Intertemporal complementarity and optimalitya study of a two-dimensional dynamical system

• 成果类型: Article; Proceedings Paper
• 署名作者: Mitra, T; Nishimura, K
• 署名单位: Kyoto University; Cornell University
• 刊物名称: INTERNATIONAL ECONOMIC REVIEW
• ISSN/ISSBN: 0020-6598
• DOI: 10.1111/j.0020-6598.2005.00311.x
• 发表日期: 2005
• 页码: 93-131
• 关键词: stationary ordinal utility; optimal-growth; ECONOMIC-GROWTH; MODEL; preferences; smoothness; altruism; PROPERTY

摘要

We study the underlying structure of the two-dimensional dynamical system generated by a class of dynamic optimization models that allow for intertemporal complementarity between adjacent periods, but preserve the time-additively separable framework of Ramsey models. Specifically, we identify conditions under which the results of the traditional Ramsey-type theory are preserved even when the intertemporal independence assumption is relaxed. Local analysis of this theme has been presented by Samuelson (Western Economic Journal 9 (1971), 21-26). We establish global convergence results and relate them to the local analysis, by using the mathematical theory of two-dimensional dynamical systems. We also relate the local stability property of the stationary optimal stock to the differentiability of the optimal policy function near the stationary optimal stock, by using the Stable Manifold Theorem.