Omitted Variable Bias

Question 1

How can multiple regression account for confounders?

Answer 1

Including controls in the model capture the effect of confounders
The coefficient for the regressor of interest is now unbiased by the controls - we only use variation in the regressor that occurs holding fixed the confounders

Question 2

How to set up OVB formula (3 regressions, dont say the formula for this one)

Answer 2

Short regression: The normal regression with no controls (just one regressor)

Long regression: The regression including the controls (more than 1 regressor)

Auxiliary regression: Control = b0 + b1regressor of interest + ui

If we have 2 controls we have 2 auxiliary regressions

Question 3

What is the OVB formula

Answer 3

Short coefficient (of regressor of interest) = Long coefficient (of regressor of interest) - [coefficient of control in long regression x coefficient of regressor of interest in the auxiliary]

b1S = b1L - (B2L x delta0)

Question 4

How to interpret the OVB formula (i.e. what does it tell us)

Answer 4

The OVB formula tells us that the short regression estimate bundles together:
1) The true causal effect of interest
2) The effect of the confounder on outcome and the variation in the confounder that is correlated with the regressor of interest

Question 5

What exactly is the OVB formula definition

Answer 5

The mathematical difference between the regression coefficients from the short regression and the long regression