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.

为了分析动物精神对经济动态的影响，我们构建了一个简单的凯恩斯商业周期模型，其中包含了动物精神。与著名的 Kaldor 模型类似，我们假设每个企业都具有依赖于需求的投资功能，其中动物精神与投资倾向的程度有关。然而，我们要强调的是，与 Kaldor 模型不同，即使每个公司的需求水平相同，投资倾向的程度（即动物精神的强度）也取决于需求的变化。因此，我们假设需求上升阶段的动物精神强于需求下降阶段的动物精神。在每个阶段，对需求的依赖程度是企业特定的。所以，我们采用统计方法将这种异构的微观投资行为与宏观投资功能联系起来。通过这种方法，某种非线性自然地被引入到宏观投资函数中。我们证明非线性宏观投资函数会产生持续的商业周期。我们还证明了广义 Hopf 分岔的发生。