Correct net-VAT liability scaling; rewrite paper on the corrected model

[MaxGhenis]

Summary

Completes the net-VAT liability fix from #15 (superseding draft PR #17), re-runs the entire pipeline on the corrected model, and rewrites the paper against the corrected numbers plus a seven-referee review (methodology, red-team, domain, citations, neutrality, style, reproducibility).

The defect and its consequences

vat_liability_k was turnover − input (no ×0.20), inflating per-firm liabilities ~5×, with ρ ∈ [0.6, 1.5] leaving ~47% of firms with negative value added. The weight optimiser compensated on band totals (aggregate scores barely moved) while distorting the near-threshold density — manufacturing the paper's "reproduction" of the administrative bunching step.

Model fixes

• v = 0.20 × (turnover − input); ρ ∈ [0.1, 0.95], mean VA share 40%, zero negative-VA firms (from Fix vat liability scaling #17, applied to current main)
• Behavioural solver rewritten: the damped fixed-point iteration has no fixed point for firms straddling a reform notch (iterates oscillate; results were iteration-parity artifacts). Replaced with a closed-form region-confined solve using the formulation-A response ratio y* = y_obs[(1−τf₁)/(1−τf₀)]^e (deductible share cancels). e→0 nesting now exact; baseline reproduction asserted; raise-to-£100k behavioural ≡ static at every e — a derived invariance, asserted in the crosscheck
• Bunching estimator: removed non-identified elasticity outputs (σ/Π/eps, incl. an ad hoc τ/2 normalisation from a deleted model); fixed bootstrap replicate weights (were scaled n/W)
• Recovery test redesigned: the old injection was invisible to the counterfactual fit by construction (donor+deposit both inside the exclusion window); new KW-consistent injection extends beyond the window and is scored by the headline estimator
• Secondary-notch mass block in dominated_region_mass; new results/static_sweep.txt artifact (the sweep table was previously figure-pixels only); voluntary-retention sensitivity on the anchor

Headline results on the corrected model

Object	Old	Corrected
Common-base menu (2023-24, base)	£183.6bn	£184.7bn
Raise to £100k	−£508m	−£698m (behavioural = static at every e)
Graduated taper	−£336m	−£466m
Reduced rate 10% / 15%	−£343m / −£171m	−£460m / −£230m
Anchor 85→90k (2025-26) vs HMRC −£185m	−£175m ("within £10m")	−£248m full-dereg / −£141m retention — brackets HMRC in all 5 years
Bunching at 85k	E=8,712, b=0.060 ("reproduces admin step")	E=0, b=−0.139
Bunching at 90k (2024-25 vintage)	—	E≈196k spurious, spec-robust — band-edge artifact
Behavioural offsets	40–75% of static	0% (raise), <4% (bands)

Paper rewrite

Every section updated. Section 5 reframed around the correction: band-calibrated synthetic data cannot support bunching inference in either direction — the corrected data show nothing at £85k while the same generator shows a huge spurious signal at the £90k band edge, robust in all 16 sensitivity cells. The earlier draft's artifact is documented openly as the sharpest demonstration of the thesis. Value-added "robustness" paragraph (which implied dominated widths above the £21,250 statutory cap) replaced by the formulation-A invariance result. Anchor mechanism corrected (uprated counterfactual threshold path, not "fiscal drag"). Citations: LLAT sample setting corrected (2004–14, £58k–£81k thresholds — not "the same £85,000 notch"); Chetty et al. credited for the polynomial counterfactual; HMT 2018 call for evidence + Council Directive (EU) 2020/285 added; URLs/DOIs throughout. Full referee reports available on request.

Upstream

• populace's experimental UK firm generator (Add experimental UK firm generator populace#223) was ported pre-fix and inherits the same mis-scaling — flagged in the appendix and README; upstream issue to follow.

Closes #15. Supersedes #17.

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