Parental income on child health

[Lilly Tee]

Hi,
I am currently looking at how changes in parental income affect infants' or children's health. Specifically, I have been looking at how a policy that improves parents' income affects children's birth weight. I have a longitudinal data set that includes information on an individual and household level. My methodology follows a DiD approach. The treatment group would be those parents' incomes that do increase, and the control group are those whose incomes do not increase. I was trying to write a regression model for this and got the following:

Where,
Yit = Child birth weight
ai = individual effects
POSTit = dummy for the time after the policy was introduced
TREATEDit = Whether the parents did receive an increase in income due to policy
Xit = individual characteristics

However, I am unsure whether my model would be correct. Specifically, if I include Xit would this need to be individual or household characteristics?

Thank you.

[Carlo Lazzaro]

Lilly:
your DID code seems correct.
However, your regression may suffer form reverse causation endogeneity.
I suspect that children with a poor health state affect parents'income (due to potentially high out-of-pocket health care-related expenses and/or health care services not covered by health insurance), whereas those in good health do not.

[Andrew Musau]

So \(i\) indexes individuals and \(t\) indexes time \((i=1, \cdots, N; \;\;t=1, \cdots. T)\). \(X_{it}\) contains a set of explanatory variables that vary over both individual and time. But since you show parameters, you need to write it as \(\gamma^{\prime}X_{it}\) so that the gamma parameters will relate to these variables. \(\beta_1\alpha_i\) makes no sense. You can write the individual effects as a set of \(N-1\) dummy variables, but you will usually indicate these simply as \(\alpha_i\). Easiest to write the generalized DID as a two-way fixed effects model, just highlighting your treatment variable.

[Lilly Tee]

Thank you to both Carlo and Andrew. I was also curious as to maybe looking at minimum wage changes. So how do minimum wage changes affect children's well-being? Parents who experience an increase in their minimum wage would be in the treatment group. The control group would be parents who don't see a wage increase. I wondered if the same model would apply and change the treatment period. Say the minimum wage increased in Texas between 2009 and 2010. Therefore, that would be the treatment period. Then you would observe the treated and control group before and after the minimum wage increase. Or would I have to change the model?

[Clyde Schechter]

Responding to #1 and #2 in this thread, I think there is some confusion about what the research question is. #1 begins by saying that this is a study of the impact of parental income on children's health. But the data, and the model (as amended per the advice in #3) is not about that. It is about the impact of a particular policy. While it is apparently the case that the direct intended effect of the policy is to increase parental income, the analysis will be only about the effects of implementing the policy. It may be that the policy affects children's health through other indirect paths that are different from income. It isn't even necessarily the case that the policy will increase parental income: some parents may find that they lose their jobs and, at least temporarily, have decreased income. Or it may be that few parents were actually affected by the policy. To study effects of parental income you would need actual data on the parents' income, and that data would need to appear in the analysis.

The important point is that the data you have and the analysis you plan will not enable you to estimate the effects of parental income on anything, only the effects of implementation of that policy.

[Lilly Tee]

Thanks Clyde, your response was helpful. Relating to my previous post about an alternative research question of how do minimum wage changes affect children's well-being? Parents who experience an increase in their minimum wage would be in the treatment group. The control group would be parents who don't see a wage increase. I wondered if the same model would apply and change the treatment period. Say the minimum wage increased in Texas between 2009 and 2010. Therefore, that would be the treatment period. Then you would observe the treated and control group before and after the minimum wage increase. Or would I have to change the model?

[Clyde Schechter]

What you propose in #6 sounds right to me. I guess my only reservation would be wondering how you can accurately ascertain who received a wage increase and who didn't. But assuming you can get good data on that, this seems like an analysis that is appropriate to the question.

[Lilly Tee]

I would have data available on this information but I was also worrying about endogeneity. So would it we worth running the same regression but changing the outcome variable say to income or parental wage?

[Clyde Schechter]

I'm reluctant to advise you on this, as expectations and standards differ across disciplines, and I'm not sure what discipline you work in. In my area, epidemiology, if you are studying the effects of an intervention on a health outcome, and if you claim that the intervention works, at least in part, because it affects some mediating variable, like income, you would be expected to demonstrate first that the intervention does in fact affect income, and then demonstrate the effect on the health outcome. (And ideally a mediation analysis would be done as well.)

Your particular situation also raises other issues. Your intervention is a community-level intervention: a policy relating to minimum wage. It is entirely possible that following implementation of the policy, wages go up, and health outcomes improve, but the improved health outcomes are taking place among households other than those whose wages were increased. This kind of situation is sometimes referred to as the "ecological fallacy," although it isn't so much a fallacy as just a reminder of the need to be aware that things that are observed at the community level are not necessarily direct reflections of what is happening at the individual level. In any case, you will need to be careful in your analyses to distinguish whether the income effect on health outcomes is actually taking place at the individual (or household) level, or is a community-level phenomenon that is not mirrored at the lower level. Either way, it would be an interesting finding, but be careful not to confuse the two when you describe your results.