A sunspot paradox

Calibrated models of the business cycle typically assume a certain frequency at which economic agents take decisions. In this paper I show that the local stability properties of dynamic stochastic general equilibrium macro models may depend on the length of a period in the model economy. This leads to the following paradoxical situation: For given parameters, and in particular those assigning values of imperfections in the economy, the economy may be driven by sunspots at some frequencies while sunspots can have no impact at other frequencies.