Dif-in-dif estimators of multiplicative treatment effects

Abstract

We consider a difference-in-differences setting with a continuous outcome,
such as wages or expenditure. The standard practice is to take its logarithm
and then interpret the results as an approximation of the multiplicative treat-
ment effect on the original outcome. We argue that a researcher should rather
focus on the non-transformed outcome when discussing causal inference. Fur-
thermore, it is preferable to use a non-linear estimator, because running OLS
on the log-linearised model might confound distributional and mean changes.
We illustrate the argument with an original empirical analysis of the impact
of the UK Educational Maintenance Allowance on households’ expenditure,
and with a simulation exercise.