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From |
Daifeng He <dhe.statlist@gmail.com> |

To |
statalist@hsphsun2.harvard.edu |

Subject |
st: Weak instruments in models with more than one endogenous variable |

Date |
Sun, 26 May 2013 15:37:07 -0400 |

Dear all, I have a question about which statistics to look at for weak instrument in models with more than one endogenous variable. In particular, I have the following model: y1=a0+a1*y2+ a2*X2 +e1 y2=b0+b1*Z +b2*X2 +e2 Where y1 is the outcome variable of interest, y2 is an endogenous explanatory variable, X2 is another set of exogenous controls, and Z is an instrument for Y2. Because I want to know whether the effect of y2 on y1 is similar, say, across race (Black, White, and Hispanic), I interact the instrument Z with the Hispanic and White indicators, and then use the three instruments (Z, Z*Hispanic, Z*Black) to instrument for y2, y2*Hispanic, and y2*Black in the full sample. (I do not want to split the sample by race and estimate the above model separately for each race because my instrument becomes very weak in the Hispanic and Black subsamples given the much smaller sample sizes). My questions are: (1) What is the right statistics to look at for weak instruments? The A-F statistics which examines whether a particular instrument is weak (so I should look at the A-F statistics separately for each of the two instruments of interest, Z*Hispanic and Z*Black)? Or I should use the F version of the Cragg-Donald Wald Statistics suggested by the -ivreg2- help file (I am clustering standard errors), which is to test whether the three instruments are jointly weak? (2) Currently my results show quite large A-F statistics (above 10) but very small Cragg-Donald F-statistcs (in the magnitude of 0.0x). Does this inconsistency (or non-robustness) signal any underlying problems of my model? (3) If I were to look at the A-F statics, what should I conclude about the instrument strength if one of the A-F statistics (say for Z*black) is large (above 15) but the other one (for say Z*Hispanic) is much smaller (about 5)? -- I run into this issue when I looked at the heterogeneous effect across income tertiles instead across race. (4) Finally, is there any source that contains the critical values for either of those statistics? If you know the answer to any of my questions or can point me to some source for further reading, I'd appreciate a great deal! Thank you. Daifeng * * For searches and help try: * http://www.stata.com/help.cgi?search * http://www.stata.com/support/faqs/resources/statalist-faq/ * http://www.ats.ucla.edu/stat/stata/

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