  We analyze a simple macroeconomic model where rational inflation expectations
is replaced by a boundedly rational, and genuinely sticky, response to changes
in the actual inflation rate. The stickiness is introduced in a novel way using
a mathematical operator that is amenable to rigorous analysis. We prove that,
when exogenous noise is absent from the system, the unique equilibrium of the
rational expectations model is replaced by an entire line segment of possible
equilibria with the one chosen depending, in a deterministic way, upon the
previous states of the system. The agents are sufficiently far-removed from the
rational expectations paradigm that problems o indeterminacy do not arise.
  The response to exogenous noise is far more subtle than in a unique
equilibrium model. After sufficiently small shocks the system will indeed
revert to the same equilibrium but larger ones will move the system to a
different one (at the same model parameters). The path to this new equilibrium
may be very long with a highly unpredictable endpoint. At certain model
parameters exogenously-triggered runaway inflation can occur.
  Finally, we analyze a variant model in which the same form of sticky response
is introduced into the interest rate rule instead.
