 The Duality of Dynamics: Real-Time Indeterminacy and Notional-Time InstabilityKatsuyuki Shibayama () Studies in Economics from School of Economics, University of Kent Abstract: Applying Arrow and Hurwicz fs (1958a) classical notional-time (NT) stability analysis to dynamic general equilibrium models, we ask whether local Hamiltonian gradients, often interpreted as prices and shadow prices, provide correct signals to restore equilibrium following a deviation. Under some assumptions, a gduality h emerges between reduced real-time (RT) dynamics and the corresponding NT adjustment, both involving only dynamic variables. Let m denote RT indeterminacy (stable roots minus state variables), and n the number of unstable roots in this reduced NT adjustment (n . 0). We show that m and n have the same parity. Thus, in this reduced system, odd RT indeterminacy (e.g., m = 1) implies that the specified local NT adjustment has at least one unstable direction. Under concavity, boundary, and regularity conditions, we also establish global NT convergence for finite-horizon planner problems. Keywords: Dynamic General Equilibrium Models; Blanchard and Kahn Condition; Indeterminacy; Stability of General Equilibrium; Notional Time Adjustment (search for similar items in EconPapers) Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:ukc:ukcedp:2603 Ordering information: This working paper can be ordered from Access Statistics for this paper More papers in Studies in Economics from School of Economics, University of Kent School of Economics, University of Kent, Canterbury, Kent, CT2 7FS. |
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