Aggregate sentiment dynamics: A canonical modelling approach and its pleasant nonlinearities

• A canonical approach to modelling the adjustments of an aggregate sentiment variable.
• The approach is microfounded.
• The approach has an inherent nonlinearity that can give rise to a sequence of local and global bifurcations.

The paper is an attempt at an alternative to the rational expectations assumption in macroeconomic modelling. Emphasizing the concept of sentiment in contrast to the expectations of a single selected variable, it is meant to take an important step forward towards a canonical heterodox framework for the microfounded modelling of irreducible uncertainty and, specifically, herding. Referring to a large population of agents who repeatedly face a binary decision problem, two stylized approaches are considered to describe the aggregate sentiment dynamics: the transition probability and the discrete choice approach. After a slight modification of the latter, the two specifications are shown to give rise to essentially the same adjustment equations. In addition to these conceptual issues, a two-dimensional prototype model is put forward which can illustrate the rich potential of an inherent nonlinearity to generate scenarios with single and multiple (point and set) attractors.