Transcription of Weak IV. 1. What are Weak Instruments? - MIT …
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Weak IV. 1. What are Weak Instruments? - MIT …
1. What are Weak instruments ? Time Series Analysis, Fall 2007 Professor Anna MikushevaPaul Schrimpf, scribeNovemeber 13, 2007corrected September 2012 LectureWeak lecture extensively uses lectures given by Jim Stock as a part of mini-course at the NBER What are Weak Instruments? Consider the simplest classical homoskedastic IV model:yt= xt+utxt=Zt +vt,whereytare one-dimensional,xtisn 1,Ztisk 1 andEutZt= 0, one observes data{yt,xt,Zt}.Assume thatn k. In generalutandvtare correlated, and thus,xtis an endogenous (since we assumed thatEutZt= 0), if it also relevant (EZ xhas rankn), then it can serveas instrument and the model is identified.
2 ˙ where (z. u;z. v) ˘N(0;), = u uv. Q ˙ ˙ 2 . = C. 0. Q. 1=2 ZZ, ZZ = EZ. t. Z. t 0. uv v. What is also important here is that under this nesting (weak instrument asymptotics) the rst-stage F-statistic (for testing all coe cients on instruments are zeros) converges in distribution to a non-central ˜ 2 k. with non-centrality parameter 2 ...
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