{ "schema": { "meta": "Run settings: number of runs, agents per run, seeds, runtime, software versions.", "parameters": "Every model parameter: baseline value, kind (EVIDENCE / CALIBRATED / ASSUMPTION) and source or justification.", "derived_parameters": "Values solved inside the model from report evidence (venture logit, Pareto tail, displacement scars, sigma_alpha).", "validation": "Model outputs compared with the report figures they were calibrated to or should reproduce.", "versions": "Object keyed by version id (A_with_income, B_no_income, C_tvl_reference). Each has: description; metrics {name: {mean, ci95_low, ci95_high, run_p2_5, run_p97_5, n_runs}} where mean is the average over runs, ci95_* is the 95% confidence interval of that mean, and run_p* is the 2.5-97.5% range across individual runs (run-to-run variability of a 1,000-person population); histogram {log10_bin_edges, counts, share} of log10(final wealth / initial wealth) pooled over all agents in all runs; pooled_percentiles; by_talent_decile and by_effort_decile (list of 10 rows: decile 1 = lowest; mean_wealth, median_wealth, prob_top1pct, share_worse_off); by_background_decile (same, by background); talent_by_wealth {by_wealth_percentile: 100 rows (1 = richest 1%) and by_top_rank: 50 rows (1 = richest person), each the mean talent z-score with CIs}; richest_talent_pct_histogram (counts of runs by the talent percentile of the richest agent, 20 bins of 5 percentiles from 0 to 100); wealth_by_age (A and B: pooled mean/p10/p50/p90/p99 of wealth at ages 23..63); twin_lives (A and B: same people re-simulated with new luck; sample_pairs holds log10 wealth in both lives for the 1,000 agents of run 0).", "metric_definitions": "Plain-language definition of each metric name.", "comparison_A_minus_B": "Paired differences (A minus B, same people and same luck) for each metric with 95% CI.", "sensitivity": "{A_with_income: [...], B_no_income: [...], C_tvl_reference: [...]}: one row per one-at-a-time variant: parameter, label (value tried), overrides (all parameters changed), metrics (same format as versions.*.metrics).", "robustness": "For each version and metric: baseline value, min and max over all sensitivity variants (with the variant that produced them) and swing_by_parameter sorted from most to least influential.", "robustness_checks": "Qualitative conclusions and in how many sensitivity variants each one holds.", "agents_sample": "1,000 agents from run 0. Fields: id, talent_z (standard-normal talent score), talent_percentile (0-1 within the population), effort_z, background_z, venture_success_prob, initial_wealth, final_wealth_with_income (version A), final_wealth_no_income (version B: the same person with the same luck but no wage), lifetime_earnings_pv, entered_in_recession, and counts of opportunities, successes, windfalls, losses, displacements and health_shocks. Wealth is in units of one year of median entry-level earnings.", "agents_sample_tvl": "1,000 agents from run 0 of the TvL reference: talent (0-1 scale), talent_percentile, initial_capital (10), final_capital, counts of lucky events, exploited lucky events and unlucky events.", "units": "All money amounts are in units of one year of median earnings at age 23. TvL capital is in TvL units (start = 10)." }, "metric_definitions": { "median": "Median final wealth across the 1,000 agents of a run.", "mean": "Mean final wealth.", "p10/p90/p99/max": "Percentiles / maximum of final wealth within a run.", "top1_share / top10_share / top20_share": "Share of total final wealth held by the richest 1% / 10% / 20%.", "bottom50_share": "Share of total wealth held by the poorest 50%.", "gini": "Gini coefficient of final wealth (0 = equal, 1 = one person has everything).", "share_worse_off": "Share of agents whose final wealth is below their own starting