Using diff-in-diff and fixed effects

[Jonathan Thorsell]

I am doing research on state-level contraception policy effects on male labour outcomes (e.g. wages). I am utilizing the laws between 1960-1976 when roe.vs.wade was not ruling and the states themselves could have their own laws. The treatment here would be to live in a state where women had access to contraception technologies. i have defined a man as treated in four different ways. First i create a dataset where i plug in the year for which 16 year old women having access to birth controll pills by law in that state (c16) and also 18 year old women having access to birth controll pills(c18) by law (abortion rights are coded the same way(a16 and a18)). If the state did restrict all of this, the value would be 0. So if a man turned 16 after a state enforced a law stating that abortion was allowed for 16-year olds, he would be considered as treated in the c16-variable and vice versa. Further i merge this dataset with my IPUMS data which contains census-samples from 1970, 1980, 1990 and 2000 of men born between 1934 and 1982. Now to my concerns: i would think i need to use fixed effects and xtreg but i am not sure how? Many thanks!

[Clyde Schechter]

The Census samples you will be using are not panel data: they do not follow the same people over time. Each sample will contain (mostly) different people. There is no role for person-level fixed effects in the analysis of this data. However, it would be appropriate to introduce state-level fixed effects in the analysis.

Also, you need to make a distinction between access to contraception and access to abortion, and also get your facts clearer about abortion. While Roe v Wade 410 US 113 established, until recently, a constitutional right to abortion in the United States, thereby nullifying state-level laws, it was handed down in 1973, not 1976. Moreover, there were some states that allowed abortion even prior to that decision. The right to use contraception was established by a different decision, Griswold v Connecticut 381 US 479 in 1965. And, again, prior to that ruling the states were heterogeneous in their policies about that.

[Jonathan Thorsell]

Thank you for your input! I was not expressing myself clearly, i do distinguish between abortion and birth controll pills (so there are four "treatment variables". Do you think i should run the regressions with each treatment variable seperatly? I did not mean person-level fixed effects but birth state fixed effects, birth year fixed effects and perhaps dummies for Census year?

[Clyde Schechter]

I would not run the regressions with each treatment variable separately, because there is no easy way to then compare the different treatments.

I would create a four-level discrete variable to represent treatment: 0 = contraception and abortion banned, 1 = contraception allowed but abortion banned, 2 = abortion allowed but contraception banned, and 3 = abortion and contraception both allowed. (This is a bit of an oversimplification in that there are many varieties of abortion bans, and perhaps contraception bans as well, but probably it is the best one can do.) Use factor variable notation (-help fvvarlist- if you are not familiar with factor-variable notation) in your model so that Stata will properly handle this as a categorical, not continuous, variable.

Why do you want to use birth year fixed effects? Is there reason to think that there are strong birth cohort effects at play here? (The subject matter of your project is out of my area of expertise, so I'm asking that as a question, not expressing an opinion about what the answer to it should be.) My intuitions (which you should not rely on as the subject matter is not within my expertise) are that the survey year would be a greater influence.

The one I will express an opinion about is birth state: why would we use that? People move around a lot, and their exposure to laws and regulations depends on where they currently reside, not where they were born. Wouldn't state of current residence be more important here?

[Jonathan Thorsell]

"I would create a four-level discrete variable to represent treatment: 0 = contraception and abortion banned, 1 = contraception allowed but abortion banned, 2 = abortion allowed but contraception banned, and 3 = abortion and contraception both allowed. (This is a bit of an oversimplification in that there are many varieties of abortion bans, and perhaps contraception bans as well, but probably it is the best one can do.) Use factor variable notation (-help fvvarlist- if you are not familiar with factor-variable notation) in your model so that Stata will properly handle this as a categorical, not continuous, variable." The reason i chose the method mentioned is to differentiate between different abortion/birth control laws. An abortion bann might have different effects on 21 year olds than on 16 year old. In fact, i got then idea partly from a similar post that you commented, here is a link:https://www.statalist.org/forums/for...specifications Further, there is a working paper that investigates the effects of these laws using this method but with different outcome variables. So what would you say is the problem with coding it as I have (plugging in the year a law was enforced, example: if year_individual_turn_18 < year_law_implemented = treated (1)) done? Regarding the fixede effects, byy including state fixed effects, i think i can control for any non-time-varying characteristics of a state related to men’s socio-economics outcomes that might influence their likelihood of passing more lenient reproductive laws, such as political leanings which may impact not only reproductive laws but also educational investment or welfare generosity. By including year fixed effects, control for any cohort level trends in outcomes that do not vary across state lines would be my argument. birth state is problematic, i know, but i do not have data on where each individual was living at the time of their 16th or 18th birthday so this was the best i could get.

[Clyde Schechter]

Well, for what you describe about birth year, I think I would just want to know how old they are at the time of the survey. You can then classify them as < 16, 16-21, or > 21 in a 3-level categorical variable, and then you can interact that with your exposure (law enforced) variable. I don't see how a birth year fixed effect in the model is useful: you don't mention anything that sounds like a birth cohort effect.

As for the state fixed effects, IPUMS data does include state of residence in the year before the survey, which seems to me to be much better than state of birth for all of the things you wish to capture using a state fixed effect. At least a large majority of people would be in the same state at the time of survey as they were in the preceding year. A much smaller fraction would be in the same state where they were born.

[Jonathan Thorsell]

Ok, but then i would not be able to differentiate between the varieties of abortion/birth control laws, right? An idea would be to use three definitions of "treated" as in the paper i mentioned earlier. " In the first, we assign a man as ‘treated’ if women of his same age had access to contraception (abortion) based on the policy in the man’s state of birth when he was 16 and when he was 18. In the second, we assign a man based on the average age difference between men and their spouses, where a man is treated is women two years younger than him had access to contraception (abortion) in the man’s state of birth when he was 18 and 20. In the third, we use a continuous measure: the proportion of years between ages 15 and 20 that a man’s partner of the same age would have access to contraception (abortion). For example, California had legal confidential access to contraception for 18 year olds in 1972 and for 16 year olds in 1976. Based on the first definition of treatment, a man born in 1959 would be considered treated based on laws granting access to women at age 18, but not at age 16. Based on the second definition, he would be treated for both types of laws since when he is 18 in 1977, 16-year old women have confidential access to contraception. In the third definition, his treatment value would be 0.67, based on women aged 17, 18, 19, or 20 having access when he was those ages". But even this, i find difficult to code.

[Clyde Schechter]

With #7 I have a better understanding of what you are trying to do. It's pretty complicated as some of the treatments overlap each other on some people. This does not seem to lend itself to the approach I suggested earlier of having a single multi-level treatment variable. You will need a separate indicator ("dummy") variable for each treatment. And you may also want to include interaction terms between treatments that can overlap because the combined effect may be different from the simple sum of the separate effects. It's going to be a complicated model. It will require a large data set, but I think you have that. It may prove difficult to estimate; and it will prove difficult to interpret and explain.