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

Finding correct elasticities in log-linear and exponential models allowing heteroskedasticity AbstractLog-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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Studies in Nonlinear Dynamics & Econometrics de Gruyter

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

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References (7)

Publisher
de Gruyter
Copyright
© 2020 Walter de Gruyter GmbH, Berlin/Boston
ISSN
1558-3708
eISSN
1558-3708
DOI
10.1515/snde-2018-0099
Publisher site
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Abstract

AbstractLog-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.

Journal

Studies in Nonlinear Dynamics & Econometrics – de Gruyter

Published: Jun 14, 2021

Keywords: exponential model; log-linear model; mean elasticity; quantile elasticity; C21; C24; I10

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