model;
stoch_simul(order=1);
stoch_simul;
evaluate_planner_objective;
It computes the first order approximation of the
It computes an 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
@ -10342,20 +10436,9 @@ conditions in the ``model``-block and a ``planner_objective`` as well as potenti
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
or ``stoch_simul``-command can also contain multiplier names, but
in a case-sensititve way (e.g. ``MULT_1``). In that case, Dynare
will for example display the IRFs of the respective multipliers
when ``irf>0``.
@ -10376,16 +10459,12 @@ conditions in the ``model``-block and a ``planner_objective`` as well as potenti
``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`.
see above.
*Steady state*
@ -10409,7 +10488,8 @@ Optimal policy under discretion
It is possible to use the :comm:`estimation` command after the
``discretionary_policy`` command, in order to estimate the model with
optimal policy under discretion.
optimal policy under discretion and :comm:`evaluate_planner_objective`
to compute welfare.
*Options*