Computation of LQ Approximations to Optimal Policy Problems in Different Information Settings under Zero Lower Bound Constraints

This paper describes a series of algorithms that are used to compute optimal policy under full and imperfect information. Firstly we describe how to obtain linear quadratic (LQ) approximations to a nonlinear optimal policy problem. We develop novel algorithms that are required as a result of having agents with forward-looking expectations, that go beyond the scope of those that are used when all equations are backward-looking; these are utilised to generate impulse response functions and second moments for the case of imperfect information. We describe algorithms for reducing a system to minimal form that are based on conventional approaches, and that are necessary to ensure that a solution for fully optimal policy can be computed. Finally we outline a computational algorithm that is used to generate solutions when there is a zero lower bound constraint for the nominal interest rate.