Monetary policy¶

By default the model's own policy rule sets the policy rate. With policy.mode = 'ramsey' the rule is switched off and the instrument follows optimal policy under commitment from the forecast origin.

Option	Values (default first)	Meaning
`policy.mode`	`'rule'`, `'ramsey'`	The model's own rule, or Ramsey optimal policy (needs `spec.policy`)
`policy.type`	`'commitment'`, `'discretion'`	Ramsey under commitment; discretion is indeterminate in IRIS for SW07
`policy.loss`	`struct('pinf', 1, 'ygap', 0.5, 'r', 0.1, 'dr', 0)`	Non-negative weights by target name. Replaced as a whole: targets left out get weight 0
`policy.discount`	`[]` or a number in (0, 1]	`[]` = `spec.policy.discount`
`policy.loss_horizon`	`[]` or a number of quarters	Horizon of the reported loss; `[]` = the forecast horizon. A longer one continues the scenario with zero shocks and no conditions

The policy section of a model package¶

Ramsey policy and the loss need a policy field in model_spec.m. For SW07:

spec.policy = struct( ...
    'instrument', 'r', ...                                                   % policy instrument
    'rule_label', 'Monetary policy rule, Taylor rule on the output gap y-yf', ...  % exact equation label
    'targets', struct('pinf', '4*pinf', 'ygap', 'y - yf', 'r', '4*r', 'dr', '4*(r - r{-1})'), ...
    'discount', '$cbetabar$*$cgamma$');                                     % expression in parameters

The rule equation is found by its exact label in the model file and switched off under Ramsey policy. The targets are linear expressions in model variables; policy.loss gives their weights by name. The discounted loss is

\[ L = \sum_{h=1}^{H} \delta^{h} \sum_{j} w_j\, \text{target}_{j,h}^2 . \]

Every run of a package with a policy section reports this loss with the policy.loss weights, rule runs included, so rule and Ramsey runs are compared on the same weights: res.loss and results/<id>/loss.csv (target, expression, weight, contribution, share, discount, horizon, continuation, mode, type).

Examples¶

% Ramsey policy under commitment, balanced weights, loss over 80 quarters
cfg = a4_rule_learn(); cfg.id = 'my_ramsey_learn';
cfg.policy.mode = 'ramsey';
cfg.policy.type = 'commitment';
cfg.policy.loss = struct('pinf', 1, 'ygap', 0.5, 'r', 0.1, 'dr', 0);
cfg.policy.loss_horizon = 80;
res = hetlearn.run(cfg);

% The rule, with the loss reported under other weights (the path does not change)
cfg = a1_learn(); cfg.id = 'a1_rule_loss';
cfg.policy.loss = struct('pinf', 1, 'ygap', 1, 'r', 0, 'dr', 0.5);
cfg.policy.discount = 0.99;
res = hetlearn.run(cfg, 'save', false);
res.loss                                   % total and contributions

Under learning the planner treats the current beliefs and shares as permanent, re-optimises every quarter with the beliefs and shares in force, and honours its past commitments. The plan starts at the origin with zero Lagrange multipliers.

Restrictions¶

Ramsey policy needs expectations.re_info = 'current': with 'lagged' the run stops with hetlearn:options:unsupported. The project's Application 4 sets 'current' for this reason.
Ramsey policy is not available with the agent types and transforms of Further expectation rules.
A package without spec.policy cannot run 'ramsey', and its runs report no loss.

Anchored RE agents and Ramsey policy¶

Anchored RE agents forecast with the RE solution of the model under the rule, also in mode 'rational'. So a Ramsey run with anchored RE agents is not an RE Ramsey plan. For the RE benchmark use model-consistent RE agents:

cfg = a4_ramsey_balanced_re(); cfg.id = 'a4_ramsey_balanced_re_mc';
cfg.expectations.re_variant = 'model_consistent';

In a learning Ramsey run the anchored RE agents also keep the rule's forecast, so its loss is not a clean measure of the gain from optimal policy. Under the rule the two variants give the same RE path.

In the project¶

Application 4 compares the rule and Ramsey policy for four weight sets under RE and learning. With balanced weights over 80 quarters the loss falls from 230.1 to 127.7 under RE and from 359.4 to 184.5 under learning. Details and figure: Application 4.