wealth.", "pearson_talent": "Pearson correlation between talent score and final wealth (raw levels; sensitive to outliers).", "pearson_talent_logw": "Pearson correlation between talent score and log final wealth.", "spearman_talent / spearman_effort / spearman_background": "Spearman rank correlation of each trait with final wealth.", "richest_talent_pct": "Talent percentile (0-1) of the single richest agent in the run.", "talent_top1 / talent_top2_10": "Mean talent z-score of the richest 1% / of agents ranked in the top 2-10% by wealth.", "denrell_liu_gap": "talent_top1 minus talent_top2_10 (negative = the very top is less talented than the next tier).", "top1_from_top_talent_decile": "Share of the richest 1% who are in the top 10% of talent (10% = no link)." }, "meta": { "n_runs": 1000, "n_agents_per_run": 1000, "n_years": 40, "seeds": { "trait": 20261113, "shock": 20261114, "shock_twin": 20261115, "tvl": 20261116, "calibration": 20261119 }, "numpy": "2.5.3", "python": "3.13.18", "generated_by": "simulation/model.py", "quick_mode": false, "runtime_seconds": 1064.16 }, "parameters": { "n_years": { "baseline": 40, "kind": "ASSUMPTION", "source": "Working life of 40 annual steps, ages 23-62. Start age 23 is the age at which Huggett, Ventura & Yaron (2011) measure initial conditions (report s.3.4); 40 years is also the Talent-vs-Luck horizon (report s.3.1)." }, "talent_effort_corr": { "baseline": 0.0, "kind": "ASSUMPTION", "source": "Correlation between talent and effort scores. The report gives no estimate; 0 keeps the two channels separable. 0.3 is tested." }, "hvy_target_share": { "baseline": 0.615, "kind": "EVIDENCE", "source": "Share of the variance of (log) lifetime earnings due to conditions fixed at age 23: 61.5% in the Huggett, Ventura & Yaron (2011) benchmark (report s.3.4 and table s.4; range 53.8-66%; Keane & Wolpin give ~90%)." }, "sigma_alpha": { "baseline": null, "kind": "CALIBRATED", "source": "SD of the persistent person-specific log-earnings level. Solved by simulation so that the model's initial-conditions share of lifetime-earnings variance equals hvy_target_share." }, "w_talent": { "baseline": 0.333333, "kind": "ASSUMPTION", "source": "Share of the persistent earnings component's variance coming from talent. The report cannot split 'initial conditions' into talent, effort and background, so the three get equal shares. Todd & Zhang (report s.3.4: family background <10%, plus cognitive ability 14%) suggest talent+background could be smaller; 0.10-0.60 is tested." }, "w_effort": { "baseline": 0.333333, "kind": "ASSUMPTION", "source": "Share from effort (see w_talent)." }, "w_background": { "baseline": 0.333333, "kind": "ASSUMPTION", "source": "Share from unchosen background (see w_talent)." }, "talent_growth": { "baseline": 0.004, "kind": "EVIDENCE", "source": "Extra annual log-earnings growth per SD of talent (learning ability). HVY (report s.3.4): +1 SD learning ability raises expected lifetime wealth by ~8%; 0.004/yr x ~20 yrs average exposure = ~8%. Tested 0 and 0.008." }, "age_slope": { "baseline": 0.05, "kind": "ASSUMPTION", "source": "Hump-shaped age-earnings profile (linear term). Not in the report; a conventional shape that roughly doubles median earnings between 23 and the early 50s." }, "age_curvature": { "baseline": -0.0009, "kind": "ASSUMPTION", "source": "Quadratic term of the age profile (peak about age 51)." }, "rho_persistent": { "baseline": 0.97, "kind": "ASSUMPTION", "source": "Annual persistence of the persistent earnings shock. The report says many shocks are persistent (Guvenen et al. 2021) but gives no number; 0.97 is a near-unit-root value." }, "shock_large_prob": { "baseline": 0.1, "kind": "CALIBRATED", "source": "Normal-mixture earnings shock (report s.4 guidance: 'mostly small changes, with rare large ones (a normal mixture fits