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From |
Austin Nichols <austinnichols@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
Re: st: Question on Wooldridge's Procedure 18.1 |

Date |
Thu, 9 Aug 2012 13:37:27 -0400 |

Brent Gibbons <brent.gibbons@gmail.com>: You are misunderstanding what pure noise refers to in my post at http://www.stata.com/statalist/archive/2010-01/msg00144.html I proposed a thought experiment where you generate pure noise variables z1-z20 (say) to serve as (very bad) excluded instruments Z, where the predicted value of an endogenous X might still be highly correlated with observed X, leading you to think you had strong instruments using Procedure 18.1 (naively treating the predicted X as your sole excluded instrument). Nonlinearity of the first stage is not required for this problem to be observed--only an incorrect understanding of what the weak instrument tests are designed for. No bias is introduced by the nonlinear transformation of exogenous variables in forming a generated instrument, however. The bias would come only from violating the 2 crucial assumptions required for instruments: Z correlated with X and uncorrelated with the error (the first assumption fails in the thought experiment). E.g. clear set seed 12345 drawnorm z1-z20 e, n(1000) g x=e/4+rnormal() g y=x+e qui reg x z* predict xhat ivreg2 y (x=xhat) ivreg2 y (x=z*) Note how the 18.1 approach does not catch the weak instruments problem, but using the original instruments does. Also note that the paper I cited as an example of the flawed test for weak instruments is now published: http://www.aeaweb.org/articles.php?doi=10.1257/aer.102.5.1927 mostly without discussion of weak instruments, with a note (to Table 5) that "F-statistics are for tests that all instruments equal zero in first-stage equations" where the minimum eigenvalue of the Cragg-Donald stat should be reported (see e.g. http://www.nber.org/papers/t0284.pdf). The instruments look weak in all specifications, by the Stock-Yogo standard, but the paper appears in a top econ journal, so take heart. On Wed, Aug 8, 2012 at 7:00 PM, Brent Gibbons <brent.gibbons@gmail.com> wrote: > Hopefully the list server will recognize this response in the correct > thread. I was trying to use nabble (and only get the digest) but it > wasn't allowing me to respond. In case it doesn't recognize it > correctly, the last 2 threads are below. > > Austin, thanks for your response. Let me see if I can explain a bit better. > > I was partly trying to ask why exactly you have stated weak instrument > tests for proc. 18.1 are problematic. You mention that "weak > instrument diagnostics should come from straight IV, not procedure > 18.1--note that procedure 18.1 would go through if Z was pure noise, > and the predicted value of your endogenous variable could be very > highly correlated with the endogenous variable, leading you to think > you had very strong instruments." > > As I understand the 18.1 procedure, mainly coming from Wooldridge > (2002), you have an extra component in the predicted probabilities > besides what is specified in the probit model, which Wooldridge says > allows for identification in the subsequent 2SLS even if there are no > instruments (p. 624). The extra component comes from the probit > estimator's "nonlinear function of x" - which is what I figured you > were referring to with 'pure noise'. Hence my first question - is it > this reason alone that the weak instrument tests are problematic? > > My second question relates to a scenario where you have both strong > instruments and this same component from above, that is also highly > correlated with the endogenous variable. So you can test the strength > of the instruments with the linear 2SLS. But is there any reason to > worry that this extra component could bias the result? I don't think > so, but I'm having trouble explaining why to myself. > > Thanks again for all comments, Brent > > Below posted Aug. 7, 2012 > > B.Gibbons <brent.gibbons@gmail.com>: > This question is not clear to me--the point is that weak IV > diagnostics work fine for the linear probability model but not > Procedure 18.1, as evidenced by a thought experiment (or simulation) > using white noise variables as excluded instruments as in my 2010 > post. When you say "can't test the exclusion restriction" you are > apparently confusing several tests of quality of inference in > instrumental variables. I have no idea what you mean by "the > non-linearity in the probit may be correlated with..." (did you mean > some component of the error? a generalized residual?) > > Below posted Aug. 2, 2012 > > Hi Austin, I'm currently using the 18.1 method in a project and have seen > your warnings about using tests of instrument strength through the 18.1 > method. > > My 1st question is whether those warnings are solely because of the > potential that the non-linearity in the probit may be correlated with the > binary endogenous variable - and falsely show good instrument strength. > > 2nd - what if there is both strong correlation between the non-linearity in > the probit AND strong instruments in the model: is there reason to worry > about this non-linearity as having a potential bias, especially since you > can't test the exclusion restriction for that? > > Thanks for any comments, Brent > * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/statalist/faq * http://www.ats.ucla.edu/stat/stata/

**References**:**Re: st: Question on Wooldridge's Procedure 18.1***From:*Brent Gibbons <brent.gibbons@gmail.com>

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