Document employer National Insurance incidence assumptions

changelog.d/2168.changed.md

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+- Documented employer NI incidence assumptions, input handling, revenue measures and current household examples.

docs/book/assumptions/employer-ni-incidence.md

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+# Employer National Insurance incidence
+
+Employer National Insurance reforms can change wages, tax receipts and household
+income through the model's incidence assumptions. The parameters under
+`gov.contrib.policyengine.employer_ni` default to:
+
+| Parameter | Default | Implemented role |
+|---|---:|---|
+| `employee_incidence` | 1 | Scales the computed fixed-employer-cost pay adjustment |
+| `consumer_incidence` | 0.5 | Allocates remaining employer-cost changes by consumption shares |
+| `capital_incidence` | 0.5 | Allocates remaining employer-cost changes by corporate wealth shares |
+
+These values are adjustable model assumptions. No empirical estimate is claimed
+for the defaults, and this page does not select a preferred incidence assumption.
+
+## Wage adjustment and supplied income
+
+The wage channel compares the baseline and reform employer-NI rate, secondary
+threshold and employer-pension exemption. For its eligible earnings branch, it
+solves for pay holding modeled employer cost fixed, then multiplies the pay change
+by `employee_incidence`. At `1`, the full computed adjustment applies in the same
+model year. The formula returns zero without a baseline, without a relevant
+parameter change, at employee incidence zero, or for prior pay below the baseline
+secondary threshold. This describes the implemented calculation, including its
+threshold guard; it does not assert a general equilibrium response for every worker.
+
+`employment_income` adds this adjustment to `employment_income_before_lsr` and
+other earnings components. An input actually stored in the final
+`employment_income` holder overrides its formula. The UK `Simulation` constructor
+moves situation inputs named `employment_income` to `employment_income_before_lsr`.
+Consequently, putting that field in a constructor situation can still allow the
+wage response. The example below demonstrates an override with `set_input` after
+construction and before calculation. Dataset and other input routes should be
+checked for which earnings holder they populate.
+
+The [wage formula](https://github.com/PolicyEngine/policyengine-uk/blob/b4dbaf57a4ebb1d1f0ba5f7a384795422828db75/policyengine_uk/variables/contrib/policyengine/employer_ni/employer_ni_fixed_employer_cost_change.py),
+[earnings components](https://github.com/PolicyEngine/policyengine-uk/blob/b4dbaf57a4ebb1d1f0ba5f7a384795422828db75/policyengine_uk/variables/input/employment_income.py)
+and [constructor remapping](https://github.com/PolicyEngine/policyengine-uk/blob/b4dbaf57a4ebb1d1f0ba5f7a384795422828db75/policyengine_uk/simulation.py#L350)
+provide the implementation details.
+
+## Consumer and capital channels
+
+Consumer and capital incidence apply to the remaining change in modeled employer
+cost after the wage response. Each is zero when its own parameter is zero or
+employee incidence is one. Otherwise, the formulas use person weights and allocate
+that change using household consumption or corporate wealth per person. Their
+weighted aggregate exposure must be nonzero; they also return zero when the
+simulation has no dataset attribute.
+
+An attribute can be present with `dataset=None`, so that guard alone is not a
+promise that every household calculation has zero residual incidence. The example
+below has no representative dataset or consumption/wealth exposures and returns
+zero for both residual channels. It cannot show their population effects.
+
+Setting `employee_incidence` to zero alone leaves the consumer and capital
+parameters at `0.5`. Set **all three parameters to zero** to disable these three
+employer-NI incidence channels. This does not disable unrelated labor-supply or
+other behavioral responses.
+
+The response amounts enter `household_tax`; those same variables are not added to
+`gov_tax`. See the [consumer](https://github.com/PolicyEngine/policyengine-uk/blob/b4dbaf57a4ebb1d1f0ba5f7a384795422828db75/policyengine_uk/variables/contrib/policyengine/employer_ni/employer_ni_response_consumer_incidence.py)
+and [capital](https://github.com/PolicyEngine/policyengine-uk/blob/b4dbaf57a4ebb1d1f0ba5f7a384795422828db75/policyengine_uk/variables/contrib/policyengine/employer_ni/employer_ni_response_capital_incidence.py)
+allocation formulas.
+
+## Measures and aggregation
+
+Report these quantities separately:
+
+- Gross employer-NI liability or its reform change: `ni_employer`, a person amount.
+- Net government balance: `gov_balance = gov_tax - gov_spending`, a household amount.
+  A positive reform change improves the modeled balance. Wage changes can affect
+  income tax, employee NI and benefits, so this is not a gross employer-NI yield.
+- Household incidence here: the change in nominal `household_net_income`, defined
+  as `household_market_income + household_benefits - household_tax - pension_contributions`.
+  A negative change is a household loss under this measure.