this)'). Probability of a draw from the large component. The five mixture/transitory values are set jointly so that annual log-earnings changes have kurtosis inside the report's 10-30 band and strong negative skew (Guvenen et al. 2021)." }, "shock_small_sd": { "baseline": 0.04, "kind": "CALIBRATED", "source": "SD of the small (common) mixture component." }, "shock_large_mean": { "baseline": -0.15, "kind": "CALIBRATED", "source": "Mean of the large mixture component (negative -> negative skew). The small component's mean is set so the overall shock has mean zero." }, "shock_large_sd": { "baseline": 0.4, "kind": "CALIBRATED", "source": "SD of the large mixture component." }, "sigma_transitory": { "baseline": 0.04, "kind": "CALIBRATED", "source": "SD of a purely transitory (one-year) log-earnings shock." }, "guvenen_asymmetry": { "baseline": true, "kind": "EVIDENCE", "source": "Guvenen et al. 2021 (report s.3.3): large positive shocks to high earners are transitory while negative ones persist; the reverse for low earners. Implemented for large shocks using earnings terciles (the tercile cut-offs are our choice). Switched off in sensitivity." }, "earnings_sd_target": { "baseline": 0.6, "kind": "ASSUMPTION", "source": "Cross-sectional SD of log annual earnings, averaged over ages 23-62. The report pins the SHAPE of earnings shocks (kurtosis, skew) and the variance SHARE due to initial conditions (HVY), but not the overall spread of earnings. 0.6 is our approximate reading of typical values for working-age U.S. earners (published estimates span roughly 0.5-0.9 depending on sample); it is NOT from the report. Tested 0.45 and 0.80." }, "earnings_shock_scale": { "baseline": null, "kind": "CALIBRATED", "source": "Multiplier on the five earnings-shock values above (mixture SDs/means and transitory SD). Solved jointly with sigma_alpha so that the model hits BOTH earnings_sd_target and hvy_target_share. Discrete events (displacement, health, recession entry) are not scaled: their sizes are evidence-based." }, "shock_distribution": { "baseline": "mixture", "kind": "ASSUMPTION", "source": "'mixture' (baseline) or 'gaussian' (same variance, no fat tails) - sensitivity only." }, "displacement_rate": { "baseline": 0.02, "kind": "ASSUMPTION", "source": "Annual probability of a mass-layoff job loss. The report flags this as a gap ('no good direct estimate'). 2%/yr means ~55% of people are displaced at least once in 40 years. Tested 1% and 4%." }, "displacement_pv_loss_low": { "baseline": 1.4, "kind": "EVIDENCE", "source": "Present-value earnings loss from displacement when unemployment <6%: 1.4 years of pre-displacement earnings (20-yr horizon, 5% discount; Davis & von Wachter 2011, report s.3.5)." }, "displacement_pv_loss_high": { "baseline": 2.8, "kind": "EVIDENCE", "source": "Same when unemployment >8%: 2.8 years (Davis & von Wachter 2011)." }, "displacement_high_unemp_share": { "baseline": 0.25, "kind": "ASSUMPTION", "source": "Share of displacements that happen in high-unemployment years. Not in the report. Tested 0 and 1." }, "displacement_decay": { "baseline": 0.9, "kind": "ASSUMPTION", "source": "Annual persistence of the displacement earnings scar. The year-0 loss is then solved so the 20-year PV loss matches 1.4 / 2.8 years exactly (gives ~20% / ~39% initial losses)." }, "health_rate_start": { "baseline": 0.003, "kind": "ASSUMPTION", "source": "Annual probability of a major health shock (hospital admission) at age 23; rises linearly to health_rate_end at 62. The report has no frequency estimate (gap). About 35% of people are hit at least once. Scaled x0.5 and x2 in sensitivity." }, "health_rate_end": { "baseline": 0.02, "kind": "ASSUMPTION", "source": "Annual probability at age 62 (see health_rate_start)." }, "health_rate_scale": { "baseline": 1.0, "kind": "ASSUMPTION", "source": "Multiplier