On the interaction between public and private capital in economic growth

Abstract

This paper introduces two forms of interaction between private and public capital in an endogenous growth model in which productive government expenditure takes the form of a stock-variable and public capital is used in part as an input in the production of final output and in part to increase its own supply. While the first form of interaction involves the stocks of the two capital-goods and takes place within the final output sector through the specification of the aggregate production function (Cobb–Douglas vs. CES), the second one concerns the rates of investment in the two kinds of capital. The share of productive public expenditure devoted to output production can be either exogenous or endogenous. Our results suggest that when this share is exogenous, along the balanced growth path the optimal growth rate of the economy is a positive function of the degree of complementarity between the two forms of investment. When the share of productive public expenditure devoted to output production is endogenous, the public capital share in GDP becomes, along with the model’s preference parameters, an important determinant of the economy’s long run growth. We also find that the optimal growth rate is an increasing function of the elasticity of substitution between public and private capital inputs in goods production, and is independent of the complementarity/substitutability between the two forms of investment.