Equilibrium cycles in an overlapping generations economy with production

Fertility-related pensions and cyclical instability

“…As is known, cyclical behaviour can occur in many-good OLG models (Grandmont, 1985) as well as in the one-good Diamond-type OLG context (Farmer, 1986;Reichlin, 1986), but only when production factors are relatively complement. Moreover, with myopic foresight, the steady state may be oscillatory and exhibit deterministic complex cycles (Michel and de la Croix, 2000, de la Croix and Michel, 2002;Fanti and Spataro, 2008), but only when the inter-temporal elasticity of substitution in the utility function is higher than unity (i.e., higher than in the case of Cobb-Douglas preferences).…”

Local indeterminacy under dynamic efficiency in a two-sector overlapping generations economy

“…Considering an aggregate model with endogenous labor and consumption in the second period of life only, Reichlin [9] has shown that Hopf cycles and thus local indeterminacy arise with a unique Pareto optimal steady state when the technology is Leontief. This conclusion has had a strong echo in the literature as it implies that the introduction of a public policy based on taxes and transfers could at the same time stabilize the economy and reach the Pareto optimal steady state along which all generations get an equal level of utility.…”

“…Our main objective in this paper is to show that Reichlin's [9] result is a robust property in a two-sector OLG economy. Assuming gross substitutability and a capital intensive consumption good sector, we prove indeed that local indeterminacy can occur under dynamic efficiency when intermediary values for the elasticity of intertemporal substitution in consumption and low enough but positive sectoral elasticities of capital-labor substitution are considered.…”

Indeterminacy, bifurcations and chaos in an overlapping generations model with negative environmental externalities

“…These are quite new results because the widespread view in literature on overlapping generations models is that the rise of periodic orbits and of indeterminacy is due to distortions in the production side of the economy: non perfect competition, positive externalities and so on (see e.g. Reichlin 1986;Grandmont et al 1998;Cazzavillan et al 1998;Cazzavillan 2001), while in our model these dynamic regimes can be observed assuming a very simple production technology (i.e. a Cobb-Douglas one) and perfect competition among firms.…”