If a solution corresponding to 100% of the shock can’t be found in the first
informational period, marginal linearization will be performed to extrapolate a
solution.
However, in subsequent informational periods, this extrapolated solution cannot
be used for the initial conditions of endogenous variables, because the initial
conditions are not a true solution of the nonlinear model. For those subsequent
informational periods, the correct approach is to compute the two solutions
needed for marginal linearization using as initial conditions the values
obtained in the same two solutions for the previous informational
periods (stored as oo_.deterministic_simulation.{sim1,sim2}).
– new option “endval_steady” to pf_setup command to recompute terminal
steady state in the homotopy loop
– new options “homotopy_linearization_fallback” and
“homotopy_marginal_linearization_fallback” to pf_solver and pfwee_solver
commands, to get an approximate solution when homotopy fails to go to 100%
– new options “homotopy_initial_step_size”, “homotopy_min_step_size”,
“homotopy_step_size_increase_success_count” and “homotopy_max_completion_share”
to pf_solver and pfwee_solver commands to fine tune the homotopy behaviour
– removed option “homotopy_alt_starting_point” to pf_solver command, not really
useful
– new options “steady_solve_algo”, “steady_tolf”, “steady_tolx”,
“steady_maxit”, “steady_markowitz” to pf_solver and pfwee_solver commands, to
control the computation of the terminal steady state (and remove the
equivalent options which previously had different names in pfwee_solver command)
– Remove the terminal_steady_state_as_guess_value option to pfwee_solver
– pfwee_setup now sets the same guess values as pf_setup (i.e. terminal steady
state at all periods)
– With constant_simulation_length option, pfwee_solver uses terminal steady
state as guess values for periods that are added to the simulation
This is more logical, since those values are constraints from the point of view
of the solver.
Also, this allows to have maxit and tolf options for the steady state solver,
at the level of the setup command, without a clash with the same option names
for the deterministic solver at the level of the solver command.
These command solve the problem where agents think they know perfectly the
future (they behave as in perfect foresight), but make expectation errors.
Hence they can potentially be surprised in every period, and their expectations
about the future (incl. the final steady state) may change.
Currently the sequence of information sets needs to be passed through a CSV
file. Another interface may be added in the future.
The algorithm uses a sequence of (true) perfect foresight simulations (not
necessarily as many as there are periods, because if the information set does
not change between two periods, there is no need to do a new computation).
There are two possibilities for guess values:
— the default is to use the initial steady state for the simulation using the
first-period information set; then use previously simulated values as guess
values
— alternatively, with the terminal_steady_state_as_guess_value option, use the
terminal steady state as guess value for all future periods (this is actually
what the “true” perfect foresight solver does by default)
Sébastien Villemot