Dear Statalist members,

I have a question regarding stacking diff-in-diff estimates by time period. I'm trying to estimate the heterogeneous effects of annual price shocks (P) (exposure to the price shock varies by municipalities) by lunar month (L). The outcome is daily. I first estimate this with a simple TWFE: difference-in-differences design with two-way fixed effects for municipalities and days (dates).

\begin{equation}
\begin{aligned}
Y_{mt} = \beta_{1} P_{mt} +\beta_{2} L_{t} \text{ x } P_{mt} + +\tau P_{mt} +\rho X_{mt} + t \gamma_{mt} + \pi_{t} + \Omega_{m} + \epsilon_{mt}
\end{aligned}
\end{equation}

where m indexes municipalities and t is the date. $Y_{mt}$ is the outcome. $L_{t}$ is indicator for eight lunar month. $P_{mt}$ refers to the pricing variable. $X_{mt}$ is a matrix of time-variant municipality-level controls. $\gamma_{mt}$ captures within-municipalities time trends, $\pi_{t}$ refers to day of the year (date) fixed effects, and $\Omega_{m}$ is municipality fixed effects.

My question is how I can generalize this simple diff-in-diff to estimate the heterogeneous effects of P by L: stacking diff-in-diff estimates by time period (some in L and some are not). In other words, I would like to estimate separate diff-in-diff for each time period in a pooled specification (while also estimating the ATT between these periods). In that case, should I interact P with the municipality fixed effects (and controls)? Should I interact L with municipality fixed effects (and controls)? Or should I interact (P*L*municipality fixed effects and controls)?

Looking for your suggestions.

Thanks,