The New Palgrave Dictionary of Economics

2018 Edition
| Editors: Macmillan Publishers Ltd

Approximate Solutions to Dynamic Models (Linear Methods)

  • Harald Uhlig
Reference work entry


This article explains how to obtain an approximate solution to dynamic stochastic discrete-time (DSGE) models by first log-linearizing the relevant equations and then obtaining a recursive law of motion, by using the method of undetermined coefficients. Calculations are provided based on both an eigenvector decomposition and the QZ or Schur decomposition. The role of sunspots and the relationship to the method of Blanchard and Kahn are discussed. The base example is a generic real business cycle model, for which log-linearization is described generally and in detail. The method described should be easily implemented. Further literature references and software sources are provided.


Approximate solutions to dynamic models (linear methods) Dynamic stochastic general equilibrium (DSGE) models Linearization Log-linearization QZ decomposition Real business cycles Representative agent Recursive law of motion Sunspots 

JEL Classifications

D4 D10 
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Copyright information

© Macmillan Publishers Ltd. 2018

Authors and Affiliations

  • Harald Uhlig
    • 1
  1. 1.