# What are the dynamic and static event-study?

When reading about the Difference-in-Differences for multiple groups and time periods, I see a term called "static or dynamic/event-study". Can you help me to distinguish these two settings intuitively? I tried to google but I cannot find any intuitive answer.

Static event study

$$$$y_{it} = \mu_i + \mu_t + \tau D_{it} + \varepsilon_{it},$$$$ (1)

where $$\mu_i$$ are unit fixed effects, $$\mu_t$$ are time fixed effects, and $$D_{it}$$ is an indicator for receiving treatment.

Dynamic event study

$$$$y_{it} = \mu_i + \mu_t + \sum_{k = -L}^{-2} \tau^k D_{it}^k + \sum_{k = 1}^{K} \tau^k D_{it}^k + \varepsilon_{it},$$$$ (2)

where $$D_{it}^k$$ are lag/leads of treatment (k periods from initial treatment date). Side question: what does L mean in the second equation?

Reference updated