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Paper: describe the bunching estimator's E, b_LLAT and censored y_R as implemented - #43

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Paper: describe the bunching estimator's E, b_LLAT and censored y_R as implemented#43
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fix/bunching-estimator-definitions

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Text-only change to the Methodology paragraph of paper/Sections/bunching.tex so it describes the estimator in src/firm_microsim/bunching/model.py as implemented:

  • y_R is found by walking missing mass upward from the threshold within the search window; when missing mass runs out (Delta_R = 0 in the headline run) it is censored at the window edge (£100k). The old text said mass conservation locates it "endogenously (excess mass below must equal missing mass above)", which the headline run violates. The appendix already said "the search cap"; body and appendix now agree.
  • The displayed equation integrated the counterfactual g over the bunching interval. Replaced with E = ∫ [f − g]_+ dy over the below window, which is what locate_marginal_buncher computes, and labelled gross rather than net.
  • b_LLAT is described as the positive-part gap over [y*−W, y_R] (both sides) divided by mean counterfactual height, "in the spirit of" LLAT's normalisation but not an exact reproduction, and explicitly not E divided by a density. The b ≈ Δy*/y* sentence, which matched neither b nor b_LLAT in the code, is removed.

No numbers change. The code-side items (a y_R_censored flag, separate E_gross/E_net, exact LLAT normalisation, recovery tests) are tracked in #38.

Refs #38, #32 (finding 5).

🤖 Generated with Claude Code

…he code defines them

Section 6 described a mass-conservation restriction that locates y_R
endogenously and wrote excess bunching as the integral of the counterfactual
density. The code sums the positive part of f_obs - f_cf below the threshold
for E, searches for y_R only up to the window edge (censored at £100k in the
headline run, where Delta_R = 0), and normalises b_LLAT over both sides of
the threshold. Say so, and drop the b ≈ Δy*/y* relation that matches
neither statistic.

Refs #38, #32 (finding 5).

Co-Authored-By: Claude Fable 5.1 <noreply@anthropic.com>
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