It has been shown that progressive income taxation may stabilize an otherwise standard representative-agent real business cycle model with an indeterminate steady state against aggregate fluctuations caused by agents’ animal spirits. By contrast, within an identical model that allows for sustained economic growth, progressive taxation could lead to equilibrium indeterminacy and sunspot-driven fluctuations. In the context of household heterogeneity that gives rise to income and asset inequality, the fiscal authority has (at least) two options of setting the baseline level of taxable income: (i) the economy-wide average level of income and (ii) the economy’s steady-state level of per capita income. I show that the adoption of a fiscal rule (i) invalidates the effects that a progressive tax can exert on the model’s local stability properties. Progressive income taxation thus no longer operates as an automatic stabilizer that mitigates belief-driven cyclical fluctuations in a no-growth economy, nor as an automatic destabilizer that leads to local indeterminacy in a sustained-growth economy. If a tax policy rule (ii) is instead adopted, then the existing literature’s findings of the (de)stabilizing roles of progressive taxation are robust to the inclusion of household heterogeneity.
