Complex dynamics and optimal control of monetary policy in a New Keynesian model with government debt
One of the central tasks of macroeconomic analysis is forecasting and control of economic agents’ expectations for key macroeconomic indicators such as inflation, gross domestic product (GDP), prices and others, etc., so that to achieve maximum level of their welfare through monetary and fiscal policy. This problem is solved within the framework of the optimal control theory using New Keynesian (NK) models that can demonstrate complex behavior, including periodic and chaotic dynamics, even in conditions of dynamical economic equilibrium. Revealing the economic mechanism for the emergence of such irregular dynamics can improve forecasting behavior of the model of the economy and stabilize undesirable dynamics. We consider this complex mechanism from two sides. First, we analyze how various monetary and fiscal policy regimes, active as well as passive, stimulate the emergence of different types of dynamics, both locally determinate and explosive ones, using the NK model with government debt as an example. Second, we clarify how government debt affects optimal monetary policy. A non-trivial backward integration algorithm is implemented to identify the initial state of the model, which leads to optimal dynamic equilibrium and the achievement of targeted values of key macroeconomic indicators.