We develop a stylized model of economic growth with bubbles in which changes in investor sentiment lead to the appearance and collapse of macroeconomic bubbles or pyramid schemes. These bubbles mitigate the effects of financial frictions. During bubbly episodes, unproductive investors demand bubbles while productive investors supply them. These transfers of resources improve economic efficiency thereby expanding consumption, the capital stock and output. When bubbly episodes end, there is a fall in consumption, the capital stock and output. We argue that the stochastic equilibria of the model provide a natural way of introducing bubble shocks into business cycle models. (JEL E22, E23, E32, E44, O41)