Add postgraduate loan interest rate variable and interest rate tests

.beads/issues.jsonl

@@ -1,3 +1,6 @@
 {"id":"policyengine-uk-5qy","title":"Update student loan validation notebook with deeper analysis","description":"","status":"closed","priority":2,"issue_type":"task","created_at":"2025-11-29T21:01:35.49966-05:00","updated_at":"2025-11-29T21:02:51.469593-05:00","closed_at":"2025-11-29T21:02:51.469593-05:00"}
 {"id":"policyengine-uk-75j","title":"Add student loan calibration targets to policyengine-uk-data","description":"Add student loan repayment and balance calibration targets to policyengine-uk-data loss function.\n\n## Proposed Calibration Targets (from SLC 2024-25 statistics)\n\n### Total Repayments by Country\n| Country | Repayments | Source |\n|---------|------------|--------|\n| England (HE) | £5.0bn | SLC 2024-25 |\n| Scotland | £203m | SLC 2024-25 |\n| Wales | £229m | SLC 2024-25 |\n| Northern Ireland | £182m | SLC 2024-25 |\n| **UK Total** | **~£5.6bn** | |\n\n### Repayments by Plan Type (England)\n| Plan | Amount | Share |\n|------|--------|-------|\n| Plan 1 | £1.9bn | 37% |\n| Plan 2 | £2.8bn | 55% |\n| Postgraduate | £0.3bn | 7% |\n| Plan 5 | £41m | 0.8% |\n\n### Number of Borrowers Repaying (England)\n- 3.0m via HMRC\n- 187k scheduled direct\n- 147k voluntary direct\n\n### Outstanding Balances\n- UK Total: £294bn (March 2025)\n\n## Implementation Notes\n1. Add targets to `loss.py` in policyengine-uk-data\n2. May need to adjust for timing (FRS year vs SLC reporting year)\n3. Consider whether to calibrate on modelled (`student_loan_repayment`) or reported (`student_loan_repayments`)\n\n## Sources\n- https://www.gov.uk/government/statistics/student-loans-in-england-2024-to-2025\n- https://www.gov.uk/government/statistics/student-loans-in-scotland-2024-to-2025\n- https://www.gov.uk/government/statistics/student-loans-in-northern-ireland-2024-to-2025\n- https://www.gov.uk/government/statistics/student-loans-in-wales-2024-to-2025","status":"closed","priority":2,"issue_type":"feature","created_at":"2025-11-29T21:01:37.038332-05:00","updated_at":"2025-11-30T12:42:25.851958-05:00","closed_at":"2025-11-30T12:42:25.851958-05:00"}
+{"id":"policyengine-uk-e55","title":"Impute student loan balance from WAS to FRS","description":"Impute student loan balance from WAS to FRS.\n\n**GitHub Issue:** https://github.com/PolicyEngine/policyengine-uk-data/issues/238\n\n## WAS Data (Round 7, 2018-2020)\n- Derived from: Tot_LosR7_aggr - Tot_los_exc_SLCR7_aggr\n- 1.66m weighted households with SLC debt\n- Mean balance: £20k, Total: £33.4bn\n- Undercounts vs admin (~24% of SLC total) but captures distribution shape\n\n## Implementation in policyengine-uk-data\n1. Add variables to wealth.py\n2. Impute to FRS\n3. Consider scaling to admin totals\n\n## Then in policyengine-uk\n1. Create student_loan_balance variable\n2. Use for capping repayments (policyengine-uk-exv)\n3. Use for interest accrual (policyengine-uk-lo8)","status":"open","priority":2,"issue_type":"feature","created_at":"2025-11-30T13:00:55.693284-05:00","updated_at":"2025-11-30T21:22:35.720239-05:00"}
