Linear-Quadratic Approximation, External Habit and Targeting Rules

48 Pages Posted: 28 Jun 2007

See all articles by Paul Levine

Paul Levine

School of Economics, University of Surrey

Joseph Pearlman

London Metropolitan University - Department of Economics, Finance and International Business (EFIB)

Richard G. Pierse

University of Surrey - Department of Economics; National Institute of Economic and Social Research (NIESR)

Date Written: June 2007

Abstract

We examine the linear-quadratic (LQ) approximation of non-linear stochastic dynamic optimization problems in macroeconomics, in particular for monetary policy. We make four main contributions: first, we draw attention to a general Hamiltonian framework for LQ approximation due to Magill (1977). We show that the procedure for the 'large distortions' case of Benigno and Woodford (2003, 2005) is equivalent to the Hamiltonian approach, but the latter is far easier to implement. Second, we apply the Hamiltonian approach to a Dynamic Stochastic General Equilibrium model with external habit in consumption. Third, we introduce the concept of target-implementability which fits in with the general notion of targeting rules proposed by Svensson (2003, 2005). We derive sufficient conditions for the LQ approximation to have this property in the vicinity of a zero-inflation steady state. Finally, we extend the Hamiltonian approach to a non-cooperative equilibrium in a two-country model.

Keywords: Linear-quadratic approximation, dynamic stochastic general equilibrium

JEL Classification: E52, E37, E58

Suggested Citation

Levine, Paul L. and Pearlman, Joseph G. and Pierse, Richard G., Linear-Quadratic Approximation, External Habit and Targeting Rules (June 2007). ECB Working Paper No. 759. Available at SSRN: https://ssrn.com/abstract=989603

Paul L. Levine (Contact Author)

School of Economics, University of Surrey ( email )

Guildford
Surrey GU2 7XH
United Kingdom
+44 1483 259 380 Ext. 2773 (Phone)
+44 1483 259 548 (Fax)

Joseph G. Pearlman

London Metropolitan University - Department of Economics, Finance and International Business (EFIB) ( email )

Economics Subject Group, LMBS
London EC2M 6SQ, EC2M 6SQ
United Kingdom

Richard G. Pierse

University of Surrey - Department of Economics ( email )

Guildford
Surrey GU2 7XH
United Kingdom

National Institute of Economic and Social Research (NIESR) ( email )

2 Dean Trench Street
Smith Square
London SW1P 3HE
United Kingdom

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