Orfeas — Archaeological ABM course
PortusSIM (agent-based model of ancient marketplace economies)
A pre-registered experiment tested whether PortusSIM's inheritance mechanism reproduces the pattern predicted by Piketty, Postel-Vinay & Rosenthal (2014) — that inheritance is the engine of perpetuating wealth concentration. The hypothesis was rejected in the opposite direction, with high statistical significance. Post-hoc analysis reveals that PortusSIM operates at a scale (small population, multi-generation mortality) where the dynamics observed by Alfani (2017) regarding the Black Death dominate over Piketty-style rentier dynamics. The result is informative about both the model's scope and about which historical mechanism is being captured.
Piketty, T., Postel-Vinay, G., & Rosenthal, J.-L. (2014). Inherited vs self-made wealth: theory and evidence from a rentier society (Paris 1872–1927). Explorations in Economic History, 51, 21–40.
Central claim: Inherited wealth accounted for approximately 70% of total private wealth in Paris 1872–1927, indicating that inheritance is the dominant mechanism by which wealth concentration is sustained across generations — not within-lifetime accumulation.
Predicted PortusSIM behavior: If PortusSIM captures this mechanism, varying the inheritance_fraction parameter should produce a monotonic increase in final Gini coefficient. Higher inheritance → more concentration.
| Element | Value |
|---|---|
| Treatments | NONE (inheritance_fraction = 0.0), MODERATE (0.5), FULL (1.0) |
| Replications | 20 random seeds per treatment (seeds 2000-2019) |
| Total simulations | 60 |
| Simulation length | 1500 days (~125 historical years, 4-5 generations) |
| Population | 5 elite + 10 middle + 5 poor merchants |
| Trust regime | trust_max = 0.05 (default, below the cliff) |
| Generations | Enabled |
| Other parameters | All at default values |
Pre-registered hypotheses:
- H1 (primary): Gini(NONE) < Gini(MODERATE) < Gini(FULL). Confirmation would support Piketty et al.'s mechanistic claim.
- H2 (secondary): The effect grows with simulation length.
- H3 (secondary): Inheritance has no significant effect on within-class bankruptcy rates.
| Treatment | Mean Gini | Stdev | 95% CI | n |
|---|---|---|---|---|
| NONE | 0.866 | 0.043 | [0.847, 0.885] | 20 |
| MODERATE | 0.450 | 0.043 | [0.431, 0.469] | 20 |
| FULL | 0.383 | 0.022 | [0.374, 0.393] | 20 |
| Comparison | t | df | One-tailed p | Mean diff |
|---|---|---|---|---|
| NONE vs MODERATE | 30.59 | 38.0 | < 0.0001 | +0.416 |
| MODERATE vs FULL | 6.17 | 28.3 | < 0.0001 | +0.067 |
| NONE vs FULL | 44.55 | 28.2 | < 0.0001 | +0.483 |
| Treatment | Elite | Middle | Poor |
|---|---|---|---|
| NONE | 67% ± 9% | 78% ± 4% | 100% ± 0% |
| MODERATE | 54% ± 9% | 1.5% ± 2% | 45% ± 10% |
| FULL | 41% ± 8% | 0% ± 0% | 34% ± 8% |
- H1: REJECTED. Gini decreased monotonically as inheritance increased, opposite to the predicted direction.
- H2: Not tested in this experiment (would require additional simulation lengths).
- H3: REJECTED. Inheritance has a large, significant effect on bankruptcy rates — particularly for the middle class (78% with NONE, 0% with FULL).
The data reveals a structural mechanism that was not anticipated:
Without inheritance, the poor class undergoes 100% generational bankruptcy in every single run. This is because:
- The poor class's daily income (5 coins) equals their daily expenses (5 coins) by default. Net daily wealth = 0.
- They accumulate wealth only through trade, which depends on encountering other merchants and successful trust-based exchange.
- Once a poor merchant goes bankrupt, the replacement (new generation) starts with poor starting wealth = 50.
- Without inheritance, the cycle never breaks: every generation of poor merchants is structurally guaranteed to deplete over time.
A sensitivity check confirmed this is a regime trap: even raising poor starting wealth to 400 (8× default) or increasing trust_max to 0.30 does not lift poor survival above 0% when inheritance = 0.
With inheritance, this collapse is prevented. Poor survivors transmit wealth to the next generation, keeping the bottom of the distribution alive.
Mechanism implication: At PortusSIM's scale, generational continuity itself is an equality-preserving mechanism — not because of fairness, but because the alternative (zero inheritance) means the poor are deterministically eliminated as a class. The remaining "economy of survivors" has extreme inequality (Gini ≈ 0.87) measured among the elite-and-middle who happened to make it.
The result aligns with a different literature than the one we tried to test:
Alfani, G. (2017). The rich in historical perspective: evidence for preindustrial Europe (ca. 1300–1800). Cliometrica, 11(3), 321–348.
Alfani documents that the Black Death (1348) reduced European wealth inequality by approximately 20-30% because mass mortality redistributed property. The mechanism: mortality disrupts intergenerational transmission, which had been the engine of inequality persistence.
PortusSIM at this configuration tests the inverse of Alfani's finding: it shows that disabling intergenerational transmission (high mortality with no inheritance) produces an outcome similar to a sustained Black-Death-level shock — but in a population so small that the bottom class is eliminated rather than just shrunk.
This is consistent with Alfani, not Piketty. Two genuine claims in the same literature, but operating at different scales:
| Mechanism | Scale | Direction |
|---|---|---|
| Piketty's rentier hypothesis | Large population, century timescales | Inheritance → more inequality |
| Alfani's mortality-disruption observation | Mortality shocks in pre-modern societies | Inheritance → less collapse-driven inequality |
PortusSIM (20 merchants, 4-5 generations) operates in the Alfani regime, not the Piketty regime.
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The tool is honest about its scope. It does not pretend to test centuries-scale rentier dynamics. The result revealed which scale it does operate at.
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The "100% poor bankruptcy without inheritance" is a structural feature of the parameter design, not a bug. The poor's net daily wealth = 0 by default, making generational survival impossible without buffers. This is documented in the model.
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Generational continuity is now identified as an equality-preserving mechanism within the model's scope. This was added as Finding 5 to PortusSIM's bundled findings.
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The four previously-established findings (trust cliff, Goldilocks zone, geography dominance, inheritance amplifies structural advantage) were re-verified to hold qualitatively when generations are enabled. Quantitative values shift but directions are preserved.
The exact configuration is captured in the pre-registration document (inheritance_experiment_preregistration.md). The raw data is in RESULTS.xlsx with 60 individual run records. To reproduce:
- Open PortusSIM
- Parameter sweep mode → 1D sweep
- Sweep parameter:
inheritance_fraction, values 0.0 → 1.0, 3 steps, 20 runs per value - Base config: defaults + generations_enabled = True + simulation_days = 1500, seed = 2000
Use the new "Export per-seed CSV" button to extract per-run records identical to RESULTS.xlsx.
- Alfani, G. (2017). The rich in historical perspective: evidence for preindustrial Europe (ca. 1300–1800). Cliometrica, 11(3), 321–348.
- Piketty, T., Postel-Vinay, G., & Rosenthal, J.-L. (2014). Inherited vs self-made wealth: theory and evidence from a rentier society (Paris 1872–1927). Explorations in Economic History, 51, 21–40.
- Scheidel, W., & Friesen, S.J. (2009). The size of the economy and the distribution of income in the Roman Empire. Journal of Roman Studies, 99, 61–91.