Impute salary sacrifice participation to full population

[MaxGhenis]

Problem

The current dataset only uses raw FRS SPNAMT (salary sacrifice pension amount) field, which has only 371 observations with non-zero values out of ~36,000 persons. This represents £5bn weighted, but the HMRC target is ~£24bn.

PR #216 attempted to add calibration targets for salary sacrifice, but this requires ~5x weight scaling which inflates population from 68M to 74M (6% over target vs 2% tolerance).

Root Cause

Salary sacrifice is NOT imputed - unlike consumption, wealth, VAT, services, income, and capital gains which all have imputation steps in create_datasets.py. The raw FRS severely under-reports SS participation.

Proposed Solution

Implement ML-based imputation for salary sacrifice participation, similar to how other variables are imputed.

Key Finding: We CAN Distinguish Non-Response from Zero

The FRS SALSAC variable is a routing question that asks "Does your employer offer a salary sacrifice scheme for pension contributions?":

SALSAC Value	Meaning	Count
'1'	Yes, participates in SS	224 jobs
'2'	No, doesn't participate	3,803 jobs
' ' (blank)	Skip/not asked	13,265 jobs

This provides:

• Training data: 4,027 observations with definite Yes/No responses
• Imputation candidates: 13,265 observations where the question was skipped

External Validation Target

Per HMRC surveys, approximately 30% of private sector employees use salary sacrifice for pension contributions. This can be used to validate imputation results.

HMRC Table 6.2 Targets (2023-24)

• Total SS pension contributions: ~£24bn
• IT relief from SS: ~£7.2bn
  • Basic rate: £1.6bn
  • Higher rate: £4.4bn
  • Additional rate: £1.2bn

Implementation Steps

1. Create imputation model using SALSAC='1'/'2' as training labels
2. Predict SS participation probability for SALSAC=' ' (skipped) observations
3. Impute SS amounts based on participation probability and employee characteristics
4. Validate against HMRC 30% participation rate target
5. Remove calibration targets from loss function (or reduce their weight significantly)

Related Issues/PRs

• Issue Calibrate salary sacrifice pension contributions to external benchmarks #215: Documents SS under-reporting problem
• Issue Calibration inflates UK population from 69M to 74M (should be ~70M) #217: Documents calibration inflating population from 69M to 74M
• PR Salary sacrifice pension variable #214: Added raw FRS SPNAMT field (no imputation)
• PR Add salary sacrifice pension contributions as calibration target #216: Attempted calibration targets (causes population inflation)

Files to Modify

• policyengine_uk_data/datasets/frs.py - Add SALSAC extraction
• policyengine_uk_data/datasets/create_datasets.py - Add SS imputation step
• New file: policyengine_uk_data/datasets/imputations/salary_sacrifice.py