Optimal grid selection in numerical approaches to dynamic heterogeneous agent macroeconomic models

A well-known fact about household savings behaviour is that it depends on an individual's own wealth holdings and income expectations. In understanding how these decisions aggregate and respond to policy, we must therefore confront the substantial heterogeneity in these features which is present in the macro economy. One persistent challenge in the literature which aims to provide this understanding is the need to keep track of and forecast the decisions of every single individual in the economy. Such a feat is not possible in practice, so that some grouping of individuals is typically needed to sidestep the issue. This article considers the dividing of households into representative groups to optimally represent savings decisions across the wealth distribution. Such a division is guided by the principle that many groups are needed where there is a large amount of variation in savings propensities. Combining numerical analysis with theory on consumption behaviour, it is shown in the context of a simple model that the savings behaviour of wealthy and poor households can be captured by including a single representative for each category. Meanwhile, several groups are needed to describe the behaviour of the middle class. Middle class households face uncertain future income comparable in size to current wealth holdings, leading to a wide range of savings propensities when compared to poor hand-to-mouth individuals and wealthy savers.