st: Multiple endogenous regressors

["Lim, Elizabeth" <nxl091000@utdallas.edu>]

Hello,

I'm new to the STATA list, and I don't have much econometrics background, so please forgive me if my questions sounded too basic. I've also read the discussion threads in the archives but did not find the information adequate for my purpose/understanding.

I am running the two-stage least squares (2SLS) test for 5 endogenous regressors. Here are my questions:-

(1) Theoretically, the literature suggests that it is possible to generalize the 2SLS mechanism for a single endogenous regressor to multiple endogenous regressors. I've read articles in finance, accounting, economics, etc, that control for endogeneity. So far, the studies that I've come across only control for one endogenous variable. I suspect that it's complicated to run 2SLS for multiple endogenous regressors. From an implementation standpoint, what are the potential econometrics and statistical problems related to running multiple endogenous regressors with 2SLS? 

(2) If I can't find sufficient instruments to run all 5 endogenous regressors at the same time, what potential problems might arise if I run each of the 5 endogenous regressors independently in 5 different 2SLS models?

(3) Assuming that I can find adequate instruments, I want to run the first stage F statistics to check the validity of my instruments for these 5 endogenous regressors. For a single endogenous regressor, the literature suggests that the first stage F statistics greater than 10 indicates a valid instrument. Can I use this same rule of thumb for multiple endogenous regressors?

(4) Again assuming that I can find adequate instruments, I want to run the overidentification test akin to Basmann's F test and Hansen's J test. Can I still use these same overidentification tests for multiple endogenous variables?

References related to any of these four questions would be greatly appreciated.  Thanks in advance for your advice and suggestions.

Regards,
Elizabeth

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