Chaos and Unpredictability with Time Inconsistent Policy Makers
We study the existence of equilibria with complex dynamics in a policy problem with time inconsistent policy makers. We consider a simple economy where a policy maker every period selects the level of a durable public good (or bad) that strategically links policy making periods, such as the state of the environment. When the decision process is time consistent, as when a benevolent planner selects the policy, the economy has a unique equilibrium in which the state converges to a deterministic steady state. When the decision process is not time consistent, as in a political equilibrium, equilibria with complex cycles and aperiodic, chaotic dynamics exist under easily satisfied conditions. Depending on the fundamentals of the economy, these equilibria may generate ergodic distributions that consistently overshoot the planner's steady state, or that fluctuate around it. The size of the support of the cycles and the chaotic region depends on the degree of time inconsistency: as the degree of time inconsistency converges to zero, the support of the cycles or the chaotic behavior converges to zero as well.