2.14. Resimulation and counterfactuals

Given a solved model and a filter output, the resim_bridge package reconstructs the latent regime path and structural shock sequence consistent with the observed data, then re-simulates under user-chosen perturbations. Five reconstruction methods are exposed; three decomposition utilities consume the reconstructed baseline.

The bridge does not modify filter(m), the solver, or any class method. It reads the filter output and dispatches into the underlying +resim package (also under classes/utils/).

2.14.1. Adapter

resim_bridge.adapt packages the model and filter output into the canonical tuple used by every reconstruction method:

adapter = resim_bridge.adapt(m, f);

The returned struct exposes:

Field	Meaning
`Tfunc(x, eps, r)`	One-step state propagator on the full endogenous vector.
`Pfunc(x)`	`(h x h)` regime transition matrix at state `x`. Constant for exogenous Markov chains; state-dependent for endogenous TVTPs.
`smoothed.x`	`(nx x h x T)` regime-conditional smoothed state means.
`smoothed.eps`	`(ne x h x T)` regime-conditional smoothed shocks.
`smoothed.pi`	`(h x T)` smoothed regime probabilities.
`alpha`	`(h x T)` filtered regime probabilities (self-normalised inside the methods).
`pi0`	`(h x 1)` initial regime distribution.
`x0`	`(nx x 1)` pi-weighted initial state.

2.14.2. Reconstruction methods

resim_bridge.run(m, f, method, opts) dispatches over four deterministic / stochastic reconstruction methods:

`method`	What it returns
`'viterbi'`	The MAP regime path (single deterministic sequence) and the state path obtained by forward-simulating along it with the regime-conditional smoothed shocks.
`'ffbs'`	`M` draws from the posterior regime-path distribution via forward-filter backward-sample. Exact up to filter approximation.
`'independent'`	`M` regime paths drawn independently at each date from the smoothed marginals. Ignores the transition law; correct only marginally. Useful for fast exploratory analysis.
`'rao_blackwell'`	Deterministic pi-weighted mixture across regimes. Exact for linear models; biased for nonlinear ones, with bias growing in regime uncertainty.

The 'particle' method requires a particle-filter output rather than a Kalman smoother; run raises resim_bridge:run:notWired in that case. Call resim.particle directly with a particle container.

2.14.3. Counterfactuals

resim_bridge.counterfactual(m, f, mode, spec) reconstructs a deterministic baseline and re-simulates under one of three perturbations:

`mode`	`spec` fields	Effect
`'shock'`	`shock_ids`, optional `values`	Zeroes (or replaces) the listed shocks on the reconstructed baseline; the regime path is held fixed.
`'regime'`	`r_path`	Replaces the reconstructed regime path with a user-supplied sequence; shocks held fixed.
`'param'`	`parameters` struct	Re-sets parameters, re-solves, re-filters on the same data, and re-runs the reconstruction.

The return struct carries baseline, counter, and delta = counter.x - baseline.x.

2.14.4. Shock decompositions

Two flavours, both along the reconstructed regime path:

resim_bridge.shock_decomp(m, f) – leave-one-out:

delta_k(t) = x_t^full - x_t^(-k)

Exact for linear models; the interaction residual is not allocated.

resim_bridge.shapley(m, f) – Shapley:

phi_k(t) = (1/ne!) sum_sigma [ v(S U {k}, t) - v(S, t) ]

The Shapley decomposition is exactly additive even for nonlinear models:

sum_k phi_k(t) = x_t^full - x_t^base

Exact mode enumerates all \(2^{n_e}\) subsets and runs for ne <= opts.exact_threshold (default 10). Sampled mode ([Castro et al., 2009]) is used otherwise.

2.14.5. Ergodic variance decomposition

resim_bridge.var_decomp(m, kind) works at the model’s ergodic distribution; it does not need f. Three games:

kind

Decomposition

'shocks'

Shapley allocation of total variance across the ne shocks. The regime process runs freely under Pfunc.

'joint'

Shapley allocation across the ne shocks and a regime player. Removing the regime player fixes the chain at its ergodic distribution via Pfunc_erg.

'anova'

Between-vs-within decomposition via the law of total variance:

Var(x) = W + B

where W = sum_j pi_j * Var(x | r_t=j) and B = sum_j pi_j * (mu_j - mu)(mu_j - mu)'. Always exact; no Shapley enumeration.

A worked example using a switching New-Keynesian model is provided in Chapter 22 - Nonlinear filtering under regime switching of the RISE lecture notes (T22_6_Resimulation.m).