Introduction to Causal Inference

Question 1

predictive

Answer 1

value or feature of a unit we do not observe

Question 2

causal

Answer 2

the causal effect of a treatment on an outcome in the population

Question 3

causal effect

Answer 3

a change in some feature of the world Y that WOULD result from a change to some other feature of the world D

Question 4

‘would result’

Answer 4

counterfactual comparison between outcome in actual world and outcome in counterfactual world

Question 5

only difference?

Answer 5

only difference in worlds is one group gets treated and the other does not

Question 6

treatment notation

Answer 6

D

Question 7

For each unit i, we define two potential outcomes corresponding to the control, D= 0 and the treatment states D=1

Answer 7

Ydi = Y1i potential outcome for unit i in the treatment state, and Y0i potential outcome for unit i in the control state

Question 8

what are those quantities

Answer 8

hypothetical, the POTENTIAL outcomes

Question 9

Causal effect of the treatment on the outcome for unit i is the difference between its two potential outcomes

Answer 9

Ti = Y1i -Y0i

Question 10

what happens if in the real world a unit is is assigned to the random state

Answer 10

observed outcome will be their potential outcome under the treatment state

Question 11

fundamental problem of causal inference

Answer 11

impossible to directly observe the individual treatment effects because we only observe one state of the world

Question 12

how to fix this?

Answer 12

take averages

Question 13

ATE

Answer 13

treatment effects within a group

Question 14

ATE sum

Answer 14

E(Y1i - Y0i -> sum of Y1i/N - sum of Y0i/N

Question 15

ATT

Answer 15

adding together the potential outcomes for those under treatment and taking an average

Question 16

what are we not calculating?

Answer 16

before and after - this is PARALLEL worlds

Question 17

assignment mechanism

Answer 17

the procedure that determines what units are selected for treatment

Question 18

examples of assignment mechanisms

Answer 18

random assignment, selection on observables, selection on unobservables

Question 19

SUTVA

Answer 19

That the observed outcomes are only affected and determined by individual i’s treatment assignment, other observed outcomes are NOT impacted by others treatment assignments

Question 20

What is SUTVA

Answer 20

An assumption of causal effect stability

Question 21

what happens if SUTVA is violated?

Answer 21

then there are so many different potential outcomes

Question 22

and then…

Answer 22

cannot truly understand the causal effect

Question 23

examples of SUTVA violation

Answer 23

contagion, testing

Question 24

peer effects

Answer 24

the effects of ur peers on ur observed outcome

Question 25

naive estimator for the ATE

Answer 25

comparing observed outcomes of individuals that had treatment to observed outcomes of the control group

Question 26

why is the NAIVE ATE bad?

Answer 26

overestimating the ATE, misleading conclusions

Question 27

Potential issues when naively comparing

Answer 27

1. Correlation is not causation 2. Confounding 3. Reverse causality

Question 28

Confounder satisfies two conditions

Answer 28

Affects whether units are assigned to treatment (Di) and has an effect on the outcome over-and-above it has through its effect on treatment status

Question 29

Reverse causality

Answer 29

Instead of the treatment Di leading to the observed outcome Yi, it is the outcome variable that leads units to be treated

Question 30

Selection bias

Answer 30

changes how those individuals may be chosen to receive treatment

Question 31

thus naive ATT

Answer 31

E[Y1i - Y01|D = 1] - BIAS

Question 32

what happens when you naively compare?

Answer 32

You get the ATT