Since Dynare 4.1, the Dynare preprocessor modifies the model given by the user, under certain circumstances, by adding auxiliary variables to it.
# Dynare's use of auxiliary variables
The Dynare preprocessor modifies the model given by the user, under certain circumstances, by adding auxiliary variables to it.
Auxiliary variables are created in the following cases:
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 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
- 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.
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`.
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`.
In most cases, auxiliary equations are added along with auxiliary variables, in order to keep equal the number of equations and endogenous.
In most cases, auxiliary equations are appended along with auxiliary variables, so that the number of equations and endogenous variables stays constant.
In order to get information about auxiliary variables and equations added by the preprocessor, the `write_latex_dynamic_model` and `write_latex_static_model` commands can be useful tools.
In order to get information about auxiliary variables and equations added by the preprocessor, the `write_latex_dynamic_model` and `write_latex_static_model` commands can be useful tools.
The vector structure `M_.aux_vars` also contains information about auxiliary variables. For each auxiliary variable, the following fields are declared:
# The `M_.aux_vars`-structure
*`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 informations depending on the type of the auxiliary variable.
# 0. Auxiliary variable for endogenous with lead >= 2
This is an auxiliary variable which is a substitute for an expression in the original model where a lead of 2 or more on an endogenous variable appears.
The name of such an auxiliary variable begins with `AUX_ENDO_LEAD_`.
This kind of auxiliary variable has `M_.aux_vars(i).type = 0`.
# 1. Auxiliary variable for endogenous with lag >= 2
This is an auxiliary variable which is a substitute for an endogenous variable in the original model which has a lag of 2 or more.
The name of such an auxiliary variable begins with `AUX_ENDO_LAG_`.
The vector structure `M_.aux_vars` also contains information about auxiliary variables. For each auxiliary variable, the following fields are declared:
`M_.aux_vars(i).orig_index` contains the index of the endogenous variable for which it is a substitute, and `M_.aux_vars(i).orig_lead_lag` contains the lag of the original variable (as a negative value).
This kind of auxiliary variable has `M_.aux_vars(i).type = 1`.
# 2. Auxiliary variable for exogenous with a lead
This is an auxiliary variable which is a substitute for an expression in the original model where a lead on an exogenous variable appears.
-`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 name of such an auxiliary variable begins with `AUX_EXO_LEAD_`.
The structure can also contain other information, depending on the type of the aux var:
This kind of auxiliary variable has `M_.aux_vars(i).type = 2`.
-`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_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.
# 3. Auxiliary variable for exogenous with a lag
# Types of auxiliary variables
This is an auxiliary variable which is a substitute for an exogenous variable in the original model which has a lag.
## Type 0: Leads of endogenous >=2
This kind of aux var has `M_.aux_vars(i).type = 0` and substitutes for an expression in the original model where a lead of 2 or more appears on an endogenous variable.
The name of such an aux var begins with `AUX_ENDO_LEAD_`.
The name of such an auxiliary variable begins with `AUX_EXO_LAG_`.
## Type 1: Lags of endogenous >=2
`M_.aux_vars(i).orig_index` contains the index of the exogenous variable for which it is a substitute, and `M_.aux_vars(i).orig_lead_lag` contains the lag of the original variable (as a negative value).
This kind of aux var has `M_.aux_vars(i).type = 1` and substitutes for an expression in the original model where a lag of 2 or more appears on an endogenous variable.
The name of such an aux var begins with `AUX_ENDO_LAG_`.
This kind of auxiliary variable has `M_.aux_vars(i).type = 3`.
## Type 2: Lead of exogenous
# 4. Aux var for expectation operator using the (full) information set of another period
This kind of aux var has `M_.aux_vars(i).type = 2` and substitutes for an expression in the original model where a lead on an exogenous variable appears. The name of such an aux var begins with `AUX_EXO_LEAD_`.
This is an auxiliary variable which is a substitute for an expression like `EXPECTATION(-1)(...)`.
## Type 3: Lag of exogenous
The name of such an auxiliary variable begins with `AUX_EXPECT_LEAD_` or `AUX_EXPECT_LAG_`.
This kind of aux var has `M_.aux_vars(i).type = 3` and substitutes for an expression in the original model where a lag on an exogenous variable appears. The name of such an aux var begins with `AUX_EXO_LAG_`.
This kind of auxiliary variable has `M_.aux_vars(i).type = 4`.
## Type 4: `EXPECTATION()`-operator
# 5. Auxiliary variable for the differentiate of a forward variable (since 4.4)
This kind of aux var has `M_.aux_vars(i).type = 4` and results from the `EXPECTATION()`-operator employing the (full) information set of another period. It substitutes for an expression like `EXPECTATION(-1)(...)`. The name of such an aux var begins with `AUX_EXPECT_LEAD_` or `AUX_EXPECT_LAG_`.
This is an auxiliary variable which is a substitute for a forward variable, when the`differentiate_forward_vars`option of `model` is used.
## Type 5: `differentiate_forward_vars`-option
The name of such an auxiliary variable begins with `AUX_DIFF_FWRD_`.
This kind of aux var has `M_.aux_vars(i).type = 5` and results from `differentiate_forward_vars`-option of `model` (since Dynare 4.4). In this case, forward variables are differentiated and and the difference replaced by an aux var, whose name begins with `AUX_DIFF_FWRD_`.
`M_.aux_vars(i).orig_index` contains the index of the endogenous variable of which it is the differentiate.
`M_.aux_vars(i).orig_index` contains the index of the endogenous variable of which it is the differentiate.
This kind of auxiliary variable has `M_.aux_vars(i).type = 5`.
## Type 6: Lagrange multipliers of the `ramsey_model`
# 6. Auxiliary variable for multipliers for first order conditions of the Ramsey problem (since 4.3)
This kind of aux var has `M_.aux_vars(i).type = 6` and corresponds to the Lagrange multipliers attached to the first order conditions of the Ramsey problem (since Dynare 4.3). They will appear whenever `ramsey_model` is used. Their name begins is `MULT_i`, where `i` is the equation number with which the multiplier is associated.
This is an auxiliary variable which is created for a lagrange multiplier of the ramsey problem.
The name of such an auxiliary variable begins with `MULT_i`, where `i` is the equation number with which the multiplier is associated.
`M_.aux_vars(i).eq_nbr` contains the number of the equation (constraint) with which the multiplier is associated.
`M_.aux_vars(i).eq_nbr` contains the number of the equation (constraint) with which the multiplier is associated.
This kind of auxiliary variable has `M_.aux_vars(i).type = 6`.
# 7. Auxiliary variable to account for difference between `var_model` order and max lag in model (since 4.6)
# 7. Auxiliary variable to account for difference between `var_model` order and max lag in model (since 4.6)
This is an auxiliary variable to account for the difference in lags between that declared in the `var_model` statement and those present in the model.
This is an auxiliary variable to account for the difference in lags between that declared in the `var_model` statement and those present in the model.
