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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.

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  • $\begingroup$ 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. $\endgroup$
    – Adam Bailey
    Jun 28, 2022 at 10:23
  • $\begingroup$ 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. $\endgroup$
    – Anna Bokun
    Jun 28, 2022 at 16:14
  • $\begingroup$ 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. $\endgroup$
    – Adam Bailey
    Jun 28, 2022 at 18:54
  • $\begingroup$ 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. $\endgroup$
    – Anna Bokun
    Jun 28, 2022 at 20:21

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It looks to me like your control group would be all families with 1 or 0 kids. This is not ideal as you mention.

If you observe all households before and after the transfer, then you could do a diff-in-diff.

$$y_{it} =\beta_0 +\beta_1 Eligible_i +\beta_2 Post_t +\beta_3 Eligible_i\cdot Post_t +u_{it} $$

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.

You could also add in other controls to improve precision or if you believe the parallel trends assumption only holds conditional on other covariates.

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  • $\begingroup$ Thanks for everyone’s thoughts. I also thought about using RDD, but having 0 or 1 kids vs 2+ kids is nothing like having an 85 or 86 vs 87 or 88 on a test when what's being compared is fertility…When a program is implemented in a way that is universally applied to everyone eligible, it limits which quasi-experimental methods can be applied to evaluate its effects, which is what I’m struggling with now. $\endgroup$
    – Anna Bokun
    Jun 28, 2022 at 16:16

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