on both health rates (sensitivity knob)." }, "health_earnings_loss": { "baseline": 0.2, "kind": "EVIDENCE", "source": "A hospital admission cuts annual earnings by ~20% (Dobkin et al. 2018, report s.3.5)." }, "health_decay": { "baseline": 1.0, "kind": "EVIDENCE", "source": "Persistence of the health earnings loss. The report says the decline 'is persistent', so baseline = no recovery. A recovering version (0.90/yr) is tested." }, "entry_recession_prob": { "baseline": 0.2, "kind": "ASSUMPTION", "source": "Chance of entering the labour market in a recession. Not in the report; roughly one entry year in five." }, "entry_recession_loss": { "baseline": 0.1, "kind": "ASSUMPTION", "source": "Initial earnings loss for recession graduates. The report gives the duration (~10 years) but not the size. Tested 0 and 0.20." }, "entry_recession_years": { "baseline": 10, "kind": "EVIDENCE", "source": "The loss fades linearly to zero over 10 years: 'persistent earnings declines lasting ten years' (Oreopoulos, von Wachter & Heisz 2012, report s.3.5)." }, "entry_recession_disadvantage": { "baseline": 0.3, "kind": "ASSUMPTION", "source": "Losses are larger for the less advantaged (direction: report s.3.5). Size is our choice: loss x exp(-0.3 z_B)." }, "work_income": { "baseline": true, "kind": "ASSUMPTION", "source": "Version switch: True = people work and save part of their earnings (version A); False = no earnings enter wealth (version B)." }, "savings_rate": { "baseline": 0.1, "kind": "ASSUMPTION", "source": "Share of each year's earnings added to wealth. Not in the report. Tested 0.05 and 0.20." }, "savings_income_elasticity": { "baseline": 0.0, "kind": "ASSUMPTION", "source": "0 = everyone saves the same share of earnings. >0 = higher earners save a larger share (rate proportional to (earnings/typical earnings)^elasticity, rescaled so the aggregate saving rate is unchanged, capped at 50%). Not in the report; 1.0 is tested." }, "initial_wealth": { "baseline": 1.0, "kind": "ASSUMPTION", "source": "Starting wealth at 23, in units of one year of median entry-level earnings (all money in the model uses this unit). Equal for everyone at baseline so 'worse off than at the start' is well defined. Tested 0.25 and 4." }, "initial_wealth_sigma": { "baseline": 0.0, "kind": "ASSUMPTION", "source": "Log-SD of unequal starting wealth, tied to background z_B (HVY include initial wealth in 'initial conditions'). 0 at baseline; 1.0 tested." }, "return_rate": { "baseline": 0.03, "kind": "ASSUMPTION", "source": "Real annual return on wealth. Not in the report. Tested 0 and 0.05." }, "le_discount": { "baseline": 0.03, "kind": "ASSUMPTION", "source": "Discount rate for the present value of lifetime earnings (used only for the HVY variance decomposition)." }, "opp_rate": { "baseline": 0.1, "kind": "ASSUMPTION", "source": "Annual probability that an average-effort person meets a business/investment opportunity (~4 per career). The report: 'no good direct evidence' on the frequency of major positive events (gap); Elvidge (2020) finds the lucky-event probability is the most influential TvL input. Tested 0.05 and 0.20." }, "effort_opp_elasticity": { "baseline": 0.3, "kind": "ASSUMPTION", "source": "Effort raises the number of 'shots' (report s.5: 'maximise the number of independent shots'): rate x exp(0.3 z_E - 0.045). No magnitude in the report. Tested 0 and 0.6." }, "stake_fraction": { "baseline": 0.25, "kind": "ASSUMPTION", "source": "Share of current wealth put into each opportunity. Not in the report. Tested 0.10 and 0.50." }, "venture_base_success": { "baseline": 0.2, "kind": "EVIDENCE", "source": "Average success probability of a venture: 18% (NBER) / 21% (JFE) for first-time founders (Gompers et al.); ~25% of VC-backed founders get something at exit (Hall & Woodward). Tested 0.18, 0.21, 