+
+The example sums each output over one person or one household, as appropriate.
+Population results require the matching person or household weights. Do not sum
+household values repeated on person records as if they were distinct households.
+These measures do not by themselves establish a representative budget costing.
+
+## Worked household example
+
+For model year 2026, consider one 40-year-old London employee with £40,000 of
+pre-response earnings, no pension contributions and no other supplied income.
+Raise the employer rate from 15% to 16%, holding the other parameters fixed. Current
+main includes the annual secondary-threshold correction: £5,000 rather than the
+old rounded-weekly equivalent of £4,992. Each comparison below applies the same
+incidence assumptions to its baseline and reform.
+
+Annual changes in pounds, rounded to two decimal places:
+
+| Input and incidence assumptions | Employer NI | Income tax | Employee NI | Gross pay | Government balance | Household net income |
+|---|---:|---:|---:|---:|---:|---:|
+| Components; employee 1, consumer/capital 0.5 | +301.72 | −60.34 | −24.14 | −301.72 | +217.24 | −217.24 |
+| Components; employee 0, consumer/capital 0.5 | +350.00 | 0.00 | 0.00 | 0.00 | +350.00 | 0.00 |
+| Components; all three zero | +350.00 | 0.00 | 0.00 | 0.00 | +350.00 | 0.00 |
+| Pay set after construction; employee 1 | +350.00 | 0.00 | 0.00 | 0.00 | +350.00 | 0.00 |
+
+At fixed pay, the extra liability is `0.01 × (40,000 − 5,000) = £350`.
+With full wage incidence, the baseline employer cost is £45,250. Solving
+`pay + 0.16 × (pay − 5,000) = 45,250` gives pay of approximately £39,698.28.
+The income-tax and employee-NI changes partly offset the wage fall. The last three
+rows coincide in this example; they do not imply identical population incidence.
+
+Run this snippet from a checkout's supported Python environment:
+
+```python
+from policyengine_core.reforms import Reform
+from policyengine_uk import Simulation
+
+YEAR = 2026
+SPAN = "2026-01-01.2026-12-31"
+INCIDENCE = "gov.contrib.policyengine.employer_ni."
+RATE = "gov.hmrc.national_insurance.class_1.rates.employer"
+VARIABLES = [
+    "ni_employer",
+    "income_tax",
+    "ni_employee",
+    "employment_income",
+    "gov_balance",
+    "household_net_income",
+]
+
+
+def result(employee, consumer, capital, direct_pay=False):
+    pay_input = "employment_income" if direct_pay else "employment_income_before_lsr"
+    situation = {
+        "people": {"worker": {"age": {YEAR: 40}, pay_input: {YEAR: 40_000}}},
+        "benunits": {"family": {"members": ["worker"]}},
+        "households": {"home": {"members": ["worker"], "region": {YEAR: "LONDON"}}},
+    }
+    assumptions = {
+        INCIDENCE + "employee_incidence": {SPAN: employee},
+        INCIDENCE + "consumer_incidence": {SPAN: consumer},
+        INCIDENCE + "capital_incidence": {SPAN: capital},
+    }
+    baseline = Simulation(
+        situation=situation,
+        reform=Reform.from_dict(assumptions, country_id="uk"),
+    )
+    reform = Simulation(
+        situation=situation,
+        reform=Reform.from_dict({**assumptions, RATE: {SPAN: 0.16}}, country_id="uk"),
+    )
+    if direct_pay:
+        # UK construction moves situation earnings to the pre-response input.
+        # Explicitly supply the final earnings holder after construction.
+        baseline.set_input("employment_income", YEAR, [40_000])
+        reform.set_input("employment_income", YEAR, [40_000])
+    before = {v: float(baseline.calculate(v, YEAR).sum()) for v in VARIABLES}
+    after = {v: float(reform.calculate(v, YEAR).sum()) for v in VARIABLES}
+    return {
+        "baseline": before,
+        "reform": after,
+        "delta": {v: after[v] - before[v] for v in VARIABLES},
+        "residual_channels": {
+            v: float(reform.calculate(v, YEAR).sum())
+            for v in (
+                "employer_ni_response_consumer_incidence",
+                "employer_ni_response_capital_incidence",
+            )
+        },
+    }
+
+
+rows = {
+    "Employee 1; consumer/capital 0.5": result(1, 0.5, 0.5),
+    "Employee 0; consumer/capital 0.5": result(0, 0.5, 0.5),
+    "All three zero": result(0, 0, 0),
+    "Pay set after construction; employee 1": result(1, 0.5, 0.5, direct_pay=True),
+}
+for label, row in rows.items():
+    print(label, {v: round(value, 2) for v, value in row["delta"].items()})
+```
+
+The residual-channel outputs are retained in `rows` for inspection. No private
+microdata, representative population estimate or empirical calibration is used.
+
+## Comparing an official costing
+
+Match the definition and horizon of the specific official figure before comparing
+it with a model result. For example, the
+[OBR's October 2024 Economic and fiscal outlook](https://obr.uk/efo/economic-and-fiscal-outlook-october-2024/)
+reported £25.7 billion of employer-NICs revenue in 2029–30 before indirect economic
+effects (overview paragraph 1.7). Its paragraph 2.14 assumed about 60% of the cost
+would pass to employees in the short term, with more adjustment later through
+prices and nominal wages. These are dated forecast assumptions, not evidence for
+the model's defaults. Other official headlines can use different definitions.

