<p>I am thinking about a DID approach. Typical DID can be written as follows:
<span class="math-container">$$Y_i=\beta_0+\beta_1D_i+\beta_2T_i+\beta_3 T_i D_i+\epsilon_i$$</span>
<span class="math-container">$Y_i$</span> is an outcome, <span class="math-container">$D_i$</span> is a binary treatment, and <span class="math-container">$T_i$</span> is a time dummy. <span class="math-container">$\beta_3$</span> would be the estimate of the effect.</p>
<p>If there are two groups (e.g., the group dummy <span class="math-container">$G_i$</span>) and want to get the difference between two groups after the treatment,</p>
<p><span class="math-container">$$Y=\gamma_0+\gamma_1D_i+\gamma_2T_i+\gamma_3G_i + \gamma_4 D_i T_i + \gamma_5 D_i G_i + \gamma_6 T_iG_i +\gamma_7 T_i D_i G_i+\epsilon_i$$</span></p>
<p>Does <span class="math-container">$\gamma_7$</span> provide the effects? Is this approach the right way?</p>

CC BY-SA 4.0
2022-02-22T20:15:53.953Z
It is relevant to know whether treatment timing for the two groups is the same or whether you are considering a case of staggered treatment. More precision in defining dummy variables would also improve question quality/clarity. Finally, time indexation on variables are missing
Jesper Hybel
CC BY-SA 4.0
2022-03-06T07:45:31.383Z
By “group dummy” are you referring to *subgroups* within $T_i$ that are possibly more sensitive to the treatment?
Thomas Bilach
<difference-in-difference>
DiD with 2 groups
hrkshr
# DiD with 2 groups

(Asked by: username_0 on 2022-02-22)

I am thinking about a DID approach. Typical DID can be written as follows:
$$Y\_i=\beta\_0+\beta\_1D\_i+\beta\_2T\_i+\beta\_3 T\_i D\_i+\epsilon\_i$$
$Y\_i$ is an outcome, $D\_i$ is a binary treatment, and $T\_i$ is a time dummy. $\beta\_3$ would be the estimate of the effect.

If there are two groups (e.g., the group dummy $G\_i$) and want to get the difference between two groups after the treatment,

$$Y=\gamma\_0+\gamma\_1D\_i+\gamma\_2T\_i+\gamma\_3G\_i + \gamma\_4 D\_i T\_i + \gamma\_5 D\_i G\_i + \gamma\_6 T\_iG\_i +\gamma\_7 T\_i D\_i G\_i+\epsilon\_i$$

Does $\gamma\_7$ provide the effects? Is this approach the right way?

**Tags:** difference-in-difference

> **Comments:**
> **username_1**: It is relevant to know whether treatment timing for the two groups is the same or whether you are considering a case of staggered treatment. More precision in defining dummy variables would also improve question quality/clarity. Finally, time indexation on variables are missing  
> **username_2**: By “group dummy” are you referring to *subgroups* within $T_i$ that are possibly more sensitive to the treatment?  

---

## 0 answers

