Correct the two-child limit full roll-out page for the modelled exceptions and the FYE 2011 line

changelog.d/2708.fixed.md

@@ -0,0 +1 @@
+Corrected the two-child limit full roll-out page: it now describes the modelled exceptions to the limit and uses the FYE 2011 absolute poverty variables instead of overriding the thresholds.

docs/book/validation/two-child-limit-full-rollout.md

@@ -26,44 +26,73 @@ any child's birth. The same date also preserves the higher Universal Credit
 child element for a first child born before 6 April 2017, so full roll-out
 removes that too. IFS full roll-out analysis likewise removes the Child Tax
 Credit family premium, its legacy equivalent ([IFS, 2024][ifs-2024], Table 6.5).
+Tax credits ended on 5 April 2025 (`gov.dwp.tax_credits.active` is false from
+6 April 2025), so in 2025-26 Child Tax Credit is zero and only the Universal
+Credit settings change the results.
 
-**Take-up.** Universal Credit claiming comes from `would_claim_uc`, set in the
-data, and does not respond to the reform. For full take-up, set it to true for
-every benefit unit with `set_input` before calculating anything.
+**Take-up.** Universal Credit claiming (`claims_universal_credit`) comes from
+`would_claim_uc` and, for a family moved off legacy benefits,
+`would_claim_uc_at_legacy_closure`. Both are set in the data, and neither
+responds to the reform. For full take-up, set `would_claim_uc` to true for
+every benefit unit with `set_input` before calculating anything that depends
+on it; every benefit unit then claims.
 
 **Poverty measure.** The poverty flags are household variables. Count children
 by mapping them to people and multiplying by `is_hbai_dependent_child`, the
 HBAI definition of a child:
 
 | Variable | Measure |
 |---|---|
-| `in_poverty_ahc` | Absolute low income, after housing costs |
-| `in_poverty_bhc` | Absolute low income, before housing costs |
+| `in_poverty_ahc` | Absolute low income on HBAI's current FYE 2025 line, after housing costs |
+| `in_poverty_bhc` | The same, before housing costs |
 | `in_poverty` | Same as `in_poverty_bhc` (via the poverty gap) |
+| `in_absolute_poverty_fye2011_ahc` | Absolute low income on the FYE 2011 line, after housing costs |
+| `in_absolute_poverty_fye2011_bhc` | The same, before housing costs |
 | `in_relative_poverty_ahc` | Relative low income (60% of the contemporary median), after housing costs |
 | `in_relative_poverty_bhc` | Relative low income, before housing costs |
 
