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dynare-preprocessor-w-json.rst
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Using JSON Output from the Dynare Preprocessor
##############################################
:date: 2020-01-23
:date: 2020-01-24
:tags: Dynare, Preprocessor, JSON, MATLAB
:category: Dynare
:slug: dynare-preprocessor-w-json
......@@ -459,29 +459,28 @@ Together, these functions return matrices corresponding to the observed
variable, ``Y``, the regressors, ``X``, the constant term, ``lhssub``, and the
first and last periods of the observed data (``fp`` and ``lp``).
Parsing proceeds as follows in ``parse_ols_style_equation.m``. After, the
function arguments are verified at the beginning of the function (lines 38-66),
we know that the LHS contains either a ``VariableNode`` or a ``UnaryOpNode``.
Parsing proceeds as follows in ``parse_ols_style_equation.m``. First, the
function arguments are verified (lines 38-66). After this, we know that the LHS
contains either a ``VariableNode`` or a ``UnaryOpNode``.
.. note:: Several different types of nodes that can appear in the AST,
corresponding to the types of operations that are available in a
``.mod`` file equation. The nodes are:
#. ``NumConstNode``: e.g. non-negative integer or double
#. ``NumConstNode``: non-negative integers or doubles
#. ``VariableNode``: endogenous, exogenous, or parameter
#. ``UnaryOpNode``: unary operation on a node, e.g. ``log``, ``abs``,
unary minus, ...
#. ``BinaryOpNode``: binary operation on a node, e.g. arithmetic
operations, ``max``, comparison operators
operations, ``min``, ``max``, ``=``, comparison operators, ...
#. ``TrinaryOpNode``: trinary operation on a node, e.g. ``normcdf``,
``normpdf``
#. ``ExternalFunctionNode``: external function node
Assured that the type of the LHS is valid for OLS, the value of ``Y`` is set by
evaluating the LHS of the specified equation. Given that all equations are
represented as ``BinaryOpNodes`` (the two arguments being the LHS, ``arg1``,
and the RHS, ``arg2``), the call to evaluate the LHS of the equation is as
follows:
represented as ``BinaryOpNode``'s (the two arguments being the LHS, ``arg1``,
and the RHS, ``arg2``), the call to evaluate the LHS of the equation is:
.. code-block:: MATLAB
:linenos: inline
......@@ -555,20 +554,19 @@ this node given the ``dseries`` contained in ``ds``.
end
In the evaluation of the observed variable (``X`` in this local function, ``Y``
in the main routine), what's important to us is lines 313-342. In particular,
our OLS routine handles an observable variable declared as an endogenous or
exogenous variable, with or without a unary operator applied to it. Given the
case it falls in (``VariableNode`` or ``UnaryOpNode``), the LHS (``node``) is
evaluated using the ``dseries`` (``ds``) and the corresponding ``dseries``
vector is returned.
in the main routine), what's important to us is lines 313-342 as we know it's
either a ``VariableNode`` or a ``UnaryOpNode``. Regardless of the type of node
it is, it's evaluated using the ``dseries`` (``ds``) and the corresponding
``dseries`` vector is returned. In our case, the interest rate ``r`` is
evaluated on line 317 by looking up its value in ``ds``.
Though our work for ``Y`` was easy, the work to compute the matrix of
regressors and the vector of constants, will take a bit more work.
Though our work for ``Y`` was easy, computing the matrix of regressors and the
vector of constants will be a bit more involved.
Back in the main function, before we can create the matrix of regressors ``X``,
we decompose the RHS (``arg2``) of the equation into additive terms, storing
them in a cell array called ``terms``. We do this by calling the locally
defined function ``decomposeAdditiveTerms``:
defined function:
.. code-block:: MATLAB
:linenos: inline
......@@ -603,11 +601,10 @@ As you can see, ``decomposeAdditiveTerms`` is a recursive, tree-traversal
function that breaks down terms separated by ``+`` or ``-``, storing them in
the return value, ``terms``. Each cell in the return value is comprised of a
pair of elements: the root node of the sub-tree representing the additive node
and the sign in preceding this node. That sign will be used in the construction
of the matrix, setting the sign of the data accordingly.
and the sign preceding this node (``1`` or ``-1``).
