<p>It looks to me like your control group would be all families with 1 or 0 kids. This is not ideal as you mention.</p>
<p>If you observe all households before and after the transfer, then you could do a diff-in-diff.</p>
<p><span class="math-container">$$y_{it} =\beta_0 +\beta_1 Eligible_i +\beta_2 Post_t +\beta_3 Eligible_i\cdot Post_t +u_{it} $$</span></p>
<p>where <span class="math-container">$Eligible_i$</span> is a binary variable for being eligible, and <span class="math-container">$Post_t$</span> is a binary variable for being after the transfer. <span class="math-container">$\beta_3$</span> would be your coefficient of interest.</p>
<p>You could also add in other controls to improve precision or if you believe the parallel trends assumption only holds conditional on other covariates.</p>

CC BY-SA 4.0
2022-06-28T16:16:48.247Z
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.
Anna Bokun
CC BY-SA 4.0
2022-06-28T07:06:15.677Z
2022-06-28T07:06:15.677Z
Michael Gmeiner
<p>I’m working on a project examining the effect of a 2016 cash transfer on fertility.</p>
<p>Who is eligible for the cash?
All families with:</p>
<ul>
<li>2+ children, or</li>
<li>1 low-income or disabled child.</li>
</ul>
<p>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 &amp; control groups based on eligibility.</p>
<p>However, I keep getting stuck on how to define the treatment &amp; 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?</p>
<p>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”).</p>
<p>I think I’m getting tripped up by how the cash transfer is both universal and birth-dependent.</p>
<p>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?</p>
<p>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.</p>

CC BY-SA 4.0
2022-06-28T10:23:45.187Z
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.
Adam Bailey
CC BY-SA 4.0
2022-06-28T16:14:29.830Z
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.
Anna Bokun
CC BY-SA 4.0
2022-06-28T18:54:21.613Z
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.
Adam Bailey
CC BY-SA 4.0
2022-06-28T20:21:49.527Z
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.
Anna Bokun
<econometrics><regression><difference-in-difference><demographics><synthetic-control>
How to define treatment & control groups properly?
Anna Bokun
# How to define treatment & control groups properly?

(Asked by: username_0 on 2022-06-27)

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.

**Tags:** econometrics, regression, difference-in-difference, demographics, synthetic-control
> **Comments:**
> **username_1**: 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.  
> **username_0**: 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.  
> **username_1**: 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.  
> **username_0**: 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.  

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## 1 answers

### Answer by username_2 on 2022-06-28. Score: 2

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.

> **Comments:**
> **username_0**: 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.  

---

