Taking logarithm when the independent variable contains zeros in regression analysis: a new approach

ABSTRACT

We propose a two-part model to deal with the problem of taking logarithm when the independent variable in a regression contains zeros. In particular, we generalize the conventional approach by choosing the optimal constant to add to the variable before taking logarithm, treating observations with zero values as a separate group. The empirical evidence supports our proposed model.

KEYWORDS:

• Started logarithm
• inverse hyperbolic sine
• two-part model
• elasticity
• zero values

JEL CLASSIFICATION:

• C1
• C5

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

¹ The scaled IHST in Carroll et al. (2003), $ln(k{x}_i+{\left(k^2{x_i}^2+1\right)}^{1/2})=ln(k)+ln(x_i+{\left({x_i}^2+k^{-2}\right)}^{1/2})$, can be viewed as GIHST plus a constant.

² See Table A1 of the Appendix for the complete results.

³ See Table A2 of the Appendix for the complete results.

⁴ Although we focus on the log–log model, a similar method is applicable to the semi-log model as well.