<p>No, here the correct interpretation would be that on the average the treatment led to 0.5 decrease in number of rich people per million, conditional on all other covariates. Here (I am adding t subscript because I think you must have omitted it):</p>
<p><span class="math-container">$$-0.5=\beta = E[Y_{it1} -Y_{it0}]$$</span></p>
<p>There is no <em>per year</em> there, this is one off effect that reduces the amount of rich people  after the treatment is implemented not a negative growth that will decrease the number of rich people period after period.</p>

CC BY-SA 4.0
2021-09-21T09:48:43.103Z
I thought it would be we calculate the ATT(Average treatment effect on treated), and we account for the average effect of all years later, so the result would be yearly average, I may fall into a fallacy, please let me know then.
Phil Nguyen
CC BY-SA 4.0
2021-09-21T09:49:31.017Z
If saying that "on the average the treatment led to 0.5 decrease in number of rich people per million", meaning that we does not mention anything about time then?
Phil Nguyen
CC BY-SA 4.0
2021-09-21T10:12:25.433Z
@Louise the raw output from DiD is ATE $\beta=E[Y_{it1}-Y_{it0}]$ under some conditions you can show that ATE=ATT but the raw output is just ATE, also neither ATT or ATE here would tell you what is happening per year, they only tell you how Y changed on average over all subsequent time periods within your study not how it changed per year
1muflon1
CC BY-SA 4.0
2021-09-21T10:19:46.317Z
ah, I see, becuase when calculating the DiD, we already calculated the average first then we derive the difference in average of outcome before and after of treatment by that of control, so it is a one-off effect. Is it a correct explanation? Many thanks
Phil Nguyen
CC BY-SA 4.0
2021-09-21T10:23:58.073Z
@Louise yes you could also get an effect on growth rate of rich people but then you need to use $\Delta Y$ - however in that case you need to recheck all assumptions again because there might be parallel trend when u use Y and not $\Delta Y$ and vice versa
1muflon1
CC BY-SA 4.0
2021-09-21T10:36:42.720Z
I see, many thanks and warm regards, @1muflon1
Phil Nguyen
CC BY-SA 4.0
2021-09-21T09:19:58.247Z
2021-09-21T10:21:02.423Z
2021-09-21T10:21:02.423Z
1muflon1
<p>Considering a Difference-in-Differences (DiD) equation with a dummy variable:</p>
<p><span class="math-container">$$
y_i = \alpha + \beta D_i + Xit + \varepsilon_i.
$$</span>
While <span class="math-container">$$Xit$$</span>
is a set of covariates.
Let's say the DiD here has the frequency is year and unit level is country. The outcome variable is number of rich people per million (yearly data).</p>
<p>Can I explain that <span class="math-container">$\beta$</span> as below:
Let's say  <span class="math-container">$\beta$</span>= -0.5</p>
<p><strong>The number of rich people in the treatment group <em>decrease 0.5 per million of people per year (annually average) compared to that of control group</em> after the event date?</strong></p>

<econometrics><nonexpert>
How to explain the meaning of the coefficient of interest of Difference-in-Differences?
Phil Nguyen
# How to explain the meaning of the coefficient of interest of Difference-in-Differences?

(Asked by: username_0 on 2021-09-21)

Considering a Difference-in-Differences (DiD) equation with a dummy variable:

$$
y\_i = \alpha + \beta D\_i + Xit + \varepsilon\_i.
$$
While $$Xit$$
is a set of covariates.
Let's say the DiD here has the frequency is year and unit level is country. The outcome variable is number of rich people per million (yearly data).

Can I explain that $\beta$ as below:
Let's say $\beta$= -0.5

**The number of rich people in the treatment group *decrease 0.5 per million of people per year (annually average) compared to that of control group* after the event date?**

**Tags:** econometrics, nonexpert


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## 1 answers

### Answer by username_1 on 2021-09-21. Score: 1 | Accepted answer

No, here the correct interpretation would be that on the average the treatment led to 0.5 decrease in number of rich people per million, conditional on all other covariates. Here (I am adding t subscript because I think you must have omitted it):

$$-0.5=\beta = E[Y\_{it1} -Y\_{it0}]$$

There is no *per year* there, this is one off effect that reduces the amount of rich people after the treatment is implemented not a negative growth that will decrease the number of rich people period after period.

> **Comments:**
> **username_0**: I thought it would be we calculate the ATT(Average treatment effect on treated), and we account for the average effect of all years later, so the result would be yearly average, I may fall into a fallacy, please let me know then.  
> **username_0**: If saying that "on the average the treatment led to 0.5 decrease in number of rich people per million", meaning that we does not mention anything about time then?  
> **username_1**: @Louise the raw output from DiD is ATE $\beta=E[Y_{it1}-Y_{it0}]$ under some conditions you can show that ATE=ATT but the raw output is just ATE, also neither ATT or ATE here would tell you what is happening per year, they only tell you how Y changed on average over all subsequent time periods within your study not how it changed per year  
> **username_0**: ah, I see, becuase when calculating the DiD, we already calculated the average first then we derive the difference in average of outcome before and after of treatment by that of control, so it is a one-off effect. Is it a correct explanation? Many thanks  
> **username_1**: @Louise yes you could also get an effect on growth rate of rich people but then you need to use $\Delta Y$ - however in that case you need to recheck all assumptions again because there might be parallel trend when u use Y and not $\Delta Y$ and vice versa  
> **username_0**: I see, many thanks and warm regards, @username_1  

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