I have a question regarding what terminology should I use in my paper when I consider the following model:

$y_{it} = \alpha + \beta_0T_i + \beta_1\text{Time}_{t} + \beta_2(\text{Time}_{t} \times T_i) + \chi'_{it}\gamma + \epsilon_{it}$

In this case the regression is based on the individual-year unit and $T_i$ is a binary variable for treatment and $\text{Time}_{t}$ is a binary variable for the time period (there are only 2).

Since I wanted to use individual and time fixed effects and I have only 2 time periods I took the first difference and ran the following regression:

$\Delta_t(y_i) = \beta_1 + \beta_2T_i + \Delta_t(\chi'_i)\gamma + \Delta_t(\epsilon_i)$

What should I say that I have used: a fixed effects or differences in differences approach?


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