-The absolute line is 60% of the FYE 2025 median held constant in real terms,
-the reference year HBAI adopted in March 2026. Estimates published before then,
+HBAI's absolute line is 60% of a reference year's median held constant in real
+terms. Since March 2026 the reference year is FYE 2025, applied from FYE 2022,
+and `in_poverty_ahc` and `_bhc` follow it. Estimates published before then,
 including the IFS comment and DWP's Budget 2025 poverty impact notes, use 60% of
-the FYE 2011 median. To use that line, override
-`household.poverty.absolute_poverty_threshold_bhc` and `_ahc` for the year, as
-below. The snippet approximates the FYE 2011-based line by its FYE 2021 value
-in the parameter file (£305.70 a week BHC, £261.92 AHC, for a couple without
-children), uprated by the model's CPI index; HBAI uprates by its own CPI
-variants, so this is close but not exact.
-
-**Exceptions.** The model does not apply the statutory exceptions to the limit
-(multiple births, adoption, non-parental caring arrangements and non-consensual
-conception; [Universal Credit Regulations 2013, Schedule 12][sch12]). DWP
-counted 26,300 households with an exception in April 2025, out of about
-470,000 affected ([UC two-child limit statistics, April 2025][dwp-2cl]).
+the FYE 2011 median. From policyengine-uk 2.155.0,
+`in_absolute_poverty_fye2011_ahc` and `_bhc` compare equivalised income with
+that line in every year (`poverty_threshold_fye2011_ahc` and `_bhc`, from the
+parameters `household.poverty.absolute_poverty_threshold_fye2011_ahc` and
+`_bhc`). The parameters hold HBAI's published values up to FYE 2025 and uprate
+later years by headline OBR CPI, where HBAI uses its own CPI variants, so the
+2025-26 line is close to HBAI's but not exact.
+
+**Exceptions.** From policyengine-uk 2.161.0 the model applies the statutory
+exceptions to the limit: multiple births, adoption, non-parental caring
+arrangements, non-consensual conception and the continuation of an earlier
+exception ([Universal Credit Regulations 2013, regulation 24A][reg24a] and
+[Schedule 12][sch12]; [Child Tax Credit Regulations 2002, regulations 9 to
+14][ctc-reg9]). Each is a person-level input that defaults to false:
+`child_limit_multiple_birth_exception`, `child_limit_adoption_exception`,
+`child_limit_non_parental_caring_exception`,
+`child_limit_non_consensual_conception_exception` and
+`child_limit_continuation_exception`. In Universal Credit, a third or later
+child with the multiple births, non-consensual conception or continuation
+exception gets the child element (`uc_child_limit_exception`). An adopted child
+or one in non-parental care gets it whatever their place, and is left out of
+the order of children that the limit counts (`uc_child_limit_disregarded`).
+Child Tax Credit has its own equivalents (`is_CTC_child_limit_exception`).
+
+The Microcosm release does not supply these inputs. The FRS does not record the
+exceptions, so Microcosm leaves all five at their default
+([`policyengine_uk_concepts.py`][microcosm-defaults]), and no child in the run
+below has one. A child who would have an exception is then subject to the
+limit in the baseline, so for those families the run overstates the loss from
+the limit and the gain from removing it. DWP counted 26,300 households with an
+exception in April 2025, out of about 470,000 affected ([UC two-child limit
+statistics, April 2025][dwp-2cl]).
 
 ## Code
 
 ```python
 import numpy as np
-from policyengine_uk import CountryTaxBenefitSystem, Microsimulation
+from policyengine_uk import Microsimulation
 
 # Local path to the Microcosm UK 2024-25 national release file.
 DATASET = "microcosm_uk_2024_25.h5"
@@ -76,105 +105,159 @@ CTC = "gov.dwp.tax_credits.child_tax_credit.limit"
 # removes the higher first-child element, which the same date preserves.
 FULL_ROLLOUT = {f"{p}.born_before": {WINDOW: 10000101} for p in (UC, CTC)}
 
-# Optional: the FYE 2011-based absolute line used by HBAI before March 2026,
-# approximated as its FYE 2021 value uprated by the model's CPI index.
-cpi = CountryTaxBenefitSystem().parameters.gov.economic_assumptions.indices.obr
-uprate = cpi.consumer_price_index(f"{YEAR}-01-01") / cpi.consumer_price_index(
-    "2020-01-01"
-)
-FYE2011_LINE = {
-    "household.poverty.absolute_poverty_threshold_bhc": {WINDOW: 305.7 * uprate},
-    "household.poverty.absolute_poverty_threshold_ahc": {WINDOW: 261.92 * uprate},
+# Absolute low income after and before housing costs, on HBAI's current
+# FYE 2025 line and on the FYE 2011 line used before March 2026.
+LINES = {
+    "FYE 2025 line": ["in_poverty_ahc", "in_poverty_bhc"],
+    "FYE 2011 line": [
+        "in_absolute_poverty_fye2011_ahc",
+        "in_absolute_poverty_fye2011_bhc",
+    ],
 }
 
 
 def child_limit(n):
     return {f"{p}.child_count": {WINDOW: n} for p in (UC, CTC)}
 
 
-def run(extra, full_take_up=False):
-    sim = Microsimulation(dataset=DATASET, reform=extra or None)
+def run(reform, full_take_up=False):
+    sim = Microsimulation(dataset=DATASET, reform=reform or None)
     if full_take_up:
         n = len(sim.calculate("benunit_weight", YEAR))
         sim.set_input("would_claim_uc", YEAR, np.ones(n, dtype=bool))
     child = sim.calculate("is_hbai_dependent_child", YEAR)
-    benefits = (
-        sim.calculate("universal_credit", YEAR).sum()
-        + sim.calculate("child_tax_credit", YEAR).sum()
+    # Universal Credit and Child Tax Credit for each benefit unit, and the
+    # same amounts against each of its members.
+    benefits, per_person = (
+        sim.calculate("universal_credit", YEAR, map_to=entity)
+        + sim.calculate("child_tax_credit", YEAR, map_to=entity)
+        for entity in (None, "person")
     )
     poor = {
         m: (sim.calculate(m, YEAR, map_to="person") * child).sum()
-        for m in ["in_poverty_ahc", "in_poverty_bhc"]
+        for measures in LINES.values()
+        for m in measures
     }
-    return benefits, poor
+    return benefits, per_person, child, poor
 
 
 def compare(setting, full_take_up=False):
-    base_cost, base_poor = run(setting, full_take_up)
+    base, base_per_person, child, base_poor = run(setting, full_take_up)
     for name, n in [("abolish", np.inf), ("three-child limit", 3)]:
-        cost, poor = run({**setting, **child_limit(n)}, full_take_up)
-        lifted = {m: (base_poor[m] - poor[m]) / 1e3 for m in poor}
+        reformed, per_person, _, poor = run({**setting, **child_limit(n)}, full_take_up)
+        cost = (reformed.sum() - base.sum()) / 1e9
+        # Benefit units gaining more than £1 a year, and their children.
+        units = (reformed > base + 1).sum() / 1e3
+        children = ((per_person > base_per_person + 1) * child).sum() / 1e6
         print(
-            f"{name}: cost £{(cost - base_cost) / 1e9:.2f}bn, children lifted "
-            f"(thousands) AHC {lifted['in_poverty_ahc']:.0f}, "
-            f"BHC {lifted['in_poverty_bhc']:.0f}"
+            f"{name}: cost £{cost:.2f}bn; {units:.0f}k benefit units gain, "
+            f"with {children:.2f}m children"
         )
+        for line, (ahc, bhc) in LINES.items():
+            lifted = [(base_poor[m] - poor[m]) / 1e3 for m in (ahc, bhc)]
+            print(
+                f"  children lifted (thousands), {line}: "
+                f"AHC {lifted[0]:.0f}, BHC {lifted[1]:.0f}"
+            )
 
 
 compare({})  # current law: pre-April 2017 children protected
 compare(FULL_ROLLOUT)
 compare(FULL_ROLLOUT, full_take_up=True)
-compare({**FULL_ROLLOUT, **FYE2011_LINE}, full_take_up=True)
 ```
 
