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4.16 Optimal policy

Dynare has tools to compute optimal policies for various types of objectives. You can either solve for optimal policy under commitment with ramsey_policy, for optimal policy under discretion with discretionary_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:

$\max_\gamma E(y'_tWy_t)$

such that:

$A_1 E_ty_{t+1}+A_2 y_t+ A_3 y_{t-1}+C e_t=0$

where:

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).

The value of the objective is stored in the variable oo_.osr.objective_function, which is described below.

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.

An 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;
MATLAB/Octave variable: oo_.osr.objective_function

After an execution of the osr command, this variable contains the value of the objective under optimal policy.

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.

See section Auxiliary variables, for an explanation of how this operator is handled internally and how this affects the output.

Options

This command accepts all options of stoch_simul, plus:

planner_discount = EXPRESSION

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

instruments = (VARIABLE_NAME,…)

Declares instrument variables for the computation of the steady state under optimal policy. Requires a steady_state_model block or a …_steadystate.m file. See below.

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.

Steady state

Dynare takes advantage of the fact that the Lagrange multipliers appear linearly in the equations of the steady state of the model under optimal policy. Nevertheless, it is in general very difficult to compute the steady state with simply a numerical guess in initval for the endogenous variables.

It greatly facilitates the computation, if the user provides an analytical solution for the steady state (in steady_state_model block or in a …_steadystate.m file). In this case, it is necessary to provide a steady state solution CONDITIONAL on the value of the instruments in the optimal policy problem and declared with option instruments. Note that choosing the instruments is partly a matter of interpretation and you can choose instruments that are handy from a mathematical point of view but different from the instruments you would refer to in the analysis of the paper. A typical example is choosing inflation or nominal interest rate as an instrument.

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

Description

This command computes an approximation of the optimal policy under discretion. The algorithm implemented is essentially an LQ solver, and is described by Dennis (2007).

You should ensure that your model is linear and your objective is quadratic. Also, you should set the linear option of the model block.

Options

This command accepts the same options than ramsey_policy, plus:

discretionary_tol = NON-NEGATIVE DOUBLE

Sets the tolerance level used to assess convergence of the solution algorithm. Default: 1e-7.

solve_maxit = INTEGER

Maximum number of iterations. Default: 3000.

Command: planner_objective MODEL_EXPRESSION;

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

You need to give the one-period objective, not the discounted lifetime objective. The discount factor is given by the planner_discount option of ramsey_policy and discretionary_policy.

With ramsey_policy, you are not limited to quadratic objectives: you can give any arbitrary nonlinear expression.

With discretionary_policy, the objective function must be quadratic.


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