# Macroeconomic Model of Small Open Economy: Adaptive Parameter Estimation, Behavior Analysis and Optimal Control

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## Abstract

Internal so-called state-space representation of dynamic systems became dominating approach in the control theory in 1960s. This paper focuses on taking advantage of such a system description for dynamic economic system identification as well as on using a quantified economic model in search of suitable strategies for short-run economic development. Solving the filtration, prediction and interpolation tasks expressed by internal system description is conditioned by estimating the states of system on the basis of measured system inputs and outputs. Time-varying parameters of a system are often regarded and handled as states. The identification task is written as a stochastic problem in sense of search for an optimal linear unbiased state estimate. A recursive algorithm called Kalman filter is at our disposal to obtain the above estimate that we evaluate as conditional mean (minimizing variance) of an unknown state on the basis of data set affected by disturbances. Choice of a strategy for short-run economic development is then considered to be an optimal control task defined as two-point boundary problem of discrete-time linear-quadratic control (the optimal output and input trajectories track as close as possible the nominal trajectories entered as "wanted" or "planned"). The paper contains an analytical solution of that problem as well as an algorithm applicable to the control of a controlled economic system's model. Identification and optimal control algorithms have been applied to quarterly econometric model of the Czech economy development.

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