First-order approximation methods are a standard technique for analyzing the local dynamics of dynamic stochastic general equilibrium (DSGE) models. Although for a wide class of DSGE models linear methods yield quite accurate solutions, some important economic issues such as portfolio choice and welfare cannot be adequately ad- dressed by first-order methods. This paper provides yet another case where first-order methods may be inadequate for capturing a DSGE model’s business-cycle properties. In particular, we show that increasing returns to scale (due to production externalities) may induce asymmetric business cycles and nonlinear income effects that are not fully appreciated by linear approximation methods. For example, hump-shaped output dynamics can emerge even when externalities are below the threshold level required for indeterminacy, and output expansion tends to be smoother and longer while contraction tends to be deeper but shorter-lived, as observed in the U.S. economy.