I am a bit confused about the recent difference-in-differences/ two-way fixed effects literature.
For example, in this paper the authors analyse a policy effect that happened at a state level on prescription shares of a specific medicine for different medical practices in "treatment" and "control" states. They estimate separate TWFE regressions for each state. I figure that's to avoid the problems arrising from staggered designs in TWFE regressions as pointet out by Goodman-Bacon and others. They estimate the following regression:
$$Y_{it} = \alpha_i + \delta_t + \beta D_{it} + \epsilon_{it} $$
$Y_{it}$ is the outcome variable, $D_{it}$ is the treatment indicator variable, which is equal to 1 if a physician belongs to the treatment group and if $t > T_0$, where $T_0$ represents the quarter of introducing a prescription target. $\beta$ is the estimate of the average treatment effect (ATE) of the prescription target in the respective intervention state in comparison to the control state without any intervention. $\alpha_i$ represents physician fixed-effects and §\delta_t§ represents time fixed-effects. The error term $\epsilon_{it}$ is clustered at physician level.
In their online appendix, the authors provide information about the evolution of mean outcomes over time in order to support the parallel trends assumption.
I have the following questions:
Since the authors have included physician fixed effects instead of state fixed effects, isn't the underlying parallel trends assumption rather that outcomes in each individual physician practice would have evolved in parallel if the intervention had not taken place?
Why would you include fixed effects at the micro level instead of at the treatment level anyway? (I get the clustering because of the serial correlation problem as pointed out by Bertrand et al. but why fixed effects?)
