Instrumental variables - Weak instruments

5 important questions on Instrumental variables - Weak instruments

When do we have a weak instrument?

  1. When corr(z,x) is very low
  2. Also when cov(z,x) is close to 0.

Creates problems with the distributional properties of the estimator:
  1. Expectation: The finite-sample bias will be larger
    • Consistent estimator with "n<"
  2. Variance: expect it to be far of from the true value, visible from high standard error

What is the definition of a confidence interval?

A 95 % confidence interval for the population parameter Bj is an interval estimator of Bj such that, across repeated samples,
Pr (Bj<Bj<Bj)=0.95

How do we detect weak instruments?

If the level of correlation is "too low" (cor(z,x)).
  1. Depends on the sample size
  2. 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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What is the Local Average Treatment Effect (LATE) ?

It estimates the treatment effect on the compliers. That is a subgroup of the population.

What is the Intention to treat effect (ITT) ?

It is always smaller than LATE. It is a randomized study where the participants either got treated or not.

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