 Reform keys use the `YYYY-MM-DD.YYYY-MM-DD` form, which the dictionary and
 `Reform.from_dict` routes read the same way.
 
 ## Results, 2025-26
 
-Run on 23 October 2026 with policyengine-uk 2.147.2 and the Microcosm UK
-2024-25 national release `microcosm-uk-2024-25-national-20261023T075039Z-a133f37a`
-(SHA-256 `64f83900…`). Cost is the change in Universal Credit and Child Tax
-Credit spending. Children lifted are children out of absolute low income.
+These results come from running the snippet above on 28 October 2026 with
+policyengine-uk 2.162.14 and the Microcosm UK 2024-25 national release
+`microcosm-uk-2024-25-national-20261028T061416Z-3c0d11b6` (SHA-256
+`a5ae72ae…`), which was built with that version. Only the `DATASET` path was
+changed. The run is nine microsimulations: a baseline and two reforms for each
+setting. policyengine.py 6.11.1 certifies policyengine-uk 2.151.0, which has
+neither the exception rules nor the FYE 2011 line variables, so this pair is
+not a certified one. Cost is the change in Universal Credit and Child Tax
+Credit spending. A benefit unit gains if those two rise by more than £1 a year.
+
+| Setting | Abolish: cost | Abolish: benefit units gaining (their children) | Three-child limit: cost | Three-child limit: benefit units gaining (their children) |
+|---|---:|---:|---:|---:|
+| Current law (protection for pre-April 2017 children) | £1.91bn | 459k (1.64m) | £1.15bn | 351k (1.13m) |
+| Full roll-out | £3.07bn | 639k (2.21m) | £2.13bn | 632k (2.17m) |
+| Full roll-out, full UC take-up | £3.56bn | 767k (2.62m) | £2.52bn | 757k (2.57m) |
+| IFS, fully rolled out | about £3.6bn | over 800,000 households | about £2.6bn | — |
+
+Children lifted out of absolute low income, in thousands, after / before
+housing costs:
 