+{"id":"policyengine-uk-exv","title":"Cap student loan repayments at outstanding balance","description":"## Summary\nCurrently `student_loan_repayment` is calculated as:\n```python\nrepayment = rate * max_(0, income - threshold)\n```\n\nThis has no cap, so high earners can have modelled repayments exceeding their actual loan balance.\n\nExample from validation:\n- Person with £420k income\n- Modelled repayment: £35,470\n- Reported repayment: £1,903\n- Likely explanation: they paid off their loan during the year\n\n## Implementation\n1. Depends on: policyengine-uk-e55 (impute student loan balance)\n2. Add cap: `repayment = min_(repayment, student_loan_balance)`\n3. Consider interest accrual dynamics\n\n## References\n- Real repayments stop when balance reaches zero\n- SLC sends notification when approaching final payment","status":"open","priority":2,"issue_type":"feature","created_at":"2025-11-30T13:01:04.290596-05:00","updated_at":"2025-11-30T13:01:04.290596-05:00","dependencies":[{"issue_id":"policyengine-uk-exv","depends_on_id":"policyengine-uk-e55","type":"blocks","created_at":"2025-11-30T13:01:32.464187-05:00","created_by":"daemon"}]}
+{"id":"policyengine-uk-lo8","title":"Add student loan interest accrual calculation","description":"## Summary\nWe have `student_loan_interest_rate` but no calculation of actual interest accrued. This would require:\n1. Outstanding balance (see policyengine-uk-e55)\n2. Interest rate (already implemented)\n3. Decision on timing: interest on opening or closing balance?\n\n## UK Rules\n- Interest is calculated daily on the outstanding balance\n- For Plan 2, rate varies by income (RPI to RPI+3%)\n- Interest is added monthly\n\n## Implementation\n```python\ninterest_accrued = student_loan_balance * student_loan_interest_rate\n```\n\n## Use cases\n- Calculating lifetime loan costs\n- Analysing distributional impact of interest rate changes\n- Understanding real cost of higher education","status":"open","priority":2,"issue_type":"feature","created_at":"2025-11-30T13:01:12.269846-05:00","updated_at":"2025-11-30T13:01:12.269846-05:00","dependencies":[{"issue_id":"policyengine-uk-lo8","depends_on_id":"policyengine-uk-e55","type":"blocks","created_at":"2025-11-30T13:01:32.503041-05:00","created_by":"daemon"}]}
 {"id":"policyengine-uk-occ","title":"Research official student loan repayment aggregates for calibration","description":"## Research Findings\n\n### UK Student Loan Repayments 2024-25 (SLC Official Statistics)\n\n**England (HE):** £5.0bn total repayments\n- Plan 1: £1.9bn (37%)\n- Plan 2: £2.8bn (55%)\n- Plan 3/Postgraduate: £0.3bn (7%)\n- Plan 5: £41m (0.8%, voluntary only)\n\n**Scotland:** £203m total repayments (primarily Plan 4)\n\n**Wales:** ~£229m total repayments (6.9% increase from prior year)\n\n**Northern Ireland:** £182m total repayments\n\n**UK Total (estimated):** ~£5.6bn HE repayments\n\n### Borrowers Making Repayments (England)\n- 3.0m via HMRC (39.5% of those liable)\n- 187k scheduled direct to SLC\n- 147k voluntary direct to SLC\n\n### Outstanding Balances\n- England: £236.4bn (end March 2025)\n- Scotland: £9.4bn\n- Northern Ireland: £5.6bn\n- Wales: ~£9-10bn (estimated)\n- **UK Total: ~£260-295bn**\n\n### Sources\n- https://www.gov.uk/government/statistics/student-loans-in-england-2024-to-2025\n- https://www.gov.uk/government/statistics/student-loans-in-scotland-2024-to-2025\n- https://www.gov.uk/government/statistics/student-loans-in-northern-ireland-2024-to-2025\n- https://www.gov.uk/government/statistics/student-loans-in-wales-2024-to-2025","status":"closed","priority":2,"issue_type":"task","created_at":"2025-11-29T21:01:36.199753-05:00","updated_at":"2025-11-30T12:41:52.88068-05:00","closed_at":"2025-11-30T12:41:52.88068-05:00","dependencies":[{"issue_id":"policyengine-uk-occ","depends_on_id":"policyengine-uk-75j","type":"blocks","created_at":"2025-11-29T21:01:47.791464-05:00","created_by":"daemon"}]}

