Fiscal policy, increasing returns, and endogenous fluctuations

We examine the quantitative implications of government fiscal policy in a discrete-time one-sector growth model with a productive externality that generates social increasing returns to scale. Starting from a laissez-faire economy that exhibits an indeterminate steady state (a sink), we show that the introduction of a constant capital tax or subsidy can lead to various forms of endogenous fluctuations, including stable 2-, 4-, 8-, and 10- cycles, quasi-periodic orbits, and chaos. In contrast, a constant labor tax or subsidy has no effect on the qualitative nature of the model's dynamics. We also show that the use of local steady-state analysis to detect the presence of multiple equilibria in this class of models can be misleading. For a plausible range of capital tax rates, the log-linearized dynamical system exhibits saddle-point stability (suggesting a unique equilibrium) while the true nonlinear model exhibits global indeterminancy. Finally, we explore the use of a state-contingent capital subsidy/tax scheme for stabilization purposes. We show that a local control policy designed using the log-linearized model can rule out sunspot equilibria near the steady state but may not prevent fluctuations arising from global indeterminacy. We proceed to use the nonlinear model to design a policy that can stabilize the economy against all forms of endogenous fluctuations and select a globally unique equilibrium.