DiD regression with two treatment groups and one control group (panel data regression)

[Guest]

Hi,
For my research question I have a treatment group that can be divide into two separate groups (I suggest that the effect for one group is stronger than for the other group. So they only difference between these two groups is the intensity of the treatment). I have one control group.
There is only one dummy variable that is equals 0 for the pre-event period and 1 for the post period. Eligible is a dummy variable equals 1 if the firm is one of the treatment group, otherwise zero.

My question now is what is the best solution to see whether there is a significant difference between the treatment groups or whether it does not matter how strong the received treatment is.

The command I use so far is as follows:

reghdfe leverage postxeligible log_total assets growth tangibility if reg_treated==1, absorb(...) (treated == 1 is for the group that received probably a weaker treatment effect) and

reghdfe leverage postxeligible log_total assets growth tangibility if reg_targeted==1, absorb(...) (targeted ==1 is for the group that received probably a stronger treatment effect).

Then I compare the results of these two regression.

Would this works? Should I use other regression commands (teffects, tregress?) I cannot use the teffects command due to multicollinearity.

Kind regards

[Clyde Schechter]

I would do this by creating a single 3-category variable for the treatment groups: 0 = untreated, 1 = weaker version of treatment, 2 = stronger version of treatment. Let's call that variable group3. Then I'd do the regression as:

reghdfe leverage i.group3##i.post c.(log_total assets growth tangibility), absorb(...)

(Note: Here assuming log_total, assets, growth, and tangibility are all continuous variables. Modify accordingly if this is not correct.)
The absorbed variables should include, at a minimum, one for the unit of analysis (firms?).

Then to contrast the effect in the two active treatment groups, you follow that up with:

lincom 2.group#1.post - 1.group#1.post

which will give you the expected difference in effect of the two treatments along with test statistics.

[Guest]

Hello,

First of all thank you for you fast reply. I actually already created a 3-category variable but then I added another interaction term for only the group that probably receive a stronger effect - multicollinearity was an issue again.

I have got two continuous variables more (current ratio and EBIT over total assets). And yes, as fixed effects I have got firm fixed effects, sector and country fixed effects (you are correct, my analysis is about firms).

I will try your answer, thank you!

Kind regards

[Guest]

Hi,

would you also suggest to generate a category variable for comparing the impact of the countries on the dependent variable? I have got ca. 12 countries to look at. To create a dummy variable for each country does not work with the "reghdfe" command. I am not sure whether it is better to generate a single 12-category variable or to generate single dummy variables for each country and use a different regression command, for example "areg"?

Kind regards

[Clyde Schechter]

If, as is usually the case in data sets like yours, each firm operates in the same country at all times, then country becomes a time-invariant attribute of the firm. Consequently, it is mathematically impossible to estimate the effect of country on the dependent variable using a model with firm fixed-effects. (This is true regardless of whether you use -reghdfe-, -xtreg, fe-, -areg-, or any other fixed-effects estimator in Stata or any other software. It's linear algebra and there is no getting around it.)

Is estimating the effect of country on your outcome variable one of your research goals? If not, then just forget about country. There is no issue of omitted variable bias, because the firm fixed effects automatically adjust for all time-invariant attributes of the firm, including country. If estimation of country effects is a part of your goals, then you cannot use a fixed-effects estimator. You probably would be best off using the -xthybrid- command, by Francisco Perales and Reinhard Schunck, available from SSC. (Note: if you do go to the -xthybrid- command, because it is fairly old, it does not support factor-variable notation. So you will need to go back to creating indicator ("dummy") variables for the levels of your categories.)

[Guest]

Hi,

I have a question regarding the 3 single categorical variable. Normally Stata automatically sets a baseline. In this case the baseline would be the untreated group, right? So I have to interpret the coefficient of the two treatment groups relative to the untreated group, is this correct? I also created two dummy variables: Targeted = 1 if the treatment group receives the prob. stronger treatment and Treated = 1 if the treatment group receives the weaker treatment. So as far as I know, the Targeted dummy variable is relative to the untreated and weaker treatment group. I got the same results as with the 3 single categorical variable that should only consider the effect compared to the baseline group. So I am little bit confused about the same results and how I should interpret the results of the 3 single categorical variable correctly.

[Clyde Schechter]

Normally Stata automatically sets a baseline. In this case the baseline would be the untreated group, right?

Without seeing the actual code you used to work with this variable, I can't be certain. If your variable is named treatment and coded 0 = untreated, 1 = weaker treatment, 2 = stronger treatment, and if you referenced it in your analysis as i.treatment, then, yes, the untreated group will be the reference group. The coefficient for 1.treatment will be the estimated mean response difference between weaker treatment and no treatment, and that of 2.treatment will be the estimated mean response difference between stronger treatment and no treatment. If you need an estimate of the mean response difference between the weaker and stronger treatments, you can get that with -lincom 2.treatment - 1.treatment-.