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## 4.6 Auxiliary variables

The model which is solved internally by Dynare is not exactly the model declared by the user. In some cases, Dynare will introduce auxiliary endogenous variables—along with corresponding auxiliary equations—which will appear in the final output.

The main transformation concerns leads and lags. Dynare will perform a transformation of the model so that there is only one lead and one lag on endogenous variables and, in the case of a stochastic model, no leads/lags on exogenous variables.

This transformation is achieved by the creation of auxiliary variables and corresponding equations. For example, if `x(+2)` exists in the model, Dynare will create one auxiliary variable `AUX_ENDO_LEAD = x(+1)`, and replace `x(+2)` by `AUX_ENDO_LEAD(+1)`.

A similar transformation is done for lags greater than 2 on endogenous (auxiliary variables will have a name beginning with `AUX_ENDO_LAG`), and for exogenous with leads and lags (auxiliary variables will have a name beginning with `AUX_EXO_LEAD` or `AUX_EXO_LAG` respectively).

Another transformation is done for the `EXPECTATION` operator. For each occurence of this operator, Dynare creates an auxiliary variable equal to `AUX_EXPECT_LAG_1 = x(+2)`, and replaces the expectation operator by `AUX_EXPECT_LAG_1(-1)`.

Once created, all auxiliary variables are included in the set of endogenous variables. The output of decision rules (see below) is such that auxiliary variable names are replaced by the original variables they refer to.

The number of endogenous variables before the creation of auxiliary variables is stored in `M_.orig_endo_nbr`, and the number of endogenous variables after the creation of auxiliary variables is stored in `M_.endo_nbr`.

See Dynare Wiki for more technical details on auxiliary variables.

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