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Computational Methods for the Study of Dynamic Economies$
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Ramon Marimon and Andrew Scott

Print publication date: 2001

Print ISBN-13: 9780199248278

Published to Oxford Scholarship Online: November 2003

DOI: 10.1093/0199248273.001.0001

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Linear Quadratic Approximations: An Introduction

Linear Quadratic Approximations: An Introduction

Chapter:
(p.13) 2 Linear Quadratic Approximations: An Introduction
Source:
Computational Methods for the Study of Dynamic Economies
Author(s):

Javier Díaz‐Giménez

Publisher:
Oxford University Press
DOI:10.1093/0199248273.003.0002

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

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