Charge VAT on private school fees at current law

changelog.d/2318.fixed.md

@@ -0,0 +1,2 @@
+- Charge VAT at the standard rate on private school fees from 1 January 2025 (Finance Act 2025 ss.47 and 49), through the new `gov.hmrc.vat.private_school_fees_exempt` parameter. The contributed rate `gov.contrib.labour.private_school_vat` now raises the rate rather than adding to it, so reforms that set it to 20% score nothing from 2025. Household taxes include private school VAT as a change from baseline (`private_school_vat_change`), as they do VAT; government tax revenue includes the level.
+- Allocate school-fee VAT out of receipt-calibrated general VAT before counting it separately: general VAT is gross VAT less private school fees' official share of VAT receipts (new parameter `gov.simulation.vat.private_school_share_of_receipts`, HMRC's OBR-certified costing over OBR VAT receipts). No household's general VAT is made negative, school-specific reforms move only private school VAT, and standard-rate reforms move each head once.

docs/engineering/vat-coverage.md

@@ -3,7 +3,11 @@
 `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, so that total VAT matches receipts:
+factors. This gross amount, plus VAT on households' energy bills (see
+[Energy bills are not grossed up](#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
@@ -68,8 +72,17 @@ product         = pre-scaling VAT / OBR VAT receipts      (same year)
 survey coverage = product / household share (0.7)
 ```
 
-`vat` divides each household's statutory VAT by the product, so total `vat`
-equals receipts when the product matches the dataset.
+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](#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](https://github.com/PolicyEngine/policyengine-uk/actions/runs/40116746457)).
 
 ### Results
 
@@ -88,7 +101,11 @@ equals receipts when the product matches the dataset.
 The parameter takes the Microcosm 2024-25 value, 0.67 (product 0.469), the
 latest outturn year.
 
-With that product, total `vat` against receipts is:
+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:
 
 | Dataset | 2024-25 | 2025-26 | 2026-27 |
 |---|---|---|---|
@@ -148,6 +165,7 @@ For Enhanced FRS, download `enhanced_frs_2024_25.h5` from the model repository
 
 ## 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.
@@ -197,3 +215,116 @@ 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](https://www.gov.uk/government/publications/vat-on-private-school-fees/applying-vat-to-private-school-fees)
+(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`:
+
+```text
+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 (March 2026 EFO, table 3.8):
+
+| Fiscal year | School-fee VAT (£m) | VAT receipts (£m) | Share |
+|---|---:|---:|---:|
+| 2025-26 | 1,505 | 180,169 | 0.8353% |
+| 2026-27 | 1,560 | 187,704 | 0.8311% |
+| 2027-28 | 1,610 | 195,923 | 0.8218% |
+| 2028-29 | 1,665 | 204,591 | 0.8138% |
+| 2029-30 | 1,725 | 213,118 | 0.8094% |
+
+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, 0.8353% 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](https://github.com/PolicyEngine/policyengine-uk/actions/runs/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.

policyengine_uk/data/fiscal_partition.yaml

@@ -60,7 +60,8 @@
 #     measure for. With the heads' obr_line values they account for every
 #     tax row of the table.
 #   overlap_guards[]: the places double counting could occur, and the
-#     property the tests check for each. The aggregate-impact report also
+#     property the tests check for each. overlapping_base records a receipt
+#     allocation between heads sharing an imputed base. The report also
 #     checks the geographic_exclusivity guards on the certified dataset.
 #   spending_heads[]: as tax_heads, without obr_line, obr_table_3_1 and
 #     payer, plus caseload (default true): whether reports count recipients.
@@ -119,9 +120,9 @@ totals:
     label: Taxes borne by the household
     description: >-
       Taxes subtracted from household net income. VAT and employer NI enter
-      only as reform-induced changes (vat_change and the employer NI response
-      incidence), because baseline VAT and employer NI are not deducted from
-      the incomes the model starts from.
