Working Paper: NBER ID: w30735
Authors: John Mullahy; Edward C. Norton
Abstract: Dependent variables that are non-negative, follow right-skewed distributions, and have large probability mass at zero arise often in empirical economics. Two classes of models that transform the dependent variable y — the natural logarithm of y plus a constant and the inverse hyperbolic sine — have been widely used in empirical work. We show that these two classes of models share several features that raise concerns about their application. The concerns are particularly prominent when dependent variables are frequently observed at zero, which in many instances is the main motivation for using them in the first place. The crux of the concern is that these models have an extra parameter that is generally not determined by theory but whose values have enormous consequences for point estimates. As these parameters go to extreme values estimated marginal effects on outcomes' natural scales approach those of either an untransformed linear regression or a normed linear probability model. Across a wide variety of simulated data, two-part models yield correct marginal effects, as do OLS on the untransformed y and Poisson regression. If researchers care about estimating marginal effects, we recommend using these simpler models that do not rely on transformations.
Keywords: dependent variable transformations; regression models; skewed outcomes; zero outcomes; marginal effects
JEL Codes: C18; C20; I10
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| transformations like the natural logarithm or inverse hyperbolic sine (C51) | biased estimates of marginal effects (C51) |
| parameters associated with transformations approach extreme values (C51) | estimated marginal effects converge to those from untransformed linear regression or a linear probability model (C51) |
| presence of zeros in dependent variable (C29) | influence on estimated coefficients (C51) |
| transformations do not lead to reliable estimates of policy parameters (C51) | recommend using simpler models (C52) |