Existence of adaptively stable sunspot equilibria near an indeterminate steady state

We examine the nonlinear one-step forward-looking model, in which the current state is a function of the (subjective) expected value of a nonlinear function of the state next period. Stationary Markov Sunspot Equilibria (SSEs) are known to exist near an indeterminate steady state, i.e. when the derivative of the function at the steady state is bigger than one in absolute value. We show that there exist Markov SSEs that are E-stable, and therefore locally stable under adaptive learning, if the value of this derivative is less than minus one. JEL Classification: C62, D83, D84, E31, E32.