Alternative Policies

This section describes forecasting under an alternative monetary policy rule. That is:

1. The state space system is split into two exogenous and unanticipated regimes,

the "historical" regime and the "forecast" regime. The historical policy rule applies during the "historical" regime, and the alternative policy rule applies to the "forecast' regime.

1. Filtering and smoothing is done under the historical monetary policy rule, i.e. the one defined in the eqcond method for the given model.
2. Forecasts and IRFs are computed under the alternative rule.

See Regime-Switching Forecasts for details on how forecasting works when the state space system includes exogenous regime-switching.

Alternative policies can be either permanent or temporary. To use alternative policies, the user needs to ensure that the model can be solved with regime-switching (see Regime-Switching).

Procedure for Permanent Alternative Policies

The user defines some instance of the AltPolicy type (described below) and then calls the function setup_permanent_altpol!. Then the function calls made to forecast and compute means and bands remain the same as usual (see Forecasting and Computing Means and Bands).

For example, suppose you have defined the functions taylor93_eqcond and taylor93_solve corresponding to Taylor (1993)'s proposed monetary policy rule. Then you can run:

m = AnSchorfheide()
setup_permanent_altpol!(m, AltPolicy(:taylor93, taylor93_eqcond, taylor93_solve); cond_type = :none)
forecast_one(m, :mode, :none, [:forecastobs, :forecastpseudo])
compute_meansbands(m, :mode, :none, [:forecastobs, :forecastpseudo])

Permanent alternative policies utilize some of the same machinery as temporary alternative policies, but they use different algorithms for converting the equilibrium conditions from gensys form to the reduced form transition matrices for a state space system. The function setup_permanent_altpol! performs the setup required to interface with this machinery. The keyword argument cond_type is necessary because when the alternative policy is applied depends on whether the forecast is conditional or not. If a forecast is conditional, it is assumed that the alternative policy does not occur until after the conditional horizon, to maintain the idea that the alternative policy is entirely unanticipated.

Procedure for Temporary Alternative Policies

Another counterfactual exercise is temporarily imposing a different monetary policy rule, i.e. a temporary alternative policy, before switching back to either the historical rule or some (permanent) alternative rule. To implement this, we utilize exogenous regime switching in the forecast horizon.

In a rational expectations equilibrium, agents will take into account the fact that the temporary policy is expected to terminate. A different algorithm than Chris Sims's standard gensys algorithm is required, which we have implemented as gensys2. Note that this gensys2 is different from the gensys2 Chris Sims has implemented to calculate second-order perturbations.

To set up a temporary alternative policy, a user first needs to specify alternative policy using the type AltPolicy. For instance, this code implements a Nominal GDP targeting policy, and the AltPolicy is constructed by calling DSGE.ngdp(), or equivalently

AltPolicy(policy, DSGE.ngdp_eqcond, DSGE.ngdp_solve, forecast_init = DSGE.ngdp_forecast_init)

where the inputs to AltPolicy here are

ngdp_eqcond(m::AbstractDSGEModel, reg::Int = 1)

ngdp_solve(m::AbstractDSGEModel)

init_ngdp_forecast(m::AbstractDSGEModel, shocks::Matrix{T}, final_state::Vector{T})

Note that ngdp_replace_eq_entries is called by ngdp_eqcond but is not a direct input to AltPolicy.

The user also needs to complete the following steps to apply temporary alternative policies.

• Adding a regime for every period during which the alternative policy applies, plus one more regime for the policy which will be permanently in place after the temporary policies end.

• Adding the setting Setting(:gensys2, true) to indicate gensys2 should be used. If this setting is false or non-existent, then alternative policies will be treated as if they are permanent. Their equilibrium conditions will be solved using gensys, which can lead to determinacy and uniqueness problems if the alternative policy should be temporary (e.g. a temporary ZLB).

• Adding the setting Setting(:replace_eqcond, true) to indicate equilibrium conditions will be replaced.

• Adding the setting Setting(:regime_eqcond_info, info), where info should be a Dict{Int, DSGE.EqcondEntry} mapping regimes to instances of EqcondEntry, a type which holds any information needed to update equilibrium conditions to implement a given alternative policy. Borrowing the example of temporary NGDP targeting, the relevant EqcondEntry would be constructed as EqcondEntry(DSGE.ngdp()). Note that the user only needs to populate this dictionary with regimes in which the eqcond function differs from the default.

To see an example of using temporary alternative policies, see the example script for regime-switching.

Alternative Policy Uncertainty and Imperfect Awareness

Click on the section header for details on how to add policy uncertainty or imperfect credibility to alternative policies (both permanent and temporary).

MultiPeriodAltPolicy

Click on the section header to see the primary use of the type MultiPeriodAltPolicy, which extends AltPolicy to specify multiple regimes. In particular, one of the fields of MultiPeriodAltPolicy is regime_eqcond_info, which stores a dictionary that can be used to update a model's regime_eqcond_info Setting, i.e.

m <= Setting(:regime_eqcond_info, multi_period_altpol.regime_eqcond_info)

Types

mutable struct AltPolicy

mutable struct EqcondEntry

mutable struct MultiPeriodAltPolicy