policyengine_uk/parameters/gov/hmrc/student_loans/interest_rates/postgraduate_additional_rate.yaml

@@ -0,0 +1,11 @@
+description: Additional interest rate above RPI for Postgraduate loans
+metadata:
+  label: Postgraduate additional rate
+  unit: /1
+  period: year
+  reference:
+    - title: Education (Student Loans) (Repayment) Regulations 2009, Regulation 21B(1)
+      href: https://www.legislation.gov.uk/uksi/2009/470/regulation/21B
+
+values:
+  2016-09-01: 0.03

policyengine_uk/tests/policy/baseline/gov/hmrc/student_loans/student_loan_interest_rate.yaml

@@ -1,121 +1,153 @@
-# Tests for student loan interest rate variables
-# Plan 1/4: min(RPI, BoE base rate + 1%)
-# Plan 2: RPI below lower threshold, tapered to RPI+3% at upper threshold
-# Plan 5: RPI only
-#
-# Uses OBR RPI forecasts from gov.economic_assumptions.yoy_growth.obr.rpi:
-# 2025: RPI 4.33%, BoE 4% -> Plan 1/4 = min(4.33%, 5%) = 4.33%
-# 2026: RPI 3.71%, BoE 3.6% -> Plan 1/4 = min(3.71%, 4.6%) = 3.71%
-
-# Plan 2 tests
-- name: Plan 2 - 2025 - Income below lower threshold (RPI only)
+# Test student loan interest rate calculations
+# Interest rates vary by plan type and income (for Plan 2)
+# Note: RPI for 2025 is ~4.33% per OBR forecasts
+
+# Plan 2 income-contingent interest rate tests
+# Below lower threshold: RPI only
+# Above upper threshold: RPI + 3%
+# Between: linear taper
+
+- name: Plan 2 - Low income gets base rate (RPI only)
   period: 2025
-  absolute_error_margin: 0.001
+  absolute_error_margin: 0.005
   input:
     people:
       person:
         student_loan_plan: PLAN_2
-        adjusted_net_income: 25_000
+        adjusted_net_income: 20_000
   output:
-    # Below £28,470: RPI only (4.33%)
-    student_loan_interest_rate: 0.0433
+    # Below lower threshold, should be RPI (~4.33%)
+    plan_2_interest_rate: 0.0433
 
-- name: Plan 2 - 2025 - Income above upper threshold (RPI + 3%)
+- name: Plan 2 - High income gets max rate (RPI + 3%)
   period: 2025
-  absolute_error_margin: 0.001
+  absolute_error_margin: 0.005
   input:
     people:
       person:
         student_loan_plan: PLAN_2
         adjusted_net_income: 60_000
   output:
-    # Above £51,245: RPI (4.33%) + 3% = 7.33%
-    student_loan_interest_rate: 0.0733
+    # Above upper threshold, should be RPI + 3% (~7.33%)
+    plan_2_interest_rate: 0.0733
 
-- name: Plan 2 - 2026 - Income below lower threshold (RPI only)
-  period: 2026
-  absolute_error_margin: 0.001
+- name: Plan 2 - Mid income gets tapered rate
+  period: 2025
+  absolute_error_margin: 0.01
   input:
     people:
       person:
         student_loan_plan: PLAN_2
+        adjusted_net_income: 40_000
+  output:
+    # Between thresholds, tapered rate ~5.8%
+    plan_2_interest_rate: 0.058
+
+# Plan 5 interest rate (RPI only, regardless of income)
+
+- name: Plan 5 - High income still gets RPI only
+  period: 2025
+  absolute_error_margin: 0.005
+  input:
+    people:
+      person:
+        student_loan_plan: PLAN_5
+        adjusted_net_income: 100_000
+  output:
+    # RPI only regardless of income (~4.33%)
+    plan_5_interest_rate: 0.0433
+
+# Postgraduate interest rate (RPI + 3%)
+
+- name: Postgraduate - Gets RPI + 3% regardless of income
+  period: 2025
+  absolute_error_margin: 0.005
+  input:
+    people:
+      person:
+        student_loan_plan: POSTGRADUATE
         adjusted_net_income: 25_000
   output:
-    # Below £29,385: RPI only (3.71%)
-    student_loan_interest_rate: 0.0371
+    # RPI + 3% regardless of income (~7.33%)
+    postgraduate_interest_rate: 0.0733
+
+# Unified student_loan_interest_rate dispatch tests
+
+- name: No loan returns zero interest rate
+  period: 2025
+  input:
+    people:
+      person:
+        student_loan_plan: NONE
+        adjusted_net_income: 50_000
+  output:
+    student_loan_interest_rate: 0
 
-- name: Plan 2 - 2026 - Income above upper threshold (RPI + 3%)
-  period: 2026
-  absolute_error_margin: 0.001
+- name: Dispatch to Plan 2 rate
+  period: 2025
+  absolute_error_margin: 0.005
   input:
     people:
       person:
         student_loan_plan: PLAN_2
         adjusted_net_income: 60_000
   output:
-    # Above £52,885: RPI (3.71%) + 3% = 6.71%
-    student_loan_interest_rate: 0.0671
+    # Should match plan_2_interest_rate at high income (~7.33%)
+    student_loan_interest_rate: 0.0733
 
