This paper empirically investigates the possibility of self-sustained oscillations at business cycle frequency. The theoretical model considers aggregate economic activity and the functional income distribution in the spirit of Goodwin (1967). In the empirical investigation, we utilize four measures each of economic activity and the labor share for the US post-war macroeconomy. Using Schuster’s periodogram, we first show that these time series have an important frequency peak at about forty quarters. We therefore detrend them with wavelet methods. To allow for nonlinear dynamic interaction, we introduce a feedforward neural network (FNN). This method is first shown to correctly identify stability or a limit cycle in simulations of the theoretical model with reasonable noise and sample size. Estimation results provide some support for a limit cycle in the post-war US, but this evidence is not independent of detrending methods used.

本文实证研究了在商业周期频率下自我维持振荡的可能性。理论模型本着 Goodwin (1967) 的精神考虑了总体经济活动和功能性收入分配。在实证调查中，我们使用了美国战后宏观经济的经济活动和劳动力份额四个指标。使用 Schuster 的周期图，我们首先表明这些时间序列在大约 40 个季度有一个重要的频率峰值。因此，我们用小波方法去除它们的趋势。为了允许非线性动态交互，我们引入了前馈神经网络 (FNN)。该方法首先被证明可以在具有合理噪声和样本大小的理论模型的模拟中正确识别稳定性或极限环。