E Pluribus Unum: Macroeconomic Modelling for Multi-agent Economies

From the point of view of the average macroeconomist, agent based modelling has an obivious drawback: It makes impossible to think in aggregate terms. The modeller, in fact, can reconstruct aggregate variables only "from the bottom up" by summing the individual quantities. As a consequence the interpretation of the trasmission mechanism of shocks is somehow arbitrary. We propose a modelling strategy which reduces the dimensionality of an agent based framework by replacing the actual distributional features (in our model: the distribution of firms'financial conditions) with the first and second moments of the distribution itself. The main message is that the di¢ culty of thinking in macroeconomic terms when dealing with multi-agent economies can be circumvented by means of an appropriate aggregation procedure --which we label the Modified-Representative Agent -- such that the distribution of agents'characteristics can be approximated by (at least) the (first and second) moments of the distribution. The moments of the distribution play the role of macroeconomic variables. We put this strategy at work in a model of the financial accelerator in which firms' heterogeneous degree of financial robustness affect investment in a bankruptcy risk context (à la Greenwald-Stiglitz).