Interpreting regression results if some clusters are not treated

[Penelope Smart]

I am a bit confused about how to interpret the regression results in the following scenario:

I compare observations within countries by including fixed effects in my regression. The distribution of the sample in control and treatment group is similar to the following:

Country	# observation C	# observation T	Type of Treatment
A	200	300	1
B	300	200	2
C	250	250	3
D	250	600	1
...	...	...	...

C = control group
T = treatment.

I run the following regressions:

xtset country

gen treatment1=0
replace treatment1=1 if treatment==1


*regression type 1
xtreg y treatment1 ,fe vce (robust)

*regression type 2
xtreg y treatment1 treatment2 treatment3 ,fe vce (robust)

My confusion is caused by the fact that each country is actually treated only by ONE treatment. With the inclusion of country fixed effects, we would compare observations within each country. Would this mean, given how we have defined the treatment variable (treatment1), all countries are included in the regression and the interpretation of the estimate for treatment1 can be interpreted as the effect "comparing respondents in the treatment1 group with all other respondents (including whose who were not treated at all + those who are in treatment2 and treatment3)". Or is it "comparing control and treatment1 group without considering any observations from the countries that are not treated with treatment 1 (treatment1=0 for all observations in these countries)?

And how would one interpret the different coefficients resulting from regression type 2?

[Clyde Schechter]

The first regression you show contrasts those who received treatment 1 with all others (whether untreated or treated with a different treatment).

The second regression separately contrasts each of the three treatments with those who are untreated.

[Penelope Smart]

Clyde, thank you for the answer.

If I would only consider control and treatment group in country A:

Country	#observations C	#observations T	Treatment
A	200	300	regardless of type

Where you can split the treatment group into:

Treatment Type	#observations
1	100
2	100
3	100

and run the regressions mentioned above for only Country A, I can totally understand the interpretation you have given.


But given the table in my original post following points confuse me:
I use country fixed effects in my regression, which I understand as comparing only the observations within a country. Since in each country only one type of 3 treatment types is assigned , I imagine that the following is calculates as a first step:

Country	Interpretation of estimate	Treatment
A	Effect of treatment 1 compared to those who do not receive treatment 1 (comparison within country A)	1
B	Effect of treatment 2 compared to those who do nor receive treatment 2 (comparison within country B)	2
C	Effect of treatment 3 compared to those who do not receive treatment 3 (comparison within country C)	3
D	Effect of treatment 1 compared to those who do not receive treatment 1 (comparison within country D)	1

If I run the regression of type 1 on treatment1, does the estimate result from aggregating the effects of only country A and country D (total# observations:500+850), adjusted for country fixed effects OR are all the observations including those that were assigned treatment 2, 3 in country B and C respectively, also taken into consideration? If the latter, wouldn't it be that we have for all observations in country B and C treatment1=0, which would result in just taking the average of y for those countries? If we only have averages for those countries not treated with treatment 1, why is it logical to say that the estimate of treatment1 in regression of type 1 contrasts those who received treatment 1 with all others (not treated and treated by A and B) as we do not have any effects calculated calculated for treatment 2 and 3?