It has been shown that under perfect competition and constant returns-to-scale, a onesector real business cycle model may exhibit indeterminacy and sunspots when income tax rates are determined by a balanced-budget rule with a pre-set level of government expenditures. This paper shows that indeterminacy disappears if the government finances endogenous public spending and transfers with fixed income tax rates. Under this type of balanced-budget formulation, the economy exhibits saddle-path stability and equilibrium uniqueness, regardless of the source of government revenue and/or the existence of lumpsum transfers.
This paper examines 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 local indeterminacy, 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, quasiperiodic orbits, and chaos. In contrast, a constant labor tax or subsidy has no effect on the qualitative nature of the model's dynamics. We 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, whereas the true nonlinear model exhibits global indeterminacy. This result implies that stabilization policies designed to suppress sunspot fluctuations near the steady state may not prevent sunspots, cycles, or chaos in regions away from the steady state. Overall, our results highlight the importance of using a model's nonlinear equilibrium conditions to fully investigate global dynamics.
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