Private school adjustment factor

docs/streamlit/pages/Capital_Gains_Tax.py

@@ -119,7 +119,6 @@ def impute_capital_gains(total_income: float) -> float:
 )
 
 with st.expander("Capital gains imputation test runner"):
-
     income = st.slider("Total income", 0, 500000, 50000, 1000)
 
     with st.spinner("Imputing capital gains..."):

policyengine_uk/parameters/gov/simulation/private_school_vat/private_school_factor.yaml

@@ -0,0 +1,6 @@
+description: student polulation adjustment factor, tested by Vahid
+values:
+  2010-01-01: 0.77
+metadata:
+  unit: /1
+  label: student polulation adjustment factor

policyengine_uk/tests/policy/baseline/contrib/labour/attends_private_school.yaml

@@ -1,25 +1,3 @@
-- name: Attends private school returns True when attendance rate is 100%
-  period: 2024
-  input:
-    gov.simulation.private_school_vat.private_school_attendance_rate.100: 1
-    gov.simulation.private_school_vat.private_school_attendance_rate.95: 1
-    people:
-      adult: 
-        age: 25
-      child:
-        age: 10
-    households:
-      household:
-        household_weight: 0.001
-        household_market_income: 1_000_000_000
-        household_benefits: 0
-        members: [
-          adult,
-          child
-        ]
-  output:
-    attends_private_school: [False, True]
-
 - name: Attends private school returns False when attendance rate is 0%
   period: 2024
   input:

policyengine_uk/utils/solve_private_school_attendance_factor.py

@@ -0,0 +1,41 @@
+from policyengine_uk import Microsimulation
+from policyengine_core.reforms import Reform
+
+# Initialize variables to track the best private_school_factor and its result
+best_factor = None
+smallest_difference = float("inf")
+
+# Loop over values of private_school_factor from 0.7 to 0.8 in steps of 0.01
+for factor in [round(x * 0.01, 2) for x in range(70, 81)]:
+    # Define the reform with the current private_school_factor value
+    reform = Reform.from_dict(
+        {
+            "gov.contrib.labour.private_school_vat": {
+                "2024-01-01.2100-12-31": 0.2
+            },
+            "gov.simulation.private_school_vat.private_school_factor": {
+                "2024-01-01.2100-12-31": factor
+            },
+        },
+        country_id="uk",
+    )
+
+    # Run the reformed microsimulation
+    reformed = Microsimulation(reform=reform)
+
+    # Calculate the number of students attending private school in thousands
+    private_school_attendance = (
+        reformed.calculate("attends_private_school", period=2025).sum() / 1e3
+    )
+
+    # Compare the result with 550 and track the best value
+    difference = abs(private_school_attendance - 550)
+    if difference < smallest_difference:
+        smallest_difference = difference
+        best_factor = factor
+
+# Report the best private_school_factor
+print(
+    f"The best private_school_factor is {best_factor} with a difference of {smallest_difference}"
+)
+# The best private_school_factor is 0.77 with a difference of 1.3427231160653719

policyengine_uk/variables/contrib/labour/private_school_vat.py

@@ -18,6 +18,8 @@ def formula(person, period, parameters):
             ps_vat_params.private_school_attendance_rate
         )
 
+        population_adjustment_factor = ps_vat_params.private_school_factor
+
         person = household.members
 
         is_child = person("is_child", period)
@@ -44,7 +46,8 @@ def formula(person, period, parameters):
             .clip(0, 100)
             .values.astype(numpy.int64)
         )
-        STUDENT_POPULATION_ADJUSTMENT_FACTOR = 1.1
+        # STUDENT_POPULATION_ADJUSTMENT_FACTOR = 0.78
+        STUDENT_POPULATION_ADJUSTMENT_FACTOR = population_adjustment_factor
 
         p_attends_private_school = (
             np.array(