Endogenous business cycles in overlapping generations models with time inconsistency

This paper investigates the implications of incorporating quasi-hyperbolic discounting preferences and extending the economic lifespan for the emergence of endogenous business cycles. Using a three-period overlapping generations model, we examine how quasi-hyperbolic discounting influences the dynamics of deterministic cycles and local sunspot equilibria. The presence of a middle-aged generation plays a key role in generating an elasticity of intertemporal substitution that is lower than the inverse of risk aversion, interacting with consumers’ time-inconsistent behavior. A lower EIS strengthens gross complementarity between dated goods and thereby contributes to the existence of multiple equilibria and self-fulfilling, belief-driven fluctuations. We show that our three-period model with time-inconsistent preferences makes two-period cycles and local indeterminacy more plausible than in a standard two-period framework with exponential discounting, as it expands the set of parameter values under which such endogenous fluctuations can arise.