# How to define treatment & control groups properly?

I’m working on a project examining the effect of a 2016 cash transfer on fertility.

Who is eligible for the cash? All families with:

• 2+ children, or
• 1 low-income or disabled child.

The data doesn’t have a variable indicating who got the cash transfer, so as I understand it, I would be doing an “intent to treat” analysis by defining the treatment & control groups based on eligibility.

However, I keep getting stuck on how to define the treatment & control groups. I guess my question is since the cash transfer is universal for ALL families with 2+ kids, what would be the control group then? Theoretically, there should be two similar groups of families with 2+ kids (one who get the cash transfer and the other who don’t), but that’s not possible in this case?

Comparing eligible families (2+ kids or 1 poor/disabled kid) to ineligible families (1 kid that is not poor/disabled or zero kids) would violate one of the core assumptions of causal inference (that the treatment and control groups be similar and only differ in the “treatment”).

I think I’m getting tripped up by how the cash transfer is both universal and birth-dependent.

I’m exploring using a linear probability model with FE or a DID model, but not sure if a DID makes sense? Synthetic control? Any thoughts on modeling strategies?

More context: The data comes from a household survey, which I’ve organized into a panel with fertility histories for each childbearing-aged woman (e.g. each woman has 17 observations, or 18 years containing her time-variant birth information). I have data from 2010-2018 and the program started in 2016. The program grandfathers in anyone who falls in either one of two eligibility categories. The cash transfer is not means or work tested.

• What is the geographical scope of eligibility for the cash, eg a whole country, a region within a country? That may give a clue as to a suitable control group. Jun 28, 2022 at 10:23
• The context is a European country and the cash transfer applied to all of the country's regions equally at the same time. So unfortunately, I wouldn’t be able to use different regions as controls. Jun 28, 2022 at 16:14
• Wouldn't the ideal control group be families with 2+ children etc in another European country which does not have such a cash transfer, the country being chosen to be similar in socio-economic characteristics to the treatment group country? I appreciate however that it may not be practicable to obtain data for such a control group. Jun 28, 2022 at 18:54
• That's my thinking too, but procurement of such data requires a rather extended process. All the same, I'm looking into it bc it seems to be the most appropriate empirical approach in this case. Jun 28, 2022 at 20:21

$$y_{it} =\beta_0 +\beta_1 Eligible_i +\beta_2 Post_t +\beta_3 Eligible_i\cdot Post_t +u_{it}$$
where $$Eligible_i$$ is a binary variable for being eligible, and $$Post_t$$ is a binary variable for being after the transfer. $$\beta_3$$ would be your coefficient of interest.