Chaos and unpredictability with time inconsistent policy makers

We analyze the existence of equilibria with complex dynamics in a policy framework with time-inconsistency. We consider an economy where, in each period, the policy maker in power determines the level of a durable public good (or bad) that creates strategic linkages across policy periods. When the decision-making process is time-consistent---such as when a benevolent planner sets policy in every period---the economy exhibits a unique equilibrium where the state converges to a deterministic steady state. When the identity of the decision-maker changes probabilistically over time as in a political equilibrium, the decision-making process becomes time-inconsistent. In this scenario, we identify conditions under which equilibria with cycles of more than two periods and chaotic dynamics can emerge. Depending on the economy's fundamental parameters, these equilibria may produce ergodic distributions in which the state variable either persistently overshoots the planner's steady state or fluctuates around it. The extent of chaotic behavior is influenced by the degree of time inconsistency: as the degree of time inconsistency approaches zero, the size of the support of the ergodic distribution converges to zero as well.