policyengine_uk/parameters/gov/contrib/policyengine/employer_ni/README.md

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-# Employer NI
+# Employer NI incidence
+
+These parameters describe how the model allocates a change in employer National
+Insurance costs. Their defaults, unchanged from 2010, are employee incidence `1`,
+consumer incidence `0.5` and capital incidence `0.5`. They are adjustable modeling
+assumptions; no empirical estimate is claimed for the defaults.
+
+For eligible earnings computed from components, employee incidence `1` applies the
+computed fixed-employer-cost pay adjustment in the same model year. This changes
+income tax and employee NI as well as gross pay. A supplied final
+`employment_income` holder overrides that formula. The UK `Simulation` constructor
+moves situation earnings into `employment_income_before_lsr`, so a constructor
+field alone does not demonstrate that override.
+
+Setting employee incidence to `0` leaves the consumer and capital channels active
+where population weights and exposure totals support them. Set all three incidence
+parameters to `0` to disable these three channels. Other labor-supply responses
+have separate controls.
+
+Report employer-NI liability, net `gov_balance` and household income effects
+separately. The [assumptions page](../../../../../../docs/book/assumptions/employer-ni-incidence.md)
+explains the implemented guards, aggregation, current worked example and a dated
+OBR comparison. A single-household example does not establish population incidence.

policyengine_uk/parameters/gov/contrib/policyengine/employer_ni/capital_incidence.yaml

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-description: Fraction of (remaining after employee incidence) employer NI that is borne by capital.
+description: >-
+  Share of the remaining employer-cost change allocated to capital after employee incidence; set all three incidence parameters to 0 to disable these channels.
 values:
   2010-01-01: 0.5
 metadata:
   label: Employer NI capital incidence
   unit: /1
+  reference:
+    - title: PolicyEngine-UK implemented employer NI incidence mechanism
+      href: https://github.com/PolicyEngine/policyengine-uk/blob/b4dbaf57a4ebb1d1f0ba5f7a384795422828db75/policyengine_uk/variables/contrib/policyengine/employer_ni/employer_ni_response_capital_incidence.py

policyengine_uk/parameters/gov/contrib/policyengine/employer_ni/consumer_incidence.yaml

@@ -1,6 +1,10 @@
-description: Fraction of (remaining after employee incidence) employer NI that is borne by consumers.
+description: >-
+  Share of the remaining employer-cost change allocated to consumers after employee incidence; set all three incidence parameters to 0 to disable these channels.
 values:
   2010-01-01: 0.5
 metadata:
   label: Employer NI consumer incidence
   unit: /1
+  reference:
+    - title: PolicyEngine-UK implemented employer NI incidence mechanism
+      href: https://github.com/PolicyEngine/policyengine-uk/blob/b4dbaf57a4ebb1d1f0ba5f7a384795422828db75/policyengine_uk/variables/contrib/policyengine/employer_ni/employer_ni_response_consumer_incidence.py

policyengine_uk/parameters/gov/contrib/policyengine/employer_ni/employee_incidence.yaml

@@ -1,6 +1,10 @@
-description: Fraction of employer NI that is borne by employees.
+description: >-
+  Share of the fixed-employer-cost pay change passed to employees in the same model year; set all three incidence parameters to 0 to disable these channels.
 values:
   2010-01-01: 1
 metadata:
   label: Employer NI employee incidence
   unit: /1
+  reference:
+    - title: PolicyEngine-UK implemented employer NI incidence mechanism
+      href: https://github.com/PolicyEngine/policyengine-uk/blob/b4dbaf57a4ebb1d1f0ba5f7a384795422828db75/policyengine_uk/variables/contrib/policyengine/employer_ni/employer_ni_fixed_employer_cost_change.py