VAT grossing to receipts

vat and baseline_vat compute the statutory liability on each household’s recorded consumption (the standard rate on full_rate_vat_consumption plus the reduced rate on reduced_rate_vat_consumption) and divide it by two factors. This gross amount, plus VAT on households’ energy bills (see Energy bills are not grossed up), is calibrated to total VAT receipts. The private school component is then allocated to private_school_vat, as explained below, so the receipts comparison uses vat + private_school_vat:

• gov.simulation.vat.household_share_of_receipts (0.7): the share of VAT liabilities that falls on household final consumption. HMRC’s VAT gap estimates put household consumption at around 70% of the VAT total theoretical liability; the rest falls on government, charities, VAT-exempt businesses and new housing. This is a published quantity and does not depend on the dataset.

• gov.simulation.vat.survey_consumption_coverage (0.67): the share of household VAT liability that the dataset’s consumption captures. This depends on the dataset’s consumption imputation and must be re-derived when the default dataset changes.

The incidence assumption is that every pound of receipts, including VAT that government, charities and exempt businesses pay on their inputs, is passed on to households in proportion to their own VAT-liable spending.

These two factors replace gov.simulation.microdata_vat_coverage, a single undated 0.38 added in January 2023 against an older LCFS-based consumption imputation, with no derivation recorded. Its product with today’s datasets put 2024-25 VAT 24% above OBR receipts on Microcosm UK 2024-25 and 71% above on Enhanced FRS 2024-25 (policyengine-uk-data 1.56.16).

gov.simulation.microdata_vat_coverage is kept as a deprecated parameter so that existing reforms to it still work. Its value is now the product of the two factors (0.469). If a reform sets it to any other value, vat and baseline_vat use that value in place of the two factors (policyengine_uk/utils/vat.py); otherwise they use the two factors. New reforms should change the two factors instead.

Which datasets the factor applies to¶

The survey coverage of 0.67 is calibrated to one dataset: the certified Microcosm UK 2024-25 national release. It does not carry over to other datasets, because their consumption imputations capture a different share of household VAT. On Enhanced FRS 2024-25 it puts VAT 35% to 44% above receipts, depending on the release and year (see the tables below). Re-derive the coverage, with the calculation below, whenever the dataset it should match changes.

Derivation (October 2026)¶

Inputs¶

Model year 2024 is the 2024-25 fiscal year. All dataset totals are weighted sums from Microsimulation, computed with policyengine-uk as of #2187 (before energy bills were split out, see below) and policyengine-core 3.33.2.

Formula¶

pre-scaling VAT = 0.20 x sum(full_rate_vat_consumption)
                + 0.05 x sum(reduced_rate_vat_consumption)
product         = pre-scaling VAT / OBR VAT receipts      (same year)
survey coverage = product / household share (0.7)

Dividing each household’s statutory VAT by the product gives the gross amount, G; VAT on energy bills, E, is added to it without grossing (see Energy bills are not grossed up). At current law, total vat + private_school_vat is close to G + E but not equal to it: combined receipts are (1 - s) * sum(w * G) + sum(w * E) + sum(w * P0) (see the receipt-partition derivation below), so they differ from G + E by sum(w * P0) - s * sum(w * G). On the certified Enhanced FRS (policyengine-uk-data 1.58.1) that difference is -£5.5m to -£142.5m a year from 2025-26 to 2031-32, at most 0.06% of VAT (Aggregate impact run 40116746457).

Results¶

The parameter takes the Microcosm 2024-25 value, 0.67 (product 0.469), the latest outturn year.

With that product, the gross amount against receipts was as below, before energy bills were split out. On the certified Enhanced FRS (policyengine-uk-data 1.58.1), current-law vat + private_school_vat is within 0.06% of the receipt-calibrated G + E (see above); the other rows weren’t checked against that bound:

Bound¶

Total VAT depends only on the product, so the household share being a rounded “around 70%” changes how the product is split between the two factors, not the totals. On Microcosm the product is bounded by:

• the receipts route across 2024-25 to 2026-27: 0.459 to 0.471 (coverage 0.655 to 0.672);

• the ready reckoner, which does not use the level of receipts: one point on the standard rate raises £4.24bn before scaling in 2026-27 (1% of £423.66bn), so matching HMRC’s £8.8bn needs a product of 0.481 (coverage 0.688).

So on Microcosm the product lies between 0.459 and 0.481, and the coverage between 0.655 and 0.688 at a household share of 0.7. The value used, 0.469 (0.67), sits inside that range, and the totals it gives are within 2.2% of receipts from 2024-25 to 2026-27. The implied product moves by less than 3% over those years, so the factors are not dated by year.

