https://www.bradyneal.com/causal-inference-course
Introduction to Causal Inference라는 강의를 듣고 정리했습니다.

9. Difference-in-Difference

9-1. Motivation and Preliminaries

Average Treatment Effect on the Treated (ATT)

9-2. Difference-in-Differences Overview

Introducing Time

• without time을 계산할 때는 unconfoundedness($Y(0)\perp T$)를 가정

Tolerates Time-Invariant Unobserved Confounding

unobserved confounder가 constant하면 괜찮다.

9-3. Assumptions and Proof

Consistency Assumption Extended to Time

• Observed value of outcome = potential outcome in time $\tau$ if getting treatment t

Parallel Trends Assumption

• treatment group과 control group의 변화량의 기울기가 평행하다.

No Pretreatment Effect

$E[Y_0(0)|T=1]$ 을 알기 위해

Assumptions Change

DID 증명

9-4. Problems with Difference-in-Differences

Violations of Parallel Trends

Treatment and time 사이의 interaction이 있으면 violation이 생김

Parallel Trends is Scale-Specific

log scale일 때는 parallel 안 됨

The parallel trends assumptions isn’t nonparametric