HBAI

These are:

• hbai_household_net_income: Household net income, before housing costs, with a negative figure reset to zero

• hbai_household_net_income_before_reset_to_zero: The same income before a negative figure is reset to zero

• hbai_household_net_income_ahc: Household net income, after housing costs

• equiv_hbai_household_net_income: Equivalised household net income, before housing costs (BHC)

• equiv_hbai_household_net_income_ahc: Equivalised household net income, after housing costs (AHC)

These variables are used in the HBAI income distribution and poverty statistics, which are published by the Department for Work and Pensions (DWP) in the UK. The HBAI income concepts are defined in the FYE 2025 background information and methodology report.

Property income¶

HBAI income counts a landlord’s profit after mortgage interest. The Family Resources Survey asks for rent from property “AFTER paying for any of the things on this card”, and show card K6 lists mortgage payments and interest on a loan to buy the property (FRS 2023–24 question instructions, question PropRent, page 302). PolicyEngine’s property_income is the profit before those finance costs, because income tax no longer deducts them (ITTOIA 2005 s. 272A(4)) and relieves them with a tax reduction instead (s. 274A). So hbai_household_net_income, market_income and household_market_income count property_income_after_finance_costs: property_income less property_finance_costs, and nil where the costs exceed a positive profit. The tax reduction itself is in income_tax. Interest on a let property is not a housing cost; only the household’s own mortgage_interest_repayment is deducted after housing costs.

Negative incomes¶

HBAI resets a negative income before housing costs to zero: “Negative incomes BHC are reset to zero, but negative AHC incomes calculated from the adjusted BHC incomes are possible. Where incomes have been adjusted to zero BHC, income AHC is derived from the adjusted BHC income.” (HBAI Background Information and Methodology report FYE 2025).

PolicyEngine does the same. hbai_household_net_income is hbai_household_net_income_before_reset_to_zero reset to zero when negative, and hbai_household_net_income_ahc subtracts all five housing costs listed above from the reset figure, so it can be negative. The equivalised incomes, household_income_decile, the poverty flags and the poverty gaps all use the reset figure. A household whose income was negative is below every absolute poverty line, and its before-housing-costs poverty gap is the whole line. It is below the relative line while the median person’s income is positive; if half or more of people had BHC income at or below zero, the reset would make the BHC median, and so the BHC relative line, zero. Households with equal incomes share the rank at the top of their group, so households at zero are in the bottom decile while they hold at most a tenth of people. On the enhanced FRS under 1% of people have an income at or below zero before the reset, so both conditions hold. The labour supply responses use the figure before the reset, which is the household’s actual budget constraint. hbai_household_net_income_ahc deducts all five housing-cost rows above from the reset hbai_household_net_income. Ground rent and service charges (housing_service_charges) are the fifth cost. Housing costs can exceed income, leaving negative AHC income. The equivalised AHC income and AHC poverty measures use that result; household_income_decile uses BHC income.

Income deciles¶

household_income_decile ranks households by equivalised BHC income. household_income_decile_ahc ranks them by equiv_hbai_household_net_income_ahc. Both use household survey weight multiplied by household size, so the distribution counts people. Calculate the decile on the population to be ranked; a single-household calculation does not locate that household in the national income distribution.

The AHC decile follows the existing BHC ranking conventions: it resets negative values to zero for ranking, and equal values share the cumulative rank at the top of their group. A tied group can therefore span a decile boundary without being split. This ranking adjustment leaves AHC income and AHC poverty measures unchanged, including their negative values. It is a model ranking convention, not a claim to reproduce DWP’s published AHC decile groups exactly.

In FRS-based datasets, housing_service_charges contains the annualised property charges recorded in CHRGAMT1–CHRGAMT9: ground rent, chief rent, service charges, regular maintenance, caravan site rent, factoring charges, other regular charges and combined charges. CHRGAMT2, historically feu duty, is unused in the FRS 2024–25 dictionary. The combined-charge question is an alternative to recording individual amounts. Water and sewerage and rent are separate inputs; calculator users should supply each cost once, with service charges additional to the other housing-cost inputs. See the FRS 2024–25 question instructions, property charges section (pages 98–99), and its variable dictionaries.

Normalized squared poverty gaps¶

squared_poverty_gap_bhc and squared_poverty_gap_ahc are annual household, dimensionless components of the Foster–Greer–Thorbecke poverty-severity measure (FGT2). Each is the square of its existing nonnegative poverty_gap_bhc or poverty_gap_ahc, divided by the matching positive poverty_line_bhc or poverty_line_ahc before squaring:

For example, income at or above the line gives zero, income halfway to the line gives 0.25, and zero income gives one. Scaling income and its line by the same positive factor leaves the component unchanged. These are normalized components, not GBP-squared poverty gaps or sums.

The statistical definition follows the World Bank PIP methodology, section 4.1. The variables retain the UK HBAI basis described above: negative BHC income is reset to zero, while AHC income can be negative. The AHC component can therefore exceed one. PIP’s own negative-welfare preprocessing is not reproduced here, and these components are not an official DWP severity estimate.

For a person-based population index, map each household’s component to every person and take the existing survey-weighted mean, not a sum or a household-weighted mean. Given an already configured Microsimulation named sim:

component = sim.calculate("squared_poverty_gap_bhc", 2025, map_to="person")
fgt2 = component.mean(skipna=False)

For example, a one-person household with survey weight 2 and component 0.25, plus a three-person household with survey weight 1 and component 1, gives (2 * 0.25 + 3 * 1) / (2 + 3) = 0.7. A household-weighted mean would instead give 0.5. This tiny synthetic example is not a national estimate.

A zero or negative poverty line has an undefined normalized component, returned as NaN. The explicit skipna=False preserves that invalid-domain signal in a weighted mean rather than silently dropping people; alternatively validate that all included poverty lines are positive before aggregation. No new income, poverty-line, equivalence, survey-weight or dataset assumptions are introduced.

Nowcasting/forecasting¶