Restore VAT-liability-by-sector as a calibration target

[vahid-ahmadi]

Background

vat_liability_sector (HMRC net VAT liability by trade sector) has been removed from the calibration objective — see Config.calibrate_vat_liability_sector = False (gated in firm_microsim/calibration.py). It is still computed and reported as an informational diagnostic in firm_microsim/validate.py, but it no longer feeds the weight optimizer.

Why it was removed

The model fixes firm inputs and sets liability = turnover − input, but does not yet calibrate the input/output tax structure. As a result the sector-level net liability is structurally unhittable — it over/under-shoots for individual sectors (badly for small ones) and competed with the dimensions the paper relies on. Concretely it scored 43.9% (2023-24) and −121.1% (2024-25, sign-broken), dragging the naive 6-dimension mean down even though the five core dimensions calibrate well (~89–90%).

Removing it lets the optimizer focus on the five calibrated dimensions (HMRC turnover bands, ONS population, employment, sector counts, VAT liability by band) and gives a cleaner, defensible headline accuracy.

What restoring it requires

Restoration should come after the input/output calibration work (tracked in #1), specifically:

• Calibrate the input/output tax structure using HMRC T9 Input and output tax and/or ONS ABS intermediate consumption, so per-sector net liability is reproducible rather than a by-product of unconstrained input draws.
• Then re-enable the target by setting Config.calibrate_vat_liability_sector = True and (likely) raising vat_liability_sector_importance.
• Consider flooring the per-sector accuracy metric at 0 (the current sign-aware metric is uncapped and over-penalizes tiny sectors), so the dimension is scored fairly once calibrated.

Acceptance

• With input/output calibration in place, vat_liability_sector accuracy is positive and reasonable (target ≥ ~70%).
• Re-enabling it does not materially degrade the five core dimensions.

Related: #1 (broader future calibration extensions).

[MaxGhenis]

Connecting this to today's corrections (PR #21, merged) and to the sector-heterogeneity concern raised around the IMA presentation:

What the current build does. Per-firm input shares come from one rescaled-Beta distribution with sector shifts only, so the liability-by-sector diagnostic scores 45.2% on the corrected 2023-24 build (informational, excluded from the optimiser — see results/calibration_accuracy.txt).

Why this does not undermine the paper's current claims:

1. The costings are pinned by band-level liability targets. Every headline number (raise/taper/reduced-rate menu, the 85k→90k anchor) is a band or sub-band liability sum; sector composition within a band cannot move a calibrated band total.
2. The analytic core is sector-invariant by construction. Under the value-added formulation, the deductible share δ (and hence the input/output structure) cancels out of both the dominated-region width a = T*·τ/(1−τ) and the intensive-margin response ratio — the two objects the distortion and behavioural sections rest on.
3. Sectoral incidence is explicitly out of scope. The conclusion's limitations paragraph states it, and PR Correct net-VAT liability scaling; rewrite paper on the corrected model #21 adds the sharper caveat that the sub-band split of band-total liability (which the anchor and relocation costings use) rests on the generator's common input-share distribution rather than sector-composition data.

Where it genuinely binds (the reason this issue should stay open): sectoral incidence of any reform in the menu; the within-band liability profile if near-threshold sector mix is skewed (e.g. toward high-value-added consumer services); and rated-structure work (zero-rated sectors → repayment traders), which is unrepresentable without sector-level input/output detail.

Fix path, as this issue already says: calibrate the input/output tax structure by sector first — ONS Supply-Use / ABS value-added shares per SIC section give sector-specific ρ distributions — and only then restore liability-by-sector as a target. Today's v = 0.20(y − x) correction is what makes that calibration meaningful at all (under the old mis-scaled liability, sector targets were unhittable by construction). The same design should carry into the populace port (PolicyEngine/populace#258).

[MaxGhenis]

Addendum to the assessment above, from the adversarial review round (PR #26): the dominated-region/input-share invariance in point 2 is a property of the value-added formulation, in which unregistered firms bear no unreclaimed input VAT. If deregistered firms instead bore VAT on inputs, the width would shrink in the input share — a(δ) = T*τ(1−2δ)/[(1−δ)(1−τ)] — and vanish for δ > ½, which is exactly the input-reclaim motive behind the ~43% voluntary registration rate. The paper now states this condition (model section + background). It does not change the conclusion here (band-total costings remain target-pinned), but it is one more reason sector-level input/output structure is the right next calibration step: with sectoral ρ distributions the formulation itself can be relaxed.