Calibration inflates UK population from 69M to 74M (should be ~70M)

[MaxGhenis]

Summary

The dataset calibration process is inflating the UK population significantly above ONS targets. The base FRS 2025 dataset has ~69M people, but after calibration this jumps to ~74M - about 6% above the ONS mid-2024 actual estimate of 69.3M.

Evidence

Dataset	2025 Population
Base dataset (frs_2025_with_ss.h5)	68.97M
Calibrated dataset (frs_2025_calibrated_v3.h5)	73.57M
ONS mid-2024 actual estimate	69.3M
ONS 2022-based projection for 2025	~70M

Root Cause Investigation

1. The uk_population target IS included in the calibration loss function (loss.py line 318)
2. The population index in policyengine-uk (ons.population) uses reasonable growth rates
3. BUT the calibration is not constraining population properly - other targets are pulling weights in a direction that inflates total population

Potential Solutions

1. Increase the weight on population targets in the calibration loss function
2. Add a hard constraint that total population must match the target
3. Review conflicting targets that may be inflating population (e.g., regional age bands sum to more than national total)

Impact

This is causing CI test failures in PR #216:

• Test expected: 69.5M (ONS 2022-based)
• Test got: 73.7M

Data Sources

• ONS mid-2024 population estimate: 69.3M
• ONS 2022-based population projections

[MaxGhenis]

Root Cause Found

The calibration loss function gives equal weight to all 556 targets. Population is just 1/556 of the total loss, so it gets overridden by other targets.

Targets breakdown:

• Total targets: 556
• Population target: ons/uk_population = 69.90M
• Largest targets: employment_income 1,133bn, income_tax 328bn, etc.

The loss function uses symmetric relative error:

sre = ((1 + x) / (1 + y) - 1) ** 2
return mse_local + mse_national  # all targets weighted equally

Solution Options:

1. Add population weight multiplier in calibrate.py:

   population_loss = sre(pred_pop, y_pop)
   return mse_local + mse_national + 10 * population_loss  # Give 10x weight

2. Hard constraint: Rescale all weights after optimization so total population matches exactly:

   final_weights *= target_pop / actual_pop

3. Target-specific weights: Allow specifying weights for "anchor" targets like population