Budget Deficits, Stochastic Population Size and Consumption

This paper analyzes the effects on present consumption of budget deficits under different assumptions regarding demographics. In the first part, birth and death rates are deterministic, and in the second part, birth rates are assumed to be stochastic. In the case of a deterministic population size, an increase in public debt raises present consumption, if the (deterministic) birth rate is greater than zero, while with a zero birth rate we obtain debt neutrality. This is consistent with the results in Blanchard [1985] and Buiter [1988]. However, for the case of stochastic birth rates, it is shown that we can obtain the result that present consumption will decrease when public debt is increased, both when we have a zero expected birth rate, and when the expected population size is assumed to be constant, so that the expected birth rate is positive and equal to the death rate. The explanation is that with an uncertain birth rate, the future tax base is uncertain, which makes per capita taxes uncertain in the future. Shifting taxes to the future thus implies greater uncertainty about future net income, and induces precautionary savings.