Finding Correct Elasticities in Log-Linear and Exponential Models Allowing Heteroskedasticity
- Authors
- Lee, M.-J.
- Issue Date
- 6월-2021
- Publisher
- De Gruyter Open Ltd
- Keywords
- exponential model; log-linear model; mean elasticity; quantile elasticity
- Citation
- Studies in Nonlinear Dynamics and Econometrics, v.25, no.3, pp.81 - 91
- Indexed
- SSCI
SCOPUS
- Journal Title
- Studies in Nonlinear Dynamics and Econometrics
- Volume
- 25
- Number
- 3
- Start Page
- 81
- End Page
- 91
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/128812
- DOI
- 10.1515/snde-2018-0099
- ISSN
- 1081-1826
- 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. © 2020 Walter de Gruyter GmbH, Berlin/Boston.
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