Chaos, sunspots and automatic stabilizers

We consider a real business cycle model with an externality in production. Depending on parameter values, the model has sunspot equilibria, cyclical and chaotic equilibria, and equilibria with deterministic or stochastic regime switching. We study the implications of this model environment for automatic stabilizer tax systems. Stabilization is desirable because the efficient allocations are characterized by constant employment and output growth. We identify an automatic stabilizer income tax-subsidy schedule with two properties: (i) it specifies the tax rate to be an increasing function of aggregate employment, and (ii) earnings are subsidized when aggregate employment is at its efficient level. The first feature eliminates inefficient, fluctuating equilibria, while the second induces agents to internalize the externality.