## Transformation of variables for imposing terminal condition in terms of growth rates

The object of the task will be to define a new option for the Dynare preprocessor for deterministic simulations. The convergence of deterministic simulations is sometimes hindered by sub-optimal use of terminal conditions. Especially for level variables and Lagrange multipliers, bad values for terminal conditions in the case of very persistent dynamics or permanent shocks can hinder correct solutions or any convergence. To this end, it will be useful to consider an option for the Dynare preprocessor that defines auxiliary forward looking variables expressed in first differences or growth rates of the actual forward looking variables defined in the model. These new variables have obvious zero terminal conditions whatever the simulation context and this in many cases helps convergence of simulations. Allowing the preprocessor to automatically define these auxiliary variables would avoid modelers to modify/edit the model for simulation purposes.

The specific objectives for the deliverables will be:

- define the specifications and preprocessor options that trigger the definition of auxiliary forward looking variables with zero terminal conditions;
- the default behavior of this new option will be to transform all forward looking variables in the model: a further option will be to allow the modeler to explicitly define the list of variables to be transformed. This may be useful in the case some forward looking variables in the model (like inflation in Phillips curve) have already the trivial zero terminal condition, thus reducing the number of new variables defined by the preprocessor (namely only Lagrange multipliers and level variables).