Capital externalities in OLG economies

The recent literature has stressed that externalities, however small, may lead to indeterminacy and endogenous fluctuations while, on the contrary, intertemporal substitution in consumption leads to local uniqueness. This paper introduces increasing returns, through aggregate capital externalities, into the overlapping generations model with endogenous labor and consumption in both periods of life. We show that local determinacy of the steady state prevails, when externalities are arbitrarily small, as long as the fraction of young-age consumption out of wage income is large enough. Conversely, local indeterminacy with small externalities requires both labor supply to be close to indivisible and irrealistic values of the propensity to save out of the wage income. More surprising is the fact that increasing the size of externalities indeed reduces the range of values of the consumption-to-wage ratio associated with multiple equilibria, because of two conflicting effects on savings that operate through wage and interest rate.