Dynare now incorporates new features which significantly speed-up deterministic simulation and steady state computation in middle and large scale models.

The speed-up is achieved by the combination of three new features:

/!\ The various options in this page only work with deterministic simulation at this time: they won't work with stochastic simulation, estimation or Ramsey policy. For the very same reason, in Dynare 4.1 they are also not compatible with the check command. This latter restriction has been alleviated in Dynare 4.2.

1. Block decomposition of the model

1.1. Description of the steps of the algorithm

1.1.1. Model simplification

In a first step, to get rid of nearly zero elements in the jacobian, a threshold (cutoff) is used to determine whether a jacobian element has to be considered as null or not. If the absolute value of a jacobian element is below the threshold then it is considered as null and is discarded form the sparse representation of the jacobian. Eliminating nearly zero elements improves the sparsity of the model and hence the simulation time. Note that if the cutoff value is too high then the model properties could be strongly modified and the simulation could fail.

1.1.2. Prologue and Epilogue determination

In a second step, the equations and the variables of the model could be reordered to get purely recursive initial and final blocks. The purely recursive equations are easily found.

1.1.3. Model normalization

To get a block decomposition of the model, each endogenous variable has to be assigned unambiguously to an equation or equivalently the model has to be normalized: this normalization is performed using the maximum cardinality matching with Edmonds’ matching algorithm (Boost-graph library). Attention has to be paid to potential singularity in the matching process (to avoid for example a normalisation where the variable

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[Thu Sep 09 08:40:18.812051 2021] [wsgi:error] [pid 3351:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
is assigned to the following equation:
latex error! exitcode was 2 (signal 0), transscript follows:

[Thu Sep 09 08:40:18.859799 2021] [wsgi:error] [pid 3352:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
). The matching algorithm is applied iteratively using the normalized Jacobian matrix (each row is divided by its maximum absolute value component) with a decreasing cutoff (all the elements in the Jacobian matrix below the cutoff are set to zero) until a matching is found.

1.1.4. Equations renormalization

Once the model has been normalized, the preprocessor tries to rewrite the equations in a normalized form: for the variable

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[Thu Sep 09 08:40:18.909939 2021] [wsgi:error] [pid 3353:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
associated to the equation
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[Thu Sep 09 08:40:18.951479 2021] [wsgi:error] [pid 3354:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
, the equation has of the following form
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[Thu Sep 09 08:40:18.991714 2021] [wsgi:error] [pid 3355:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
. For equations belonging to a recursive block, the normalized equation has not to be solved but only evaluated. For equations normalized belonging to a simultaneous block, they could be simply evaluated if they belong to the recursive set of the block in the feedback variables determination.

1.1.5. Block decomposition

The simultaneous block composed of equations and endogenous variables that do not belong to the prologue or the epilogue could be split sub recursive blocks. Those sub recursive blocks form the strong component of the graph representation of the model. To find them a depth search Tarjan algorithm is used.

1.1.6. Splitting the variables of a simultaneous block in feedback and recursive variables

The simultaneous blocks computed in the previous step are rewritten in a quasi triangular form. The non normalized equations that could not be evaluated are forced to belong to the feedback variables set. In addition, for dynamic model the static variables associated with non static equation or the non static variables are imposed in the feedback variables set. The equations of the block are reordered as follow:

1.2. Dynare syntax

1.2.1. Computing block decomposition

The block decomposition of the model is triggered by the block option of the model keyword:

model(block);
...
end;

1.2.2. Controlling the model simplification

The default value of the cutoff described in the first step of the algorithm is

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[Thu Sep 09 08:40:19.051819 2021] [wsgi:error] [pid 3356:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
. It can be modified with cutoff option of the model keyword:
model(block,cutoff=1e-13);
...
end;

/!\ Note that the jacobian is evaluated considering the initial value of the parameters provided in the mod file. If the parameters value are modified (the model is estimated for example) before the simul command, some components of the jacobian could be wrongly discarded. To prevent such a result you may need to decrease the cutoff (or even set it to zero).

1.2.3. Controlling equation renormalization and the set of feedback variables

The mfs option of the model keyword controls equation renormalization and the set of feedback variables:

Example:

model(block,mfs=2);
...
end;

1.2.4. Exploring the block structure of the model

The model_info command provides information about:

There are five different types of blocks depending on the simulation method used:

Synopsis:

model(block);
...
end;

model_info;

2. Bytecode representation of the model

By default, the Dynare preprocessor creates two M-files (one for the static model, one for the dynamic model) which are used by the MATLAB routines of Dynare. With big models, these M-files can become huge, and consume a lot of computing ressources.

