Chapter

Linear Quadratic Approximations: An Introduction

Javier Díaz‐Giménez

in Computational Methods for the Study of Dynamic Economies

Published in print October 2001 | ISBN: 9780199248278
Published online November 2003 | e-ISBN: 9780191596605 | DOI: http://dx.doi.org/10.1093/0199248273.003.0002
 Linear Quadratic Approximations: An Introduction

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This is a brief introduction to dynamic programming and the method of using linear quadratic (LQ) approximations to the return function; the method is an approximation because it computes the solution to a quadratic expansion of the utility function about the steady state or the stable growth path of model economies. The main purpose of the chapter is to review the theoretical basis for the LQ approximation and to illustrate its use with a detailed example (social planning). The author demonstrates that, using the LQ approximation approach and the certainty equivalence principle, solving for the value function is a relatively easy task. The different sections of the chapter describe the standard neoclassical growth model, present a social planner problem that can be used to solve the model, give a recursive formulation of the social planner's problem, and describe an LQ approximation to this problem. Exercises are included throughout, and an appendix presents a MATLAB program to illustrate the LQ method.

Keywords: certainty equivalence principle; dynamic economics models; dynamic programming; economic theory; linear models; linear quadratic approximations; macroeconomics; MATLAB programs; model economies; neoclassical growth model; return function; social planning; utility function; certainty equivalence principle

Chapter.  8570 words. 

Subjects: Macroeconomics and Monetary Economics

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