The continuous variable used in a regression discontinuity design pattern to determine whether an individual receives a treatment.
Let $X_i$ be the running variable, $c$ the cutoff, and $D_i$ the treatment indicator:
$D_i = \mathbb{1}_{X_i \geq c}$
or equivalently,
$D_i = \begin{cases} 1, & X_i \geq c \\ 0, & X_i < c \end{cases}$
where:
* $D_i$: Treatment assignment
* $X_i$: Running variable (continuous)
* $c$: Cutoff value
> [!info]- Last updated: November 5, 2025