how to correct the standard errors when using multiple IVs for only one endogenous variable

[William Cheung]

Hello:

I would like to ask that when dealing with only one endogenous variable, say X1, is it correct to instrument X1 by multiple IVs, say Z1, Z2, and Z3? That is, putting Z1 Z2 and Z3 all together in the first stage regression? Or it is better to use the IVs separately in the regression?

From my understanding, it is ok, but the standard errors may be somewhat unusual. The paper suggests a way how the standard errors can be corrected: https://economics.mit.edu/files/1106

Could anyone tell me the STATA code for correcting the standard errors when using multiple IVs? Thank you!

[Jeff Wooldridge]

With three IVs there’s no need to do anything special if the first-stage F is sufficiently strong.

[William Cheung]

With three IVs there’s no need to do anything special if the first-stage F is sufficiently strong.

Hi Dr. Wooldridge, Thank you very much for your answer. May I ask in your opinion, to deal with the endogeneity, which method is preferable? Throw all three IVs in the first stage regression or do three separate regressions with each of the three IVs respectively?

[Jeff Wooldridge]

Put all three in the first stage. The optimal linear combination (under the standard assumptions) will be selected. Use ivregress or ivreg2.