Last updated on September 27, 2018
In the capharnaum leading to the start of the fall semester, I had somehow lost sight of the idea of posting the newest version of my paper with Casey Wichman in which we derive elasticities for regressions involving the inverse hyperbolic sine (IHS) transformation.
Here it is. The results haven’t changed much, but this version is considerably better, and we are grateful to those who have read the first version. 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.
I was reminded that I hadn’t yet posted about this new version last week, in the context of a thread about whether the IHS transformation was really better than the ln(x + 1) transformation.
For me, that is neither here nor there. For better or for worse, applied microeconomists have settled on the IHS transformation as the thing to do when dealing with ln(0) instead of on the ln(x + 1) (or on some kind of ln(x + e), where e is a small but arbitrary constant) transformation–an example of a fads or fashion in applied econometrics. No transformation is perfect, and ideally, one will want to show that one’s results are robust to many different specifications. Because this is what the social norm is nowadays, and because people tend to follow the norm, we thought we could usefully contribute by deriving the associated elasticities.