UK: source the extended-hours usage draw from DfE additional-hours PTEs (#1126)

changelog.d/1126-uk-extended-hours-usage-dfe.changed.md

@@ -0,0 +1 @@
+Source the UK `maximum_extended_childcare_hours_usage` draw from DfE: the mean moves from the frozen 15.019 to 31.141 (sd 4.972, clip [0, 30]), so a working-parent 3- or 4-year-old averages the 28.5 weekly hours implied by DfE's January 2025 additional-hours PTEs, lifting 2026-27 free early-years spending from £5.81bn to about £9.30bn against DfE's £9.9bn (#1126).

packages/microcosm-build/src/microcosm/build/uk/take_up_contract.json

@@ -520,19 +520,19 @@
       "output": "maximum_extended_childcare_hours_usage",
       "entity": "benunit",
       "distribution": "normal",
-      "mean": 15.019,
+      "mean": 31.141,
       "sd": 4.972,
       "lower": 0,
       "upper": 30,
       "source": {
-        "source": "FRS empirical fit, frozen by microcosm#834 adjudication",
-        "agency": "PolicyEngine",
-        "citation": "Incumbent offline childcare usage fit, clipped to [0, 30] hours. Frozen because it is underidentified without an independent extended-spending observation; replacing it needs evidence on hours actually used.",
-        "status": "frozen_by_adjudication",
-        "freeze": {
-          "decision": "Hold 15.019 / 4.972 / 0 / 30 fixed while fitting only four take-up rates",
-          "followup": "microcosm#834"
-        }
+        "source": "DfE 2026 to 2027 early years national funding formulae technical note (3- and 4-year-old additional-hours PTEs, January 2025 censuses) and DfE Education provision: children under 5 years of age, January 2025 (3- and 4-year-olds registered for the working parent entitlement)",
+        "agency": "DfE",
+        "status": "sourced_administrative_derived",
+        "url": "https://www.gov.uk/government/publications/early-years-funding-2026-to-2027/2026-to-2027-early-years-national-funding-formulae-technical-note",
+        "registrations_url": "https://explore-education-statistics.service.gov.uk/find-statistics/education-provision-children-under-5/2025",
+        "derivation": "15 + 15 * 341,988.09 additional-hours PTEs / 379,000 registered 3-4-year-olds = 28.535 mean weekly funded hours for a working-parent 3- or 4-year-old (one PTE is 15 hours a week for 38 weeks); mean solves E[clip(N(mean, 4.972), 0, 30)] = 28.535 with the sd and bounds held",
+        "citation": "Replaces the frozen 15.019 / 4.972 incumbent fit (microcosm#834), which #834 held pending evidence on hours actually used. The DfE additional-hours PTEs are that evidence: observed January 2025 census volumes, not a forecast. The variable caps a family's total weekly extended hours, so its mean is the total (universal plus additional) for a 3- or 4-year-old. Only the 3-4 cohort anchors the mean; DfE's under-2 and 2-year-old PTEs are partly forecast. The sd is not identified by any source and keeps the incumbent value. Re-mapping the 2024-25 national release's own draws through this distribution gives 2026-27 free-entitlement spending of 9.30bn against DfE's illustrative 9.9bn (5.81bn before); see microcosm#1126.",
+        "followup": "microcosm#1126"
       }
     }
   ]

packages/microcosm-build/tests/engine_free/uk/test_uk_take_up_contract.py

@@ -1,6 +1,8 @@
 """Tests split from packages/microcosm-build/tests/test_uk_take_up_contract.py."""
 
 # ruff: noqa: F403, F405
+import numpy as np
+
 from test_support.microcosm_build.uk_take_up_contract import *
 from test_support.paths import paths_for
 
@@ -191,3 +193,31 @@ def test_forbidden_source_dependency_strings_absent_from_uk_resources() -> None:
         text = files("microcosm.build.uk").joinpath(resource).read_text().lower()
         assert "policyengine_" + "uk_data" not in text
         assert "policyengine-" + "uk-data" not in text
+
+
+def test_extended_hours_usage_reproduces_dfe_additional_hours_ptes() -> None:
+    """The clipped draw's mean is the DfE-implied total weekly hours (#1126).
+
+    DfE funds 341,988.09 additional-hours PTEs (15 hours x 38 weeks each) for
+    the 379,000 3- and 4-year-olds registered for the working parent
+    entitlement in January 2025, on top of the universal 15 hours.
+    """
+
+    from microcosm.build.stochastic_assignment import clipped_normal_from_uniforms
+
+    contract = load_uk_take_up_contract()
+    entry = contract.continuous_entry("maximum_extended_childcare_hours_usage")
+    assert entry["source"]["status"] == "sourced_administrative_derived"
+    assert (entry["lower"], entry["upper"]) == (0, 30)
+
+    n = 200_000
+    uniforms = (np.arange(n) + 0.5) / n
+    draws = clipped_normal_from_uniforms(
+        uniforms,
+        mean=float(entry["mean"]),
+        sd=float(entry["sd"]),
+        lower=float(entry["lower"]),
+        upper=float(entry["upper"]),
+    )
+    dfe_mean_hours = 15 + 15 * 341_988.09 / 379_000
+    assert draws.mean() == pytest.approx(dfe_mean_hours, abs=0.01)