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Linear-Quadratic Approximation, Efficiency and Target-Implementability

  • Paul Levine

    (University of Surrey)

  • Joseph Pearlman

    (London Metropolitan University)

  • Richard Pierse

    (University of Surrey)

We examine linear-quadratic (LQ) approximation of stochastic dynamic optimization problems in macroeconomics (and elsewhere), in particular in policy analysis using Dynamic Stochastic General Equilibrium (DSGE) models. We first define the problem that is solved by a social planner, given that the objective of the latter is to maximize average welfare; this yields the efficient solution. We then comment on the LQ approximation when a tax or subsidy can be imposed such that the zero-inflation competitive steady state output level is equal to the efficient level. We then examine the correct procedure for replacing a stochastic non-linear dynamic optimization problem with a linear-quadratic approximation. We show that a procedure proposed by Benigno and Woodford (2004) for large underlying distortions in the economy can be more easily implemented through a second-order approximation of the Hamiltonian used to compute the ex ante optimal policy with commitment (the Ramsey problem). We then define the notion of Target-Implementability, which is also a sufficient condition for a particular steady-state maximum of the Ramsey problem, and explain the usefulness of this in the context of stabilization policy

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Paper provided by Society for Computational Economics in its series Computing in Economics and Finance 2006 with number 441.

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Date of creation: 04 Jul 2006
Handle: RePEc:sce:scecfa:441
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  1. Svensson, Lars E. O., 2005. "Monetary policy with judgment: forecast targeting," Working Paper Series 0476, European Central Bank.
  2. Svensson, Lars E.O. & Faust, John, 1998. "Transparency and Credibility: Monetary Policy with Unobservable Goals," Seminar Papers 636, Stockholm University, Institute for International Economic Studies.
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  10. Clarida, R. & Gali, J. & Gertler, M., 1998. "Monetary Policy Rules and Macroeconomic Stability: Evidence and some Theory," Working Papers 98-01, C.V. Starr Center for Applied Economics, New York University.
  11. Nicoletta Batini & Alejandro Justiniano & Paul Levine & Joseph Pearlman, 2004. "Robust Inflation-Forecast-Based Rules to Shield against Indeterminacy," School of Economics Discussion Papers 0804, School of Economics, University of Surrey.
  12. Clarida, Richard & Gali, Jordi & Gertler, Mark, 2002. "A simple framework for international monetary policy analysis," Journal of Monetary Economics, Elsevier, vol. 49(5), pages 879-904, July.
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