Fix vat liability scaling#17
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Implements corrections from a policy / economics / statistics referee panel.
Substantive (theory):
- Secondary dominated region: a banded reduced rate reverts to 20% at the
£105k band top, creating a second notch (a' = T1(τ−r)/(1−τ)). Total
dominated width is therefore £21,562 (15%) and £22,569 (10%), essentially
unchanged vs the £21,250 baseline — the reduced rate splits the empty band
rather than shrinking it. Only the taper removes the distortion; the level
move relocates it. Corrected in model.tex, intro.tex, conclusion.tex.
- Reconcile notch rate: the £21,250 width uses the statutory 20% turnover
rate while the costing/behavioural layers use each firm's ~3% net wedge.
Reframe "model-free" → "exact, elasticity-free (conditional on the
turnover-tax notch)"; clarify the 137k count indexes exposed population,
not optimal locators.
- Demote e=0.17 from "headline" to "illustrative midpoint"; anchor the
e-range's only external point (Kleven–Waseem ≈0.05); note 0.17/0.32 are
notch-implied, not data-identified.
Statistics / inference:
- Caveat that bootstrap SEs/CIs reflect resampling dispersion of a synthetic
file of analyst-chosen size, not population sampling error.
- Reconcile appendix elasticities (notch-width ≈0.45, marginal-buncher ≈0.66)
vs body sweep {0.05,0.17,0.32}: different objects, all non-identified.
- Fix estimator contradictions: bin width £100 → £1,000 (bunching.tex);
counterfactual polynomial "cubic" → degree-7 (a_data.tex), matching code.
Policy:
- Reconcile £203.8bn base as a theoretical-liability (VTTL-style) aggregate
above cash receipts (footnote); cite HMT Spring Budget 2024 for the £185m
anchor.
- Add compliance-cost caveat (cite Keen & Mintz 2004) to the distortion
ranking limitations.
Housekeeping:
- Correct the static-sweep convexity mechanism (higher per-firm liability,
not denser mass) and three sec:bunching → sec:behavioural cross-refs.
- Move orphaned/contradictory model sections (results, counterfactuals,
literature) to paper/future/; update body.tex comments.
- README firm count 2.0M → 2.5M; conclusion voluntary-reg wording → 43%.
- Rebuild paper/main.pdf.
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
The reduced-rate case needs the secondary-notch identity, so the opening of "How each reform changes the dominated region" now references both eq:dominated and eq:dominated-secondary rather than implying everything follows from the single primary-notch formula. Rebuild main.pdf. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Second-pass revisions from the three-referee re-review (all minor):
- Base reconciliation: intro now flags the £508m (£85k data-year base) vs the
£374m £90k-sweep figure for the same £100k move; static.tex notes both
£183.6bn and £203.8bn are VTTL-style theoretical-liability bases.
- "HMRC's £185m" → "the Government's published £185m" (cite is HM Treasury).
- model.tex: own that the 137k dominated-band count is conditional on the
uniform within-band fill and would shift under another shape; the width a,
not the count, is exact.
- behavioural.tex: resolve the Δy* symbol collision (structural marginal-buncher
excess now Δy_H ≡ n_H−T*, distinct from the appendix's £5.6k bunching span);
note the body's 0.17/0.32 differ from the appendix's ≈0.66 marginal-buncher
elasticity, both non-identified.
- data.tex: note ρ_i up to 1.5 permits negative value added (input-VAT-reclaim
positions).
- conclusion.tex: flag absent sectoral incidence of the menu reforms as future
work (VAT-by-sector excluded from the optimiser).
- a_inference.tex: complete tab:degwin to the full {5,6,7,8}×{£10–25k} grid
(16 cells, from the released estimator output) so it matches the prose.
- Rebuild main.pdf (35pp).
Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
… ~0.6 Per-firm net VAT liability is now STANDARD_VAT_RATE*(turnover-input) (was raw value added, missing the rate); input/output ratio re-centred ~0.98 -> ~0.6 and clamped [0.1,0.95] so value added is always positive (eliminates the ~47% negative-VA firms). Applied consistently in generate/calibration/validate/dynamic. Calibration knob l1_reg_coef is PROVISIONAL (repair of near-threshold density in progress). Results/figures intentionally not committed yet. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
Knob-tuning (l1_reg_coef, vat_liability_band_importance) was explored to repair the near-threshold density but did NOT restore positive bunching excess mass (E stays 0 even when the simple below/above density step turns positive). So the branch keeps the v_i/rho fix with DEFAULT knobs; the bunching reproduction issue is deferred to a tracking issue. Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>
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What this does
Fixes a per-firm scaling defect in the synthetic-data model:
vat_liability_kwas storing raw value added (turnover − input), missing the ×0.20 VAT rate — per-firm "net VAT" was ~5× too large.The fix:
v_i = STANDARD_VAT_RATE · (turnover − input)and ρ re-centred to ~0.6 (clamped[0.1, 0.95], so value added is always positive), applied consistently acrossconfig / generate / calibration / validate / dynamic.What's verified good ✅
Why it's a DRAFT and must not merge ❌
The corrected (turnover-correlated) liability makes the weight optimiser pile weight just above £85k, which reverses the near-threshold density step and collapses the bunching signal: excess mass E: 8,712 → 0, ratio b: +0.06 → −0.14. The 2024-25 vintage also degrades. Calibration-knob tuning (
l1_reg_coef,vat_liability_band_importance) can flip the simple density step positive but the estimator still returns E=0 — knob-tuning does not restore it. So merging this would ship a paper whose headline bunching result is broken.What remains (see #15)
Decide the bunching story under the corrected model — either a deeper calibration change (e.g. a near-threshold density target) or an honest reframing of Section 5 — then a full re-run and propagation of all headline numbers.
Notes
main(paper/Sections/data.tex,paper/main.pdf); needs a rebase before it could ever be considered.🤖 Generated with Claude Code