POL222 - week 12

Threats to validity in Observational Research

Reverse causality (Y → X instead of X → Y)

Omitted confounding variables, especially unobservable ones that correlate with both X and Y

Natural Experiment

observational design where a naturally occurring event assigns units to different values of X as if randomly

depends on the strength of the argument that assignment was as-if random

Regression Discontinuity Design

Units get treatment when their running variable (RV) crosses a threshold

Units just above and below the cutoff are marginally treated vs. marginally controlled and are assumed to be as-if randomly assigned

This allows estimation of the Average Treatment Effect at the Threshold

External validity is limited to cases near the cutoff

EX. Scholarship given at score ≥ 85; 84 does not receive. 84 vs. 85 scorers are extremely similar → treatment (scholarship) is as-if random. Mechanism: scholarship → less work hours → more study time → better performance

Instrumental Variables

Affects X (the main causal variable), affects Y only through X (no direct path), is uncorrelated with unobservable confounders (U)

IVs help solve reverse causality and unobservable confounding problems

Two-Stage Least Squares

First stage: regress X on W (+ controls)

Produces predicted value X̂, the component of X driven by W (not by unobserved confounders U)

Second stage: regress Y on X̂ (+ controls)

Estimates causal effect of X on Y using only variation in X that is validly exogenous

X̂ = clean causal part of X; Ux = part influenced by confounders