This paper analyzes local and global equilibrium dynamics in an optimizing endogenous growth model under expenditure-based fiscal austerity feedback policies expressed relative to the private capital stock—prescribing spending cuts in reaction to public debt accumulation. Because the present value of equilibrium primary surpluses turns to be a nonlinear function of debt, two steady state equilibria are shown to emerge, one exhibiting low debt and high growth, one exhibiting high debt and low growth. Local analysis reveals that the low-debt/high-growth steady state is saddle-path stable while the high-debt/low-growth steady state is unstable—the latter thus indicating the possibility of self-defeating austerity, characterized by off-equilibrium upward spirals in debt because of persistent policy-induced adverse effects on growth dividends and fiscal revenues. However, when global nonlinear dynamics are taken into account, it is demonstrated that the two steady states are endogenously connected. In particular, global analysis reveals that even if the high-debt/low-growth steady state is locally unstable, there exists a unique and possibly nonmonotonic saddle connection making the economy converge to the low-debt/high-growth steady state. The existence of the saddle connection guarantees global determinacy of perfect foresight equilibrium should the high-debt/low-growth steady state be a node, ruling out multiple explosive paths incompatible with the government's intertemporal budget constraint and the private agents' transversality condition. The foregoing results are robust with respect to the adoption of an output-based—rather than a capital-based—policy function as long as the rule is nonlinear and sufficiently reactive to debt changes.

中文翻译：

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财政紧缩真的会弄巧成拙吗？

本文分析了在基于支出的财政紧缩反馈政策下优化内生增长模型中的局部和全球均衡动态，该政策表示相对于私人资本存量——规定削减支出以应对公共债务积累。由于均衡基本盈余的现值变为债务的非线性函数，因此出现了两种稳态均衡，一种表现为低债务和高增长，另一种表现为高债务和低增长。局部分析表明，低负债/高增长稳态是马鞍路径稳定的，而高负债/低增长稳态是不稳定的——后者表明紧缩政策可能会适得其反，由于政策对增长红利和财政收入的持续不利影响，债务呈非均衡螺旋式上升。然而，当考虑全局非线性动力学时，证明两个稳态是内生连接的。特别是，全局分析表明，即使高债务/低增长稳态在局部不稳定，也存在独特且可能非单调的鞍点连接，使经济收敛到低债务/高增长稳态。如果高债务/低增长稳态是一个节点，鞍座连接的存在保证了完美预见均衡的全局确定性，排除了与政府跨期预算约束和私人代理的横向条件不相容的多个爆炸路径。