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## 4.16 Optimal policy

Dynare has tools to compute optimal policies for quadratic objectives. You can either solve for optimal policy under commitment with `ramsey_policy` or for optimal simple rule with `osr`.

Command: osr [VARIABLE_NAME…];
Command: osr (OPTIONS…) [VARIABLE_NAME…];

  Description

  This command computes optimal simple policy rules for linear-quadratic problems of the form:

  such that:

  where:

  - are parameters to be optimized. They must be elements of matrices , , ;
  - are the endogenous variables;
  - are the exogenous stochastic shocks;

  The parameters to be optimized must be listed with `osr_params`.

  The quadratic objectives must be listed with `optim_weights`.

  This problem is solved using a numerical optimizer.

  Options

  This command accept the same options than `stoch_simul` (see section Computing the stochastic solution).

Command: osr_params PARAMETER_NAME…;

  This command declares parameters to be optimized by `osr`.

Block: optim_weights ;

  This block specifies quadratic objectives for optimal policy problems

  More precisely, this block specifies the nonzero elements of the quadratic weight matrices for the objectives in `osr`.

  A element of the diagonal of the weight matrix is given by a line of the form:

      VARIABLE_NAME EXPRESSION;

  An off-the-diagonal element of the weight matrix is given by a line of the form:

      VARIABLE_NAME,  VARIABLE_NAME EXPRESSION;

Command: ramsey_policy [VARIABLE_NAME…];
Command: ramsey_policy (OPTIONS…) [VARIABLE_NAME…];

  Description

  This command computes the first order approximation of the policy that maximizes the policy maker objective function submitted to the constraints provided by the equilibrium path of the economy.

  The planner objective must be declared with the `planner_objective` command.

  Options

  This command accepts all options of `stoch_simul`, plus:

  `planner_discount = DOUBLE`

    Declares the discount factor of the central planner. Default: `1.0`

  Note that only first order approximation is available (i.e. `order=1` must be specified).

  Output

  This command generates all the output variables of `stoch_simul`.

  In addition, it stores the value of planner objective function under Ramsey policy in `oo_.planner_objective_value`.

Command: planner_objective MODEL_EXPRESSION;

  This command declares the policy maker objective, for use with `ramsey_policy`.

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