Units of Measurement and the Inverse Hyperbolic Sine Transformation

The inverse hyperbolic sine (IHS) transformation is frequently applied in econometric studies to transform right-skewed variables that include zero or negative values. We confirm a previous study that shows that regression results can largely depend on the units of measurement of IHS-transformed variables. Hence, arbitrary choices regarding the units of measurement for these variables can have a considerable effect on recommendations for policies or business decisions. In order to address this problem, we suggest a procedure for choosing units of measurement for IHS-transformed variables. A Monte Carlo simulation assesses this procedure under various scenarios and a replication of the study by Bellemare and Wichman (2019) illustrates the relevance and applicability of our suggested procedure.