PolicyEngine Macro
model 06 — overlapping generations · psl-og · UK · local
Model long-run behavioural change.
Estimate how reforms affect work, saving, investment, and public finances over decades, for the UK.
Two UK overlapping-generations models, side by side.
OG-UK — the UK calibration of OG-Core, maintained by the Policy Simulation Library — against the OBR UK OLG model of OBR Working Paper No. 22 (Brzezinski, Hantzsche & Watson, April 2025), the closest available external check for a model of this kind.
| Dimension | OG-UK strength | OBR UK OLG strength |
|---|---|---|
| Transition dynamics | Full year-by-year paths | Steady-state only |
| UK institutional detail | Smooth approximations | Explicit bands and rates |
| Within-cohort inequality | Permanent types | Stochastic earnings |
| Production structure | Multi-sector CES | Single-sector Cobb-Douglas |
| Tax instruments | 5 instruments | 3 instruments (more detailed) |
| Fiscal policy levers | G, TR, UBI, Ig | RBI, age-dependent transfers |
| Openness | Open-source, Python | MATLAB, closed toolkit |
Production technology.
| OG-UK | OBR UK OLG | |
|---|---|---|
| Production function | CES (nests Cobb-Douglas as special case) | Cobb-Douglas only |
| Industries | M industries (multi-sector) | Single sector |
| Public capital | Yes — generates rents to private capital | No |
| Capital share | Configurable per industry | α = 0.33 |
| Labour input | Efficiency-weighted across permanent types | Efficiency-weighted by age + stochastic shocks |
| TFP | Varies by industry and over time | Normalised to 1, with labour-augmenting growth g = 1.2% |
| Depreciation | Configurable per industry | δ = 5% |
Household heterogeneity.
How households differ within each cohort — the deepest structural difference between the two models.
| OG-UK | OBR UK OLG | |
|---|---|---|
| Within-cohort variation | J permanent ability types (deterministic) | Stochastic earnings shocks (AR(1) persistent + i.i.d. transitory) |
| Income inequality driver | Fixed type assignment at birth | Random shocks each period (ρz = 0.9, σz = 0.05, σe = 0.7) |
| Precautionary savings | Not a primary channel | Yes — driven by earnings uncertainty |
| Utility function | CRRA on consumption; elliptical labour disutility | Cobb-Douglas over consumption and leisure (non-separable) |
| Labour disutility | Elliptical function — always interior solutions | Implicit in Cobb-Douglas composite — corner solutions possible |
| Risk aversion parameter | σ = 1.5 on consumption only | σ₂ = 2 on consumption-leisure composite |
| Consumption aggregation | Stone-Geary Cobb-Douglas (subsistence levels, I goods) | Single consumption good |
| Discount factor | β = 0.965, fixed and uniform (per-type βj supported, not used here) | β = 0.99, calibrated to the WAS asset profile |
Bequest motive.
| OG-UK | OBR UK OLG | |
|---|---|---|
| Motive | "Warm glow" weighted by mortality probability ρs | "Warm glow" with target level, kicks in at age j* = 91 |
| Varies by type | Yes — χbj calibrated per ability type | Uniform (φ₁ = 10, φ₂ = 4.55) |
| Distribution | To surviving households | Equal distribution to ages 55–75 |
Tax system.
Government & fiscal policy.
The fiscal closure rule — which item adjusts to keep debt sustainable — determines who bears the long-run burden of any reform.
| OG-UK | OBR UK OLG | |
|---|---|---|
| Budget constraint | Revenue + new debt = debt service + G + Ig + pensions + TR + UBI | Revenue = welfare transfers + RBI + debt service (growth-adjusted) |
| Fiscal closure rule | Configurable: adjust G, TR, or combination after period TG1 | Residual Budgetary Item (RBI) adjusts to stabilise debt/GDP at 100% |
| Debt target | Configurable | Fixed at 100% of GDP |
| Public investment | Explicit (Ig contributes to public capital stock) | Not modelled as productive |
| Welfare transfers | Lump-sum TR | Age-dependent transfers (γj scaling) calibrated to OBR welfare spending projections |
| State pension | Part of transfers | Explicitly modelled as age-dependent welfare transfer from state pension age onwards |
| Spending categories | G (public goods) + Ig (infrastructure) + pensions + TR + UBI | Welfare transfers + residual non-interest spending (G⁰) |
Open economy.
