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Finding correct elasticities in log-linear and exponential models allowing heteroskedasticity

Myoung-jae Lee

Studies in Nonlinear Dynamics & Econometrics, 2020, vol. 25, issue 3, 81-91

Abstract: Log-linear models are popular in practice because the slope of a log-transformed regressor is believed to give an unit-free elasticity. This widely held belief is, however, not true if the model error term has a heteroskedasticity function that depends on the regressor. This paper examines various mean – and quantile-based elasticities (mean of elasticity, elasticity of conditional mean, quantile of elasticity, and elasticity of conditional quantile) to show under what conditions these are equal to the slope of a log-transformed regressor. A particular attention is given to the ‘elasticity of conditional mean (i.e., regression function)’, which is what most researchers have in mind when they use log-linear models, and we provide practical ways to find it in the presence of heteroskedasticity. We also examine elasticities in exponential models which are closely related to log-linear models. An empirical illustration for health expenditure elasticity with respect to income is provided to demonstrate our main findings.

Keywords: exponential model; log-linear model; mean elasticity; quantile elasticity (search for similar items in EconPapers)
JEL-codes: C21 C24 I10 (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1515/snde-2018-0099

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