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Instrumental variables - stage OLS (2SLS)

4 important questions on Instrumental variables - stage OLS (2SLS)

What is 2-stage least squares? And what are the stages?

2SLS is another useful way to view the IV estimator.

The first stage is to regress x on the instrument Z to obtain fitted values of x.
Then regress y on the fitted values of x. The estimated coefficient will then be identical as the IV estimator.

What does the MLR6 assumption mean for the estimate parameter?

The population error u ~ N(0,o2) independently from the explanatory variables x=(x1,x2, ..,xk)
Under assumptions MLR1-MLR6, conditional on the independent variables, the Bj also have a joint normal distribution.

What happens if we estimate 2 or more instruments separately?

If we have two or more instruments and estimated the coefficient separately, we could get different estimates. Possible reasons:

Sampling variation
One or more instruments are invalid
The observations affected by each instrument have a different response to x.

What is structural form, reduced form, first stage and second stage?

The structural form is our causal model of interests
The reduced form is a regression of y on instruments
The first stage is a regression of x on the instruments
The second stage is the regression stage with the fitted values of x from the first stage.