The application of RD in quasi-experimental experiments is different from the model of adding dummy directly and using OLS estimation in natural random experiments.

The estimation methods are different. RD usually adopts the method of local linear regression (that is, selecting samples within a certain bandwidth rather than all samples later), which is essentially an estimation of the local average processing effect around the breakpoint. Imbens and Kalyanaraman(2009) provided an estimate of the optimal bandwidth, and usually provided results with different bandwidths to show the robustness of the results. Sometimes, RD also adopts nonparametric method of kernel regression.

RD needs to test the problem of endogenous sorting, that is, if individuals know the grouping rules in advance and can completely control the grouping variables through their own efforts, it will lead to the failure of breakpoint regression.

If covariates are added to RD, it is necessary to check whether the conditional density of covariates is continuous at the breakpoint, that is, the "jump" at the breakpoint is not caused by the "jump" of covariates.

Note: The above contents mainly focus on whether the dummy (called z) of grouping variables is greater than the breakpoint as a tool variable to deal with variables (called d, that is, the main estimator). Z is obviously related to D. Z is equivalent to a local random experiment near the breakpoint, so the variable Y is only influenced by D, which has nothing to do with the disturbance term, so the externality is satisfied. Z can be used as the tool variable of d and 2SLS for estimation.