An Alternative Proof of the Theorem of Woodford on the Existence of a Sunspot Equilibrium in a Continuous-Time Model

Abstract

Nishimura and Shigoka, Int J Econ Theory 2:199–216, (2006) has proved a continuous-time version of the theorem of Woodford, Stationary sunspot equilibria: the case of small fluctuations around a deterministic steady state, mimeo, (1986) to the effect that there exists a stationary sunspot equilibrium for a continuous-time model with a predetermined variable and with an unstable root, if equilibrium is indeterminate near either a steady state or a closed orbit, and if a stable manifold is well-located in an ambient space. The present study provides this theorem with an alternative proof that is due to Murakami et al. Homoclinic orbit and stationary sunspot equilibrium in a three-dimensional continuous-time model with a predetermined variable forthcoming in: Nishimura K, Venditti A, Yannelis NC (eds) Sunspots and non-linear dynamics. Springer, (2016) and simpler than that of Nishimura and Shigoka, Int J Econ Theory 2:199–216, (2006).