First-order approximation methods are a standard technique for analyzing the local dynamics of dynamic stochastic general equilibrium (DSGE) models. Although linear methods yield quite accurate solutions for a broad class of DSGE models, some important economic issues (e.g., portfolio choice and welfare) cannot be adequately addressed by first-order methods. This paper provides yet another case when first-order methods may be inadequate for capturing the business cycle properties of a DSGE model. In particular, the authors show that increasing returns to scale (due to production externalities) may induce asymmetric business cycles and nonlinear income effects that are not fully captured 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, whereas contraction tends to be deeper but shorter-lived, as observed in the U.S. economy.