从平衡增长到创新周期：一个索洛型半内生增长模型
From Balanced Growth to Innovation Cycles:A Solow-Type Semi-Endogenous Growth Model
- PSE, CNRS, IPAG Business School, FTU Vietnam（巴黎社会科学中心, 法国国家科学研究中心, IPAG商学院, 越南外交学院）
- EconomiX, University of Paris Nanterre（埃科米克斯研究中心, 巴黎楠泰尔大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文构建含研发部门的索洛型半内生增长模型，研究创新知识弹性为负时平衡增长路径的存在性、稳定性及创新周期涌现条件，并通过比较静态与数值模拟为研发和人口政策提供指导。
AI中文摘要：
我们开发了一个包含研发部门的增长模型，其中创新相对于现有知识的弹性可以为负。我们研究了平衡增长路径（BGP）的存在性和唯一性，并推导了闭式增长因子，表明生产率和产出增长是半内生的且由人口驱动。我们还在一般生产函数下建立了全局稳定性。在可检验的参数限制下，经济收敛到平衡增长路径。然而，当知识弹性足够低时，基于雅可比矩阵的条件意味着不稳定性，并且可能出现N期创新周期。我们进行了比较静态分析，以探讨包括研究效率、投入弹性和人口增长在内的几个因素的影响。数值模拟描绘了转变过程，并标出了稳定性丧失的点。它们清楚地说明了创新摩擦何时危及平衡增长，并为研发和人口政策提供了实用指导。
英文摘要：
We develop a growth model with an R\&D sector in which the elasticity of innovation with respect to existing knowledge can be negative. We investigate the existence and uniqueness of a balanced growth path (BGP) and derive closed-form growth factors, showing that productivity and output growth are semi-endogenous and population-driven. We also establish the global stability under a general production function. Under testable parameter restrictions, the economy converges to the BGP. However, when the knowledge elasticity is sufficiently low, a Jacobian-based condition implies instability, and an N-period innovation cycle can emerge. Comparative statics are conducted to explore the impact of several factors, including research efficiency, input elasticity, and population growth. Numerical simulations map out transitions and mark the points at which stability is lost. They make clear when innovation frictions endanger balanced growth and provide practical guidance for R\&D and demographic policy.
