A (pedagogical) note on the log-linearization of functions of several variables. (June 2021)

• Record Type: Journal Article
• Authors: Solis-Garcia, Mario
• Is Part Of: International review of economics education. Volume 37(2021)
• Publication Date: 2021-06
• Subjects: C65 -- E00; DSGE models -- Log-linear approximation; Economics -- Study and teaching -- Periodicals; Economics -- Study and teaching; Periodicals; 330.0711
• DOI: 10.1016/j.iree.2021.100210
• Languages: English
• ISSNs: 1477-3880

Abstract

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.