When changes occur, people do not know how long they will persist. Using a simple stochastic structure that incorporates temporary and permanent changes in an augmented IS-LM model, we show that rising prices and rising unemployment — stagflation is likely to follow a large permanent reduction in productivity. All markets clear and all expectations are rational. People learn gradually the permanent values which the economy will reach following a permanent shock and gradually adjust anticipations. In our model, optimally perceived permanent values take the form of a Koyck lag of past observations.