Income elasticity of labor supply
Labor and tax subpanel · pooled centers and 90 percent intervals from 15 independent runs per model · shaded region marks the review range [-0.15, -0.05].
What the models were asked
Percent change in annual hours worked from a 1 percent increase in non-labor income, holding the net-of-tax wage fixed and excluding participation responses.
- In standard notation:
- ε = ∂ ln h / ∂ ln ynon-labor, holding wnet fixed (shorthand for display; the models received only the prose definition above)
- Population:
- Prime-age workers in the United States who are already working
- Interpretation:
- Intensive-margin annual-hours elasticity conditional on employment
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: Income elasticity of labor supply
- Definition: Percent change in annual hours worked from a 1 percent increase in non-labor income, holding the net-of-tax wage fixed and excluding participation responses.
- Target interpretation: Intensive-margin annual-hours elasticity conditional on employment
- Population/context: Prime-age workers in the United States who are already working
- Units: elasticity
Sign convention for this quantity:
- An elasticity of ε means that a 1 percent increase in non-labor income changes annual hours worked by ε percent; for example, if ε = 0.5, a 1 percent increase in non-labor income changes annual hours worked by 0.5 percent (not 50 percent).
- ε > 0 if and only if additional non-labor income raises annual hours worked.
- ε < 0 if and only if additional non-labor income reduces annual hours worked.
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; 22 of 29 models received exactly this text, and the other 7 an earlier v4 wording — every model's prompt is archived verbatim, and the two-wording comparison below shows the four models elicited under both. 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.
Review-range sources: CBO 2012; Blundell and MaCurdy 1999; Imbens, Rubin, and Sacerdote 2001 (marginal propensity to earn, converted to an elasticity). These are hand-coded literature anchors, not benchmark truths.
Same model, two clarifier wordings
The sign clarifier for this quantity was revised two days into the April 2026 wave: plain conditionals with the conventional direction first became symmetric if-and-only-if clauses. Seven April models keep the original wording (the split disclosed above), while the four April premium models were re-elicited in full under the revision — so those four answered this quantity under both wordings. Their superseded April 19 runs remain in git history and pool to:
| Model | April 19 center (original wording) | April 21 center (revised wording) | Change |
|---|---|---|---|
| Claude Opus 4.7 | -0.05 | -0.05 | 0.000 |
| Claude Sonnet 4.6 | -0.09 | -0.10 | -0.003 |
| Gemini 3.1 Pro | -0.05 | -0.07 | -0.023 |
| Grok 4.20 | -0.10 | -0.11 | -0.011 |
Pooled centers under the paper's piecewise-uniform construction, 15 runs per cell on both sides. The comparison is not a pure wording experiment — the April 21 re-elicitation also moved to the per-quantity harness that added request logging, and two days elapsed — so wording is confounded with harness path and time (paper, Appendix Tables A18–A19).
Alternative estimators (REML and Bayesian hierarchical)
| Model | Pooled 90% | REML predictive 90% | Bayes predictive 90% |
|---|---|---|---|
| grok-4.20 | [-0.48, 0.10] | [-0.35, 0.12] | [-0.24, 0.03] |
| grok-4.5 | [-0.34, 0.05] | [-0.27, 0.06] | [-0.19, -0.01] |
| claude-sonnet-4.6 | [-0.35, 0.05] | [-0.26, 0.06] | [-0.19, -0.01] |
| deepseek-v4-pro | [-0.42, 0.04] | [-0.22, 0.08] | [-0.17, 0.03] |
| grok-4.3 | [-0.37, 0.08] | [-0.25, 0.06] | [-0.18, -0.00] |
| glm-5.2 | [-0.37, 0.09] | [-0.24, 0.08] | [-0.17, 0.02] |
| gpt-5.6-sol | [-0.34, 0.03] | [-0.23, 0.06] | [-0.16, 0.00] |
| grok-4.1-fast | [-0.50, 0.30] | [-0.42, 0.25] | [-0.26, 0.13] |
| gpt-5.6-terra | [-0.30, 0.04] | [-0.22, 0.05] | [-0.16, -0.00] |
| claude-haiku-4.5 | [-0.25, 0.09] | [-0.21, 0.06] | [-0.15, 0.00] |
| gpt-5.6-luna | [-0.53, 0.19] | [-0.36, 0.19] | [-0.23, 0.08] |
| gemini-3.1-pro-preview | [-0.30, 0.02] | [-0.18, 0.05] | [-0.13, 0.00] |
| kimi-k3 | [-0.38, 0.05] | [-0.21, 0.09] | [-0.15, 0.03] |
| claude-fable-5 | [-0.30, 0.02] | [-0.20, 0.07] | [-0.14, 0.01] |
| gpt-5.4-mini | [-0.25, 0.09] | [-0.18, 0.06] | [-0.13, 0.01] |
| qwen-3.7-max | [-0.28, 0.09] | [-0.18, 0.07] | [-0.13, 0.02] |
| gemini-3.1-flash-lite-preview | [-0.23, 0.01] | [-0.13, 0.03] | [-0.10, -0.01] |
| claude-opus-4.8 | [-0.25, 0.02] | [-0.16, 0.06] | [-0.11, 0.01] |
| kimi-k2.6 | [-0.24, 0.03] | [-0.14, 0.04] | [-0.10, 0.00] |
| gpt-5.4 | [-0.20, 0.06] | [-0.14, 0.04] | [-0.10, -0.00] |
| claude-opus-4.7 | [-0.20, 0.02] | [-0.16, 0.05] | [-0.11, 0.01] |
| gemini-3-flash-preview | [-0.15, 0.00] | [-0.13, 0.02] | [-0.09, -0.01] |
| claude-sonnet-5 | [-0.20, 0.02] | [-0.16, 0.05] | [-0.11, 0.01] |
| claude-opus-5 | [-0.32, 0.01] | [-0.18, 0.08] | [-0.12, 0.03] |
| gemini-3.6-flash | [-0.23, 0.02] | [-0.13, 0.05] | [-0.09, 0.01] |
| gpt-5.5 | [-0.23, 0.03] | [-0.12, 0.06] | [-0.08, 0.02] |
| minimax-m3 | [-0.37, 0.27] | [-0.23, 0.18] | [-0.14, 0.10] |
| gpt-5.4-nano | [-0.24, 0.29] | [-0.21, 0.16] | [-0.13, 0.09] |
| gemini-3.5-flash | [-0.15, 0.15] | [-0.11, 0.13] | [-0.12, 0.14] |
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: grok-4.20-elasticities-batch15, grok-4.5-elasticities-batch15, claude-sonnet-4.6-elasticities-batch15, and 26 more.