Explain UK growth and inflation.

Two blocks

Eight quarterly variables in two blocks: global — world GDP and world CPI (both UK-trade-weighted) plus the real oil price in sterling — and UK — Bank Rate, the sterling exchange-rate index, CPI, CPI energy, and real GDP.

Sample and specification

Estimation covers the inflation-targeting era, 1992Q1–2025Q1, in both the paper replication and the hosted adapter — in levels, with \(p = 4\) lags and exogenous Covid dummies for 2020Q1–2021Q2.

Conditioning versus estimation

The hosted forecast conditions on observations through 2026Q1 without re-estimating coefficients on them.

The prior

Estimation is Bayesian with a Minnesota (normal-inverse-Wishart) prior plus sum-of-coefficients and dummy-initial-observation priors — the framework of Giannone, Lenza & Primiceri (2015).

The posterior

The output is a posterior over the reduced-form coefficients \(\Pi\) and error covariance \(\Sigma\); every downstream object — impulse responses, decompositions, fan charts — is a posterior distribution, not a point estimate.

Zero and sign restrictions

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.

Corrections

Importance weights correct the sampler's non-uniformity; the Chan–Matthes–Yu (2025) permutation search cuts rejections.

Accept/reject sampling

This is accept/reject sampling. The production run drew 10,000 posterior \((\Pi, \Sigma)\) 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 run

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 published current-outlook chart on the overview comes from a larger 5,600-draw run of the same pipeline (385 accepted, ESS 176.3).

Why a satellite

The unemployment rate is not one of the eight VAR variables, so the published unemployment outlook comes from a deliberately separate satellite: a small dynamic Okun's-law regression that maps the VAR's UK GDP growth forecast into a path for the ONS unemployment rate (MGSX). The replication core is untouched.

How it is fitted

The quarterly change in unemployment is regressed by OLS on year-on-year GDP growth and its own lag, on the VAR's 1992Q1–2025Q1 sample. The furlough quarters (2020Q1–2021Q2) are dummied out: GDP printed ~−20% year on year while unemployment barely moved, and including them attenuates the Okun coefficient about threefold (β −0.047 → −0.016).

How the bands work

Conditional on the fit, the mapping is monotone decreasing in GDP growth, so the GDP median and bands pass through directly (with the bounds swapped — high growth means low unemployment). The bands carry GDP-forecast uncertainty only, no Okun residual uncertainty, so they are a lower bound on the true uncertainty. In the 73-origin rolling test the published path is capped at four quarters, where the satellite stops beating a no-change benchmark.