A business-cycle model connecting heterogeneous micro investment behaviors with macro dynamics

To analyze the effect of animal spirits on economic dynamics, we construct a simple Keynesian business-cycle model with animal spirits incorporated into it. Similar to the well-known Kaldor model, we assume that each firm possesses the investment function depending on demand, in which the animal spirits are connected with the degree of the propensity to invest. However, we would like to emphasize that, unlike the Kaldor model, even if the level of demand for each firm is the same, the degree of propensity to invest (i.e., the strength of animal spirits) depends on the change in demand. Thus, we assume that animal spirits in demand-upswing phases are stronger than those in demand-downswing phases. In each phase, the degree of dependence on demand is firm specific. Therefore, we adopt a statistical approach to connect such heterogeneous micro-investment behaviors with a macro-investment function. Through this approach, some kind of nonlinearity is naturally introduced into the macro-investment function. We demonstrate that the nonlinear macro-investment function yields persistent business cycles. We also demonstrate the occurrence of a generalized Hopf bifurcation.