A (pedagogical) note on the log-linearization of functions of several variables

Mario Solis-Garcia

International Review of Economics Education, 2021, vol. 37, issue C

Abstract: Dynamic stochastic general equilibrium (DSGE) models are analytically intractable and numerical methods must be used to approximate a solution. A key input shared by many solution methods is log-linearization. While the basics of the procedure have been extensively documented, applying the methodology to complicated functions of model variables remains uncharted territory, often resulting in cumbersome and error-prone calculations. This paper offers a procedure – the log-linear product approach – that automates and simplifies this task, as I show with a full working example. The procedure relies on the basic fact that the product of second order terms is zero when dealing with a linear expansion.

Keywords: DSGE models; Log-linear approximation (search for similar items in EconPapers)
JEL-codes: C65 E00 (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ireced:v:37:y:2021:i:c:s1477388021000025

DOI: 10.1016/j.iree.2021.100210

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