| OG-UK | OBR UK OLG | |
|---|---|---|
| Approach | Parameterised capital mobility (ζK for capital, ζD for debt) | Binary switch: fully open (r = 5% exogenous) or fully closed (r endogenous) |
| Foreign capital | Continuous degree of openness | Either all or nothing |
| Net foreign assets | Derived from capital mobility parameters | NFA residually determined in open economy |
| Interest rate | Endogenous (influenced by openness parameters) | Either fixed at 5% (open) or MPK − δ (closed) |
Solution method & calibration.
Both are rational-expectations dynamic general equilibrium; they solve different problems.
Calibration differs mainly in data sources and anchors.
Sources: OBR Working Paper No. 22; OG-Core documentation and OG-UK calibration code.
No ground truth. Calibration targets instead.
| Quantity | Official UK value | Source | Model treatment | Deviation |
|---|---|---|---|---|
| Government debt-to-GDP | 94.9% (June 2026) | ONS · HF6X, vintage 2026-07-26 | imposed via closure target | +0.1pp vs latest ONS (target 95.0%) |
| Household saving ratio | 8.9% (2026Q1, down from 9.6%) | ONS quarterly sector accounts | not targeted — β = 0.965 fixed, not estimated | no model-produced value to compare |
| Potential growth | ≈1.1% / yr | OBR EFO | imposed, gy = 0.011 | ≈0 |
| Depreciation / capital | ≈6–7% (CFC / net stock) | ONS capital stocks bulletin | imposed, δ = 0.065 | within range |
| Labour share of income | ≈0.59–0.60, rising in 2024 | ONS labour-share series / Blue Book 2025 | imposed, γ = 0.35 (OG-Core default) | ≈5pp — the capital share is not yet re-anchored to ONS factor shares |
| Net capital stock | £5.6tn (2024) whole-economy net stock; the model's K maps to the narrower business-capital concept | ONS capital stocks bulletin | emergent — checked, not imposed | concept-adjusted; no published reconciliation |
An imposed target cannot disagree, so a zero deviation above is an anchor, not evidence. Only the emergent row is a check.
The nearest external benchmark is OBR Working Paper 22, Table 5.1 — a 1pp basic-rate rise in the long run: GDP/person −0.1%, labour supply −0.2%, productivity +0.1%. Those are the figures a future OG-UK run will be judged against, not a match claimed today.
What would count as over-identifying evidence, and the dating and structural caveats
The genuinely over-identifying checks are the ones the steady state must deliver: the capital–output ratio and the interest rate implied by the calibrated (γ, δ, β) triple. Both emerge in an economically sensible range, but no systematic published reconciliation of achieved-versus-target moments exists for OG-UK 0.3.2. Producing one from logged solves is the most valuable next step for this member.
Two dating caveats: the official column reports mid-2026 figures while the deployed calibration was frozen against slightly earlier vintages, and the saving ratio is volatile quarter to quarter, so the fixed β was set against a smoothed level rather than the latest print. Two structural caveats from OG-Core: the ability types and lifetime earnings profiles are still the US tax-microdata estimates, and UK re-estimation is open.
Experimental limitations.
| limit | detail |
|---|---|
| Version pin | oguk 0.3.2 pins policyengine-uk==2.88.0. Versions ≥ 2.89 renamed the microdata dataset keys, so mixing them fails with a KeyError at calibration time; the adapter traps it and raises an actionable error. Until the pin lifts, the OLG member scores against an older statute vintage than the microsimulation member — a declared inconsistency, not a hidden one. |
| Gated data | Calibration needs the private enhanced-FRS microdata, so a HUGGING_FACE_TOKEN with access is a hard prerequisite. |
| Thin CI | CI cannot exercise a seventeen-minute solve on every commit, so regressions in solve behaviour are caught by scheduled runs and by hand, not continuously. |
| Steady-state-only in the CLI | The CLI exposes steady-state solves only (Code, step 7): the long-run destination is reachable through the suite, the path there is not. |
| Ability profiles not UK-estimated | Lifetime-ability profiles are inherited rather than re-estimated on UK microdata. On the roadmap. |