On Dynamic Decoupling and Dynamic Path Controllability in Economic Systems

In the theory of economic policy making a standard question deals with the ability of guiding a given set of target variables along arbitrarily chosen time paths by a suitable selection of the policy instruments at each time instant. The rationale of having a positive answer to this question of dynamic path controllability or perfect controllability is of course that in such a situation the policymaker can steer the target variables along desired paths. This could be interpreted as a dynamic generalization of the well-known Tinbergen concept of static controllability. Dynamic path controllability has been studied in the economics literature by various authors, e.g., Aoki (1974,1975,1976), Buiter (1979), Aoki and Canzoneri (1979), Preston and Pagan (1982), Wohltmann (1984, 1985b), Wohltmann and Kramer (1983, 1984), and others. There also exists a large engineering literature on dynamic path controllability in that context often referred to as right-invertibility or functional reproducibility see, e.g., Brockett and Mesarovic (1965), Sain and Massey (1969) Wolovich (1974), and others. In all forementioned references one has to assume that the underlying (economic) model is a linear one in state space form. The linearity requirement is clearly usually not met. To avoid nonlinearities in the model a common approach is that one linearizes the economic model around a fixed equilibrium point and then one applies the linear theory on dynamic path