On economic growth and automatic stabilizers under linearly progressive income taxation

I analytically show that the adoption of a linearly progressive income tax scheme destabilizes the endogenously growing economy of Barro (1990) by giving rise to dual balanced growth path equilibria, wherein the low-growth equilibrium exhibits local indeterminacy and belief-driven growth fluctuations, and the high-growth equilibrium displays saddle-path stability. I propose that both a sufficiently high lump-sum taxes-to-capital ratio and a sufficiently high consumption tax rate operate as automatic stabilizers that eliminate the indeterminate low-growth trap, thereby ensuring the existence of a unique determinate balanced growth path equilibrium that displays high output growth. In these cases, both the welfare- and the growth rate-maximizing marginal income tax rate on the high-growth balanced growth path are lower than the elasticity of output with respect to government spending. I further show that, when the marginal income tax rate is optimally set, investment subsidies are unable to eliminate the low-growth trap. Finally, government spending on goods and services cannot serve as an automatic stabilizer whether or not the income tax rate is optimally set.