Given the equation we want to estimate (shown here from
``Smets_Wouters_2007.mod`` as a reminder),
``Smets_Wouters_2007.mod`` as a reminder):
.. include:: sw2007/Smets_Wouters_2007.mod
:code:
......@@ -628,13 +625,78 @@ Hence, in this case, 4 nodes of ``terms`` contain ``BinaryOpNode``'s
(corresponding to the binary operation ``*``) and one term contains a
``VariableNode``.
To understand how the terms are stored, one need only look at the following
output for the first term, ``crpiMcrpiXcrr*pinf``:
.. code-block:: text
>> terms
terms =
1x5 cell array
{1x2 cell} {1x2 cell} {1x2 cell} {1x2 cell} {1x2 cell}
>> terms{1}
ans =
1x2 cell array
{1x1 struct} {[1]}
>> terms{1}{1}
ans =
struct with fields:
node_type: 'BinaryOpNode'
op: '*'
arg1: [1x1 struct]
arg2: [1x1 struct]
>> terms{1}{1}.arg1
ans =
struct with fields:
node_type: 'VariableNode'
name: 'pinf'
type: 'endogenous'
lag: 0
>> terms{1}{1}.arg2
ans =
struct with fields:
node_type: 'VariableNode'
name: 'crpiMcrpiXcrr'
type: 'parameter'
lag: 0
Here, the second element of ``terms{1}`` is ``1`` as it is not preceded by a
minus sign. The node itself is a ``BinaryOpNode`` as it represents the
multiplication of an endogenous variable (the first argument of the node) and a
parameter (the second argument of the node).
.. note:: The elements of ``terms`` are not necessarily in the same order as
written in the equation in the ``.mod`` file. This is because, for
efficiency reasons (e.g. node sharing), the AST created by the
preprocessor does not guarantee this ordering.
preprocessor does not guarantee this ordering. By the same token, the
elements of a node are not guaranteed to be in the same order as they
appear in the ``.mod`` file, as you can see above where the first
argument of the ``BinaryOpNode`` in ``terms{1}{1}`` is the endogenous
variable ``pinf`` whereas ``pinf`` appears second in the
multiplication as written in the ``.mod`` file:
``crpiMcrpiXcrr*pinf``.
Now that we have ``terms`` set, we can enter the loop in the main function of
``parse_ols_style_equation.m`` that constructs the regressor matrix ``X``:
Now that we have ``terms`` set, we can construct the regressor matrix ``X`` by
entering the loop on line 75 of ``parse_ols_style_equation.m``:
.. code-block:: MATLAB
:linenos: inline
......@@ -718,44 +780,47 @@ Now that we have ``terms`` set, we can enter the loop in the main function of
X = [X Xtmp];
end
When the loop starts, certain variables are set. ``Xtmp`` is where we will
construct the regressor column to be appended to ``X`` at the end of each
loop. ``node_to_parse`` and ``node_sign`` are simply the corresponding parts of
the pair stored in each ``terms`` cell, as described above.
Entering the loop, we set 3 variables: ``Xtmp``, ``node_to_parse``, and
``node_sign``. ``Xtmp`` is where we will construct the regressor column to be
appended to ``X`` at the end of each loop. ``node_to_parse`` and ``node_sign``
are simply the corresponding parts of the pair stored in each ``terms`` cell,
as described above.
With these variables set, we take different actions, depending on the type of
node encountered in ``node_to_parse``. The following subsections explain those
actions.
VariableNode
````````````````
Condition 1: VariableNode (lines 79-97)
```````````````````````````````````````
If ``node_to_parse`` is a ``VariableNode`` it is an additive variable in the
equation. If it was declared as a parameter in the ``.mod`` file, then it's the
intercept of the equation. It is thus stored in ``Xtmp`` with the value of the
parameter at every period. If it's a lone exogenous variable, we treat it as
the residual. If there are more than one such variable, then it's an error. If
it's an endogenous variable, we add it to the ``dseries`` ``lhssub``, a
parameter at every period. If it's a lone exogenous variable that is not
present in ``ds``, we treat it as the residual. If there are more than one such
variable, then it's an error. If it's an endogenous variable or an exogenous
variable present in ``ds``, we add it to the ``dseries`` ``lhssub``, a
``dseries`` that will be subtracted from the LHS before returning. If the type
of the ``node_to_parse`` doesn't fall into any of these categories, parsing
ends with an error.
