Finding Correct Elasticities in Log-Linear and Exponential Models Allowing Heteroskedasticity

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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.

Original languageEnglish
JournalStudies in Nonlinear Dynamics and Econometrics
DOIs
Publication statusAccepted/In press - 2020

Keywords

  • exponential model
  • log-linear model
  • mean elasticity
  • quantile elasticity

ASJC Scopus subject areas

  • Analysis
  • Social Sciences (miscellaneous)
  • Economics and Econometrics

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