Method-Oriented Calibration for Economic ABMs

Classical Economic Simulation Methods

1. Indirect Inference

Authors: Gourieroux, C., Monfort, A., & Renault, E. (1993)
Link: https://onlinelibrary.wiley.com/doi/abs/10.1002/jae.3950080507

Method: Use auxiliary model to match moments; choose parameters so auxiliary estimates from simulated and real data are close.

Why it works: Achieves consistent estimation even when auxiliary model is misspecified, as long as structural parameters have independent effects on auxiliary parameters.

Best for: Dynamic economic models, DSGE-like ABMs, continuous-time models.

Data types: Moments from empirical time-series; cross-sectional moments.

2. Simulated Method of Moments (SMM)

Authors: McFadden, D. (1989); Pakes, A., & Pollard, D. (1989)
Link: https://opensourceecon.github.io/CompMethods/struct_est/SMM.html

Method: Match moments (e.g., mean, variance, autocorrelation) from simulated data to observed data via optimization.

Why it works: Consistent and asymptotically normal estimator under identifiability conditions (order: #moments ≥ #parameters; rank: parameters differentially affect moments).

Best for: Heterogeneous-agent models, financial market ABMs, any model where likelihood is intractable.

Data types: Empirical moments from time-series or cross-sectional data.

3. On the Problem of Calibrating an Agent-Based Model for Financial Markets

Authors: Fabretti, A. (2013)
Link: https://link.springer.com/article/10.1007/s11403-012-0096-3

Method: Combine Nelder-Mead simplex algorithm with threshold-accepting heuristic and genetic algorithms to calibrate Farmer-Joshi ABM; minimize distance between simulated and empirical moments.

Why it works: Handles non-smooth, multi-modal objective functions; genetic algorithms escape local minima better than gradient-based methods; explicitly accounts for Monte Carlo variance in objective function.

Best for: Financial market ABMs with many parameters and complex loss landscapes; applies to moment-matching calibration with stylized facts.

Data types: Financial time-series moments (returns, volatility, autocorrelation); empirical moments from real market data.

4. Efficient Calibration of a Financial Agent-Based Model Using the Method of Simulated Moments

Authors: (Recent application showing computational efficiency improvements)
Link: https://link.springer.com/chapter/10.1007/978-3-030-77967-2_27

Method: SMM with filtered neighborhood optimization to reduce computational cost while maintaining accuracy.

Why it works: Gradually narrows search space by examining local neighborhoods, exploiting structure of objective surface.

Best for: Large parameter spaces; computationally expensive financial ABMs.

Data types: Financial moments (returns, volatility, autocorrelation, fat tails).

Bayesian Approaches

5. Bayesian Calibration of Computer Models

Authors: Kennedy, M. C., & O’Hagan, A. (2001)
Link: https://www.asc.ohio-state.edu/statistics/comp_exp//jour.club/kennedy01.pdf

Method: Model computer output as Gaussian process with explicit discrepancy term δ(x); use Bayesian inference to estimate parameters and model inadequacy.

Why it works: Quantifies both parameter uncertainty AND model discrepancy; accounts for the fact that no model is perfect.

Best for: Continuous parameter spaces; when you have both empirical data and want full uncertainty quantification.

Data types: Pointwise empirical observations; works with expensive-to-evaluate models.

6. Bayesian Estimation of Agent-Based Models via Adaptive Particle Markov Chain Monte Carlo

Authors: (Recent, 2021)
Link: https://link.springer.com/article/10.1007/s10614-021-10155-0

Method: Use adaptive particle MCMC to sample from posterior distribution of parameters given observed data.

Why it works: Particle methods handle multimodal posteriors better than standard MCMC; adapts proposal distributions on-the-fly.

Best for: ABMs with moderate parameter counts; when you need full posterior distribution, not just point estimates.

Data types: Time-series data; likelihood-free inference using summary statistics.

7. Black-Box Bayesian Inference for Agent-Based Models

Authors: Dyer, J., Cannon, P., Farmer, J.D., & Schmon, S.M. (2024)
Link: https://www.sciencedirect.com/science/article/pii/S0165188924000198
Preprint: https://arxiv.org/abs/2202.00625

Method: Use neural networks to learn direct mapping from data to posterior distribution (neural posterior estimation and neural density ratio estimation); applies simulation-based inference.

Why it works: Avoids explicit likelihood; learns posterior from ensemble of simulations; amortizes cost across many observations; achieves accurate posteriors with orders of magnitude fewer simulations than traditional methods.

Best for: Very high-dimensional parameter spaces; when summary statistics are difficult to define; computationally expensive economic ABMs.

Data types: Any type of data including multivariate time-series; works with neural network emulators.

