This paper presents a new nonlinear time series model that captures a post-recession bounce-back in the level of aggregate output. While a number of studies have examined this type of business cycle asymmetry using recession-based dummy variables and threshold models, we relate the bounce-back effect to an endogenously estimated unobservable Markov-switching state variable. When the model is applied to US real GDP, we find that the Markov-switching regimes are closely related to NBER-dated recessions and expansions. Also, the Markov-switching form of nonlinearity is statistically significant and the bounce-back effect is large, implying that the permanent effects of recessions are small. Meanwhile, having accounted for the bounce-back effect, we find little or no remaining serial correlation in the data, suggesting that our model is sufficient to capture the defining features of US business cycle dynamics. When the model is applied to other countries, we find larger permanent effects of recessions.