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

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  • Solis-Garcia, Mario

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.

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  • Solis-Garcia, Mario, 2021. "A (pedagogical) note on the log-linearization of functions of several variables," International Review of Economics Education, Elsevier, vol. 37(C).
    • Handle: RePEc:eee:ireced:v:37:y:2021:i:c:s1477388021000025
    DOI: 10.1016/j.iree.2021.100210
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    More about this item

    Keywords

    DSGE models; Log-linear approximation;

    JEL classification:

    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • E00 - Macroeconomics and Monetary Economics - - General - - - General

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