Intro to causal inference

Question 1

What is the fundamental problem of causal inference?

Answer 1

We never observe the counterfactual within individuals

Question 2

Potential outcomes: assumption 1

Answer 2

Assumption 1 (SUTVA). Stable unit treatment value assumption (SUTVA): the outcome of individual i depends only on the treatment of individual i and not the treatments of others.
else.

Question 3

Relationship of Y (population RV) to potential outcomes

Answer 3

Y = (1 − D)Y_0 + DY_1 = Y_0 + D(Y_1 − Y_0)

Question 4

What does identified mean?

Answer 4

We can use observed information to identify whether D causes Y.

Question 5

Average treatment effect (ATE): formula

Answer 5

ATE ≡ E[Y1 − Y0] = E[Y1] − E[Y0]

Question 6

Average treatment on treated (ATT): formula

Answer 6

ATT ≡ E[Y_1 − Y_0 | D = 1] = E[Y_1 | D = 1] − E[Y_0 | D = 1]

Question 7

Do selection bias proof for why OLS coefficient does not necessarily equal ATE. When does beta^OLS equal ATE?

Answer 7

See lecture notes for proof. beta OLS = ATE under strict exogeneity

Question 8

When does strict exogeneity fail? Give 4 cases

Answer 8

1) Simultaneity
2) OVB
3) Measurement error - CME => attenuation bias
4) Sample selection - systemic self-selection