Empirical validation of simulated models through the GSL-div: An illustrative application

A major concern about the use of simulation models regards their relationship with the empirical data. The identification of a suitable indicator quantifying the distance between the model and the data would help and guide model selection and output validation. This paper proposes the use of a new criterion, called GSL-div and developed in Lamperti (2015), to assess the degree of similarity between the dynamics observed in the data and those generated by the numerical simulation of models. As an illustrative application, this approach is used to distinguish between different versions of the well known asset pricing model with heterogeneous beliefs proposed in Brock and Hommes (1998). Once the discrimination ability of the GSL-div is proved, model's dynamics are directly compared with actual data coming from two major stock market indexes (EuroSTOXX 50 for Europe and CSI 300 for China). Results show that the model, once calibrated, is fairly able to track the evolution of both the two indexes, even though a better fit is reported for the Chinese stock market. However, I also find that many different combinations of traders behavioural rules are compatible with the same observed dynamics. Within this heterogeneity, an emerging common trait is found: to be empirically valid, the model has to account for a strong trend following component, which might either come from a unique trend type that heavily extrapolates information from past observations or the combinations of different types with milder, or even opposite, attitudes towards the trend.