T-tests and regressions

[Helen Chang]

Hi, I want to compare the coefficient on one variable (i.e. IndVar) from the regressions based on two subsamples .

reghdfe DepVar IndVar ControlVar Tone>Median, absorb(sic2 fyear) cluster(gvkey)
reghdfe DepVar IndVar ControlVar Tone<Median, absorb(sic2 fyear) cluster(gvkey)


I was suggested to use the following code:

gen byte largetone = Tone > Median if Tone < . reghdfe DepVar i.largetone##(c.IndVar c.ControlVar) , absorb(sic2 fyear) cluster(gvkey)

The test reported next to the interaction term between 1.largetone and lndVar is the test I am looking for.


1. As an alternative method, can I use the following regression and look at the coefficient of the interaction term?

reghdfe DepVar i.largetone (or any indicator variable used to identify subgroups)##c.IndVar ControlVar, absorb(sic2 fyear) cluster(gvkey)

Does this regression aim to achieve different goals compared to the one I was suggested initially?


2. If I want to run subsample regressions separately, such as the models below:

reghdfe DepVar IndVar ControlVar if tone>median_tone, absorb(sic2 fyear) cluster(gvkey)
reghdfe DepVar IndVar ControlVar if tone<median_tone, absorb(sic2 fyear) cluster(gvkey)

Do I need to put the variable, tone, in these regressions as a control variable?

[Wouter Wakker]

Please read the FAQ on posting questions, especially regarding code delimiters. Using them would make it easier to read your code and increases your chances of getting a helpful response.

1. You can, but if you don't interact your control variable with the tone dummy you're assuming that the effect of the control variable is the same for both groups. This may be the case, but if it's not I would say it is an inferior model. The only reason I can think of to do this is if you first ran the fully interacted regression and found that there is no significant difference of the control variable between groups, and you have a small sample size and want to save some degrees of freedom.

2. This depends on theory. Do you think that tone can influence your dependent variable and may be correlated with your variable of interest? If so I would include it.

As an aside, not that running the regressions on the subsamples should yield the exact same coefficients as the interacted model if tone stays consistently above or below the median within panels. If i.largetone changes within panels and there is a large difference, there may be important interaction effects between the fixed effects and i.largetone.