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Improve manual on lmmcp

time-shift
Johannes Pfeifer 2016-07-05 13:09:26 +02:00 committed by Stéphane Adjemian (Lupi)
parent 2751ab08bb
commit 76e2112df9
1 changed files with 22 additions and 12 deletions
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doc/dynare.texi
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@ -2988,8 +2988,9 @@ Levenberg-Marquardt mixed compleproblem (LMMCP) solver
(@cite{Kanzow and Petra 2004})
@item 11
PATH 3.0 solver of @cite{Ferris and Munson (1999)}. Dynare only provides the interface
for using the solver. Due to licence restrictions, you have to download the solver yourself
PATH mixed complementarity problem solver of @cite{Ferris and Munson (1999)}. The complementarity
conditions are specified with an @code{mcp} equation tag, @pxref{lmmcp}. Dynare only provides the interface
for using the solver. Due to licence restrictions, you have to download the solver's most current version yourself
from @url{http://pages.cs.wisc.edu/~ferris/path.html} and place it in Matlab's search path.
@end table
@ -3656,14 +3657,17 @@ solved, before using a constant set of operations for the remaining
periods. Only used when @code{stack_solve_algo = 5}. Default: @code{1}.
@item lmmcp
@anchor{lmmcp}
Solves the perfect foresight model with a Levenberg-Marquardt mixed complementarity problem (LMMCP) solver
(@cite{Kanzow and Petra 2004}), which allows to consider inequality constraints on the endogenous variables
(such as a ZLB on the nominal interest rate or a model with irreversible
investment). This option is equivalent to @code{stack_solve_algo=7} @strong{and}
@code{solve_algo=10}. The inequality constraints on the endogenous variables
have to be specified with an equation tag @pxref{Model declaration}. The tag has to use
the @code{mcp} keyword. For instance,
a ZLB on the nominal interest rate would be specified as follows in the model block:
@code{solve_algo=10}. Using the LMMCP solver requires a particular model setup as the goal is to get rid of
any @code{min/max} operators and complementary slackness conditions that might introduce
a singularity into the Jacobian. This is done by attaching an equation tag (@pxref{Model declaration})
with the @code{mcp} keyword to affected equations. This tag states that the equation
to which the tag is attached has to hold unless the expression within the tag is binding.
For instance, a ZLB on the nominal interest rate would be specified as follows in the model block:
@example
model;
...
@ -3673,14 +3677,20 @@ model;
end;
@end example
where 1.94478 is the steady state level of the nominal interest rate and
@code{r} is the nominal interest rate in deviation from the steady state. In the
current implementation, the content of the @code{mcp} equation tag is not parsed by the
@code{r} is the nominal interest rate in deviation from the steady state. This construct implies that
the Taylor rule is operative, unless the implied interest rate @code{r<=-1.94478}, in which case the
@code{r} is fixed at @code{-1.94478} (thereby being equivalent to a complementary slackness
condition). By restricting the value of @code{r} coming out of this equation, the
@code{mcp}-tag also avoids using @code{max(r,-1.94478)} for other occurrences of @code{r} in the
rest of the model. It is important to keep in mind that, because the @code{mcp}-tag effectively
replaces a complementary slackness condition, it cannot be simply attached to any
equation. Rather, it must be attached to the correct affected equation as otherwise the
solver will solve a different problem than originally intended.
Note that in the current implementation, the content of the @code{mcp} equation tag is not parsed by the
preprocessor. The inequalities must therefore be as simple as possible: an endogenous
variable, followed by a relational operator, followed by a number (not a
variable, parameter or expression). Note also that the constraint on an
endogenous variable must be associated to an equation and that the mixed
complementarity solver may fail or perform poorly if the constraint is
associated with an equation not directly related to the restricted variable.
variable, parameter or expression).
@item endogenous_terminal_period
The number of periods is not constant across Newton iterations when