Instrumental Variables Flashcards
What are the requirements for a valid instrumental variable?
- No direct effect on the outcome. Only via the mediator.
- Must be a strong.
- The part of “X” coming from “Z” must not be part of the error of “Y”. (Unbiased predictor.)
What are three common types of instrumental variables in educational research?
college enrollment, test scores, health, earnings, birth weight, criminal behavior, financial aid, class size, school year, etc…
What type of treatment effect is estimated with instrumental variable methods?
local average treatment effect
What is the Wald estimator of treatment effects with instrumental variables?
biv = Cov{Y,Z}/Cov{X,Z}
The Wald estimator is also called the method of moments.
What are the steps of the two-stage least squares estimator of treatment effects with instrumental variables
Two-stage least squares estimation involves:
1. Regressing X on Z to get estimates X-hat and of X.
2. Regressing Y on X-hat to get an estimate of β1.
Any covariates included in Stage 1 must also be included in Stage 2, but covariates can be included in Stage 2 without inclusion in Stage 1.
What is the main advantage of the 2SLS estimator over the Wald estimator?
The Wald estimator only allows one instrument and no additional covariates, but allows the inclusion of additional covariates.
What is the structural equation model to estimate treatment effects with an instrumental variable?
(See PPT Slide 11) X -> Y with β1. I ->X. δi -> X. εi -> Y. δi εi (correlated).
What are two potential problems that invalidate an instrumental variable estimator?
- Failure of exogeneity (Z influences Y though other variables than X).
- Failure of relevance (Z has only a weak relation to X).
Why is the problem of a weak instrument more serious when the sample size is small?
Even when assumptions are perfectly met, IV is not unbiased in small (finite) samples.
How can instrumental variables be used to deal with non-compliance in experimental designs?
Experimental methods cannot estimate the effect of receiving the treatment, because that cannot be randomly assigned (without perfect compliance). IVs resolve this issue.
How can instrumental variable methods be used to analyze a fuzzy regression discontinuity design?
In fuzzy regression discontinuity designs, there are exemptions to the assignment cutoff. However, the cutoff can be used as an instrument for receiving the treatment.
(See PPT Slide 21 for formulas.)