-- name: Plan 2 - 2026 - Income midpoint (tapered rate)
-  period: 2026
-  absolute_error_margin: 0.001
+- name: Dispatch to Postgraduate rate
+  period: 2025
+  absolute_error_margin: 0.005
   input:
     people:
       person:
-        student_loan_plan: PLAN_2
-        # 2026 calendar year uses 2025-09-01 thresholds: 28,470 / 51,245
-        # Midpoint: (28,470 + 51,245) / 2 = 39,857.5
-        adjusted_net_income: 39_858
+        student_loan_plan: POSTGRADUATE
+        adjusted_net_income: 30_000
   output:
-    # RPI (3.71%) + half of 3% (1.5%) = 5.21%
-    student_loan_interest_rate: 0.0521
+    # Should match postgraduate_interest_rate (~7.33%)
+    student_loan_interest_rate: 0.0733
 
-# Plan 1 tests - min(RPI, BoE + 1%)
-- name: Plan 1 - 2026 - min(RPI, BoE+1%)
-  period: 2026
-  absolute_error_margin: 0.001
+# Repayment rate tests
+
+- name: No loan returns zero repayment rate
+  period: 2025
   input:
     people:
       person:
-        student_loan_plan: PLAN_1
-        adjusted_net_income: 60_000
+        student_loan_plan: NONE
   output:
-    # min(3.71%, 3.6% + 1%) = min(3.71%, 4.6%) = 3.71%
-    plan_1_interest_rate: 0.0371
+    student_loan_repayment_rate: 0
 
-# Plan 4 tests - same as Plan 1
-- name: Plan 4 - 2026 - min(RPI, BoE+1%)
-  period: 2026
-  absolute_error_margin: 0.001
+- name: Plan 2 returns 9% repayment rate
+  period: 2025
   input:
     people:
       person:
-        student_loan_plan: PLAN_4
-        adjusted_net_income: 60_000
+        student_loan_plan: PLAN_2
   output:
-    # min(3.71%, 3.6% + 1%) = min(3.71%, 4.6%) = 3.71%
-    plan_4_interest_rate: 0.0371
+    student_loan_repayment_rate: 0.09
 
-# Plan 5 tests - RPI only
-- name: Plan 5 - 2026 - RPI only
-  period: 2026
-  absolute_error_margin: 0.001
+- name: Postgraduate returns 6% repayment rate
+  period: 2025
   input:
     people:
       person:
-        student_loan_plan: PLAN_5
-        adjusted_net_income: 60_000
+        student_loan_plan: POSTGRADUATE
   output:
-    # RPI only (3.71%)
-    plan_5_interest_rate: 0.0371
+    student_loan_repayment_rate: 0.06
+
+# Postgraduate repayment integration test
+# Note: Threshold uprated by RPI so ~21,909 for 2025
 
-# No student loan
-- name: No student loan - Zero rate
-  period: 2026
+- name: Postgraduate - Repayment above threshold at 6% rate
+  period: 2025
+  absolute_error_margin: 1
   input:
     people:
       person:
-        student_loan_plan: NONE
-        adjusted_net_income: 50_000
+        employment_income: 30_000
+        student_loan_plan: POSTGRADUATE
   output:
-    student_loan_interest_rate: 0
+    # Postgraduate threshold ~£21,909 (uprated from £21,000)
+    # 6% of (30,000 - 21,909) = 6% of 8,091 = ~485
+    student_loan_repayment: 485

policyengine_uk/variables/gov/hmrc/student_loans/postgraduate_interest_rate.py

@@ -0,0 +1,23 @@
+from policyengine_uk.model_api import *
+
+
+class postgraduate_interest_rate(Variable):
+    value_type = float
+    entity = Person
+    label = "Postgraduate loan interest rate"
+    documentation = (
+        "Interest rate for Postgraduate loans (Master's and Doctoral). "
+        "Per Regulation 21B: 'RPI plus 3%'. "
+        "Unlike Plan 2, this rate applies regardless of income."
+    )
+    definition_period = YEAR
+    unit = "/1"
+    reference = "https://www.legislation.gov.uk/uksi/2009/470/regulation/21B"
+
+    def formula(person, period, parameters):
+        p = parameters(period).gov
+        # Per Regulation 21B: "RPI plus 3%"
+        return (
+            p.economic_assumptions.yoy_growth.obr.rpi
+            + p.hmrc.student_loans.interest_rates.postgraduate_additional_rate
+        )

