A striking implication of the replacement of adaptive expectations by Rational Expectations was the "Lucas Critique," which showed that expectation parameters, and endogenous variable dynamics, depend on policy parameters. We reconsider this issue from the vantage point of bounded rationality. Adaptive expectations, with an optimally tuned parameter, can provide a reasonable, if not fully rational, forecast method when the true process is unknown. We show that for a range of processes, monetary policy remains subject to the Lucas critique. However, there are also regimes in which the expectation parameter is locally invariant and the Lucas critique does not apply.