A researcher uses RD to estimate the effect of a college scholarship (awarded to students scoring above 75) on future earnings, finding a $5,000 higher annual earnings at the cutoff. What does this estimate tell us?
AThe average effect of the scholarship for all college-age students in the population
BThe effect for students near the threshold — those who scored just around 75
CThe effect for high-achieving students who scored well above 75
DThe effect for students who would have attended college regardless of the scholarship
RD estimates a Local Average Treatment Effect (LATE) at the threshold, not the ATE for the full population. Units far from the cutoff — very high scorers or very low scorers — may respond very differently to the scholarship than marginal students. This limited external validity is RD's principal weakness: the estimate is credibly causal but may not generalize beyond the narrow window around the cutoff.
Question 2 Multiple Choice
What does the McCrary density test check for in a regression discontinuity design?
AWhether the running variable is a strong predictor of the outcome
BWhether there is a suspicious discontinuous jump in the density of the running variable at the cutoff
CWhether the chosen bandwidth minimizes mean squared error
DWhether outcomes trend smoothly on each side of the cutoff
The key RD assumption is that units cannot *precisely* manipulate their position around the cutoff. If they can, the treated group just above the threshold will be systematically different (e.g., more motivated students who studied harder to score exactly above 75), breaking the local randomization logic. The McCrary test checks for a suspicious pile-up of observations just above the cutoff in the running variable's density — a red flag for sorting.
Question 3 True / False
In a regression discontinuity design, units just below the cutoff serve as a credible comparison group for units just above because they are essentially identical in both observed and unobserved characteristics.
TTrue
FFalse
Answer: True
This is the local randomization intuition behind RD. A student who scored 74 vs. one who scored 76 are separated by two points of test noise — effectively random variation. They likely have similar ability, background, and all other characteristics. This near-identical comparability makes the jump in outcomes at the cutoff a credible causal estimate, rather than reflecting underlying differences between the groups.
Question 4 True / False
Using a wider bandwidth in RD typically produces more accurate causal estimates because more observations reduce sampling error.
TTrue
FFalse
Answer: False
Bandwidth selection involves a bias-variance tradeoff. A narrow bandwidth gives highly comparable units (low bias) but few observations (high variance and imprecise estimates). A wide bandwidth increases precision but includes units farther from the cutoff who may be systematically different, introducing bias if the underlying outcome function is nonlinear. Neither extreme is always best; credible RD papers typically report results across multiple bandwidth choices.
Question 5 Short Answer
Why does precise manipulation of the running variable threaten the validity of an RD design? What does the McCrary density test look for?
Think about your answer, then reveal below.
Model answer: If agents can precisely control their score to land just above the cutoff, the treatment group will be systematically different — more motivated, higher-ability — from the control group just below, destroying the 'local randomization' logic. The McCrary test examines the density of the running variable around the cutoff. In a valid RD, the density should be smooth (continuous) at the threshold. A spike or discontinuous jump just above the cutoff suggests strategic sorting, which undermines the causal interpretation of the discontinuity.
Some manipulation is fine — students may study harder knowing the cutoff exists — but *precise* sorting is fatal to the design. The intuition: if the treated group just above the threshold is self-selected by determination or resources, the outcome jump reflects those traits rather than the treatment itself.