Standard linear macroeconomic models generate business cycles around a unique equilibrium through random productivity or preference shocks. Dynamic nonlinear models with multiple equilibria have the potential for endogenous fluctuations without exogenous shocks. This paper combines both approaches in a nonlinear model with multiple steady states due to a production externality. In the absence of policy changes, the driving forces generating fluctuations are exogenous random productivity shocks: without these shocks the economy would converge to a nonstochastic steady state. However, because there are multiple steady states, large productivity shocks of the right sign can shift the economy between high and low level stochastic steady states, providing an additional endogenous source of fluctuations. In this setting macroeconomic policy exhibits hysteresis (irreversibilities), and policy can be used to eliminate endogenous fluctuations
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