Public capital, private capital and economic growth

An endogenous growth model is presented in which productive government expenditure takes the form of a stock. Private and public capital interact with each other in two different ways. The first takes place in the final output sector and depends on the specification of the aggregate production function (Cobb-Douglas vs. CES). The second has to do with the rates of investment in the two types of capital and arises from the law of motion of public capital. The share of public capital devoted to output production can be exogenous or endogenous. Our results suggest that when this share is exogenous along the balanced growth path the optimal growth rate of the economy depends positively on the degree of complementarity between the investments in the two kinds of capital, irrespective of the form of the aggregate production function. This is also true when the share of public capital devoted to output production is endogenous, as long as the inverse of the intertemporal elasticity of substitution in consumption is sufficiently large. When the technology for final output production is CES and the social planner can choose the fraction of public capital to be devoted to goods-production, optimal growth crucially depends on the elasticity of substitution between the two forms of capital in the production of goods. We analyze the conditions for an increase in this elasticity to yield either a positive, or a negative, or else an ambiguous effect on the economy’s optimal growth rate. Unlike Barro (1990), the relationship between optimal growth and the share of productive government expenditure in GDP is nonlinear and characterized by threshold-effects.