A note on did2s syntax

Kyle Butts | March 2025

Being the author of the did2s package, I get a lot of emails from folks asking how to properly specify a first_stage and second_stage argument. A typical usage will look like:

library(did2s)
did2s(
  data = df,
  yname = "y",
  first_stage = ~ 0 | unit + year,
  second_stage = ~ i(post * treated),
  treatment = "treat",
  cluster_var = "state"
)

It is equivalent to the following:

library(fixest)
fs <- feols(
  y ~ 0 | unit + year,
  data = subset(df, treat == 0)
)
df$y_diff <- df$y - predict(fs, newdata = df)
ss <- feols(
  y_diff ~ i(post * treated),
  data = df
)

Note the first-stage is run only using observations where the treatment variable takes the value 0. These should be the untreated and not-yet-treated observations ($d_{it} = 0$). The first_stage argument is therefore your model for untreated potential outcomes, $Y_{it}(0)$. So, this could include things like state-specific linear trends, time-invariant covariates interacted with time-dummies, etc. But, it should not include any treatment variables (these are untreated $Y$).

Next, you use your estimated model (predicting $Y_{it}(0)$) to forecast for the entire sample including post-treatment observations with $d_{it} = 1$.

The second_stage is what you regress $Y_{it} - \hat{Y}_{it}(0)$ on. If you observed this $Y_{it}(0)$, this variable would take the value 0 for all $d_{it} = 0$ observations and would take the value $\tau_{it}$ for all $d_{it} = 1$ observations. Therefore, the second_stage is your model for how you want to summarize (estimated) unit-time treatment effects. This could be things like a treat x post variable, event-study indicators, or an interaction between a treat x post and some discrete variable (like gender). Of course, when you take these averages you want there to be a large number of observations (so a central limit theorem can kick in).

In summary:

1. first_stage tells you the model for $Y_{it}(0)$ you estimate with the treatment = 0 group.
2. second_stage tells you how you want to summarize estimated treatment effects