Approximate Likelihood-Free Methods

8. Calibration and Evaluation of Individual-Based Models Using Approximate Bayesian Computation

Authors: Hartig, F., Calabrese, J. M., Reineking, B., Wiegand, T., & Huth, A. (2011)
Link: https://www.sciencedirect.com/science/article/pii/S0304380015002173

Method: ABC: generate simulations under various parameters, accept those matching observed data within tolerance ε; use accepted simulations to estimate posterior.

Why it works: Works without likelihood function; asymptotic acceptance region gives valid Bayesian posterior (within tolerance).

Best for: Stochastic economic ABMs; high-dimensional parameter spaces; when summary statistics capture essential features.

Data types: Summary statistics from observed data.

9. Likelihood-Free Inference by Ratio Estimation

Authors: (Recent neural simulation-based inference)
Link: https://arxiv.org/pdf/1611.10242

Method: Train neural network classifier to estimate likelihood-to-marginal ratio p(data

θ)/p(data); use for inference.

Why it works: Avoids density estimation; directly learns the relevant ratio for inference.

Best for: Economic ABMs with expensive simulations; combines with sequential refinement for efficiency.

Data types: Summary statistics; raw simulation outputs.

Machine Learning / Surrogate-Based Methods

10. Agent-Based Model Calibration using Machine Learning Surrogates

Authors: Lamperti, F., Roventini, A., & Sani, A. (2018)
Link: https://arxiv.org/abs/1703.10639

Method: Train neural network or Gaussian process to emulate ABM; calibrate using surrogate instead of true model; expensive simulations only for training.

Why it works: Reduces computational cost by orders of magnitude; maintains uncertainty quantification; allows efficient exploration of parameter space.

Best for: Computationally expensive macro ABMs (EURACE-style); large parameter spaces.

Data types: Empirical moments; macro time-series data; trained on simulation ensemble.

11. Using Machine Learning as a Surrogate Model for Agent-Based Simulations

Authors: Lamperti, F., Roventini, A., & Sani, A. (2022)
Link: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0263150

Method: Compare ANNs, gradient-boosted trees, and GPs as surrogates; optimize via calibration on surrogate.

Why it works: Demonstrates which surrogates best preserve ABM behavior for different output types; guides method selection.

Best for: Any large ABM; practical guidance on which ML method to use.

Data types: Simulation training data; empirical targets.

Pattern-Based Calibration

12. Pattern-Oriented Modelling: A ‘Multi-Scope’ for Predictive Systems Ecology

Authors: Grimm, V., & Railsback, S. F. (2012)
Link: https://royalsocietypublishing.org/doi/abs/10.1098/rstb.2011.0180

Method: Identify patterns at multiple scales/hierarchies; calibrate to reproduce all patterns simultaneously; discard parameter sets failing any pattern.

Why it works: Multi-criteria calibration reduces overfitting risk; validates mechanisms at different scales; patterns constrain parameter space more than single moment.

Best for: Macro ABMs; when you have multiple stylized facts at different organizational levels.

Data types: Categorical/qualitative patterns; stylized facts; multi-scale observations.

Validation Framework

13. Validation of Agent-Based Models in Economics and Finance

Authors: Fagiolo, G., Guerini, M., Lamperti, F., Moneta, A., & Roventini, A. (2017)
Link: https://www.econstor.eu/bitstream/10419/174573/1/2017-23.pdf

Method: Framework comparing three calibration/validation paradigms: (i) stylized facts matching, (ii) moment matching (SMM), (iii) econometric testing.

Why it works: Clarifies when each approach is appropriate; shows trade-offs between statistical rigor and computational efficiency.

Best for: Understanding methodological choice; identifying which approach suits your economic ABM’s purpose.

Data types: Empirical moments; econometric test statistics; stylized facts.

Quick Method Selection Guide

Model Type	Primary Method	Alternative
Macro ABM (expensive)	Surrogates (10, 11) + SMM	ABC (8)
Financial market ABM	SMM with evolutionary opt. (2, 3)	Bayesian MCMC (6)
High-parameter ABM	Pattern-oriented (12)	Surrogate + ABC (10+8)
Stochastic economic ABM	ABC (8) or indirect inference (1)	Bayesian (5, 6)
Policy-focused ABM	Moment matching (2) validated with patterns (12)	Surrogate forecasting (10)
Very high-dimensional ABM	Neural SBI (7)	Surrogates + SMM (10+2)

Notes

All 13 papers are method-focused—each explains a specific calibration/inference technique and why it works for economic ABMs
Papers are ordered from classical to modern approaches
Paper 7 (Dyer et al., 2024) represents the cutting edge of simulation-based inference for ABMs using neural networks