+      only as reform-induced changes (vat_change, private_school_vat_change
+      and the employer NI response incidence), because baseline VAT and
+      employer NI are not deducted from the incomes the model starts from.
     dropped_when:
       gov.contrib.abolish_council_tax:
         - council_tax
@@ -237,7 +238,7 @@ tax_heads:
 
   # Consumption
   - id: vat
-    label: VAT
+    label: VAT excluding private school fees
     variable: vat
     entity: household
     obr_line: Value added tax
@@ -247,12 +248,16 @@ tax_heads:
     totals: [gov_tax]
     sign: nonnegative
     data_note: >-
-      Negative for 76 households on policyengine-uk-data 1.58.0
-      (enhanced_frs_2024_25) in every year from 2025 to 2030, -£72m weighted
-      in 2026: full_rate_vat_consumption is negative there because the
-      dataset's consumption (44 households) or full_rate_vat_expenditure_rate
-      (32 households) is negative. policyengine-uk-data issue 565. Measured
-      2026-10-11.
+      Grossed-up VAT on recorded consumption less private school fees'
+      official share of VAT receipts, which the separate school head counts,
+      plus VAT on energy bills. The share is below one, so the allocation
+      keeps the sign of the grossed-up amount. Negative for 76 households on
+      policyengine-uk-data 1.58.1 (enhanced_frs_2024_25) in every year from
+      2025 to 2031, -£55.7m weighted in 2026 (Aggregate impact run
+      40116746457, 2026-10-24). On 1.58.0 (measured 2026-10-11) it was also
+      76: full_rate_vat_consumption is negative there because the dataset's
+      consumption (44 households) or full_rate_vat_expenditure_rate (32
+      households) is negative. policyengine-uk-data issue 565.
   - id: vat_change
     label: Change in VAT from its baseline
     variable: vat_change
@@ -268,6 +273,11 @@ tax_heads:
       - head: vat
         route: vat_change adds vat and subtracts baseline_vat
         why: a change measure built from the level; the two are never in the same total
+  # Standard-rated from 1 January 2025: Finance Act 2025 s.47 inserts VATA
+  # 1994 Sch 9 Part 3, taking private school education, vocational training
+  # and closely related board and lodging out of the Group 6 exemption, for
+  # supplies on or after that date (s.49). Before it the head is zero unless
+  # the contributed reform rate is set.
   - id: private_school_vat
     label: VAT on private school fees
     variable: private_school_vat
@@ -276,12 +286,8 @@ tax_heads:
     obr_table_3_1: Value added tax
     report_group: vat
     payer: household
-    totals: [gov_tax, household_tax]
+    totals: [gov_tax]
     sign: nonnegative
-    zero_at_baseline: expected
-    zero_at_baseline_note: >-
-      gov.contrib.labour.private_school_vat is 0 at current law in this
-      model, so the head is reform-only here.
     reads:
       - head: income_tax
         route: private_school_vat -> attends_private_school -> income_tax
@@ -292,6 +298,30 @@ tax_heads:
       - head: council_tax
         route: private_school_vat -> attends_private_school -> household_benefits -> council_tax_benefit -> council_tax
         why: as above
+  - id: private_school_vat_change
+    label: Change in private school VAT from its baseline
+    variable: private_school_vat_change
+    entity: household
+    obr_line: Value added tax
+    obr_table_3_1: Value added tax
+    report_group: vat
+    payer: household
+    totals: [household_tax]
+    sign: any
+    zero_at_baseline: expected
+    reads:
+      - head: private_school_vat
+        route: private_school_vat_change adds private_school_vat and subtracts baseline_private_school_vat
+        why: a change measure built from the level; the two are never in the same total
+      - head: income_tax
+        route: private_school_vat_change -> private_school_vat -> attends_private_school -> income_tax
+        why: attendance is imputed from income; it decides who attends, not how much tax is counted
+      - head: nics_individual
+        route: private_school_vat_change -> private_school_vat -> attends_private_school -> (net income) -> national_insurance
+        why: as above
+      - head: council_tax
+        route: private_school_vat_change -> private_school_vat -> attends_private_school -> household_benefits -> council_tax_benefit -> council_tax
+        why: as above
   - id: fuel_duty
     label: Fuel duties
     variable: fuel_duty
@@ -645,6 +675,7 @@ exclusions:
   - {variable: student_loan_repayment, kind: component, head: student_loan_repayments}
   # Consumption
   - {variable: baseline_vat, kind: baseline_measure, head: vat_change, note: "Subtracted inside vat_change."}
+  - {variable: baseline_private_school_vat, kind: baseline_measure, head: private_school_vat_change, note: "Subtracted inside private_school_vat_change."}
   - {variable: beer_duty, kind: component, head: alcohol_duty}
   - {variable: cider_duty, kind: component, head: alcohol_duty}
   - {variable: sparkling_cider_duty, kind: component, head: alcohol_duty}
@@ -697,14 +728,30 @@ overlap_guards:
     property: >-
       Each allocates a different receipt by shareholding; none reads another.
