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Can rational stochastic asset bubbles help explain the excess volatility of stock prices? The bubble considered here is treated as an unobserved state vector in the state‐space model and is easily estimated using the Kalman filter. I find that the bubble components estimated account for a substantial portion of US. stock prices, and the model does a credible job in fitting the data, especially during several bull and bear markets in this century. Much of the deviation of stock prices from the present‐value model are captured by the bubble.