0.25." }, "venture_skill_ratio": { "baseline": 1.6, "kind": "EVIDENCE", "source": "Success probability of a +1 SD talent person relative to an average one (logit model). Report s.4 guidance: skill shifts success odds by ~1.5-1.7x for strong vs average ('strong' = +1 SD is our reading). Tested 1.0 (no skill), 1.5, 1.7 and the ~2.1 implied by Gompers' raw persistence." }, "venture_repeat_success": { "baseline": 0.3, "kind": "EVIDENCE", "source": "Success rate of founders whose previous venture succeeded (Gompers et al., report s.3.2). Used for validation and for the 'persistence-implied' skill variant." }, "venture_share_over_5x": { "baseline": 0.06, "kind": "EVIDENCE", "source": "~6% of VC-backed ventures return more than 5x (Kerr, Nanda & Rhodes-Kropf 2014, report s.3.3)." }, "venture_top_return_share": { "baseline": 0.5, "kind": "EVIDENCE", "source": "Those >5x ventures supply roughly half of gross returns (Kerr et al. 2014). Together with the two figures above this pins down a Pareto payoff for successes. Tested 0.4 and 0.6." }, "windfall_rate": { "baseline": 0.01, "kind": "ASSUMPTION", "source": "Annual probability of a pure-luck windfall (inheritance, gift, prize). Not in the report. Tested 0.005 and 0.02." }, "windfall_median": { "baseline": 1.0, "kind": "ASSUMPTION", "source": "Median windfall size (years of median entry earnings)." }, "windfall_sigma": { "baseline": 1.0, "kind": "ASSUMPTION", "source": "Log-SD of windfall size (lognormal)." }, "windfall_labour_response": { "baseline": 0.01, "kind": "EVIDENCE", "source": "Windfalls reduce annual labour earnings by ~1% of the prize, persistently (Cesarini et al. 2017, report s.3.5)." }, "loss_rate": { "baseline": 0.02, "kind": "ASSUMPTION", "source": "Annual probability of a large wealth loss (failed asset, divorce, uninsured loss, fraud). Not in the report. Tested 0.01 and 0.05." }, "loss_fraction": { "baseline": 0.5, "kind": "EVIDENCE", "source": "Share of wealth lost: the TvL unlucky event halves capital (report s.3.1). TvL is uncalibrated, so 0.25 and 0.75 are tested." }, "tvl_talent_mean": { "baseline": 0.6, "kind": "EVIDENCE", "source": "TvL talent ~ Normal(0.6, 0.1) truncated to [0,1]. The report says talent is normal but does not quote the moments; these are the original paper's values (Pluchino et al. 2018)." }, "tvl_talent_sd": { "baseline": 0.1, "kind": "EVIDENCE", "source": "See tvl_talent_mean." }, "tvl_initial_capital": { "baseline": 10.0, "kind": "EVIDENCE", "source": "Everyone starts with capital 10 (original TvL paper)." }, "tvl_steps": { "baseline": 80, "kind": "EVIDENCE", "source": "40 years in six-month steps (report s.3.1)." }, "tvl_event_prob": { "baseline": 0.05, "kind": "ASSUMPTION", "source": "Per-step probability of meeting a lucky event, and separately an unlucky one. TvL generates encounters from moving points on a grid; the report gives no rate. 0.05 gives ~4 of each per career. Tested 0.02 and 0.10." } }, "derived_parameters": { "venture_a": -1.49354, "venture_b": 0.614736, "pareto_xmin": 3.0, "pareto_alpha": 2.35692, "disp_logscar_low": -0.225236, "disp_initial_loss_low": 0.201672, "disp_logscar_high": -0.488216, "disp_initial_loss_high": 0.386279, "shock_small_mean": 0.0166667, "earnings_calibration_check": { "hvy_share_achieved": 0.615021, "earnings_sd_achieved": 0.600015 }, "earnings_shock_scale": 1.39445, "sigma_alpha": 0.470673 }, "validation": { "lifetime_earnings_variance_share_initial_conditions": { "target_HVY_2011": 0.615, "report_range": [ 0.538, 0.66 ], "model_twin_lives": 0.620265, "model_r2_on_traits": 0.615303, "r2_talent_only": 0.298087, "r2_effort_only": 0.157882, "r2_background_only": 0.158682 }, "annual_log_earnings_changes": { "report_target": "strongly negatively skewed; kurtosis ~10-30 (Gaussian = 3); most changes small, rare large jumps", "n": 