Controlling for observables

Question 1

What is the difference between prediction and estimating causal effects in a multiple regression?

Answer 1

Prediction: focus on the outcome (all independent variables equally important)
Estimating: focus on the effect of T (other variables are only control variables)

Question 2

Endogeneity + reasons

Answer 2

Correlation between the variable of interest and the error term

1. Reverse causality
2. Measurement error
3. Omitted variables: are not in the model and related to both T and Y

Question 3

Derive the omitted variable bias (OVB) formula

Answer 3

!!!!!

Question 4

Omitted variable + which control variables should not be included

Answer 4

Omitted variable has influence on both T and Y
No need to control for variables that only influence T (because it is not part of the error term) and variables that only influence Y (because it is not correlated to T)

Question 5

Reasons why including mechanisms biases the treatment effect

Answer 5

1. Takes away part of the causal effect of T

2. Reintroduces ‘composition’ selection bias

Question 6

Confounders
Non-confounders
Mechanisms
Colliders

Answer 6

Confounders = control variables 
Non-confounders = influence only Y
Mechanism = influenced by T, influence on Y
Colliders = T and Y influence C

Question 7

Conditional Independence Assumption (CIA)

Answer 7

Controlling for observables aims to solve selection bias: assumption that the difference between treated and control is only due to the observable characteristic X
E [Y(0) | X, T = 1] = E [Y(0)| X, T = 0] = alfa + betaX

Question 8

Plausibility of CIA

Answer 8

CIA does not hold:
If there are omitted variables other than X related to T and Y (treatment and control groups differ in unobserved ways)
If X is influenced by treatment (X should be measured before treatment takes place)