The Inverse Hyperbolic Sine Transformation and Retransformed Marginal Effects

Edward Norton

No 29998, NBER Working Papers from National Bureau of Economic Research, Inc

Abstract: This paper shows how to calculate consistent marginal effects on the original scale of the outcome variable in Stata after estimating a linear regression with a dependent variable that has been transformed by the inverse hyperbolic sine function. The method uses a nonparametric retransformation of the error term and accounts for any scaling of the dependent variable. The inverse hyperbolic sine function is not invariant to scaling, which is known to shift marginal effects between those from an untransformed dependent variable to those of a log-transformed dependent variable.

JEL-codes: C16 I1 (search for similar items in EconPapers)
Date: 2022-04
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Published as Edward C. Norton, 2022. "The inverse hyperbolic sine transformation and retransformed marginal effects," The Stata Journal: Promoting communications on statistics and Stata, vol 22(3), pages 702-712.

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