Present bias and the inefficiency of the centralized economy: The role of the elasticity of intertemporal substitution

We analyze an endogenous growth model considering agents with an isoelastic utility. Preferences are characterized by a utility affected by a negative externality, and a level of impatience which decays with the time distance from the present. Agents who cannot commit the actions of their future selves, play a game against them. The stationary equilibrium of this game defines a balanced growth path with a slower growth when played by subsequent central planners than when played by decision makers in the market economy. First, we prove that the fast growing market economy implies higher welfare if the negative externality is small, while the centralized economy is welfare improving above a given threshold for the externality (obtained for a specific family of non-constant discount functions). Secondly, we observe that this threshold increases with the elasticity of intertemporal substitution in consumption. Therefore, the greater this elasticity the more likely it is that the externality lies below this threshold, where policy interventions would not be adequate. Finally, as one would expect, the range of values of the externality for which the market equilibrium provides higher welfare widens the more different from constant discounting time preferences are, due either to a wider range of variation for the instantaneous discount rates or because these decay more slowly.