The idea is to represent the model under another form: a bytecode, i.e. a binary file containing a compact representation of all the equations. This bytecode is then read and used for evaluations from MATLAB, using a dedicaded DLL.

You can activate the bytecode representation with the bytecode option of the model keyword:

model(block, bytecode);
...
end;

/!\ In Dynare 4.1, bytecode without block is not possible. This restriction has been alleviated in Dynare 4.2.

3. New variants of Newton algorithm

3.1. Steady state computation

The steady option accepts a solve_algo option for choosing the nonlinear solver for the steady state. This option can take the following values:

The possible combinations are the following:

3.1.1. In Dynare 4.1

solve_algo=...

neither block nor bytecode

block without bytecode

bytecode without block

block and bytecode

0

OK (only under MATLAB with optim toolbox)

N/A

N/A

N/A

1

N/A

OK

N/A

N/A

2

N/A

OK

N/A

N/A

3

N/A

OK

N/A

N/A

4

N/A

OK

N/A

N/A

5

N/A

N/A

N/A

OK

6

N/A

N/A

N/A

N/A

7

N/A

N/A

N/A

N/A

8

N/A

N/A

N/A

N/A

3.1.2. In Dynare 4.2

solve_algo=...

neither block nor bytecode

block without bytecode

bytecode without block

block and bytecode

0

OK (except under MATLAB without optim toolbox)

OK

OK

OK

1

OK

OK

OK

OK

2

OK

OK

OK

OK

3

OK

OK

OK

OK

4

OK

OK

OK

OK

5

N/A

N/A

OK

OK

6

N/A

OK

OK

OK

7

N/A

OK (except under Octave)

OK (except under Octave)

OK (except under Octave)

8

N/A

OK

OK

OK

3.2. Deterministic simulation

The simul command has a new option, stack_solve_algo, used to specify the resolution algorithm. This option can take integer values between 0 and 5:

The possible combinations are the following:

3.2.1. In Dynare 4.1

stack_solve_algo=...

neither block nor bytecode

block without bytecode

bytecode without block

block and bytecode

0

OK

N/A

N/A

N/A

1

N/A

OK

N/A

N/A

2

N/A

OK

N/A

N/A

3

N/A

OK

N/A

N/A

4

N/A

OK

N/A

N/A

5

N/A

N/A

N/A

OK

3.2.2. In Dynare 4.2

stack_solve_algo=...

neither block nor bytecode

block without bytecode

bytecode without block

block and bytecode

0

OK

OK

OK

OK

1

N/A

OK

OK

OK

2

N/A

OK (except under Octave)

OK (except under Octave)

OK (except under Octave)

3

N/A

OK

OK

OK

4

N/A

OK

OK

OK

5

N/A

N/A

OK

OK

3.3. Sparse Gaussian Elimination

FILL IN DESCRIPTION HERE...

3.3.1. Markowitz criterion option

At each iteration of the deterministic simulation, if the linear approximation of the model is solved using a sparse gaussian elimination, two criteria could be used to select the variable to substitute:

The pivot is selected according to the highest value among

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[Thu Sep 09 08:40:19.575804 2021] [wsgi:error] [pid 3365:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
(where
latex error! exitcode was 2 (signal 0), transscript follows:

[Thu Sep 09 08:40:19.613465 2021] [wsgi:error] [pid 3366:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
is the number of possible pivots) of the following criterion:

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[Thu Sep 09 08:40:19.656263 2021] [wsgi:error] [pid 3367:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex

With:

As

latex error! exitcode was 2 (signal 0), transscript follows:

[Thu Sep 09 08:40:20.046548 2021] [wsgi:error] [pid 3376:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
the Markowitz criterion prevails. At the opposite if
latex error! exitcode was 2 (signal 0), transscript follows:

[Thu Sep 09 08:40:20.092376 2021] [wsgi:error] [pid 3377:tid 139902167504640] [client 192.168.1.1:36066] failed to exec() latex
the usual maximum pivot criterion prevails.

The default value for the Markowitz criterion is 0.5.

model(block, bytecode);
...
end;

steady(solve_algo=5, markowitz=2);

simul(periods=80, stack_solve_algo=5, markowitz=2);

3.3.2. Datafile

If the variables of the model are not constant over time, their initial values, stored in a text file, could be loaded, using the datafile option, as initial values before a deteministic simulation.

model(block, bytecode);
...
end;

simul(periods=80, stack_solve_algo=5, datafile=mark3);

DynareWiki: FastDeterministicSimulationAndSteadyStateComputation (last edited 2011-03-18 09:04:48 by FerhatMihoubi)