policyengine_uk/variables/gov/hmrc/student_loans/student_loan_plan.py

@@ -7,6 +7,7 @@ class StudentLoanPlan(Enum):
     PLAN_2 = "PLAN_2"
     PLAN_4 = "PLAN_4"
     PLAN_5 = "PLAN_5"
+    POSTGRADUATE = "POSTGRADUATE"
 
 
 class student_loan_plan(Variable):
@@ -20,6 +21,7 @@ class student_loan_plan(Variable):
         "Plan 1: Started before Sept 2012 (England/Wales) or any time (NI). "
         "Plan 2: Started Sept 2012 - Aug 2023 (England/Wales). "
         "Plan 4: Scotland. "
-        "Plan 5: Started Aug 2023 onwards (England)."
+        "Plan 5: Started Aug 2023 onwards (England). "
+        "Postgraduate: Master's or Doctoral loans."
     )
     definition_period = YEAR

policyengine_uk/variables/gov/hmrc/student_loans/student_loan_repayment.py

@@ -10,16 +10,16 @@ class student_loan_repayment(Variable):
     label = "Student loan repayment (modelled)"
     documentation = (
         "Annual student loan repayment calculated from income and plan type. "
-        "Repayments are 9% of income above the plan-specific threshold."
+        "Repayments are 9% of income above threshold for Plans 1/2/4/5, "
+        "and 6% for Postgraduate loans."
     )
     definition_period = YEAR
     unit = GBP
 
     def formula(person, period, parameters):
         plan = person("student_loan_plan", period)
         income = person("adjusted_net_income", period)
-        rate = parameters(period).gov.hmrc.student_loans.repayment_rate
-        thresholds = parameters(period).gov.hmrc.student_loans.thresholds
+        p = parameters(period).gov.hmrc.student_loans
 
         # Get threshold based on plan type
         threshold = select(
@@ -28,18 +28,20 @@ def formula(person, period, parameters):
                 plan == StudentLoanPlan.PLAN_2,
                 plan == StudentLoanPlan.PLAN_4,
                 plan == StudentLoanPlan.PLAN_5,
+                plan == StudentLoanPlan.POSTGRADUATE,
             ],
             [
-                thresholds.plan_1,
-                thresholds.plan_2,
-                thresholds.plan_4,
-                thresholds.plan_5,
+                p.thresholds.plan_1,
+                p.thresholds.plan_2,
+                p.thresholds.plan_4,
+                p.thresholds.plan_5,
+                p.thresholds.postgraduate,
             ],
             default=np.inf,
         )
 
-        repayment = rate * max_(0, income - threshold)
-        return repayment
+        rate = person("student_loan_repayment_rate", period)
+        return rate * max_(0, income - threshold)
 
 
 class has_student_loan(Variable):
@@ -76,12 +78,14 @@ def formula(person, period, parameters):
                 plan == StudentLoanPlan.PLAN_2,
                 plan == StudentLoanPlan.PLAN_4,
                 plan == StudentLoanPlan.PLAN_5,
+                plan == StudentLoanPlan.POSTGRADUATE,
             ],
             [
                 person("plan_1_interest_rate", period),
                 person("plan_2_interest_rate", period),
                 person("plan_4_interest_rate", period),
                 person("plan_5_interest_rate", period),
+                person("postgraduate_interest_rate", period),
             ],
             default=0,
         )

policyengine_uk/variables/gov/hmrc/student_loans/student_loan_repayment_rate.py

@@ -0,0 +1,31 @@
+from policyengine_uk.model_api import *
+from policyengine_uk.variables.gov.hmrc.student_loans.student_loan_plan import (
+    StudentLoanPlan,
+)
+
+
+class student_loan_repayment_rate(Variable):
+    value_type = float
+    entity = Person
+    label = "Student loan repayment rate"
+    documentation = (
+        "Percentage of income above threshold paid toward student loan. "
+        "9% for Plans 1/2/4/5, 6% for Postgraduate loans."
+    )
+    definition_period = YEAR
+    unit = "/1"
+    reference = "https://www.gov.uk/repaying-your-student-loan/what-you-pay"
+
+    def formula(person, period, parameters):
+        plan = person("student_loan_plan", period)
+        p = parameters(period).gov.hmrc.student_loans
+
+        return where(
+            plan == StudentLoanPlan.POSTGRADUATE,
+            p.postgraduate_repayment_rate,
+            where(
+                plan == StudentLoanPlan.NONE,
+                0,
+                p.repayment_rate,
+            ),
+        )