Simultaneity/Reverse Causality

Question 1

Why do we need to use 2SLS in the case of simultaneity?

Answer 1

Sometimes, aside from confounders, reverse causality can also be a concern.
The primary aim is to see how the regressor affects the outcome, but the outcome can also affect the regressor.
OLS will bundle these two effects together, since there are two channels by which the regressor and outcome affect each other, causing bias

Question 2

How to form the simultaneous equations

Answer 2

First regression is the one of interest
Second one has the original regressor as the outcome and the original outcome as the regressor (with a control as well)

Question 3

How do we overcome the reverse causality bias? Explain how it works

Answer 3

We must use an instrumental variable. We add the instrumental variable to the equation which is NOT the regression of interest.

The intuition is that the IV will create variation in the original regressor of interest that is unrelated to the reverse causality

The original regression will have 2 channels affecting the variation, but the IV will isolate to the channel that we care about, so we have isolated a situation where there is no reverse causality because the IV does not directly affect the outcome of interest like the original regressor does

Question 4

How to form the three equations for 2SLS?

Answer 4

Second stage: Original regression of interest (the one without the IV)

First Stage: Regressor of interest = a0 + a1(IV) + any controls in the original regression of interest + ni

Reduced Form: Plug first stage into second stage to derive, will also give you the relationship to estimate the coefficient of interest

Question 5

Could you estimate the slope for the second line (i.e. the coefficient on the regressor in the reverse causality equation)

Answer 5

If we don’t have an instrumental variable in the other equation we cannot because the regressor will be not identified