UnaryOpNode
```````````````
Condition 2: UnaryOpNode (lines 98-101)
```````````````````````````````````````
If ``node_to_parse`` is a ``UnaryOpNode``, we evaluate it and add it to the
``lhssub`` variable to be subtracted from the LHS.
BinaryOpNode with division operator
```````````````````````````````````
Condition 3: BinaryOpNode with division operator (lines 102-108)
````````````````````````````````````````````````````````````````
In this case, if a parameter is found in this expression, we end with a parsing
error. Otherwise, we evaluate the node and add it to ``lhssub``.
BinaryOpNode with multiplication operator
`````````````````````````````````````````
Condition 4: BinaryOpNode with multiplication operator (lines 109-137)
``````````````````````````````````````````````````````````````````````
In this case, we parse the ``node_to_parse``, by calling the local function ``parseTimesNode``
In this case, we parse the ``node_to_parse``, by calling the local function
``parseTimesNode``:
.. code-block:: MATLAB
:linenos: inline
......@@ -791,23 +856,24 @@ In this case, we parse the ``node_to_parse``, by calling the local function ``pa
end
end
This function handles returns the ``dseries`` vector/matrix ``X`` corresponding
to the regressors found. This function can handle parsing expressions of
additively-separated parameters multiplied by an expression of variables. Each
of the additively separated parameters in ``pterms`` corresponds to one column
of the returned vector/matrix ``X``.
This function returns the ``dseries`` vector/matrix ``X`` corresponding to the
regressors found. It can handle parsing expressions of additively-separated
parameters multiplied by an expression of variables. Each of the additively
separated parameters in ``pterms`` corresponds to one column of the returned
vector/matrix ``X``.
Returning from this function, we have ``Xtmp`` corresponding to the evaluated
variables and ``names`` corresponding to the parameter names. In the code that
follows, we add any columns of ``Xtmp`` that were multiplied by a constant to
``lhssub`` and then remove this column from ``Xtmp``.
follows (lines 113-137), we add any columns of ``Xtmp`` that were multiplied by
a constant to ``lhssub`` and then remove this column from ``Xtmp``.
Otherwise
`````````
Condition 5: Otherwise (line 139)
`````````````````````````````````
We have encountered a parsing error.
If none of the previous 4 conditions were satisfied, we have encountered a
parsing error.
End of loop, lines (143-151)
End of loop (lines 141-150)
````````````````````````````
At the end of the loop, we combine the temporary vector/matrix of regressors,
......@@ -847,7 +913,8 @@ assigned to the variables ``fp`` and ``lp``:
lp = min(lp, lhssub.lastobservedperiod);
end
Finally, the ``Y``, ``X``, and ``lhssub`` datasets are adjusted given ``fp`` and ``lp``:
Finally, the ``Y``, ``X``, and ``lhssub`` datasets are adjusted given ``fp``
and ``lp``:
.. code-block:: MATLAB
:linenos: inline
......@@ -883,12 +950,12 @@ the first and last observed period of the estimation range for each equation.
[Y, lhssub, X, fp, lp] = common_parsing(ds(ds_range), ast, true, param_names);
We loop over these cell arrays, running our estimation for each equation:
:math:`\hat{\beta} = (X'X)^{-1}X'Y`. [#]_ The output is set to the standard
Dynare MATLAB/Octave output structure ``oo_`` in the ``ols`` field. Each
sub-field of ``ols`` corresponds to an equation tag that was either provided by
the user or created by ``dyn_ols.m``. In this case, they will be saved to
``oo_.ols.taylor_rule``. Furthermore, the estimated parameter values are set in
``M_``.
:math:`\hat{\beta} = (X'X)^{-1}X'Y`. [#]_ The output is set to the ``ols``
field of the standard Dynare MATLAB/Octave output structure, ``oo_``. Each
sub-field of ``oo_.ols`` corresponds to an equation tag that was either
provided by the user or created by ``dyn_ols.m``. In this case, they will be
saved to ``oo_.ols.taylor_rule``. Furthermore, the estimated parameter values
are set in ``M_``.
.. code-block:: MATLAB
:linenos: inline
......
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