Could I use a difference-in-differences in the following setup?

[Mateus Maciel]

Dear users,

I am researching the behavior of same-sex marriages, and I would like to apply a differences-in-differences design according to the election results by cities. My treated units would be the cities where the president won the elections. On the other hand, the control units would be where he lost them. The dashed red line represents the election day. Therefore, I want to know if the DiD would apply here. I have parallel trends, but I do not know if the increase in the number of marriages would only be proportional and not a causal effect due to the elections.

I obtained the following figure after running the commands:

collapse (mean) marriage_women marriage_men marriage_straight, by(ano month treated year_month)

graph twoway (line marriage_women year_month if treated==1) (line marriage_women year_month if treated==0), ///
  legend(label(1 President won) label(2 President lost)) xline(2018 10, lpattern(dash))

[Clyde Schechter]

Well, you can fit a DID model to this data. But I think it would be a huge stretch to interpret the findings as showing a causal effect of the President's victory in the city on same-sex marriages.

Yes, you have parallel trends. But to infer causality you also must be able to say with a straight face that there are no other factors active at the time of the election that could account for the difference in the outcomes. Perhaps you can make that case, but it seems like a steep climb to me given how many things go on at the time of a national election and how many factors might influence decisions to marry. Then you would also need a plausible explanation why the difference post-election seems to arise suddenly several months after the election, appears as a short-lived spike, and then things return abruptly to the status quo ante in both groups. I'm not a social scientist, so maybe these things make perfect sense if one knows enough about them. But from a purely statistical perspective, I would be skeptical. But if you can build a case that explains away these concerns, then go for it.

[Jared Greathouse]

I'm not very sure I follow what the intervention is, but you may be interested in doing a differences-in-discontinuities approach, where you exploit the pre-post period AS WELL AS the cutoff for winning (50%). In other words, you'd be comparing (counties?) 0.2 (for example) to the left and right of the cutoff.


You'd need to show that theres no confounding at the discontinuity and that parallel trends holds for whatever bandwidth you'd use.


See this link for more https://www.kylebutts.com/papers/dif...iant%20sorting.

[Mateus Maciel]

Thanks for your comments, dear Jared Greathouse and Clyde Schechter!