Instrumental variables: come up with a hypothetical example in which it would be appropriate to estimate treatment effects using an instrumental variables strategy. For simplicity, stick to an example...

Instrumental variables: come up with a hypothetical example in which it would be appropriate to estimate treatment effects using an instrumental variables strategy. For simplicity, stick to an example with a binary instrument and binary treatment variable.

(a) Simulate data for this imaginary example if all the assumptions are met. Estimate the local average treatment effect for the data by dividing the intent-totreat effect by the percentage of compliers. Show that two-stage least squares yields the same point estimate.

(b) Now simulate data in which the exclusion restriction is not met (so, for instance, those whose treatment level is left unaffected by the instrument have a treatment effect of half the magnitude of the compliers) but the instrument is strong (say, 80% of the population are compliers), and see how far off your estimate is.

(c) Finally, simulate data in which the exclusion restriction is violated in the same way, but where the instrument is weak (only 20% of the population are compliers), and see how far off your estimate is.