Dif-in-dif estimators of multiplicative treatment effects
We consider a difference-in-differences setting with a continuous outcome. The standard practice is to take its logarithm and then interpret the results as an approximation of the multiplicative treatment effect on the original outcome. We argue that a researcher should rather focus on the non-transformed outcome when discussing causal inference. The first step should be to decide whether the time trend is more likely to hold in multiplicative or level form. If the former, it is preferable to estimate an exponential model by Poisson Pseudo Maximum Likelihood, which does not require statistical independence of the error term. Running OLS on the log-linearised model might instead lead to confounding distributional and mean changes. We illustrate the argument with a simulation exercise.
Journal of Econometric Methods
Open Access; ©2018 Paul Fisher et al., published by DeGruyter, Berlin/Boston. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License. BY-NC-ND 4.0