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.

🤖 Generated with Claude Code

[vahid-ahmadi]

cc @MaxGhenis — flagging some data-generation design questions on this branch before we lock it in.

Since this PR rewrites the generation pipeline substantially, I think we should capture sector heterogeneity of VAT liability properly at the same time. Right now it isn't, and the new setup makes it structurally harder:

1. Sector heterogeneity is a three-level caricature

The input/output ratio is a single global Beta(4,2) mapped to [0.2, 0.8], plus two hand-coded SIC sets (17 "negative-liability" sectors shifted up by U[0, 0.3], 5 "high-liability" sectors shifted down by U[0, 0.2]) — calibrated to nothing (generate.py:82–84, 164–170). The branch's own calibration report shows the consequence: VAT liability by sector = 45% accuracy, demoted to an "informational diagnostic", while every calibrated dimension sits at 78–94%.

2. The new clamp makes negative sectors unreachable by construction

We have the right data in-repo (data/processed/2023-24/hmrc_vat_liability_by_sector.csv, ~80 sectors) and it includes genuinely negative sectors — crop production −£2,330m, fishing −£100m, oil/gas −£460m (zero-rated outputs → repayment traders). The new ρ ∈ [0.1, 0.95] clamp forces every firm's liability strictly positive, so those sector targets can never be matched — the 45% is a ceiling, not a tuning problem. The old model was wrong at the firm level (no ×0.20) but could at least represent negative sector aggregates; this branch fixes the rate but silently deletes the repayment-trader mechanism.

This matters for the paper directly: sector composition near £85–90k sets the net-rate distribution τ₀ there, which drives the anchor cost, every behavioural wedge, and the firm-level dominated-region analysis.

3. The HMRC overshoot is mostly convention, not shape

Anchor now −358/−365 vs HMRC −150/−185 — but this branch's own artifact shows that with 43% voluntary retention (Liu et al.) of released-firm liability the series becomes −204 / −208 / −125 / −43 / +57 vs HMRC's −150 / −185 / −125 / −50 / +65: within ~£25m every year. So the headline gap is dominated by the assume-everyone-deregisters convention, not by the Beta parameters. The residual is where sector/VA-share composition near the threshold matters.

4. The near-threshold density shape is an optimizer artifact

On the corrected model the 2023-24 file has a density step up at £85k (below/above ≈ 0.74 — the opposite of admin data), and the 2024-25 vintage piles ~54k firms/£1k just below £90k vs ~6.9k above (7.8×). Root cause: turnover is drawn ~uniform within coarse ONS bands and the Adam reweighting has no target constraining within-band density shape, so it manufactures spikes to reconcile count and liability totals. No Beta(a,b) choice fixes this — it lives in the weights.

Proposed fixes (in order of value)

1. Per-sector Beta parameters, calibrated: set each sector's mean input ratio μ_s from HMRC sector liability ÷ sector turnover (or ONS Supply–Use intermediate-consumption shares), then a_s = μ_s·κ, b_s = (1−μ_s)·κ with a single concentration κ ≈ 6–10. Replaces both hand-coded sector sets. (a, b are exactly the right knobs — but per sector, matched to data, not global.)
2. Reintroduce repayment traders via the correct mechanism: a sector-level effective output rate r_s < 0.20 (zero-rating share: food, agriculture, exports), so liability = r_s·y − 0.20·x goes negative where it genuinely is — then liability-by-sector becomes a real calibration target instead of a diagnostic. (Not ρ > 1, which was the old bug's enabler.) If we'd rather keep the standard-rate approximation, we should drop negative sectors from the target explicitly and document it.
3. Constrain near-threshold density shape: a smoothness penalty (e.g. second differences of weighted density over ~£60k–£120k) or fine near-threshold count targets in the calibration loss, so the optimizer can't fabricate steps/spikes. Without this, any bunching/placebo statement on the synthetic file is at the optimizer's mercy.
4. Make the 43%-retention anchor the headline convention (or co-headline) — it closes most of the HMRC gap for a documented, literature-anchored reason. Caveat: once retention is tuned, the anchor is a consistency check, not validation.

One dependency to sequence deliberately: with per-sector rates and negative liabilities restored, the behavioural layer's creditor handling becomes first-order again (creditors rationally never deregister), so the solver convention needs to be fixed at the same time.