+
Dunare AIM Solver Subsystem
+
Contents
+
+
+ - AIM=20
+ Solver Subsystem=20
+
- APPENDIX=20
+ 1: AIM System SPecification and Dynare Mapping=20
+
- APPENDIX=20
+ 2: dynAIMsolver1 Function Specification
+
AIM Solver Subsystem
+
The AIM subsystem in the AIM subdirectory of the main Dynare matlab =
+directory=20
+contains Matlab functions necessary for using Gary Anderson's AIM 1st =
+order=20
+solver as an alternative to Dynare's default mjdgges solver (see http:/=
+/www.federalreserve.gov/Pubs/oss/oss4/aimindex.html=20
+).
+
It cosists of:
+
+
+ - New Dynare function dynAIMsolver1(jacobia_, M_, dr) which =
+is called=20
+ from dr1.m and which maps Dynare system to the AIM package =
+subsystem.=20
+ It then derives the solution for gy=3Ddr.hgx and gu=3Ddr.hgu from the =
+AIM outputs.=20
+ ("1" in the title is for 1st order solver).
+
+
+ - A subset of Matlab routines from Gary Anderson's own AIM package =
+needed to=20
+ compute and solve system passed on and returned by dynAIMsolver1 whose =
+names=20
+ start with SP.. of which SPAmalg.m is the main driver: =
+
+
+
+ - SPAmalg.m=20
+
- SPBuild_a.m=20
+
- SPSparse.m=20
+
- SPShiftright.m=20
+
- SPExact_shift.m=20
+
- SPNumeric_shift.m=20
+
- SPObstruct.m=20
+
- SPSparseSPBuild_a.m=20
+
- SPEigQZ.m=20
+
- SPEigensystem.m=20
+
- SPReduced_form=20
+
- SPCopy_w.m=20
+
- SPAimerr.m
+
The path to the AIM directory, if exists, is added by =
+dynare_config.m=20
+using addpath
+
USE:
+
Dynare DR1.m tries to invoke AIM solver instead default mjdgges if=20
+options_.useAIM =3D=3D 1 is set and, if not check only, and if 1st order =
+solution is=20
+needed, i.e.:
if (options_.useAIM =3D=3D 1) && (task =
+=3D=3D 0) && (options_.order =3D=3D 1)
+
For a start, options_.useAIM =3D 0 is set by default in=20
+global_initialization.m so that system uses mjdgges by default. =
+
+
If AIM is to be used, options_.useAIM =3D 1 needs to be set either in =
+the model=20
+modelname=
+.mod=20
+file, before invoking, estimate and/or stoch_simul, or by issuing =
+appropriate=20
+command for estimate and/or stoch_simul.
+
RELEASE NOTES:
+
In the current implementation, as of July 2008, only first order =
+solution is=20
+supported and handling of exceptions is rather fundamental and, in =
+particular,=20
+when Blanchard and Kahn conditions are not met, only a large penalty =
+value=20
+1.0e+8 is being set.
+
Hence, system may not coverge or the resluts may not be accurate if =
+there=20
+were many messages like
+
+
+ - "Error in AIM: aimcode=3D4 : Aim: too few big roots", or=20
+
- "Error in AIM: aimcode=3D3 : Aim: too many big roots" =
+
+
especially when issued close to the point of convergence.
+
However, if other exceptions occur and aimcode (see codes below) is =
+higher=20
+than 5, the system resets options_.useAIM =3D 0 and tries to use mjdgges =
+instead.=20
+
+
APPENDIX 1: AIM System SPecification and Dynare Mapping
+
AIM System for thau lags and theta leads, and:
+
![]()
+
![]()
+
where xt+i is system vectors at time t for all lag/lead t+i and zt is =
+vector=20
+of exogenous shocks.
+
The AIM input is array of matrices H:
+
![]()
+
and its solution given as:
+
![]()
+
where Xt is matrix of vectors of all current system variables and =
+forward=20
+looking leads xi for i=3Dt,...,t+theta:
+
![]()
+
and AIM output in the form of endogenous transition matrix bb: =
+
+
![]()
+
and, for simple case of one lag system, the matrix Phi derived =
+as:
+
![]()
+
For more lags, the phi equation becomes more complicated (see =
+documentation=20
+on G.Anderson's site above).
+
Dynare AIM Mapping - input
+
For Dynare jacobian =3D [fy'-tau... fy'i ... fy'+theta fu'] - where =
+-tau and=20
++theta are subscripts, we have that its subset without exogenous term =
+fu' and=20
+expanded with zero columns represents H, i.e.:
+
![]()
+
and for exogenous shocks terms:
+
![]()
+
Output Dynare solution output:
+
![]()
+
where Xt is again matrix of vectors all current system variables and =
+forward=20
+looking leads xi for i=3Dt,..., t+theta, is mapped so that:
+
+
+ - gy (or dr.ghx) is a reordered subset of AIM SPAmalg.m =
+output=20
+ bb without zero columns, and,=20
+
- gu (or dr.ghu) is derived from reordered AIM SPObstruct.m =
+output as=20
+ phi in:
+
![]()
+
APPENDIX 2: dynAIMsolver1 Function Specification
+
function [dr,aimcode]=3DdynAIMsolver1(jacobia_,M_,dr)
+
INPUTS
+
+
+ - jacobia_ - [matrix] 1st order derivative of the model=20
+
- dr - [matlab structure] Decision rules for stochastic simulations. =
+
+
- M_ - [matlab structure] Definition of the model.
+
OUTPUTS
+
+
+ - dr [matlab structure] Decision rules for stochastic simulations.=20
+
- aimcode [integer] status
aimcode status is =
+resolved by calling AIMerr as
+
+
+ - (c=3D=3D1) e=3D'Aim: unique solution.';=20
+
- (c=3D=3D2) e=3D'Aim: roots not correctly computed by real_schur.'; =
+
+
- (c=3D=3D3) e=3D'Aim: too many big roots.';=20
+
- (c=3D=3D35) e=3D'Aim: too many big roots, and q(:,right) is =
+singular.';=20
+
- (c=3D=3D4) e=3D'Aim: too few big roots.';=20
+
- (c=3D=3D45) e=3D'Aim: too few big roots, and q(:,right) is =
+singular.';=20
+
- (c=3D=3D5) e=3D'Aim: q(:,right) is singular.';=20
+
- (c=3D=3D61) e=3D'Aim: too many exact shiftrights.';=20
+
- (c=3D=3D62) e=3D'Aim: too many numeric shiftrights.';=20
+
- else e=3D'Aimerr: return code not properly specified'; =
+
+
SPECIAL REQUIREMENTS
+
Dynare use:
1) the lognormal block in DR1 is being =
+invoked for some models and changing
+ values of ghx and ghy. We need to return the AIM output
+ values before that block and run the block with the current =
+returned values
+ of gy (i.e. dr.ghx) and gu (dr.ghu) if it is needed even when the =
+AIM is used
+ (it does not depend on mjdgges output).
2) for =
+forward looking models, passing into dynAIMsolver aa =3D{Q'|1}*jacobia_
+ can produce ~ one order closer results to the Dynare solutiion
+ then when if plain jacobia_ is passed,
+ i.e. diff < e-14 for aa and diff < *e-13 for jacobia_ if Q' =
+is used.
+
GP July 2008
+
part of DYNARE, copyright Dynare Team (1996-2008) Gnu Public =
+License.
+
