Methodology

Hamilton-Perry cohort change ratio model

UK Demographics uses the Hamilton-Perry (HP) method to project ethnic composition at local authority level. The HP method computes cohort change ratios (CCRs) from two Census observations (2011 and 2021), then applies these ratios forward to project future populations by age, sex, and ethnic group.

The model covers 320 English local authorities, 20 ethnic groups, single year of age (0-100+), and both sexes. Projections extend to 2061, with 2051 as the primary horizon and 2061 as illustrative.

Data sources

• Census 2021: ONS custom dataset — single year of age by ethnic group by sex, 292 LAs (direct observations, no IPF dependency)
• Census 2011: 18-group age-sex-ethnicity dataset via NOMIS API
• ONS SNPP 2022: Subnational Population Projections used as total population envelope constraint
• DfE School Census 2024/25: Independent validation — 10 years of ethnic composition data by school and LA
• ONS Births Table 8: Age-specific fertility rates by ethnicity and IMD decile

Validation

The model achieves a mean absolute error (MAE) of 1.72 percentage points when backcasting from 2011 to 2021. This compares favourably with NEWETHPOP (Rees et al.), the previous academic benchmark, which achieves MAE 3.94pp on the same test.

School census data provides an independent out-of-sample validation for ages 0-15. School validation MAE: 2.36pp across 121 areas with 10 years of annual data.

Uncertainty quantification

1,000 Monte Carlo simulations with stochastic perturbation (sigma = 0.02) generate 80% and 95% confidence intervals for all projections. This captures the range of plausible outcomes, not a single point estimate.

Known limitations

• No international migration component — CCRs from 2011-2021 capture ~300K net migration pa, but post-2021 net migration peaked at 745K. This means the model likely understates the pace of change in high-migration areas.
• Per-group confidence intervals not yet computed (national stochastic only).
• No out-of-sample validation beyond DfE school data.
• Not peer-reviewed (submission to Demographic Research planned).
• COVID period (2020-21) may distort the 2021 Census baseline for some groups and areas.

Evidence standard

All figures on this site are categorised by evidence quality:

• Official: Published ONS, Census, DfE, or parliamentary data with stable provenance.
• Derived: Computed from official sources using documented methods (e.g., CCRs from two Census observations).
• Modelled: Output of the projection model — inherently uncertain, always shown with confidence intervals where available.
• Estimated: Best available approximation where no direct data exists. Always flagged.