Dif-in-Dif Estimators of Multiplicative Treatment Effects

We consider a difference-in-differences setting with a continuous outcome, such as wages or expenditure. The standard practice is to take the logarithm of the outcome and then interpret the results as an approximation of the multiplicative treatment effect on the original outcome. We argue that a researcher should instead focus on the original outcome when discussing causal inference. Furthermore, 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