Chapter 13 Numerical methods for linear-quadratic models

This chapter discusses the widely used control model in economics, the Linear Quadratic Control Model (LQCM).The major advantage of LQCM is that it has, in general, a unique analytical solution. However, this is not necessarily true when dealing with forward-looking behavior or stochastic models. The same holds for most nonlinear dynamic control problems. Therefore, the solution of the optimization problem has to be obtained through an approximation procedure. The stochastic version of the LQCM explicitly models stochastic parameters and provides the opportunity to address the Lucas critique within the control framework. The stochastic version has some major drawbacks that have to be worked upon.