Add marginal_tax_rate_wrt_employer_cost (#45) (#1641)

* Add marginal_tax_rate_wrt_employer_cost (#45)

Mirror the existing `marginal_tax_rate` variable but divide the change
in household net income by the change in the employer's cost of
employment rather than the change in gross pay. The denominator is
`employer_cost` (gross pay plus employer NI, employer pension
contributions, and statutory sick/maternity/paternity pay), so a pound
of employer-side NI is no longer invisible to the MTR.

Computation uses the same simulation-branching pattern as
`marginal_tax_rate` — for each adult, branch the simulation, bump
`employment_income` by the configured delta, recompute, and read both
`household_net_income` and `employer_cost` in the branch. Division-by-
zero is guarded for people whose employer cost happens not to move.

No change to the existing `marginal_tax_rate` variable. Downstream
surfaces (API, household calculator) would need a separate change to
expose the new variable to end users.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

* Test employer-cost marginal tax rate

---------

Co-authored-by: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
Co-authored-by: Max Ghenis <mghenis@gmail.com>

Author: 3 people

changelog.d/45.md

@@ -0,0 +1 @@
+- Add `marginal_tax_rate_wrt_employer_cost`, a person-level variable that reports the share of a marginal increase in the employer's cost of employment (gross pay plus employer NI, employer pension contributions and statutory sick/maternity/paternity pay) that does not flow to household net income. Computed via the same simulation-branching pattern as `marginal_tax_rate`. Useful for analysing reforms that shift incidence between worker-side and employer-side charges.

policyengine_uk/tests/policy/baseline/household/marginal_tax_rate_wrt_employer_cost.yaml

@@ -0,0 +1,16 @@
+- name: Single employee marginal tax rate with respect to employer cost
+  period: 2024
+  absolute_error_margin: 0.001
+  input:
+    people:
+      adult:
+        age: 40
+        employment_income: 50_000
+    benunits:
+      benunit:
+        members: [adult]
+    households:
+      household:
+        members: [adult]
+  output:
+    marginal_tax_rate_wrt_employer_cost: 0.457

policyengine_uk/variables/household/marginal_tax_rate_wrt_employer_cost.py

@@ -0,0 +1,53 @@
+from policyengine_uk.model_api import *
+from policyengine_core.variables import Variable
+
+
+class marginal_tax_rate_wrt_employer_cost(Variable):
+    label = "Marginal tax rate with respect to employer cost"
+    documentation = (
+        "Percent of a marginal increase in the employer's cost of employment "
+        "(gross pay plus employer NI, employer pension contributions and "
+        "statutory sick/maternity/paternity pay) that does not flow to "
+        "household net income."
+    )
+    entity = Person
+    definition_period = YEAR
+    value_type = float
+    unit = "/1"
+
+    def formula(person, period, parameters):
+        p = parameters(period).gov.simulation
+        mtr_values = np.zeros(person.count, dtype=np.float32)
+        simulation = person.simulation
+        adult_index_values = person("adult_index", period)
+        delta = p.marginal_tax_rate_delta
+        adult_count = p.marginal_tax_rate_adults
+        baseline_employer_cost = person("employer_cost", period)
+        baseline_net = person.household("household_net_income", period)
+        for adult_index in range(1, 1 + adult_count):
+            alt_simulation = simulation.get_branch(
+                f"adult_{adult_index}_employer_cost_mtr"
+            )
+            mask = adult_index_values == adult_index
+            for variable in simulation.tax_benefit_system.variables:
+                variable_data = simulation.tax_benefit_system.variables[variable]
+                if (
+                    variable not in simulation.input_variables
+                    and not variable_data.is_input_variable()
+                ):
+                    alt_simulation.delete_arrays(variable)
+            alt_simulation.set_input(
+                "employment_income",
+                period,
+                person("employment_income", period) + mask * delta,
+            )
+            alt_person = alt_simulation.person
+            new_net = alt_person.household("household_net_income", period)
+            new_employer_cost = alt_person("employer_cost", period)
+            net_increase = new_net - baseline_net
+            employer_cost_increase = new_employer_cost - baseline_employer_cost
+            safe_denominator = where(
+                employer_cost_increase != 0, employer_cost_increase, 1
+            )
+            mtr_values += where(mask, 1 - net_increase / safe_denominator, 0)
+        return mtr_values