Last updated on February 24, 2019
Casey Wichman and I have just finished revising our paper titled “Elasticities and the Inverse Hyperbolic Sine Transformation,” in which we derive exact elasticities for log-linear, linear-log, and log-log specifications where the inverse hyperbolic sine transformation is used in lieu of logs so as to be able to keep zero-valued observations instead of systematically dropping them due to the undefined nature of ln(0).
Here is the abstract:
Applied econometricians frequently apply the inverse hyperbolic sine (or arcsinh) transformation to a variable because it approximates the natural logarithm of that variable and allows retaining zero-valued observations. We provide derivations of elasticities in common applications of the inverse hyperbolic sine transformation and show empirically that the difference in elasticities driven by ad hoc transformations can be substantial. We conclude by offering practical guidance for applied researchers.
In this new version, we have made a number of changes in responses to reviewer comments. In my view, the most important of these changes is appendix B, where we provide Stata code to compute elasticities with an inverse hyperbolic sine transformation.