Mathematical Analysis of the Chaotic Behavior in Monetary Policy Games
This thesis discusses the concept of chaos in monetary policy games. The mathematical framework developed in this thesis addresses two important problems in monetary theory, namely, the time-inconsistency and the complexity in designing, conducting and predicting the impacts of monetary policy on the economy. Considering a noncooperative non-zero-sum differential monetary policy game between the central bank and the public when the coefficients of the system depend on the state and control variables, it is shown that the co-state variables of both players are controllable in all solution concepts. The controllability of the co-state variables means that the monetary policy is time inconsistent even in the open loop Nash game, which is known as a time-consistent policy game in the literature. In other words, the results confirm that the structural time-inconsistency of monetary policy is almost always unavoidable. To better understand how monetary policy affects the economy, we need to know the response of the public expectations. This can be achieved if the monetary policy behaves in a systematic manner. To this end, this thesis tests the chaotic dynamics of the trajectories of both players. The results reveal that chaotic dynamics is possible in monetary policy games, and it seems that the source of this complexity comes from the chaotic behavior in the public expectations. Chaotic behavior in the strategy of the public sector creates serious difficulties for the policymaker, who wishes to design a policy that controls the business cycles.