Reproducing¶

The two datasets are in private Hugging Face repositories. Anyone with PolicyEngine access can rerun the calculation; anyone else can check the arithmetic from the published aggregates in the results table.

from huggingface_hub import hf_hub_download
from policyengine_uk import Microsimulation

path = hf_hub_download(
    "policyengine/populace-uk-private",
    "microcosm_uk_2024_25.h5",
    repo_type="dataset",
    revision="f9d1922cddab6b54a0dd37794a9bac74e3780c88",
)
sim = Microsimulation(dataset=path)
# OBR March 2026 EFO, table 3.8, cash-basis VAT receipts
receipts = {2024: 170.994e9, 2025: 180.169e9, 2026: 187.704e9}
for year, obr in receipts.items():
    p = sim.tax_benefit_system.parameters(f"{year}-01-01").gov.hmrc.vat
    full = sim.calculate("full_rate_vat_consumption", year).sum()
    reduced = sim.calculate("reduced_rate_vat_consumption", year).sum()
    raw = full * p.standard_rate + reduced * p.reduced_rate
    print(year, raw / 1e9, raw / obr, raw / obr / 0.7)

For Enhanced FRS, download enhanced_frs_2024_25.h5 from the model repository policyengine/policyengine-uk-data-private at the release tag (for example revision="1.58.0").

Energy bills are not grossed up¶

VAT on domestic electricity and gas is charged on each household’s own bills (domestic_energy_vat, PolicyEngine/policyengine-uk#2166), and the ONS domestic fuel and power share of spending comes out of the generic reduced-rate share. Those bills are calibrated to national energy use (NEED), and households bear VAT on them in full, so neither factor applies to them:

vat = (standard rate x full_rate_vat_consumption
       + reduced rate x reduced_rate_vat_consumption)
      / (survey_consumption_coverage x household_share_of_receipts)
      + domestic_energy_vat

The electricity and gas inputs are priced including 5% VAT by the data build (Microcosm UK at DESNZ Quarterly Energy Prices average prices paid; the legacy Enhanced FRS at Ofgem price cap unit rates), so domestic_energy_vat charges the statutory rates on the input divided by 1.05. The divisor is the fixed price-basis parameter gov.simulation.vat.energy_input_price_basis_rate, not the statutory reduced rate, so a reform to a VAT rate leaves the VAT-exclusive base unchanged.

Dividing energy VAT by the household share as well would put part of government, charity and exempt-business VAT on electricity bills, and a zero rate on domestic electricity would then cost 1/0.7 times the VAT households actually pay on it.

With energy split out, the coverage is derived against receipts net of energy VAT: coverage = pre-scaling non-energy VAT / (0.7 x (receipts - energy VAT)).

On the same inputs as the derivation above:

The pre-scaling non-energy VAT is the standard-rated part alone, since the generic reduced-rate base is empty once domestic fuel and power is taken out. The Microcosm 2024-25 value rounds to the same 0.67 as the derivation above, so the parameter is unchanged, and the bound above still holds (0.650 to 0.670 by receipts, 0.688 by the ready reckoner). With it, total vat on Microcosm is within 0.1% of 2024-25 receipts and 3.0% below in 2026-27; on Enhanced FRS it is 38% (1.56.16) or 44% (1.58.0) above 2024-25 receipts.

To reproduce, run the snippet above on this version and subtract sim.calculate("domestic_energy_vat", year).sum() from the receipts before dividing.

Private school VAT: splitting the existing receipts total¶

The OBR VAT total already includes VAT on private school fees. HMRC’s VAT-only costing (Autumn Budget 2024 Table 5.1, certified by the OBR) is £460m in 2024-25, £1,505m in 2025-26, £1,560m in 2026-27, £1,610m in 2027-28, £1,665m in 2028-29 and £1,725m in 2029-30. Adding a separate school VAT head to the gross amount above would count that receipt twice. The model instead takes the fees’ share of receipts out of the gross amount, keeping the survey coverage at 0.67.

