On the Interaction between Public Investment and Private Capital in Economic Growth

This paper examines two possible sources of interaction between private capital and productive public expenditure within an endogenous growth model. On the one hand, public investment and private capital are complementary with each other in the production of goods. On the other, they can be either complementary or substitutes in the production of new productive public capital. In our model private capital and the stock of productive public spending are two reproducible productive inputs interacting with each other in goods production and in productive public capital investment. The share of productive public expenditure devoted to output production can be exogenous or endogenous, and we consider a Cobb-Douglas as well as a more general CES aggregate production function. Our main results suggest that, when the share productive public expenditure devoted to output production is exogenous along the balanced growth path equilibrium the common growth rate is a negative function of this share and a positive function of the degree of complementarity between the two forms of capital. When the sectoral allocation of productive public expenditure is endogenous, the main determinant of the economy’s long run growth rate is, along with the model’s preferences parameters, the public capital’s share in GDP. Unlike existing literature (notably, Barro 1990), we find that the relationship linking the economy’s growth rate and the productive public expenditure’s share in GDP is U-shaped, rather than monotonically decreasing.