Statistical Model Checking of the Island Model: An Established Economic Agent-Based Model of Endogenous Growth

Abstract

Agent-based models (ABMs) are increasingly used to study complex economic phenomena such as endogenous growth, but their analysis typically relies on ad-hoc Monte Carlo exercises without formal statistical guarantees. We show how statistical model checking (SMC), and in particular Multi-VeStA, can automate and enrich the analysis of a seminal ABM: the Island Model of Fagiolo and Dosi, which captures the exploration-exploitation trade-off in technological search. We reproduce key stylized facts from the original model with formal confidence intervals, confirm the optimality of moderate exploration rates, and perform a counterfactual sensitivity analysis across returns to scale, skill transfer, and knowledge locality. Using MultiVeStA's built-in Welch's t-test, 6 out of 7 pairwise parameter comparisons yield statistically different growth trajectories, while the exception reveals a saturation effect in knowledge locality. Our results demonstrate that SMC offers a principled, reproducible methodology for the quantitative analysis of agent-based economic models.

Figures (6)

• Figure 1: Agent type transitions. Miners are the productive state. Exploration (with probability $\varepsilon$) and imitation (upon receiving a stronger productivity signal) represent two distinct search strategies. Both explorers and imitators return to mining upon completing their search.
• Figure 2: Stagnation vs. sustained growth. When exploration ceases at $t=50$, log(GDP) plateaus. With continuous exploration ($\varepsilon = 0.1$), growth is sustained. Shaded bands show 95% confidence intervals.
• Figure 3: Average Growth Rate vs. exploration probability $\varepsilon$. Growth peaks at $\varepsilon \approx 0.1$, demonstrating the exploration-exploitation trade-off. Error bars show 95% confidence intervals.
• Figure 4: Effect of returns to scale $\alpha$ on average $\log(\text{GDP})$. Shaded bands show 95% confidence intervals. Bottom: pairwise t-test results ($\bullet$ = equal means, $\times$ = different means).
• Figure 5: Effect of skill transfer $\varphi$ on average $\log(\text{GDP})$. Even low skill transfer ($\varphi = 0.1$) produces higher growth than none. Bottom: pairwise t-test results ($\bullet$ = equal means, $\times$ = different means).