Imputations

PolicyEngine UK Data enhances the Family Resources Survey with variables from other surveys using statistical imputation. All imputations use Quantile Regression Forests (QRF), which predict the full conditional distribution of target variables given predictor variables.

Imputation Pipeline Order¶

The imputations are applied in this order (dependencies noted):

1. Wealth (from WAS)

2. Consumption (from LCFS) — requires num_vehicles from wealth

3. VAT (from ETB)

4. Public Services (from ETB)

5. Income (from SPI)

6. Capital Gains (from Advani-Summers data)

7. Salary Sacrifice (from FRS subsample)

8. Student Loan Plan (rule-based, from age)

Wealth Imputation¶

Source: Wealth and Assets Survey (WAS) Round 7 (2018-2020)

Imputes household wealth components using demographic and income predictors.

Predictors¶

Outputs¶

Consumption Imputation¶

Source: Living Costs and Food Survey (LCFS) 2021-22

Imputes household spending patterns for indirect tax modeling.

Predictors¶

Outputs¶

Bridging WAS Vehicle Ownership to LCFS Fuel Spending¶

LCFS 2-week diaries undercount fuel purchasers (58%) compared to actual vehicle ownership (78% per NTS 2024). We bridge this gap using WAS vehicle data:

1. In WAS: Create has_fuel_consumption from vehicle ownership:

   • has_fuel = (num_vehicles > 0) AND (random < 0.90)

   • The 90% accounts for EVs/PHEVs that don’t buy petrol/diesel

   • Source: NTS 2024 shows 59% petrol + 30% diesel + ~1% hybrid fuel use

2. Train QRF: Predict has_fuel_consumption from demographics (income, adults, children, region)

3. Apply to LCFS: Impute has_fuel_consumption to LCFS households before training consumption model

4. At FRS imputation time: Compute has_fuel_consumption directly from num_vehicles (already calibrated to NTS targets)

5. Zero non-fuel households: After imputation, set petrol_spending and diesel_spending to zero for households where has_fuel_consumption = 0

This ensures fuel duty incidence aligns with actual vehicle ownership (~70% of households = 78% vehicles × 90% ICE) rather than LCFS diary randomness.

VAT Imputation¶

Source: Effects of Taxes and Benefits (ETB) 1977-2021

Imputes the share of household spending subject to full-rate VAT.

Predictors¶

Outputs¶

Income Imputation¶

Source: Survey of Personal Incomes (SPI) 2020-21

Imputes detailed income components to create “synthetic taxpayers” with higher incomes than typically captured in the FRS. These records initially have zero weight but can be upweighted during calibration to match HMRC income distribution targets.

Predictors¶

Outputs¶

Capital Gains Imputation¶

Source: Advani-Summers capital gains distribution data

Uses a gradient-based optimization approach rather than QRF. The dataset is doubled, with one half receiving imputed capital gains amounts. Weights are then optimized to match the empirical relationship between total income and capital gains incidence.

Method¶

1. Double the dataset (original + clone)

2. Assign capital gains to one adult per household in the cloned half

3. Optimize blend weights to match income-band capital gains incidence from Advani-Summers data

Salary Sacrifice Imputation¶

Source: FRS 2023-24 (respondents asked about salary sacrifice)

Imputes pension contributions made via salary sacrifice arrangements.

Predictors¶

Outputs¶

Training Data¶

• FRS respondents with SALSAC='1' (Yes): ~224 jobs with reported amounts

• FRS respondents with SALSAC='2' (No): ~3,803 jobs with 0

• Imputation candidates (SALSAC=' '): ~13,265 jobs

Student Loan Plan Imputation¶

Source: Rule-based (not QRF)

Assigns student loan plan type based on age and reported repayments.

Logic¶

1. If student_loan_repayments > 0, person has a loan

2. Estimate university start year = simulation_year - age + 18

3. Assign plan:

   • Plan 1: Started before September 2012

   • Plan 2: Started September 2012 - August 2023

   • Plan 5: Started September 2023 onwards

Calibration Targets¶

After imputation, household weights are calibrated to match aggregate statistics from: