Significant difference in number of observations between treatment and control group

[Isha Mohanty]

I have a data set where the control group is almost 80 times larger than the treatment group. The treatment and the control group observations are almost the same as the population. I have two questions in this regard:

1) What are the potential problems of using a data set for running regressions where control group is 80 times larger than the treatment group?

2) I chose to do a propensity score matching to retain only the matched observations where the number of observations in the treatment group is same as the control group. I chose to use this sample for running regressions. Is this approach correct?

[Maxence Morlet]

First things first, was treatment assignment randomised? That is the most fundamental question fo causality (which I presume you're after).

[Isha Mohanty]

It is not an experimental study. The treatment group consists of firms belonging to a certain industry and the control group is its sector peers.

[Maxence Morlet]

OK, was treatment implemented exogenously with respect to the outcome?

[Isha Mohanty]

Yes, treatment was implemented exogenous to the outcome.

[Carlo Lazzaro]

Isha:
Maxence highlighted two relevant points.
As an aside, I would go PSM.

[Isha Mohanty]

Dear Carlo and Maxence, thank you for addressing my issue. I am uncertain as to why would PSM be an appropriate solution for this? To articulate my question better - What would be the problem in using a sample as mentioned (number of observations in treatment and control group is sognificantly high), that would be solved by adopting a PSM?

[Maxence Morlet]

You may also want to check out the comunity-contributed command sdid.

But bottom line is, as long as your treatment is plausibly exogenous, it all gets a lot easier.

Next question: do you have panel data or cross sectional data?

[Carlo Lazzaro]

Isha:
the most paramount issue that I see with your approach #1 is that, given its sky-rocketing sample size, the control group could include firms that differ in many respects from their treatment counterparts.

[Isha Mohanty]

Dear Maxence, I have panel data for an observation period of 15 years (2005-2019). Two of my mentioned approaches are as follows:

1) In the first approach, I am using the panel data of 15 years for treatment group and control group (100X treatment group observations) to conduct a fixed effects regression.
2) In the second approach, I am using only the 2005 values of the covariates to do the propensity score matching. I am then retaining the matched observations only and dropping the rest from the sample data. I am using these matched observations to conduct the fixed effects regression.

Dear Carlo, you are absolutely right. The treatment group characteristics are significantly different than the control group characteristics if I am following the first approach.

Thank you so much for your help