# Alternative Scenarios

An alternative scenario is a set of forecasted paths for a subset of observables ("targets"), along with a subset of shocks ("instruments") which get the model to hit those paths. Each scenario has a description which tells a story about the scenario targets and instruments – for example, "High Spreads" or "Persistent Consumer Optimism".

In an alternative scenario, we first solve for the values for specific shocks at specific horizons that create the paths of the observables imposed in the scenario. Only then do we run a regular forecast, imposing the path of shocks we just solved for and letting these propagate through the economy. (Compare to adding more periods of conditional data – in this case, the model is free to use as many shocks as it wants to explain the deviation of the conditional data from trend in these additional periods.) This allows us to answer questions like:

• Suppose a spread shock hits tomorrow, increasing spreads by 50 basis points. How large of a spread shock did this correspond to it? How does the economy respond? Suppose it is a discount factor shock instead.
• Suppose a discount factor shock hits for the next two quarters, causing a 100 basis point increase in spreads for two quarters, then reverting to zero (increase from baseline). How does the economy respond?

We will conceive of all alternative scenario forecasts as occuring in "deviations from baseline forecast". That is, if the scenario consists of spreads increasing by 50 basis points, then we want this to be independent of the underlying model and baseline forecast, such that in our own forecast, spreads actually are 50 basis points above our baseline forecast.

## Basic Scenarios

### The Scenario Type

The Scenario type encodes the basic information needed to forecast an alternative scenario. For now, we'll consider the following fields of the Scenario type:

• key::Symbol: scenario identifier, appearing in file names
• description::String: longer name, e.g. "High Spreads"
• target_names::Vector{Symbol}: names of the observables targeted in this scenario. For the High Spreads scenario, this would just be [:obs_spread]. These observable names should correspond to keys in m.observables
• instrument_names::Vector{Symbol}: names of the shocks used to hit the target paths, which should correspond to keys in m.exogenous_shocks. There must be at least as many instruments as there are targets. If this field is the empty array, then all model shocks will be used
• targets::DataFrame: contains the specific target values, given in deviations from some baseline forecast. No :date field is required, since the scenario is assumed to begin in the first forecasted period of the model
• instruments::DataFrame: initially empty DataFrame, which is populated after backing out the necessary shocks to hit the targets
• vintage::String: scenario vintage in yymmdd format, which can be different from the data vintage
• n_draws::Int: number of scenario draws. A scenario draw is one set of target paths. Often, multiple draws of target paths will be associated with one scenario name, which collectively make up a forecast distribution for the particular scenario. This field is usually initialized to 0 and then updated upon reading in the target draws

### Setting Up Input Target Paths

If you only want to forecast one scenario draw, it is sufficient to create an instance of the Scenario type and hard-code in the target paths. However, when forecasting multiple draws, it is convenient to load target draws from a file.

This file's name should be of the form inpath(m, "scenarios", <key>_<vintage>.jld) and should contain the following datasets:

• arr::Array{Float64, 3}: array of target values of size ndraws x ntargets x horizon
• target_indices::OrderedDict{Symbol, Int}: maps target names to their indices along the ntargets dimension

### Forecasting Scenarios

Forecasting scenarios is similar to running a normal full-distribution forecast, with some exceptions:

• All draws of a particular scenario are forecasted under the modal parameters.

• Smoothed histories, shock decompositions, and IRFs are not supported.

• We zero out the entries in the $Q$ matrix (the variance-covariance of the shocks $\epsilon_t$) corresponding to shocks which are not scenario instruments.

• Forecasting is done in deviations from baseline. That is, let $s^a_t$ and $s^b_t$ be the state vectors under the alternative and baseline scenarios respectively, and define $y^a_t$ and $y^b_t$ analogously for observable vectors. Then the state space in deviations is

\begin{aligned} s^a_t - s^b_t &= T(s^a_{t-1} - s^b_{t-1}) + R \epsilon_t & \mathrm{(transition)} \\ y^a_t - y^b_t &= Z(y^a_t - y^b_t) & \mathrm{(measurement)} \end{aligned}

The main function to run is forecast_scenario, which is similar in spirit to forecast_one. forecast_scenario loads the modal parameters for the model and calls forecast_scenario_draw, which does the following for each input draw:

1. Call load_scenario_targets! to read the ith scenario draw from the input file
2. Filter and smooth to back out the necessary shocks, treating the targeted paths like data
3. Forecast paths for all variables (not just the targeted observables) using the smoothed shocks
4. Check that the forecasted observables match the targets and return

When all draws for the scenario have been forecasted, the forecasted observables and pseudo-observables are written to the files given by get_scenario_output_files.

