INTERTEMPORAL COMPLEMENTARITY AND OPTIMALITY: A STUDY OF A TWO-DIMENSIONAL DYNAMICAL SYSTEM

Tapan Mitra and Kazuo Nishimura

International Economic Review, 2005, vol. 46, issue 1, 93-131

Abstract: 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. Copyright 2005 by the Economics Department Of The University Of Pennsylvania And Osaka University Institute Of Social And Economic Research Association.

Date: 2005
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Working Paper: Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System (2004)
Working Paper: Intertemporal Complementarity and Optimality: A Study of a Two-Dimensional Dynamical System (2002)
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