This paper shows that the dynamics of the Lucas (J Monet Econ, 22:3–42, 1988) endogenous growth model with flow externalities may give rise to a 2-torus, a compact three-dimensional manifold enclosed by a two-dimensional surface. The implications of this result are relevant for many fields of economic theory. It is first of all clear that if we choose to initialize the dynamics in the basin of attraction of this trapping region, a continuum of perfect foresight solutions may be observed. A simple econometric exercise, linking the physical-to-human capital ratio (state variable) to the 5-years forward variance of the growth rate of an unbalanced sample of 183 countries, seems to provide empirical backing for the phenomenon. Other important consequences, relevant from the point of view of endogenous cycles theory, are also scrutinized in the paper.

这篇论文表明，具有流动外部性的 Lucas (J Monet Econ, 22:3–42, 1988) 内生增长模型的动力学可能会产生一个 2 环面，一个由二维表面包围的紧凑的三维流形. 这一结果的含义与经济理论的许多领域相关。首先很明显，如果我们选择在这个诱捕区域的吸引力盆地中初始化动力学，则可以观察到完美的预见性解决方案的连续统。一个简单的计量经济学练习，将物质与人力资本比率（状态变量）与 183 个国家的不平衡样本的增长率的 5 年远期方差联系起来，似乎为这一现象提供了实证支持。从内生循环理论的角度来看，其他重要的后果也在本文中进行了详细审查。