Modeling the Lucas critique as an open loop feedback process with time-varying parameters

\\begin{abstract} Lucas (1976) pointed out, that when optimization is performed on a deterministic macro model, the resulting policy may not reflect the true optimal solution. Private agents may react to announced policies and consequently model parameters will start to drift. The aim of this paper is to develop a methodology for deriving an optimal policy in the presence of parameter drift. This drift is captured by a stochastic optimization framework with time varying parameters. The resulting optimal policy is capable of tracking changes in the parameters due to policy changes. \\\\ The methodology we have applied in this paper is based on a feedback control in a quadratic-linear stochastic control model with time varying parameters. Thus it is an extension of Kendrick (1981) which provides a similar derivation for models with constant rather than time-varying parameters. For this paper the model is augmented with equations for time-varying parameters. The vector of parameters is used to augment the original state vector, thus the linear system equations in the original states become a pair of nonlinear system equations in the original states and in the parameter vector. \\end{abstract}