as stated in the title, I'm thinking about exploring the heterogeneity of treatment effect result from a DID design based on a continuous variable. To be specific:

\begin{align} & \mathrm{Profit}_{i,t} \\[8pt] = {} & \beta_0 + \beta_1\mathrm{after}_{i,t} + \beta_2\mathrm{Treated}_i + \beta_3 \mathrm{after}_{i,t} \cdot \mathrm{Treated}_i + \varepsilon_{i,t}. \end{align}

In which $i,t$ are subscript for firm and time(year). Now I want to know whether the treatment effect differs among treated with different size (measured as sales one year before treatment). I understand that one way to do it is to create a dummy for size (1, if large, 0 if small) (see discuss here), but is that possible to use size as a continuous variable to evaluate the treatment heterogeneity for treated with different size?


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