779990, "share_person_years_below_min_earnings": 7.5e-06, "min_earnings_threshold": 0.05, "mean": 0.0155189, "sd": 0.245499, "skewness": -0.974427, "kurtosis": 15.6981, "share_abs_change_below_0.05": 0.307835, "share_abs_change_above_0.5": 0.0549956, "p1": -0.947712, "p99": 0.770356, "hist_edges": [ -2.0, -1.95, -1.9, -1.85, -1.8, -1.75, -1.7, -1.65, -1.6, -1.55, -1.5, -1.45, -1.4, -1.35, -1.3, -1.25, -1.2, -1.15, -1.1, -1.05, -1.0, -0.95, -0.9, -0.85, -0.8, -0.75, -0.7, -0.65, -0.6, -0.55, -0.5, -0.45, -0.4, -0.35, -0.3, -0.25, -0.2, -0.15, -0.1, -0.05, 0.0, 0.05, 0.1, 0.15, 0.2, 0.25, 0.3, 0.35, 0.4, 0.45, 0.5, 0.55, 0.6, 0.65, 0.7, 0.75, 0.8, 0.85, 0.9, 0.95, 1.0, 1.05, 1.1, 1.15, 1.2, 1.25, 1.3, 1.35, 1.4, 1.45, 1.5, 1.55, 1.6, 1.65, 1.7, 1.75, 1.8, 1.85, 1.9, 1.95, 2.0 ], "hist_counts": [ 99, 20, 44, 64, 66, 71, 99, 139, 148, 198, 191, 297, 357, 434, 500, 532, 674, 779, 891, 1008, 1133, 1299, 1512, 1560, 1818, 2014, 2140, 2478, 2722, 3081, 3499, 3824, 4228, 5038, 6882, 11116, 20664, 40923, 73006, 109159, 130949, 124893, 94172, 57017, 27498, 11738, 5072, 2982, 2314, 2120, 1896, 1855, 1663, 1489, 1337, 1168, 994, 950, 761, 684, 640, 491, 446, 400, 338, 247, 221, 162, 158, 126, 87, 86, 62, 44, 46, 37, 32, 20, 14, 74 ] }, "venture_payoffs": { "report_targets": { "share_zero_or_loss": "~0.73-0.75 founders get nothing (Hall & Woodward); 55% of VC deals at a loss (Kerr)", "share_over_5x": 0.06, "share_of_returns_from_over_5x": 0.5, "expert_score_correlation_with_returns": 0.1 }, "n_ventures": 80044, "share_zero_payoff": 0.798261, "share_over_5x": 0.0607166, "share_of_returns_from_over_5x": 0.501065, "mean_multiple": 1.05345, "corr_talent_with_multiple": 0.161428 }, "venture_persistence_implied_by_baseline_skill": { "report_targets": { "first_time": "0.18 (NBER) / 0.21 (JFE)", "after_success": 0.3, "after_failure": "0.20 (NBER) / 0.22 (JFE)", "consecutive_outcome_correlation": "~0.10-0.15 (report's interpretation)" }, "mean_success": 0.2, "success_after_success": 0.245414, "success_after_failure": 0.188647, "consecutive_outcome_correlation": 0.0567674, 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"mean": 0.900294, "ci95_low": 0.846113, "ci95_high": 0.954474, "run_p2_5": -0.836373, "run_p97_5": 2.56801, "n_runs": 1000 }, { "wealth_rank": 41, "mean": 0.935414, "ci95_low": 0.881117, "ci95_high": 0.989711, "run_p2_5": -0.860584, "run_p97_5": 2.55002, "n_runs": 1000 }, { "wealth_rank": 42, "mean": 0.910217, "ci95_low": 0.856975, "ci95_high": 0.963459, "run_p2_5": -0.74978, "run_p97_5": 2.50765, "n_runs": 1000 }, { "wealth_rank": 43, "mean": 0.956982, "ci95_low": 0.903266, "ci95_high": 1.0107, "run_p2_5": -0.795362, "run_p97_5": 2.74207, "n_runs": 1000 }, { "wealth_rank": 44, "mean": 0.976467, "ci95_low": 0.924452, "ci95_high": 1.02848, "run_p2_5": -0.589009, "run_p97_5": 2.60831, "n_runs": 1000 }, { "wealth_rank": 45, "mean": 0.944357, "ci95_low": 0.891821, "ci95_high": 0.996892, "run_p2_5": -0.775437, "run_p97_5": 2.53517, "n_runs": 1000 }, { "wealth_rank": 46, "mean": 0.900436, "ci95_low": 0.845237, "ci95_high": 0.955636, "run_p2_5": -0.839672, "run_p97_5": 2.59214, "n_runs": 1000 }, { "wealth_rank": 47, "mean": 0.891603, "ci95_low": 0.837904, "ci95_high": 0.945302, "run_p2_5": -0.820543, "run_p97_5": 2.58813, "n_runs": 1000 }, { "wealth_rank": 48, "mean": 0.946125, "ci95_low": 0.893614, "ci95_high": 0.998636, "run_p2_5": -0.853878, "run_p97_5": 2.45196, "n_runs": 1000 }, { "wealth_rank": 49, "mean": 0.914419, "ci95_low": 0.859004, "ci95_high": 0.969833, "run_p2_5": -0.993279, "run_p97_5": 2.68835, "n_runs": 1000 }, { "wealth_rank": 50, "mean": 0.895946, "ci95_low": 0.842006, "ci95_high": 0.949886, "run_p2_5": -0.913442, "run_p97_5": 2.54237, "n_runs": 1000 } ], "note": "Mean talent z-score (0 = average, 1 = one SD above). 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