For each household, let G be the grossed-up VAT on recorded consumption other than energy bills (the statutory liability divided by the two factors), E be domestic_energy_vat, s be gov.simulation.vat.private_school_share_of_receipts, P0 be baseline_private_school_vat (baseline policy with this simulation’s attendance, fee and VAT-basis assumptions) and P be private_school_vat:

vat          = G  * (1 - s) + E
baseline_vat = G0 * (1 - s) + E0
combined VAT = vat + P

The share comes out of G only. School fees are not energy bills, and E is not grossed up, so a reform to the VAT on energy bills changes vat by exactly the change in E.

s is the costing divided by OBR cash-basis VAT receipts for the same fiscal year (October 2026 EFO, table 4.8; 2025-26 is outturn):

Before the October 2026 EFO the shares used the March 2026 EFO’s receipts (table 3.8), 0.8353% in 2025-26 to 0.8094% in 2029-30. The coverage calibration above still uses the March 2026 EFO’s 2024-25 outturn, which the October 2026 EFO does not revise.

The 2029-30 share is held after it. Each value starts on 1 April, so a model year reads its fiscal year’s share. vat and baseline_vat both read it from the simulation’s own parameters, as baseline_private_school_vat reads its assumptions; the baseline parameter tree reads 1 January, before the fiscal year’s value takes effect.

Properties of the split:

• Because 0 <= s < 1 and E does not depend on s, the allocation never makes a household’s VAT negative where G and E are non-negative, and repealing the school charge cannot either.

• vat reads neither attendance nor fees. Restoring the school exemption sets P to zero and leaves vat unchanged, so receipts fall by the weighted school charge, sum(w * P0), with no second grossing factor. A contributed rate moves only P.

• A standard-rate change moves G * (1 - s) and P, each on its own base: recorded consumption and the fees. E moves only with the domestic electricity and reduced rates.

• With household weights w, current-law combined receipts are sum(w * G) - s * sum(w * G) + sum(w * E) + sum(w * P0). They equal the receipt-calibrated total sum(w * G) + sum(w * E) when the population’s school charge is the share s of its grossed-up VAT, and otherwise differ from it by sum(w * P0) - s * sum(w * G).

• s is a share of total receipts, but G is calibrated to receipts net of energy-bill VAT. Where G matches receipts net of energy-bill VAT exactly, s * sum(w * G) falls short of the costing by s times energy-bill VAT: on f9d1922c’s 2025-26 energy-bill VAT, 0.8368% of £2.01bn, about £17m (arithmetic on the energy table above, not a run).

The earlier design subtracted each household’s own school charge from its own gross VAT. Combined receipts then equalled G household by household, but a pupil with little recorded consumption had negative general VAT, which a repeal left in place. On the certified Enhanced FRS (policyengine-uk-data 1.58.1), before energy bills were split out, that made general VAT negative for 549 households with non-negative gross VAT in 2025-26 (306,750 weighted households, -£0.58bn), rising to 572 in 2030-31.

A share measured on each simulation’s own population, sum(w * P0) / sum(w * G), would preserve combined receipts exactly, and was considered. It makes every household’s general VAT depend on the imputed attendance of every other household, and attendance is imputed from net income. Raising any household’s income tax, National Insurance or council tax could then move every household’s VAT, by its gross VAT times the change in the share. The aggregate-impact counted-once check fails a head wherever such a response is one for one, as it did for vat in fewer than 10 households under the earlier design; spreading the response to every household makes that coincidence likelier. A household situation would also measure its own school charge against its own VAT. The official share keeps each household’s VAT a function of its own consumption.

Measured on the certified Enhanced FRS (Aggregate impact run 40116746457), the official share changes current-law combined receipts by -£0.14bn in 2025-26, -£0.13bn in 2026-27, -£0.10bn in 2027-28, -£0.08bn in 2028-29 and -£0.01bn in 2029-30, at most 0.06% of that dataset’s VAT. Two overstatements nearly offset there: VAT is 40% above OBR receipts (£252.5bn against £180.2bn in 2025-26), and the modelled school charge is £1.95bn, against HMRC’s £1.505bn, because attendance is imputed for 751,000 weighted pupils (policyengine-uk-data issue 568). The difference belongs to those two calibrations, not to the split.

The receipts check for the coverage factor is unchanged. Model year 2024 has no school charge and a zero share, so, using the rounded 2024-25 Microcosm inputs in the energy table above, 79.23 / (0.67 * 0.7) + 1.99 = £170.924bn, compared with OBR’s £170.994bn: about 0.04% below receipts. The existing differences from receipts, including Enhanced FRS’s larger overstatement, still require dataset-specific calibration. Aggregate impact CI compares the combined VAT report group against the PR’s base.

Model year 2024 represents 2024-25 but reads annual policy before the January 2025 commencement, so P0 and the share are both zero for that year. The £460m part-year receipt (0.27% of £170,994m) remains in general VAT; this change does not model its separate timing.