-| Setting | Abolish: cost | Abolish: children lifted, AHC / BHC | Three-child limit: cost | Three-child limit: children lifted, AHC / BHC |
+| Setting | Abolish: FYE 2025 line | Abolish: FYE 2011 line | Three-child limit: FYE 2025 line | Three-child limit: FYE 2011 line |
 |---|---:|---:|---:|---:|
-| Current law (protection for pre-April 2017 children) | £1.94bn | 217k / 268k | £1.17bn | 137k / 159k |
-| Full roll-out | £3.35bn | 439k / 445k | £2.32bn | 289k / 314k |
-| Full roll-out, full UC take-up | £3.58bn | 475k / 484k | £2.51bn | 312k / 374k |
-| Full roll-out, full UC take-up, FYE 2011-based line | £3.58bn | 455k / 353k | £2.51bn | 293k / 196k |
-| IFS, fully rolled out (AHC, FYE 2011-based line) | about £3.6bn | 630,000 | about £2.6bn | 420,000 |
+| Current law (protection for pre-April 2017 children) | 209 / 299 | 229 / 235 | 132 / 219 | 194 / 97 |
+| Full roll-out | 392 / 417 | 287 / 339 | 267 / 313 | 186 / 178 |
+| Full roll-out, full UC take-up | 450 / 496 | 366 / 361 | 294 / 399 | 240 / 184 |
+| IFS, fully rolled out | | 630 (after housing costs) | | 420 (after housing costs) |
 
-Under current law, 467,000 benefit units with 1.64 million children gain from
+Under current law, 459,000 benefit units with 1.64 million children gain from
 abolition in 2025-26. DWP's April 2025 statistics count 453,600 households not
 receiving the child element for at least one child, with 1.61 million children.
 
+Each children-lifted figure comes from between 59 and 196 household records,
+out of 21,086 households with children in the release, and no household moves
+into absolute low income in any comparison. The ten records that contribute
+most make up between 29% and 69% of each figure, and one record contributes up
+to 57,000 children, so two figures can differ by that much because of one
+household.
+
 ## Why the results differ from the IFS's
 
