Dynamics of externalities: a second-order perspective

We show that increasing returns to scale (due to production externalities) may induce a strong degree of asymmetric income effects and nonlinear dynamics that are not fully appreciated by linear approximation methods. For example, hump-shaped output dynamics can emerge even when externalities are significantly 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. Thus, mild degree of externalities without triggering indeterminacy can potentially explain the asymmetric property of the business cycle and the hump-shaped output dynamics found in the empirical literature. Our results also suggest exercising caution when using linear approximation methods to analyze the local dynamics of models with market frictions and non-convexities.