מסמך טכני מיומן המחקר · באנגלית, כפי שנכתב בשלב העבודה
Step 305: completing the frontier figure
Why. The interactive figure on the thesis page plots the median breakeven productivity gain g\* against the ceiling on the profit levy. Two sets of points were missing from the archives: the 30% ceiling under the step-301 costs, and a tax-base erosion elasticity of 0.9, the stronger value tested in step 304. This step computes them with the existing model and sweep; nothing else in the model changes.
Generated by scripts/frontier_v305.py, with output in data/processed/frontier_v305.json. The figure data are rebuilt from it by scripts/frontier_web.py. Model: scripts/closure_model_v304.py. With the new options off it reproduces steps 301–303, and the costless and step-301 rows below reproduce steps 277 and 301 exactly. Illustrative; not a forecast.
Method
- Sweep. The step-277 sweep over 144 combinations of the other assumptions: g from 0 to 1.5 in steps
of 0.025. g\* is the first gain at which both displaced cohorts keep 90% of their consumption.
- Rules.
- PV equity with no levy (0% ceiling); - levy up to 15% (the central specification); - levy up to 30%; - benefits only (step 271 rule).
- Variants.
- costless levy; - step-301 costs: erosion 0.5, owners consume 0.4, Tobin's q after the levy; - erosion 0.9 with the eroded base returned to owners (as in steps 301–303); - erosion 0.9 with the eroded base leaving the economy (step 304's leakage).
Results
Median g\* (quartiles), and cases preserved out of 432 in the central grid, with fiscal crises in brackets:
| Variant | No levy (PV) | Levy up to 15% | Levy up to 30% | Benefits only |
|---|---|---|---|---|
| Costless levy | 0.463 (0.344–0.625); 214 (110) | 0.325 (0.20–0.45); 277 (10) | 0.20 (0.125–0.30); 338 (56) | 0.50 (0.35–0.675); 211 (110) |
| Step-301 costs | 0.338 (0.175–0.50); 282 (49) | 0.25 (0.125–0.325); 339 (0) | 0.15 (0.10–0.20); 383 (0) | 0.35 (0.175–0.525); 277 (43) |
| Erosion 0.9, returned to owners | 0.463; 214 (110) | 0.375 (0.275–0.506); 246 (37) | 0.35 (0.275–0.425); 262 (5) | 0.50; 211 (110) |
| Erosion 0.9, leaking out | 0.463; 214 (110) | 0.375 (0.275–0.506); 245 (37) | 0.375 (0.30–0.463); 254 (4) | 0.50; 211 (110) |
New values in bold. Erosion does not affect the rules without a levy.
What it shows.
- Under the step-301 costs, a higher ceiling still lowers the threshold. It goes from 0.25 to 0.15.
The levy's ranking does not change, although all thresholds are lower because owners who consume less raise investment in this closure (see step 301).
- Strong erosion flattens the frontier.
- At elasticity 0.9 the 15% levy lowers the median threshold from 0.46 to 0.375, rather than to 0.325. Doubling the ceiling to 30% adds little: 0.35, or nothing at all (0.375) when the eroded base leaves the economy. - The levy still preserves more cases than no levy (246 or 245 against 214), and with far fewer fiscal crises (37 against 110).
- A higher ceiling buys stability more than preservation under strong erosion. At 30%, crises fall to
4–5 while preserved cases rise only to 254–262.
Limits
- Medians over a grid chosen by the researcher; the counts are not probabilities.
- Erosion is a reduced-form response of reported profits to the levy rate. An elasticity of 0.9 lies above
the estimates the thesis cites (0.13–0.58).
- Same model limits as steps 301–304.