Permanent Primary Deficits, Idiosyncratic Long-Run Risk, and Growth

We consider an economy with perpetual youth and inelastic labor supply that grows endogenously. Consumers are subject to idiosyncratic capital accumulation risk and markets are incomplete. The government purchases consumption goods, makes transfers in the form of baby bonds, and it can use consumption and wealth taxes. The wealth distribution is given in closed form. When the intertemporal elasticity of substitution ɛ is equal to 1, the government can run a permanent primary deficit, up to a finite upper bound, if the coefficient of relative risk aversion is high enough and the factor share of labor is not too close to 1. This causes the risk-free rate r to be below the growth rate g of the economy. But the government can implement Pareto improvements when r - g does not exceed zero by enough. If ɛ ≠ 1, then there may not be an upper bound on the permanent primary deficits of the government. If ɛ Є (0,1), this happens when the economy is relatively unproductive, and then taking deficits to be very large makes all consumers worse off. If ɛ Є (1,∞), very large deficits are possible if the economy is sufficiently productive, and then they imply unbounded Pareto improvements.