Elasticities and the Inverse Hyperbolic Sine Transformation

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.