Regression Discontinuity Notes Review

This set of vocabulary flashcards covers the fundamental concepts, assumptions, and terminology of Regression Discontinuity (RD) designs as applied to the study of drinking and mortality.

Sharp RD design

A design in which the cutoff value of the running variable perfectly determines treatment assignment.

Fuzzy RD design

A design in which the cutoff value of the running variable only determines the probability of treatment.

Running variable

The particular covariate, often denoted as $x$, that determines treatment assignment in a regression discontinuity design.

Minimum Legal Drinking Age (MLDA)

Laws that exogenously change drinking opportunities at age 21, used to study the effect of alcohol on mortality.

LATE (Local Average Treatment Effect)

The average treatment effect identified specifically at the cutoff $c$, defined as E(y_{1i} - y_{0i}|x_i = c) = \text{\}\_mu_1(c) - \text{\}\_mu_0(c).

Continuity assumption

The key identifying assumption for RD designs stating that the treatment and control potential outcomes (\text{\}\_mu_g(\cdot)) are continuous at the cutoff $c$.

Switching equation

The equation relating observed to potential outcomes: $y_i = y_{0i} + (y_{1i} - y_{0i})D_i$.

Centering

The practice of using $(x_i - c)$ in a regression to guarantee that the treatment coefficient \text{\}\_delta maintains a LATE interpretation at the cutoff.

Bandwidth

The specific range of the running variable around the cutoff (e.g., ages 20-22) used for analysis; its choice is vital for the sensitivity of results.

Conditional Independence Assumption (CIA)

An assumption that holds trivially in sharp RD designs because treatment is a deterministic function of the running variable.

Internal causes of death

Causes of death that are not typically alcohol-related, used as a comparison against external causes in the Carpenter and Dobkin study.

External causes of death

Potentially alcohol-related causes of death, such as those that spike significantly at the age 21 cutoff.

rdrobust

An R/Stata package that automates defensive actions and best practices for RD designs.