Instrumental Variables Estimation and Two-Stage Least Squares - Motivation: Omitted Variables in a Simple Regression Model
3 important questions on Instrumental Variables Estimation and Two-Stage Least Squares - Motivation: Omitted Variables in a Simple Regression Model
For what can instrumental variables be used and what kind of instrumental variables are there?
Let y=B0+B1x+u with E[u]=0 but possibly cov(x,u)=/= 0
We can consistently estimate B0 and B1 if we can find a variable z that satisfies two assumptions,
(1) cov(z,u)=0 (instrument exogeneity) (cannot be tested)
(2) cov(z,x)=/=0 (instrument relevance) (can be tested)
Such a variable z is called an instrumental variable for x.
We can consistently estimate B0 and B1 if we can find a variable z that satisfies two assumptions,
(1) cov(z,u)=0 (instrument exogeneity) (cannot be tested)
(2) cov(z,x)=/=0 (instrument relevance) (can be tested)
Such a variable z is called an instrumental variable for x.
What can be said about the asymptotic variance of the IV estimator?
The estimator B1 is approximately normal in large samples, with asymptotic variances
What follows for the properties of IV when instrument z is weak?
If the instrument z is weak, even a minor violation of instrument engoneity may give serious problems. ^B1 IV is less than that of ^B1 OLS if and only if corr(z,u)/corr(z,x) < corr(x,u)
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