Simple models of interacting agents can be formulated as jump Markov processes via suitably specified transition probabilities. Their aggregate dynamics might then be analyzed by the Master equation for the change of the probability distribution over time, or the Fokker-Planck equation that is obtained via a power series expansion and governs the probability distribution for fluctuations around an equilibrium. With such information on the transient density of the process, maximum likelihood estimation of its parameters becomes feasible. Even if the Fokker-Planck equation cannot be solved explicitly, one can resort to numerical approximations like the Crank-Nicolson method for approximate ML estimation. We explain this algorithm with a simple model of interacting agents and show that the approximate ML procedure works well and has desirable accuracy even in the case of bimodal limiting distributions. We illustrate possible applications by estimating the parameters of this model for a popular business climate index for the German economy.

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1. Estimation of Agent-Based Models using Sequential Monte Carlo Methods