Business Cycle Models : closing the gap between the different approaches.

This paper is concerned with the subject of how the three main approaches to model aggregate fluctuations are related. That is, we are interested in the relation between real business cycle models, endogenous business cycle models and sunspot equilibria models. It is shown that there exists an open set of parameters where the three approaches are very much related : the time series have much resemblance. Outside this set of parameters the approaches seem mutually exclusive. Moreover, we show that if the interior steady state is unique and has a saddle structure then no sophisticated deterministic fluctuations can occur. On the other hand if the nonlinear model is close to having multiple eigenvalues close to + 1 then so-called Bogdanov-Takens bifurcations can occur very close to the interior steady state : sophisticated deterministic fluctuations near unit roots occur. We will argue that if these types of bifurcations occur then a linearization is less justifiable. In addition, for parameters close to these bifurcations the linearized model may have the same structure as the real business cycle model. In this case cycles are generated by animal spirits.