Aggregate and Disaggregate Dynamic Spatial Interaction Approaches to Modeling Coin Diffusion

With the 2002 introduction of the euro as a common currency in Europe, the possibility has emerged to assess international mobility using this new tracer, given that every coin bears a specific national side. Using a simple two-country framework, four dynamic modeling strategies were designed in order to simulate the diffusion of coins and to understand how this diffusion is affected by population size, mobility rates and coin exchange processes. Methodological implications are raised with respect to aggregation, synchronicity and stochasticity issues. Although each model converges to an equilibrium, the time to reach this end stage and the level of coin mixing in each country strongly varies with the modeling strategy. Calibration is undertaken with French data, using mobility rates as adjustment variables. The experiment shows that convergence to a perfect mix of coins can only be obtained if reciprocal exchanges are modeled, with a time horizon around 2064 – while non-reciprocal models indicate an imperfect mix converging in the year 2020 at the latest.