<p>In my difference-in-difference setting (double diff), I examine the impact of anticorruption laws on firms' asset growth of all countries all over the world after the laws are implemented in each country.</p>
<p>I normally control for firm and industry * year fixed effects in this case following existing literature.</p>
<p>However, I reckon that the impacts of laws will be different between developed and developing countries. Therefore, I am thinking of using subsample tests. There are two ways of conducting a subsample test are: (1) divide the whole sample into two subsamples and then run the main regression for all subsamples or (2) add the interaction for one subsample and see the difference by reading the interactive coefficients by running the regression.</p>
<p>Regarding the method (2) in double diff, we call it diff-in-diff-in-diff or triple diff. And (2) is preferred compared to (1).</p>
<p>So, what I want to ask is, if in the main specification, I control for firm and industry * year fix effects, so what fixed effects I should control when I perform the triple diff to examine the additional impact of laws on developed countries?</p>
<p>From this answer of <a href="https://stats.stackexchange.com/questions/543504/what-fixed-effects-should-be-controlled-for-in-a-ddd-specification/543578#543578">Thomas</a>, it seems that I only need to add the second level interaction terms. I deem the regression should be adjusted as below</p>
<blockquote>
<p><span class="math-container">$$ Y_{iast} = \gamma_{st} + \lambda_{at} + \eta_{as} + \delta L_{ast}
+ u_{iast}, $$</span></p>
<p>where <span class="math-container">$Y_{iast}$</span>, which denotes the asset growth of each firm i in developed country
group <span class="math-container">$a$</span> in country <span class="math-container">$s$</span> and year <span class="math-container">$t$</span></p>
</blockquote>
<p>Up to this point, I do not know what I should do next to know what are the fixed effects should be controlled.</p>

CC BY-SA 4.0
2021-09-30T14:42:21.377Z
If `develop` is time-invariant, `develop` fixed effects are unnecessary because `firm` is finer. But `industry` isn't finer than `develop` so perhaps you may want to further include develop\*year dummies or even industry\*develop\*year (preferred). I think you should decide it depending on the interpretation. (Each industry*develop has separate time trends?)
chan1142
CC BY-SA 4.0
2021-10-01T05:23:07.433Z
@chan1142 I do not think **industry * develop * year** is reasonable in this case because the event date is not the same among country, I think, reference ( https://stats.stackexchange.com/questions/543504/what-fixed-effects-should-be-controlled-for-in-a-ddd-specification )
Nguyen Lis
CC BY-SA 4.0
2021-10-01T05:23:59.157Z
Yes, ```develop``` is assumed invariant in my sample
Nguyen Lis
CC BY-SA 4.0
2021-10-01T05:26:38.197Z
@chan1142, I just edited the question to clarify my point, could you please have a look again. Thanks a heap
Nguyen Lis
CC BY-SA 4.0
2021-10-01T13:41:44.867Z
Please clarify your question. Are you asking how to conduct DDD using a regression, or you know how to do DDD but you wonder which fixed effects should be included in order for the model to be reasonable? If it's the latter, there is nothing you _must_ do; you only _choose_ your model. Of course, some models are more reasonable than others, though.
chan1142
CC BY-SA 4.0
2021-10-01T19:01:04.437Z
@chan1142, sorry for my poor explanation, yes, it is the second point. I do not know what fixed effect I should put into the DDD. From the link I refer above, If we do not include all second level interaction fixed effects, the model will be misspecified
Nguyen Lis
<econometrics>
What fixed effects I should add when using triple difference in firm level where I want to examine the last difference by country?
Nguyen Lis
# What fixed effects I should add when using triple difference in firm level where I want to examine the last difference by country?

(Asked by: username_0 on 2021-09-30)

In my difference-in-difference setting (double diff), I examine the impact of anticorruption laws on firms' asset growth of all countries all over the world after the laws are implemented in each country.

I normally control for firm and industry \* year fixed effects in this case following existing literature.

However, I reckon that the impacts of laws will be different between developed and developing countries. Therefore, I am thinking of using subsample tests. There are two ways of conducting a subsample test are: (1) divide the whole sample into two subsamples and then run the main regression for all subsamples or (2) add the interaction for one subsample and see the difference by reading the interactive coefficients by running the regression.

Regarding the method (2) in double diff, we call it diff-in-diff-in-diff or triple diff. And (2) is preferred compared to (1).

So, what I want to ask is, if in the main specification, I control for firm and industry \* year fix effects, so what fixed effects I should control when I perform the triple diff to examine the additional impact of laws on developed countries?

From this answer of [Thomas](https://stats.stackexchange.com/questions/543504/what-fixed-effects-should-be-controlled-for-in-a-ddd-specification/543578#543578), it seems that I only need to add the second level interaction terms. I deem the regression should be adjusted as below

> $$ Y\_{iast} = \gamma\_{st} + \lambda\_{at} + \eta\_{as} + \delta L\_{ast}
> + u\_{iast}, $$
>
> where $Y\_{iast}$, which denotes the asset growth of each firm i in developed country
> group $a$ in country $s$ and year $t$

Up to this point, I do not know what I should do next to know what are the fixed effects should be controlled.

**Tags:** econometrics

> **Comments:**
> **username_1**: If `develop` is time-invariant, `develop` fixed effects are unnecessary because `firm` is finer. But `industry` isn't finer than `develop` so perhaps you may want to further include develop\*year dummies or even industry\*develop\*year (preferred). I think you should decide it depending on the interpretation. (Each industry*develop has separate time trends?)  
> **username_0**: @username_1 I do not think **industry * develop * year** is reasonable in this case because the event date is not the same among country, I think, reference ( https://stats.stackexchange.com/questions/543504/what-fixed-effects-should-be-controlled-for-in-a-ddd-specification )  
> **username_0**: Yes, ```develop``` is assumed invariant in my sample  
> **username_0**: @username_1, I just edited the question to clarify my point, could you please have a look again. Thanks a heap  
> **username_1**: Please clarify your question. Are you asking how to conduct DDD using a regression, or you know how to do DDD but you wonder which fixed effects should be included in order for the model to be reasonable? If it's the latter, there is nothing you _must_ do; you only _choose_ your model. Of course, some models are more reasonable than others, though.  
> **username_0**: @username_1, sorry for my poor explanation, yes, it is the second point. I do not know what fixed effect I should put into the DDD. From the link I refer above, If we do not include all second level interaction fixed effects, the model will be misspecified  

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## 0 answers

