Cycles and sunspots: The Poincaré-Hopf approach

P. A. Chiappori, J. Dávila

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5 Citations (Scopus)

Abstract

This paper deals with the existence of stationary sunspot equilibria (SSE) of finite order in an n-commodity economy. We first provide a simple condition that is sufficient for the existence of SSE associated with any given Markov matrix. This condition encompasses and extends previous results by Guesnerie (Journal of Economic Theory, 1986, 40, 103-128) and Chiappori and Guesnerie (in: Economic complexity, chaos, sunspots, bubbles and nonlinearity, 189, CUP). Also, we consider the order of the corresponding SSE (i.e. the cardinality of their support), and we show that almost all of these are of maximum order. Finally, we study the links between SSE and cycles, and find that the existence of cycles of order 2 detected by our condition implies that of SSE arbitrarily close to cycles of order k for any even k - although cycles of order k may not exist in such models.
Original languageEnglish
Pages (from-to)269-284
JournalJournal of Mathematical Economics
Volume26
Issue number3
DOIs
Publication statusPublished - 1 Jan 1996

Keywords

  • Cycles
  • Index theorem
  • Sunspot equilibrium

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