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

Stefano Blando; Giorgio Fagiolo; Daniele Giachini; Andrea Vandin; Ernest Ivanaj

cs.MAApr 6, 2026

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

Authors: Stefano Blando, Giorgio Fagiolo, Daniele Giachini, Andrea Vandin, Ernest Ivanaj

Organizations: Institute of Economics and L'EMbeDS, Sant'Anna School of Advanced Studies · Institute of Economics and L’EMbeDS, Sant’Anna School of Advanced Studies, Pisa, Italy · Swiss Finance Institute and University of Geneve · Swiss Finance Institute, University of Geneve, Switzerland

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 & tables

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.

Parameter	Description	Default	Economic Interpretation
$N$	Number of agents	20	Labor force size
$T$	Simulation length	201	Time horizon (steps)
$\pi$	Island density	0.1	Technological opportunity
$\alpha$	Returns to scale	1.5	Market structure
$\varepsilon$	Exploration probability	0.1	Innovation intensity
$\lambda$	Technology jump	1	Breakthrough frequency

Table 1: Island Model Parameters

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).

Figure 6: Effect of knowledge locality $\rho$ on average $\log(\text{GDP})$ . Lower $\rho$ (broader knowledge diffusion) promotes growth. Bottom: pairwise t-test results ( $\bullet$ = equal means, $\times$ = different means).

Statistical Model Checking

See all 8 papers

Statistical Model Checking of the Keynes+Schumpeter Model: A Transient Sensitivity Analysis of a Macroeconomic ABM
May 11, 2026Stefano Blando, Giorgio Fagiolo, Mauro Napoletano +2Statistical Model Checking Agent-Based Modeling
Institute of Economics and L’EMbeDS2026 Sant’Anna School of Advanced Studies, Pisa, Italy · GREDEG, CNRS, Université Côte d’Azur Sophia Antipolis, France · Maastricht University Maastricht, The Netherlands
Towards Agentic Agent-based Models: Feasibility, Performance, and Statistical Model Checking
Jul 20, 2026Stefano Blando, Emanuele Guerrazzi, Riccardo Porcedda +3Agent-Based Modeling LLM Agents
Sant’Anna School of Advanced Studies Pisa, Italy · University of Pisa, Italy · CentraleSupélec, Université Paris-Saclay, France +2
From Model-Based Screening to Data-Driven Surrogates: A Multi-Stage Workflow for Exploring Stochastic Agent-Based Models
Apr 3, 2026Paul Saves, Matthieu Mastio, Nicolas Verstaevel +1Sensitivity Analysis Agent-Based Modeling
IRIT, Université Toulouse Capitole, Toulouse, France

May 11, 2026J/K move · Enter open · S save

Statistical Model Checking of the Keynes+Schumpeter Model: A Transient Sensitivity Analysis of a Macroeconomic ABM

Stefano Blando, Giorgio Fagiolo, Mauro Napoletano, Tania Treibich+1

Institute of Economics and L’EMbeDS2026 Sant’Anna School of Advanced Studies, Pisa, Italy · GREDEG, CNRS, Université Côte d’Azur Sophia Antipolis, France · Maastricht University Maastricht, The Netherlands

Statistical Model Checking Agent-Based Modeling Sensitivity Analysis

Open paper AskPDF arXiv

Agent-based models (ABMs) are increasingly used in macroeconomics, but their analysis still often relies on ad hoc Monte Carlo campaigns with heterogeneous statistical effort across parameter settings. We show how statistical model checking (SMC), implemented through MultiVeStA, can provide a principled analysis layer for a realistic macroeconomic ABM without rewriting the simulator in a dedicated formalism. Our case study is the heuristic-switching Keynes+Schumpeter(K+S) model, analysed hrough a transient sensitivity campaign over one-parameter sweeps, two macro observables (unemployment and GDP growth), and one auxiliary micro-level probe (market share) on the post-warmup phase of a 600-step horizon. The analysis is driven by reusable temporal queries, observable-specific precision targets, and confidence-based stopping rules that automatically determine the simulation effort required by each configuration. Results show a clear contrast across parameter families: macro-financial and structural sweeps produce the strongest transient effects, whereas several heuristic-rule sweeps remain much weaker under the same precision policy. More broadly, the paper shows that SMC can support reproducible and informative quantitative analysis of substantively rich economic ABMs, while making uncertainty estimates and simulation cost explicit parts of the reported results.

Abstract

Statistical Model Checking

Explore similar work

Statistical Model Checking of the Keynes+Schumpeter Model: A Transient Sensitivity Analysis of a Macroeconomic ABM

Towards Agentic Agent-based Models: Feasibility, Performance, and Statistical Model Checking

From Model-Based Screening to Data-Driven Surrogates: A Multi-Stage Workflow for Exploring Stochastic Agent-Based Models