One of the breakthroughs of econometrics over the past two decades has been to employ "clustering" to take into account the correlation of error terms across observations. For instance, if you're evaluating the effect of an educational intervention where you have data on individual students but you suspect that teachers implemented the intervention differently, it is common to analyze the data in a way that recognizes that there are common effects at the "class" level. A common correction is to use clustering.
When you run a regression discontinuity, do you similarly have to take into account that your observations may be clustered? If so, how is the estimator implemented differently?