-- **Roll-out.** Running current law in 2025-26 gives about a third of the IFS
-  headcount, because most children in large families are still protected.
-  Full roll-out is the largest single setting.
-- **Take-up.** With full roll-out and full take-up, the cost (£3.58bn) and the
-  number of families gaining (778,000 benefit units, against the IFS's "over
-  800,000 households") match the IFS closely.
-- **The remaining gap.** Children lifted stay about a quarter to 30% short
-  of the IFS figures. These checks do not isolate the cause. Plausible
-  contributors, none of them ruled out:
-  - *Family size in the data.* At FYE 2025 the Microcosm release has about 10%
-    fewer children in families with three or more children than HBAI (4.20
-    million against 4.64 million, HBAI table 4.5db), and about 21% fewer of
-    those children in relative low income after housing costs (1.64 million
+- **Roll-out.** Under current law, abolition costs £1.91bn and lifts 229,000
+  children on the IFS's line (FYE 2011, after housing costs), just over a
+  third of its 630,000. Full roll-out raises the cost to £3.07bn and the
+  benefit units gaining from 459,000 to 639,000. For abolition it raises
+  children lifted on the FYE 2011 line after housing costs from 229,000 to
+  287,000, less than on the FYE 2025 line (209,000 to 392,000). For the
+  three-child limit it lowers them on the FYE 2011 line (194,000 to 186,000).
+  Full roll-out also removes the higher first-child element, which neither
+  reform restores, so a family that a reform lifts out of low income under
+  current law may stay in it at full roll-out. On that line the largest single
+  record contributes 57,000 children to each current-law figure, but at most
+  17,000 to a full roll-out one.
+- **Take-up.** With full roll-out and full take-up, the cost (£3.56bn to
+  abolish, £2.52bn for a three-child limit) is close to the IFS's (about
+  £3.6bn and £2.6bn), and 767,000 benefit units gain from abolition, against
+  the IFS's "over 800,000 households".
+- **The remaining gap.** On the IFS's line, children lifted are about 42% short
+  of the IFS figures: 366,000 against 630,000 for abolition, and 240,000
+  against 420,000 for a three-child limit. On the higher FYE 2025 line they are
+  about 30% short (450,000 and 294,000). These checks do not isolate the cause.
+  Plausible contributors, none of them ruled out:
+  - *Family size in the data.* At FYE 2025 the Microcosm release has about 13%
+    fewer children in families with three or more children than HBAI (4.04
+    million against 4.64 million, HBAI table 4.5db), and about 20% fewer of
+    those children in relative low income after housing costs (1.66 million
     against 2.07 million). See [PolicyEngine/microcosm#1371](https://github.com/PolicyEngine/microcosm/issues/1371).
     A shortfall in relative low income does not show how many children cross
     an absolute line after the reform, so this alone cannot size the gap.
-  - *The poverty line.* The snippet approximates the FYE 2011-based line (see
-    above), so it is not exactly the IFS line.
-  - *Exceptions.* The snippet does not apply the statutory exceptions.
+  - *The poverty line.* The model uprates the FYE 2011 line beyond FYE 2025 by
+    headline OBR CPI (see above), which may not match the IFS's uprating.
   - *Take-up.* Full take-up here sets `would_claim_uc` to true for everyone,
     which is not the IFS adjustment to reported take-up ([IFS, 2024][ifs-2024],
     Appendix 6B), and this page has not matched that adjustment.
-
-  Attributing the gap to any one of these would need a controlled comparison.
+  - *Sample size.* The two full take-up figures on the IFS's line come from 185
+    and 137 household records, and the ten that contribute most make up 29% and
+    38% of them.
+  - *Exceptions, for the three-child limit.* No child in the release has an
+    exception, and this can move the three-child figures either way. A family
+    with three children whose third child has one would already get that
+    child's element, so the run overstates its gain. A family with four
+    children whose fourth child has one would have one more child element
+    before and after the reform than the run gives it, so the run can count it
+    as lifted out of low income when it would not be, or the reverse.
+
+  For abolition the missing exceptions do not explain the gap: if anything they
+  raise the abolition figures here. Attributing the gap to any one of these
+  contributors would need a controlled comparison.
 - **Data year and method.** The IFS used TAXBEN on FRS 2022-23 and 2023-24,
   additionally reweighting 2022-23 by number of children, and FRS data as
   published before HBAI's March 2026 administrative-data linking. PolicyEngine
@@ -187,10 +270,13 @@ receiving the child element for at least one child, with 1.61 million children.
 - DWP, [Universal Credit claimants: statistics on the two-child limit policy, April 2025][dwp-2cl].
 - DWP, [Households Below Average Income FYE 2025, background information and methodology][hbai-meth], section 2.3 (absolute reference year).
 - [Universal Credit Regulations 2013, regulation 24A][reg24a] and [Schedule 12][sch12].
+- [Child Tax Credit Regulations 2002, regulations 9 to 14][ctc-reg9].
 
 [ifs-2025]: https://ifs.org.uk/articles/options-reforming-two-child-limit
 [ifs-2024]: https://ifs.org.uk/publications/child-poverty-trends-and-policy-options
 [dwp-2cl]: https://www.gov.uk/government/statistics/universal-credit-claimants-statistics-on-the-two-child-limit-policy-april-2025/universal-credit-claimants-statistics-on-the-two-child-limit-policy-april-2025
 [hbai-meth]: https://www.gov.uk/government/statistics/households-below-average-income-for-financial-years-ending-1995-to-2025/households-below-average-income-background-information-and-methodology-report-fye-2025#update-to-the-absolute-low-income-reference-year
 [reg24a]: https://www.legislation.gov.uk/uksi/2013/376/regulation/24A/2025-04-06
 [sch12]: https://www.legislation.gov.uk/uksi/2013/376/schedule/12/2025-04-06
+[ctc-reg9]: https://www.legislation.gov.uk/uksi/2002/2007/regulation/9/2025-04-06
+[microcosm-defaults]: https://github.com/PolicyEngine/microcosm/blob/daaf543023b8d3d327798c94a4028bd917a7bd73/packages/microcosm-frame/src/microcosm/frame/adapters/policyengine_uk_concepts.py#L232-L243