Capital share in production
Calibration parameters subpanel · pooled centers and 90 percent intervals from 15 independent runs per model.
What the models were asked
Output elasticity with respect to capital in an aggregate production function.
- In standard notation:
- α = ∂ ln Y / ∂ ln K (shorthand for display; the models received only the prose definition above)
- Population:
- U.S. aggregate production
- Interpretation:
- Cobb-Douglas capital share alpha
The exact prompt, verbatim
Answer from your current memory and background knowledge only.
Do not use tools, files, the web, code, or external resources.
Do not try to reconstruct a literature review or search for a consensus estimate.
Report the belief you currently endorse.
Quantity of interest:
- Name: Capital share in production
- Definition: Output elasticity with respect to capital in an aggregate production function.
- Target interpretation: Cobb-Douglas capital share alpha
- Population/context: U.S. aggregate production
- Units: share
Task:
1. Use exactly the target interpretation above. In `interpretation`, restate it briefly.
2. Give your subjective quantiles p05, p25, p50, p75, and p95 for this quantity.
3. Set `point_estimate` equal to `p50`.
4. Make the quantiles weakly increasing and numerically coherent.
5. In `citations`, list up to 3 source anchors from memory that influenced your belief. These are recall anchors only. If none come to mind confidently, return `[]`.
6. Keep `reasoning_summary` brief and substantive.
Return valid JSON only with exactly this shape:
{
"interpretation": "...",
"point_estimate": <number>,
"quantiles": {
"p05": <number>,
"p25": <number>,
"p50": <number>,
"p75": <number>,
"p95": <number>
},
"citations": ["..."],
"reasoning_summary": "..."
}Read from the archived request logs; all 29 models received this identical text. How the JSON response is enforced varies by provider — see the Methods harness table and the Process page.
Dot: pooled center (mean of run point estimates). Bar: pooled 90 percent mixture interval. Faint underlay: each run's elicited p05–p95. Models sorted by center; color = provider family. Filters change which models render; the axis stays fixed to the full panel.
Alternative estimators (REML and Bayesian hierarchical)
| Model | Pooled 90% | REML predictive 90% | Bayes predictive 90% |
|---|---|---|---|
| claude-haiku-4.5 | [0.25, 0.43] | [0.25, 0.36] | [0.27, 0.34] |
| gpt-5.4-nano | [0.20, 0.50] | [0.21, 0.43] | [0.25, 0.38] |
| grok-4.1-fast | [0.25, 0.42] | [0.25, 0.41] | [0.28, 0.37] |
| gpt-5.4 | [0.25, 0.45] | [0.24, 0.43] | [0.28, 0.39] |
| claude-opus-4.7 | [0.25, 0.42] | [0.25, 0.42] | [0.29, 0.38] |
| claude-sonnet-4.6 | [0.25, 0.42] | [0.26, 0.41] | [0.29, 0.37] |
| gemini-3-flash-preview | [0.28, 0.42] | [0.28, 0.39] | [0.30, 0.36] |
| gemini-3.1-flash-lite-preview | [0.25, 0.45] | [0.25, 0.42] | [0.28, 0.38] |
| grok-4.20 | [0.25, 0.44] | [0.26, 0.41] | [0.29, 0.38] |
| grok-4.3 | [0.25, 0.43] | [0.26, 0.40] | [0.29, 0.37] |
| gpt-5.6-terra | [0.25, 0.45] | [0.25, 0.43] | [0.28, 0.38] |
| grok-4.5 | [0.25, 0.45] | [0.25, 0.42] | [0.28, 0.38] |
| glm-5.2 | [0.23, 0.47] | [0.25, 0.42] | [0.28, 0.38] |
| claude-opus-4.8 | [0.25, 0.42] | [0.27, 0.41] | [0.30, 0.37] |
| kimi-k3 | [0.25, 0.45] | [0.25, 0.43] | [0.28, 0.39] |
| gpt-5.5 | [0.25, 0.47] | [0.25, 0.44] | [0.29, 0.39] |
| gemini-3.5-flash | [0.28, 0.42] | [0.28, 0.40] | [0.30, 0.37] |
| gemini-3.6-flash | [0.28, 0.42] | [0.28, 0.40] | [0.30, 0.37] |
| gemini-3.1-pro-preview | [0.26, 0.44] | [0.27, 0.41] | [0.30, 0.38] |
| gpt-5.4-mini | [0.23, 0.49] | [0.24, 0.45] | [0.28, 0.40] |
| deepseek-v4-pro | [0.24, 0.45] | [0.27, 0.43] | [0.30, 0.39] |
| claude-sonnet-5 | [0.28, 0.42] | [0.28, 0.41] | [0.30, 0.38] |
| qwen-3.7-max | [0.25, 0.45] | [0.27, 0.42] | [0.30, 0.39] |
| claude-fable-5 | [0.28, 0.43] | [0.28, 0.41] | [0.31, 0.38] |
| kimi-k2.6 | [0.25, 0.48] | [0.26, 0.44] | [0.29, 0.40] |
| minimax-m3 | [0.23, 0.51] | [0.25, 0.45] | [0.29, 0.40] |
| gpt-5.6-sol | [0.25, 0.48] | [0.25, 0.45] | [0.29, 0.40] |
| claude-opus-5 | [0.27, 0.43] | [0.28, 0.42] | [0.31, 0.39] |
| gpt-5.6-luna | [0.24, 0.51] | [0.25, 0.48] | [0.29, 0.42] |
The paper's headline object is the pooled mixture interval; the alternatives are robustness estimators (paper, Appendix A2).
Run-level responses
Each model answered 15 independent times. Pick a model to read every run: its elicited 90 percent interval, point estimate, and stated reasoning.
435 successful runs · elicited April and July 2026 · v4 prompts · 15 runs per model-quantity cell. Code · Raw responses · Paper (PDF)
Result directories: claude-haiku-4.5-elasticities-batch15, gpt-5.4-nano-elasticities-batch15, grok-4.1-fast-elasticities-batch15, and 26 more.