IV Flashcards
Explain the different assumptions underlying the use of instrumental variables in regression analysis.
The two primary assumptions are that the instrument has a first stage and that is satisfies the exclusion restriction. We also want the instrument to be as good as randomly assigned, and for the instrument
to impact everyone in the same direction, or not at all, which is the monotonicity assumption.
What is the reduced form in IV analysis and how is it used?
The reduced form is the effect that the instrument has on the outcome of interest. We get the LATE by dividing the reduced form by the first stage.
How does the Weak Instruments Problem arise and how can it be addressed?
The weak instrument problem comes from there being a lot of sampling variation in the estimate of the first stage when the true first stage is small. As a result, we can get too many false-positives in
the second stage. To deal with this we can inspect the first stage F-statistic or change our approach to inference in the second stage, such as using AR confidence intervals.
Explain the exclusion restriction assumption and why it is necessary for valid IV analysis.
The exclusion restriction says that corr(z, u) = 0, that is our instrument is uncorrelated with the errors in the second stage. It alternatively implies that the only path from z to y is through x. If it fails to
hold we can’t say that changes in y as a result of changes z happen because z causes x to also change.
Explain briefly how Andersen-Rubin confidence intervals tackle the weak-instruments problem.
The AR confidence intervals are an alternative way to conduct inference for instrumental variables. The way these work is that they are larger when an instrument is weak.
