Gary Solonof Michigan State University pointed out to us that our claim on p. 209 that “just identified 2SLS is median unbiased” is not quite correct and that the claim should be qualified. Gary notes that if the first stage is really zero, the just identified IV estimator is centered at the same point as the biased OLS estimator. Similarly, just identified IV is biased for instruments that are extremely weak, as has been shown in the literature.
Gary is right, of course, and we thank him for pointing this out. Just-identified IV is approximatelyly median unbiased, but if the instruments are weak enough you’ll certainly have bias. On the other hand, if a single instrument is really that weak, you’re unlikely to want to use it since a very low t-stat and high 2nd stage standard errors will warn you away. See the attached note for details.
Just-identified IV
Gary Solon of Michigan State University pointed out to us that our claim on p. 209 that “just identified 2SLS is median unbiased” is not quite correct and that the claim should be qualified. Gary notes that if the first stage is really zero, the just identified IV estimator is centered at the same point as the biased OLS estimator. Similarly, just identified IV is biased for instruments that are extremely weak, as has been shown in the literature.
Gary is right, of course, and we thank him for pointing this out. Just-identified IV is approximatelyly median unbiased, but if the instruments are weak enough you’ll certainly have bias. On the other hand, if a single instrument is really that weak, you’re unlikely to want to use it since a very low t-stat and high 2nd stage standard errors will warn you away. See the attached note for details.