Public debt, positional concerns, and wealth inequality

We consider an AK growth model with positional concerns and public debt financed by distortionary income taxes. We show that if positional concerns are not too strong, there is a threshold level of the debt-to-GDP ratio. For the debt-to-GDP ratio below this level, the economy converges to a unique egalitarian balanced-growth equilibrium, whereas if this ratio is above the threshold level, the economy eventually settles on a two-class balanced-growth equilibrium. The rate of growth in the egalitarian equilibrium is higher than that in any possible two-class equilibrium. Thus, a reduction in public debt may cause the economy to switch from the two-class regime to the egalitarian regime and accelerate growth. Our results also suggest that policies aimed at reducing initial inequality using public debt may, in fact, increase wealth inequality in the long run.