BUSN 5000E: Potential Outcomes and Causality

A set of vocabulary flashcards based on lecture notes covering causal inference, potential outcomes, and the results of the Tennessee STAR experiment.

Tennessee STAR experiment

The Tennessee Student/Teacher Achievement Ratio (STAR) experiment was a large randomized experiment starting in the 1985–86 school year that assigned kindergartners and teachers to small, regular, or regular+aide class configurations.

Confounding

A situation where a variable $Z$ affects both the treatment $X$ and the outcome $Y$, creating a spurious relationship through a backdoor path.

Backdoor path

A non-causal, spurious path in a directed acyclic graph (DAG) that connects the treatment to the outcome through a confounder.

Counterfactual

The notion of a 'road not taken,' representing the outcome that would have been observed for an individual under a treatment status different from the one actually experienced.

Potential Outcomes

The two possible states for an individual: $y_{1i}$ (the outcome if treated, $D_i = 1$) and $y_{0i}$ (the outcome if untreated, $D_i = 0$).

Switching Equation

The formula $y_i = (1 - D_i)y_{0i} + D_i y_{1i}$ (or $y_i = y_{0i} + (y_{1i} - y_{0i}) D_i$), which defines the observed outcome based on treatment assignment.

Causal inference problem

Essentially a missing data problem where counterfactual potential outcomes are unobserved, making it impossible to see the individual-level treatment effect.

Average Treatment Effect (ATE)

The expected difference between the treated and untreated potential outcomes for the entire population, defined as $ATE = E(y_{1i} - y_{0i}) = E(y_{1i}) - E(y_{0i})$.

Selection Bias

The difference in average untreated potential outcomes between the treated and untreated groups, represented as $E(y_{0i}|D_i = 1) - E(y_{0i}|D_i = 0)$.

Average Treatment Effect on the Treated (ATT)

The average treatment effect specifically for those in the treatment group, defined as $ATT = E(y_{1i} - y_{0i}|D_i = 1)$.

Ignorable assignment mechanism

A condition achieved through randomization where treatment status is independent of potential outcomes, denoted as $(y_{0i}, y_{1i}) \perp \perp D_i$.

Conditional Independence Assumption (CIA)

The claim that potential outcomes are independent of treatment assignment conditional on a set of observed variables $x_i$, denoted as $\{y_{0i}, y_{1i}\} \perp \perp D_i | x_i$.

Overlap

A requirement for estimating the ATE that ensures treated and untreated units are observed for every value of $x_i$, meaning $0 < P(D_i = 1|x_i) < 1$.

Strong Ignorability

A condition for identifying causal effects that occurs when both the Conditional Independence Assumption (CIA) and the overlap condition are met.

Covariate balance

The condition where the distributions of covariates are similar between treated and untreated units, indicating that treatment assignment was likely random.