Optimal moment set selection for the SMM using machine learning

This paper addresses the moment selection issue of the simulated method of moments, which is an estimation technique commonly applied to analytically intractable agent-based models. To reduce the arbitrariness of the choice of moments, we develop a simple machine learning extension on top of this method that offers a novel automated approach to the optimal moment set selection. The idea beyond the extension follows the stepwise regression framework. Two algorithms are proposed: forward stepwise moment selection and backward stepwise moment elimination. The methodology is tested on three models with increasing complexity and a number of estimated parameters. We use one standard time series model and two popular financial agent-based models, and we employ three sets of moments from the literature as benchmarks. We find that both selection algorithms consistently identify multiple moment sets that outperform all benchmark sets for every model. Moreover, for financial agent-based models, where one needs to address moment set selection in practice, we achieve considerable estimation precision enhancements between 9 and 67 percent. Finally, we demonstrate the overidentification issue of too many moments decreasing estimation performance