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Macroeconomic Model with Monetary and Fiscal Policy and Externality: Nonlinear dynamics, Optimization and Control
Irregular fluctuations in economy lead to unpredictable effects and disrupt its stable functioning. Various tools could be used to stabilize irregular dynamics in economic models. For example, to introduce control into the model as an external function, as well as to take into account the internal characteristics of economic agents in the economy under consideration, we consider agents that use the variables that are under their control to achieve optimum, by minimizing or maximizing cost, profit, or welfare function. However, optimal behavior in economics does not necessarily lead to simple model dynamics. It is therefore important to find the conditions for and understand the mechanism of emergence of complex dynamics. We study two New Keynesian models, including one with externalitites, in continuous-time under different monetary and fiscal policy regimes, which represent the economy where the economic agents solve constrained optimization problems. We show that in case of explosive equilibrium dynamics, limit cycles or more complicated attracting sets could appear, including chaotic attractors of various nature. In this case it is possible to control irregular dynamics, including by adjusting policy parameters that serve as bifurcation parameters, in order to alleviate the implied economic uncertainty and bring agents’ expectations in line with the intended steady state.