OLS with dummy and few observations (12 mean values from 2.5k observations)

#1
Hi all :)

Maybe you can help me with a problem I have in using OLS regression:

I have a dataset of 12 markets, in total ~2.5k trades happened over all markets.

I now calculated 6 different measures for the each markets performance (my 12 observations per measure i want to use as dependent variables)

My treatment is indicated by a dummy, 6 markets were in one treatment, 6 in the other one.

What I would like to do is, to use OLS to see, if there is a treatment effect, using the dummy variable, looking like this:

Y = cons + b*dummy + e

My question now is: Can i do this without overfitting? I dont know if I can use OLS because of my low number of observations, even though they stem from far more (and hopefully carry the statistical power / information of all my observations of transactions?)

I would also like to add (2-3) control variables and am worried that I will use too many explanatory variables on too few observations.

Thank you very much vor any help!
 
#2
Sounds like you have an N of 12. The number of trades doesn't seem relevant because you are saying things about the markets not thetrades but perhaps I misunderstood.

The rule of thumb is that you want 10 cases for each independent or control variable so you could use just the dummy variable but not any explanatory variables. If you can't get more data, then one idea is matching the cases in one treatment to those in the other; there are various ways to do this, but, with low N, one good method is via propensity scores