       corporate_tax_incidence sums two of them and is excluded.
+  - id: private_school_vat_level_and_change
+    kind: level_and_change
+    heads: [private_school_vat, private_school_vat_change]
+    property: >-
+      Never in the same total: the level is in gov_tax and the change in
+      household_tax, as for vat and vat_change. private_school_vat_change
+      reads private_school_vat.
   - id: private_school_vat_and_vat
-    kind: possible_base_overlap
+    kind: overlapping_base
     heads: [vat, private_school_vat]
     property: >-
-      vat applies to imputed consumption; if that consumption includes school
-      fees, turning on private_school_vat would tax them twice. The head is
-      zero at baseline, so baseline totals are unaffected; check the
-      consumption imputation before costing a reform that sets it.
+      Grossed-up consumption VAT is fitted to receipts net of energy-bill
+      VAT, which include school-fee VAT. vat keeps gross VAT less the fees'
+      official share of receipts
+      (gov.simulation.vat.private_school_share_of_receipts), plus VAT on
+      energy bills, which bears no share; then gov_tax adds
+      private_school_vat. vat reads neither attendance nor fees, so
+      school-specific exemption and contributed rate reforms move only the
+      school head, and a standard-rate change moves each head on its own
+      base. At current law combined receipts change by the weighted school
+      charge less the share of weighted gross VAT. Both baseline measures
+      hold this simulation's fee, attendance and share assumptions fixed.
+      See test_private_school_vat_receipts.py and
+      docs/engineering/vat-coverage.md.
   - id: council_tax_gross_and_reduction
     kind: gross_and_net
     heads: [council_tax]
@@ -729,11 +776,15 @@ overlap_guards:
       here as well.
   - id: eligibility_reads
     kind: read_not_inclusion
-    heads: [tv_licence, private_school_vat]
+    heads: [tv_licence, private_school_vat, private_school_vat_change]
     property: >-
       These heads reach other heads of the same total only through
       eligibility or imputation (see each head's reads). Raising the other
       head by a small amount leaves them unchanged on the test population.
+      For the private school heads that check is vacuous: attendance is
+      imputed only on a dataset (on a situation it is zero or an input), so
+      a tax change moves them only through re-imputed attendance on the
+      microdata (policyengine-uk-data issue 568).
 
 uncovered_receipts:
   # Rows of Table A.5 with no household measure in the model.

policyengine_uk/parameters/gov/contrib/labour/private_school_vat.yaml

@@ -1,6 +1,7 @@
-description: VAT rate applied to private schools.
+description: Contributed reform rate of VAT on private school fees. The fees bear VAT at the higher of this rate and the statutory rate (the standard rate from 1 January 2025, when the exemption ended), so the reform can raise the rate but never charges VAT on the fees twice.
 values:
   2000-01-01: 0
 metadata:
   unit: /1
-  label: Private school VAT rate
+  period: year
+  label: Private school VAT rate (reform)