I am looking for the formula of a regression discontinuity, where the independent variable is the dummy (0, 1) and the dependent variable is continuous. Furthermore, I would like to add several confounders to this formula.
Many books point me to this formula, which is not sufficient for my study:
Υ = ∝ + Dτ + Xβ + ε
where
D = dummy
τ = treatment
ε = error
Could someone point me into the right direction? I am really struggling with adding the dummy as independent variable, and including the confounders in the formula.
Your help is very much appreciated!