Accounting for fixed effects in regression discontinuity (rdrobust package in R)

Question

I'm just starting out with rd designs and have a question about accounting for fixed effects. Say I have a dataframe df with outcome variable y (observed across 100s of districts over several years), running variable x. I wish to account for district fixed effects with a 'factor' variable 'district'

I've looked at two solutions here and here.

Both give widely different estimates depending on how I specify covs:

I used --

rdrobust(df$y, df$x, covs=cbind(df$district), c=0, all=TRUE)

-- and --

blocks.d = model.matrix(~df$district+0)
rdrobust(df$y , df$x, covs=blocks.d, c=0, all=TRUE)

-- based on the answers I saw (linked above) but it is puzzling how the results are dramatically different for both these approaches. Is using covs the correct way to control for fixed effects? If so, which of the approaches above is better? I tried going through the rdrobust documentation and unfortunately could not figure it out

Answer 1

If I understand your data correctly, your first approach uses the list of districts as covariates, while the second one uses the set of indicators, which would be the right approach if you want to include fixed effects.