Logs with zeros? Some problems and solutions
Jiafeng Chen, Jonathan Roth

TL;DR
This paper examines the problems of interpreting log-like transformations of outcomes that can be zero, highlighting issues of unit-dependence and proposing alternative methods for analysis.
Contribution
It demonstrates the unit-dependence of treatment effects for log-like transformations with zeros and introduces a trilemma regarding effect interpretability, proposing alternative approaches.
Findings
Log-like transformations depend on outcome units, affecting treatment effect interpretation.
A treatment effect for outcomes with zeros cannot be both unit-invariant and point-identified.
Alternative methods include using levels, calibrating margins, or separate effects estimation.
Abstract
When studying an outcome that is weakly-positive but can equal zero (e.g. earnings), researchers frequently estimate an average treatment effect (ATE) for a "log-like" transformation that behaves like for large but is defined at zero (e.g. , ). We argue that ATEs for log-like transformations should not be interpreted as approximating percentage effects, since unlike a percentage, they depend on the units of the outcome. In fact, we show that if the treatment affects the extensive margin, one can obtain a treatment effect of any magnitude simply by re-scaling the units of before taking the log-like transformation. This arbitrary unit-dependence arises because an individual-level percentage effect is not well-defined for individuals whose outcome changes from zero to non-zero when receiving treatment, and the units of the outcome…
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Taxonomy
TopicsAdvanced Causal Inference Techniques · Labor market dynamics and wage inequality · Retirement, Disability, and Employment
