Does it make sense to "cluster" when you use a regression discontinuity? 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?
 A: Whether you take into account clustering or not only affects the standard errors of your estimates. In a situation like yours, I would not focus too much on the standard errors. It is much more important that you can justify the use of the regression discontinuity framework, and you have to be able to show that it allows recovering the parameter(s) you are interested in. Once you are sure about this you can go a step further. 
This next step would be the following. If you are concerned about these class effects, you should have a look at multilevel regression models. It should be possible to implement a regression discontinuity strategy within a multilevel model. 
A: Is it a regular linear regression model or not?
In Quantitative finance we have the same problem. we use a GARCH model to estimate volatility, however volatility does not seem to be normally distributed and seems to cluster. for this we use a switching garch model. this "switching" model differentiates and switches between different clustering regions. 
you could look into this switching it might be usefull... 
