This paper extends the standard limited-dependent, rational expectatio
ns model to allow for stochastic variations in the bounds. We show tha
t the degree of non-linearity relating expectations to fundamentals te
nds to decline as the band becomes less predictable. Monte Carlo exper
iments indicate that the assumption that the band is perfectly predict
able by the agents (when inappropriate) can seriously bias the estimat
es and the inferences based on them.