Running Variable

The running variable (or forcing variable) is the continuous variable whose value at the Cutoff determines treatment in a Regression Discontinuity design. Test score, income, vote share, age, date of birth — anything where crossing a threshold flips treatment on or off. By convention the running variable is centered at the cutoff ($\tilde r = r - c$) before estimation, so the regression intercept is read off at the threshold.

When to use

The credibility of an RDD rests on whether units can manipulate their position relative to the cutoff. If they can't (the cutoff was unannounced or the running variable is exogenous like a vote total), comparability holds. If they can (e.g. test takers studying just enough to clear the cutoff), the design is compromised — test with a McCrary Density Test. PS_5's running variable is pct_vote_union, centred at 0.5.