Instrumental variables - Weak instruments
5 important questions on Instrumental variables - Weak instruments
When do we have a weak instrument?
- When corr(z,x) is very low
- Also when cov(z,x) is close to 0.
Creates problems with the distributional properties of the estimator:
- Expectation: The finite-sample bias will be larger
- Consistent estimator with "n<
" - Variance: expect it to be far of from the true value, visible from high standard error
What is the definition of a confidence interval?
Pr (Bj<Bj<Bj)=0.95
How do we detect weak instruments?
- Depends on the sample size
- Estimate first-stage and report F-stat on instruments.
- Should have F-stat>10
- The hypothesis is that the instruments jointly are equal to 0.
- With only one instrument = F=t^2
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