Regression Discontinuity Liang Dai

Illustration Suppose we are interested in the cohort effect of elite high school A on the college entrance exam scores (高考) of graduates of middle school M. One can regress the score of M graduates on a dummy of A attendance Problem: selection bias Most talented graduates from M get into A

Way out Suppose high school enrollment is completely determined by entrance exam scores (中考) And the graduating class of M is not large enough to affect the cutoff Di=1 if score Xi>=x0, and Di=0 if Xi<x0 Then we can overcome the selection bias by comparing X graduates with score RIGHT above and below x0. Key assumption: all variables other than treatment, e.g. talent, have to be continuous at the cutoff.

Example 1 Angrist & Lavy, QJE 99 Does smaller class size enhance scholastic achievement? Hot policy debate, interesting labor economics question Challenge: ?

Example 1 Angrist & Lavy, QJE 99 Does smaller class size enhance scholastic achievement? Hot policy debate, interesting labor economics question Challenge: class size correlated with unobservable factors, e.g. student quality, teacher’s experience, etc.

Regression Discontinuity Maimonides’ rule on Israeli primary school enrollment: class size can’t exceed 40. E.g. total enrollment=80 => average class size=40; Total enrollment=81 => average class size=27. Predicted class size: f=e/[int((e-1)/40)+1]

Example 2 Raul, JF 06 Does a firm’s investment depend on its internal cash holdings, controlling for its investment opportunities (Tobin’s Q)? Evidence for financial frictions w/o financial constraints, external capital is as cheap as internal capital (Recall MM), so internal cash holdings don’t matter Challenge: ?

Example 2 Raul, JF 06 Does a firm’s investment depend on its internal cash holdings, controlling for its investment opportunities (Tobin’s Q)? Evidence for financial frictions w/o financial constraints, external capital is as cheap as internal capital (Recall MM), so internal cash holdings don’t matter Challenge: cash holdings are endogenous Persistence of profit Measurement error in Q First large-sample test

Regression Discontinuity Treatment D: Cash Running variable X: defined pension plan balance Discontinuity: when defined pension plan is in deficit, the firm has to contribute its cash to it. Not otherwise Exogeneity of cutoff: funding status mostly determined by value of the asset side of pension fund, independent of firm’s investment opportunity Analogy: Whether you are just below or above cutoff of exam scores must be independent of talent

Firms contribute mostly when funding status <0

Investment correlated with funding status only to the left of 0