RDD construction

[Mia Vorster]

Hi there,

I am looking at the French gender pay gap reporting policy, where firms above 50 employees have to report their gender pay gaps. They report scores out of 100, and if a firm is below 75 for three consecutive years they get a fine on their payroll.

I want to do an RDD around this threshold. I've made a binscatter -- below -- where I differentiate firms based on how long they've spent below the threshold (0 years, 1 yr, 2yr, 3+yrs) and then graph their current Index against their change in Index (NoteIndex - L.NoteIndex). You can see firms have different behaviours based on this characteristic: firms which have 2 or 3+ years below the threshold improve more quickly than those with only one or zero years below the threshold.

How do I capture this in an RDD?
I've done

rdplot d_NoteIndex NoteIndex, c(75) convs(consec_below) p(2) vce(cluster firm_id)

but it only controls for the years spent below, it doesn't show me how these firms behave differently.

If anyone can help, that would be much appreciated!

[Daniel Santos Torres]

Hi Mia,

I don't fully understand your question. Do you have panel data? What is your outcome of interest?

It seems to me that the comparison you are looking for to get a Regression Discontinuity Design is between two firms that have been underperforming (lower than score 75) for two years, in t-2 and t-1, and in year t one of them keep performing under 75 (being fined), and the other has overcome the threshold (not being fined). It seems plausible that these two firms could be, by adjusting for observable characteristics, very similar in unobservable characteristics, thus you could estimate the causal effect of being fined on, for example, profits in year t.

Best regards,
Daniel

PS: I don't like to use the word causal lightly, so I encourage any researcher more knowledgeable than me in these issues to correct me if I'm wrong! Thank you!

[George Ford]

I'm having a hard time grasping the idea as well. Not sure RDD fits this problem or is any better than regression analysis. The suppose the motivator is how close are you to a fine, and that is not a fixed number (could be 1 year, 2 years, or not close at all).

reg d_NoteIndex i.yearstofine spread // spread = (100 - L.NoteIndex)

reg d_NoteIndex i.yearstofine##c.spread