Regression discontinuity

We have discussed the following causal inference methods in class
• Randomized experiments
• Estimation under unconfoundedness using matching and propensity score weighting
• Instrumental variables
• Difference-in-differences
• Synthetic control
• Regression discontinuity
This assignment is about exploring how the estimators perform under different data generating processes (DGPs). Specifically, pick two or three estimators and do the following for
each estimator:
• Generate data using two DGPs

1. DGP1 - does not violate the assumptions under which the estimator works
2. DGP2 - violates at least one of the assumptions
   • For each DGP, describe it and explain how it does/does not satisfy the requirements for
   identification of the parameters (and which parameters are you identifying?)
   • Also, give a real life example of a situation which might be consistent with this DGP
   – Feel free (not required) to illustrate with a DAG
   • Run a Monte Carlo simulation. At each replication
3. Generate a random draw from the DGP
   1
4. Estimate the model
5. Save the estimates
   • Report summary statistics of parameter estimates
6. Bias
7. RMSE
8. Size
   • Comment on the results. Are the estimates from DGP1 and DGP2 as expected?

Sample Solution