### Computing Means and Bands

Computing means and bands is carried out by scenario_means_bands, which is likewise similar to compute_meansbands for regular forecasts. The default output_vars passed into scenario_means_bands are

output_vars = [:forecastutobs, :forecastobs, :forecast4qobs,
:forecastutpseudo, :forecastpseudo, :forecast4qpseudo]

The product :forecastut refers to untransformed forecasts, i.e. forecasts in model units (in deviations from baseline).

Since these forecasts are given in deviations from baseline, different transformations are used than in the usual case. These don't add back population growth to per-capita variables and approximate annualizing log differences (exponentiating and raising to the fourth power) by multiplying by four. The mapping from usual to scenario transformation is given by get_scenario_transform.

### Other Scenario Fields

The remaining fields in the Scenario type are used to forecast scenarios using additional bells and whistles:

• shock_scaling::Float64: after filtering and smoothing shocks, multiply them by shock_scaling before forecasting. Defaults to 1.0.
• draw_states::Bool: if true, use the simulation smoother rather than the Kalman smoother to smooth shocks. This generates uncertainty around the target paths. Defaults to false.
• altpolicy::AltPolicy: solve for shocks under the historical policy rule, then switch to the alternative policy (see Alternative Policies) before forecasting. Defaults to AltPolicy(:historical, eqcond, solve).

### SwitchingScenarios

Suppose you want to simulate a set of scenario draws which all start from some default scenario, switch to an alternative scenario (which we call the original scenario) with some probability in each period, and then revert back to the default scenario with some probability. This functionality is encoded in the SwitchingScenario type, which has the following fields:

• key::Symbol: identifier, not the same as the original scenario's key
• description::Symbol: defaults to the original scenario's description
• vintage::String: defaults to the original scenario's vintage
• original::SingleScenario
• default::SingleScenario
• probs_enter::Vector{Float64}: gives the probability of leaving the default scenario and entering the original scenario in each period
• probs_exit::Vector{Float64}: gives the probability of leaving the original scenario and reverting to the default scenario in each period

SingleScenario is the abstract supertype of both Scenario and SwitchingScenario.

SwitchingScenarios cannot be forecasted like ordinary Scenarios. Instead, after simulating draws from both the original and default scenarios, you call simulate_switching to use these already-forecasted draws. For each draw i of the original scenario:

1. Randomly select a draw j of the default scenario.
2. In each period t (beginning in period 1), determine whether to switch to the original scenario with probability probs_enter[t]. If remaining in the default scenario, use the period t forecasted values of the jth default scenario draw.
3. Suppose the last period in the default scenario is t0. Then for each subsequent period t0 + h, decide whether to revert to the default scenario with probability probs_exit[t0 + h]. If remaining in the original scenario, use the period h (not t0 + h) forecasted values of the ith original scenario draw.
4. Let t1 be the last period in the original scenario. Then for each remaining period t1 + h, use the period t1 + h forecasted values of the jth default scenario draw.

simulate_switching saves simulated draws in the same format as forecast_scenario. Transforming and computing means and bands for SwitchingScenarios using scenario_means_bands is the same as for regular Scenarios.

## Aggregating Multiple Scenarios

Finally, we are sometimes interested in aggregating the forecast draws from multiple scenarios. We define the ScenarioAggregate type, which has the following fields:

• key::Symbol
• description::String
• scenarios::Vector{AbstractScenario}: vector of component scenarios, some of which might be themselves ScenarioAggregates
• sample::Bool: indicates whether to
• proportions::Vector{Float64}: vector of relative scenario proportions
• total_draws::Int: desired final number of draws
• replace::Bool: indicates whether to sample with replacement
• vintage::String

In addition to the default constructor, there are two more ScenarioAggregate constructors, corresponding to the two possible values of sample. The key, description, vector of component scenarios, and vintage are always specified.

• sample = false: No additional fields are required for this constructor, as the component scenario draws are kept in their original proportions. The proportions and total_draws fields are initialized to dummy values and are updated when the component draws are read in. replace is set to false.
• sample = true: Additionally specify proportions, total_draws, and replace. Draws from scenarios[i] are sampled into the aggregate distribution with probability proportions[i]

SingleScenario and ScenarioAggregate are both subtypes of the abstract type AbstractScenario. The actual sampling and aggregating of scenario draws happens entirely in scenario_means_bands, which calls functions that dispatch on the AbstractScenario subtype passed in. In particular, this means that we don't save a separate "raw" output file with the individual draws that made it into a particular ScenarioAggregate – we only save the resulting MeansBands.