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