Employment participation elasticity of single mothers

Labor and tax subpanel · pooled centers and 90 percent intervals from 15 independent runs per model · shaded region marks the review range [0.3, 1].

labor_supply.extensive_margin.single_mothers

What the models were asked

Percent change in employment or labor-force participation from a 1 percent change in the net-of-tax wage.

In standard notation:: ε = ∂ ln Pr(employed) / ∂ ln w_net
Population:: Single mothers in the United States
Interpretation:: Medium-run employment participation elasticity with respect to the net-of-tax wage

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: Employment participation elasticity of single mothers
- Definition: Percent change in employment or labor-force participation from a 1 percent change in the net-of-tax wage.
- Target interpretation: Medium-run employment participation elasticity with respect to the net-of-tax wage
- Population/context: Single mothers in the United States
- Units: elasticity

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.

Lab29 of 29 models

0.21 [-0.05, 0.80]

0.30 [0.00, 1.37]

0.37 [-0.04, 1.37]

0.41 [0.06, 1.12]

0.42 [0.10, 1.17]

0.42 [0.10, 1.10]

0.42 [0.08, 1.17]

0.43 [0.08, 1.12]

0.45 [0.15, 1.09]

0.46 [0.07, 1.24]

0.46 [0.06, 1.08]

0.47 [0.10, 1.41]

0.47 [0.07, 1.39]

0.52 [0.06, 1.52]

0.53 [0.12, 1.39]

0.54 [0.08, 1.47]

0.54 [0.11, 1.26]

0.55 [0.16, 1.18]

Gemini 3.1 Flash-Lite

0.56 [0.10, 1.48]

0.60 [0.10, 1.46]

0.60 [0.14, 1.46]

0.62 [0.13, 1.55]

0.64 [0.08, 1.58]

0.66 [0.11, 1.64]

0.69 [0.20, 1.49]

0.70 [0.20, 1.40]

0.70 [0.20, 1.50]

0.71 [0.16, 1.85]

0.72 [0.11, 1.82]

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: Chetty, Guren, Manoli, and Weber 2013 (elasticity implied by Eissa and Liebman 1996); Meyer and Rosenbaum 2001. These are hand-coded literature anchors, not benchmark truths.

Alternative estimators (REML and Bayesian hierarchical)

Model	Pooled 90%	REML predictive 90%	Bayes predictive 90%
gpt-5.4-nano	[-0.05, 0.80]	[-0.05, 0.50]	[0.04, 0.38]
grok-4.1-fast	[0.00, 1.37]	[-0.16, 0.92]	[0.02, 0.63]
gpt-5.6-luna	[-0.04, 1.37]	[-0.10, 0.94]	[0.08, 0.67]
glm-5.2	[0.06, 1.12]	[0.05, 0.83]	[0.19, 0.64]
claude-haiku-4.5	[0.10, 1.17]	[0.08, 0.77]	[0.20, 0.61]
deepseek-v4-pro	[0.10, 1.10]	[0.06, 0.82]	[0.20, 0.63]
gpt-5.6-sol	[0.08, 1.17]	[0.02, 0.88]	[0.18, 0.66]
grok-4.3	[0.08, 1.12]	[0.07, 0.82]	[0.21, 0.64]
gemini-3-flash-preview	[0.15, 1.09]	[0.10, 0.87]	[0.25, 0.68]
gpt-5.5	[0.07, 1.24]	[0.03, 0.98]	[0.20, 0.74]
gemini-3.5-flash	[0.06, 1.08]	[0.09, 0.92]	[0.24, 0.71]
grok-4.20	[0.10, 1.41]	[0.03, 0.99]	[0.20, 0.75]
kimi-k2.6	[0.07, 1.39]	[0.03, 0.96]	[0.19, 0.74]
gpt-5.4-mini	[0.06, 1.52]	[0.02, 1.05]	[0.18, 0.82]
grok-4.5	[0.12, 1.39]	[0.10, 1.05]	[0.27, 0.81]
minimax-m3	[0.08, 1.47]	[0.07, 0.98]	[0.16, 0.86]
gemini-3.6-flash	[0.11, 1.26]	[0.09, 1.09]	[0.27, 0.84]
claude-fable-5	[0.16, 1.18]	[0.17, 1.01]	[0.32, 0.80]
gemini-3.1-flash-lite-preview	[0.10, 1.48]	[0.07, 1.14]	[0.25, 0.88]
claude-sonnet-5	[0.10, 1.46]	[0.06, 1.29]	[0.27, 0.97]
gemini-3.1-pro-preview	[0.14, 1.46]	[0.16, 1.08]	[0.30, 0.89]
gpt-5.6-terra	[0.13, 1.55]	[0.10, 1.24]	[0.30, 0.96]
claude-opus-5	[0.08, 1.58]	[0.09, 1.32]	[0.31, 1.01]
kimi-k3	[0.11, 1.64]	[0.11, 1.32]	[0.32, 1.02]
claude-opus-4.8	[0.20, 1.49]	[0.16, 1.35]	[0.38, 1.05]
claude-opus-4.7	[0.20, 1.40]	[0.20, 1.30]	[0.41, 1.02]
claude-sonnet-4.6	[0.20, 1.50]	[0.14, 1.40]	[0.37, 1.08]
gpt-5.4	[0.16, 1.85]	[0.07, 1.50]	[0.32, 1.14]
qwen-3.7-max	[0.11, 1.82]	[0.14, 1.41]	[0.37, 1.09]

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: gpt-5.4-nano-elasticities-batch15, grok-4.1-fast-elasticities-batch15, gpt-5.6-luna-elasticities-batch15, and 26 more.

Code and dataElicited April and July 2026 · 29 models · v4 prompts