The Dynare preprocessor modifies the model given by the user, under certain circumstances, by adding auxiliary variables to it.
The Dynare preprocessor modifies the model given by the user, under certain circumstances, by adding auxiliary variables to it. The aim is to bring the model into a canonical form and to simplify computations,
Auxiliary variables are created in the following cases:
- for endogenous variables with a lag or a lead of two or more (only in stochastic contexts in Dynare 4.1, in all cases in Dynare ≥ 4.2)
- for exogenous variables with a lag or a lead (only in stochastic contexts in Dynare ≤ 4.6, in all cases in Dynare ≥ 4.7)
- when the `EXPECTATION()` operator is used.
- when the `EXPECTATION()` operator is used
- when the `ramsey_model`-statement is used
- if the `diff`-operator is used.
Auxiliary variables are always endogenous variables. Internally, the indices of the original endogenous (as declared by the user) are in the range `1:M_.orig_endo_nbr`. Auxiliary variables have indices in the range `M_.orig_endo_nbr+1:M_.endo_nbr`.
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@@ -15,14 +17,14 @@ In order to get information about auxiliary variables and equations added by the
# The `M_.aux_vars`-structure
The vector structure `M_.aux_vars` also contains information about auxiliary variables. For each auxiliary variable, the following fields are declared:
The matrix structure `M_.aux_vars` also contains information about auxiliary variables. For each auxiliary variable, the following fields are declared:
-`M_.aux_vars(i).endo_index`: the index of the auxiliary variable, in the range `M_.orig_endo_nbr+1:M_.endo_nbr`
-`M_.aux_vars(i).type`: an integer representing the type of the auxiliary variable (see below for the list of types).
The structure can also contain other information, depending on the type of the aux var:
-`M_.aux_vars(i).orig_index` contains the index of the endogenous or exogenous variable for which the auxiliary variables is a substitute
-`M_.aux_vars(i).orig_index` contains the index of the endogenous or exogenous variable for whose leads/lags the auxiliary variables is a substitute
-`M_.aux_vars(i).orig_lead_lag` contains the lag or lead number of the original variable (as a negative value for lags and a positive one for leads; it will be empty for no lag).
-`M_.aux_vars(i).eq_nbr` contains the associated equation in case of Lagrange multipliers
-`M_.aux_vars(i).orig_expr` contains the original expression to which the auxiliary variable is attached, for example in case of a lead of two on a Lagrange multiplier, there will be an auxiliary variable of type `0` for the lead on an auxiliary variable of type `6` (the multiplier). In this case, `orig_expr` may contain `MULT_1(1)` to indicate that the auxiliary variable for the lead refers to that leaded multiplier.
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@@ -73,7 +75,7 @@ This kind of aux var has `M_.aux_vars(i).type = 8` and substitutes for the `diff
`M_.aux_vars(i).orig_index` contains the index of the variable contained in the `diff` operator. This field exists if the `diff` was taken of a variable, not of an expression.
`M_.aux_vars(i).orig_lead_lag` contains the lag of the variable contained in the `diff` operator. This field exists if the `diff` was taken of a variable, not of an expression.
## Type 9: lag on `diff` operator (since Dynare 4.6)
## Type 9: lag within `diff` operator (since Dynare 4.6)
This kind of aux var has `M_.aux_vars(i).type = 9` and accounts for applying the difference operator to a lag. If a `diff` operator is applied to a variable with lagged values (e.g. `diff(x(-3)`), a diff auxiliary variable is created for the `diff` operator applied to the variable with lag equal to zero (e.g. `diff(x)`) and auxiliary variables are created for the following sequence `diff(x(-1)`, `diff(x(-2))`, and `diff(x(-3)`). The name of such an auxiliary variable begins with `AUX_DIFF_LAG_`.
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@@ -84,6 +86,6 @@ This kind of aux var has `M_.aux_vars(i).type = 9` and accounts for applying the
This kind of aux var has `M_.aux_vars(i).type = 10` and substitutes for certain unary operations in the context of employing `diff`-operators, namely: `exp`, `log`, `log10`, `cos`, `sin`, `tan`, `acos`, `asin`, `atan`, `cosh`, `sinh`, `tanh`, `acosh`, `asinh`, `atanh`, `sqrt`, `abs`, `sign`, and `erf`. The name of such an auxiliary variable begins with `AUX_UOP_`.
## Type 11: lead on `diff` operator (since Dynare 4.6)
## Type 11: lead within `diff` operator (since Dynare 4.6)
This kind of aux var has `M_.aux_vars(i).type = 11` and accounts for applying the difference operator to a lead. Similarly to Type 9, it will create a sequence of auxiliary variables, but for leads.
