Productive government spending and its consequences for the growth–inequality tradeoff

This paper investigates the effects of productive government spending on the relationship between growth and inequality in an economy subject to idiosyncratic production shocks and heterogeneous endowments. Assuming lognormal distributions, we derive tractable closed form solutions describing the equilibrium dynamics. We show how the effect of government investment on the equilibrium dynamics of both inequality and growth depends crucially upon the elasticity of substitution between public and private capital in production. This has important consequences for the growth- and welfare-maximizing rates of government investment. Finally, we supplement our theoretical analysis with numerical simulations, calibrated to approximate the productive characteristics of a real world economy. With the empirical evidence strongly supporting the complementarity between public and private capital, our simulations suggest that conclusions based on the commonly employed Cobb–Douglas production function may be seriously misleading.