Working Paper: NBER ID: w29998
Authors: Edward C. Norton
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.
Keywords: Inverse Hyperbolic Sine Transformation; Marginal Effects; Linear Regression; Econometrics
JEL Codes: C16; I1
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| IHS transformation (C67) | modeling of dependent variables with non-positive values (C35) |
| IHS transformation (C67) | mitigate influence of outliers in right-skewed distributions (C46) |
| IHS transformation (C67) | retransformation essential for interpreting marginal effects (C51) |
| IHS transformation is not invariant to scaling (F12) | different interpretations of estimated marginal effects (C51) |
| scaling dependent variable (C29) | marginal effects similar to untransformed or log-transformed regression (C29) |
| Duan's smearing estimate (C51) | estimating marginal effects on original scale (C51) |
| IHS transformation (C67) | robust approach for estimating marginal effects (C51) |