Note on Woodford's Conjecture: Constructing Stationary Sunspot Equilibria in a Continuous Time-Model

If for given equilibrium dynamics there exist a continuum of non-stationary perfect foresight equilibria all converging asymptotically to a steady state (a deterministic cycle resp.), we say the equilibrium dynamics is indeterminate near the steady state (the ~terministic cycle resp.). Suppose that the fundamental characteristics of an economy are deterministic, but that economic agents believe nevertheless that. equilibrium dynamics is affected by random factors apparently irrelevant to the fundamental characteristics (sunspots). This prophecy could be self-fulfilling, and one will get a sunspot equilibrium, if the resulting equilibrium dynamics is subject toa nontrivial stochastic process and confinns the agents ' belief. See Cass-Shell [2]. Woodford [6] suggested that there exists a close relation between the indeterminacy of equilibrium near a deterministic steady state and the existence of stationary sunspot equilibria in the immediate vicinity of it. We might summarize Woodford's conjecture as what follows: "Let x be a steady state of a deterministic model which has a continuum of non stationary perfect foresight equilibria all converging asymptotically to the steady state. Then given any neighborhood U(x) of it, there exist stationar