Explain UK growth and inflation.

In July 2025 the Bank of England published Macro Technical Paper No. 3 — A structural VAR model for the UK economy — with no replication package. This project re-implements the full pipeline in Python: data assembly from public sources, Bayesian estimation, identification, and every output figure, validated against the paper's published results.

Within the suite it is the empirical, time-series member — and the baseline/conditioning member. It imposes just enough structure to name the shocks hitting the economy and to say how uncertain the baseline is, before you simulate changing it with the structural members.

A VAR in eight quarterly variables — three global, five UK — estimated over the inflation-targeting era — 1992Q1–2025Q1 in both the paper replication and the hosted adapter. The hosted forecast conditions on observations through 2026Q1, but does not re-estimate its coefficients on those later observations. It is estimated in levels, with p = 4 lags and Covid dummies for 2020Q1–2021Q2.

Estimation is Bayesian with a Minnesota (normal-inverse-Wishart) prior plus sum-of-coefficients and dummy-initial-observation priors. Identification follows Arias–Rubio-Ramírez–Waggoner (2018): zero restrictions make the UK a small open economy (UK shocks cannot move world variables on impact) and impact sign restrictions name six structural shocks — world demand, world energy, world supply, UK demand, UK supply, and UK monetary policy. Two unidentified shocks absorb residual volatility. Importance weights correct the sampler's non-uniformity and the Chan–Matthes–Yu (2025) permutation search cuts rejections.

This is accept/reject sampling. The production run drew 10,000 posterior (Π, Σ) draws, of which 751 passed the sign restrictions (7.5%), for an importance-weighted effective sample size of 355.9 — so medians and bands are correct but noisier than the paper's. The hosted forecast conditions on the current vintage — data through 2026Q1 — with a 2,000-draw default (135 accepted, ESS 65.3), while retaining the 2025Q1 coefficient-estimation endpoint.

The package installs straight from GitHub with the prepared quarterly dataset inside, so boe_var.data.load_data() works immediately with no credentials. Every input series is public: ONS (CPI, CPI energy, real GDP), Bank of England (Bank Rate, sterling ERI), and FRED (oil, exchange rates, world components).

pip install git+https://github.com/PolicyEngine/boe-var-model

The runner scripts are for development — clone the repository to rebuild the dataset or regenerate the paper outputs:

python scripts/download_data.py     # reassemble the public data

# the paper's core outputs: IRFs, FEVDs, shocks, historical decompositions
python scripts/run_replication.py

# the forecasting toolkit: fan charts, latest-quarter shock distributions,
# composite IRFs, and the forecast-revision decomposition
python scripts/run_forecast_revision.py

outputs land in results/ — the replication figures (fig2–fig6) plus the forecast figures (fig1, fig7–fig9) and two summary reports. runtime scales with draw count; the importance weights are the expensive part, since each needs a numerical Jacobian per accepted draw.

Four tools, all posterior distributions rather than point estimates:

In the current 2026Q1 round the tool reads the latest quarter as most likely hit by negative world-demand (probability 0.71) and world-energy (0.90) shocks, against positive UK demand (0.81) and expansionary monetary policy (0.84); the composite effect revises the year-on-year path by +0.27pp on GDP growth at impact and +0.22pp on CPI inflation at its peak three quarters out.

every deviation is enumerated in the repository's docs/methodology.md.