24: Regression Discontinuity

Question 1

basic logic

Answer 1

solves the biased OLS issue with discontinuity

comparing people just above and below the cutoff

Question 2

critical identification assumption

Answer 2

smoothness/continuity of X on Y
- if the only thing that is discontinuous is the cutoff, then the gap between averages is the causal effect of having been labelled

other variables vary continuously at the point of discontinuity that the regression exploits

Question 3

sharp vs. fuzzy RD

Answer 3

sharp RD where once you cross the threshold, the probability of treatment jumps from 0 to 1

fuzzy RD where the probability of treatment also jumps at the threshold but not all the way from 0 to 1

Question 4

implementing sharp RD with OLS

Answer 4

dummy for treatment/cutoff and a function capturing the effect of X on Y

Question 5

limitations of an RD

Answer 5

used only to estimate the effect of treatment at the discontinuity
- always to the extent that you can only estimate the effect that holds at the discontinuity

results contaminated if there is strategic behaviour around the cutoff
- strategic behaviour switches a non-random selection of units around the discontinuity
- identifying assumption that treatment is the only thing switching things around is no longer true

tradeoff between staying close to the discontinuity to avoid bias and the increased efficiency of including more data in the regression

Question 6

fuzzy RD where you ignore fuzziness

Answer 6

just compare average outcomes around discontinuity

captures the ITT

Question 7

fuzzy RD and IV

Answer 7

using the threshold as an instrument for treatment (just like an RCT with imperfect compliance)

IV estimate gives us TOT