Optimal Control and Filtering in Linear Forward-looking Economies: A Toolkit

We provide algorithms to solve a linear-quadratic optimal control problem with commitment. By extending to the case of imperfect information a procedure outlined in Ljungqvist and Sargent (2002), we make the results of Svensson and Woodford (2000) easy to implement. We provide a Mat-lab package that solves this class of models and analyses their properties using simulations, impulse response functions and other techniques, with both commitment and discretion. A monetary policy application, based on the “new-Keynesian” model of Clarida, Galí and Gertler (1999), is used to illustrate how the toolkit can be used.