发表机构
Colorado State University（科罗拉多州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文扩展Goodwin增长周期模型，纳入阿片类药物使用障碍对生产率的影响，通过离散选择机制和数值模拟证明系统存在极限环，并揭示OUD对就业率和波动的矛盾效应，提出社会安全网政策可稳定动态。
AI 中文摘要
本文扩展了Goodwin（1967）的捕食者-猎物增长周期模型，以纳入阿片类药物使用障碍（OUD）对劳动生产率的负面影响。利用美国1998年至2019年的州级数据，我们首先记录了劳动份额的恶化随后伴随着药物导致的死亡率上升。然后，我们通过一种新颖的离散选择机制将此联系构建到模型中，在该机制中，OUD的概率随工资份额的下降而增加，因此当实际工资未能跟上生产率增长时，阿片类药物的使用会增加。这一行为健康渠道通过生产率损害函数反馈到经济中。应用Andronov-Hopf分岔定理的存在性部分，我们证明了由此产生的三维非线性系统允许一个极限环，正如我们的数值模拟所确认的那样。沿着该循环，OUD的上升矛盾地提高了就业率，因为生产率的下降需要每单位产出更多的劳动力；然而，在各稳态之间，较高的OUD患病率与较低的就业率相关，这与阿片类药物使用障碍降低劳动力参与率的证据一致。此外，我们的数值实验表明，OUD对收入的敏感性扩大了波动，而生产率对OUD的敏感性通过一种自我纠正的反馈机制（加速工资份额的恢复）反直觉地压缩了波动。削弱收入与OUD之间联系的政策，如加强社会安全网，稳定了由此产生的动态。
英文摘要
This paper extends Goodwin's (1967) predator-prey growth-cycle model to incorporate the negative impact of Opioid Use Disorder (OUD) on labor productivity. Using U.S. state-level data for 1998--2019, we first document that deteriorations in the labor share are followed by rising drug-induced mortality. We then build this link into the model through a novel discrete-choice mechanism in which the probability of OUD decreases with the wage share, so when real wages fail to keep pace with productivity growth, opioid use rises. This behavioral health channel feeds back into the economy through a productivity damage function. Applying the existence part of the Andronov-Hopf bifurcation theorem, we show that the resulting three-dimensional nonlinear system admits a limit cycle, as confirmed by our numerical simulations. Along the cycle, rising OUD paradoxically raises the employment rate, as falling productivity requires more labor per unit of output; across steady states, however, higher OUD prevalence is associated with a lower employment rate, consistent with evidence that opioid use disorder reduces labor force participation. Moreover, our numerical experiments show that OUD sensitivity to income widens fluctuations, while productivity sensitivity to OUD counterintuitively compresses them through a self-correcting feedback that speeds the recovery of the wage share. Policies that weaken the link between income and OUD, such as stronger social safety nets, stabilize the resulting dynamics.
