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We consider piecewise linear discrete time macroeconomic models, whichpossess a continuum of equilibrium states. These systems are obtained byreplacing rational inflation expectations with a boundedly rational, andgenuinely sticky, response of agents to changes in the actual inflation rate ina standard Dynamic Stochastic General Equilibrium model. Both for alow-dimensional variant of the model, with one representative agent, and themulti-agent model, we show that, when exogenous noise is absent from thesystem, the continuum of equilibrium states is the global attractor. Further,when a uniformly bounded noise is present, or the equilibrium states aredestabilized by an imperfect Central Bank policy (or both), we estimate thesize of the domain that attracts all the trajectories. The proofs are based onintroducing a family of Lyapunov functions and, for the multi-agent model,deriving a formula for the inverse of the Prandtl-Ishlinskii operator acting inthe space of discrete time inputs and outputs.

Global stability of a piecewise linear macroeconomic model with a continuum of equilibrium states and sticky expectation