In many economies, long periods of steady growth in aggregate wealth are repeatedly interrupted by pronounced asset-price boom-bust episodes, and real activity typically moves with wealth in such episodes. I build a quantitative life-cycle model of rational bubbles that can be taken to the data at business-cycle frequency. At short horizons, bubble fluctuations transmit to output through a channel that differs from the canonical mechanisms of rational-bubble models: A positive bubble shock is a windfall to the entrepreneurs who hold the bubble on levered balance sheets. With a binding collateral constraint, their investment demand rises by a multiple of the windfall, and sticky prices translate the resulting increase in demand into output. The canonical crowding-out, liquidity, and bubble-creation channels matter mainly at longer horizons. I then use the model to jointly fit postwar US wealth, output, and inflation and decompose wealth fluctuations into bubble and fundamental components. In the model-based decomposition, the bubble component accounts for about three-fifths of the variation in postwar US wealth over five- and ten-year horizons. Most postwar recessions are not the result of bursting bubbles. The exception is the Great Recession, in which the bursting bubble accounts for about a quarter of the decline in output.