Re: re:Re: st: Multiple endogenous regressors

[Austin Nichols <austinnichols@gmail.com>]

Daniel <millimet@mail.smu.edu>, Elizabeth <nxl091000@utdallas.edu>, et al.:
I am coming to this very long thread very late, but one point of
clarification and my own answers to the numbered questions below.

If x1 through x5 are all correlated with the single instrument z it is
still possible (though in most cases implausible) for z to be a valid
instrument for each endogenous regressor in turn included as the sole
regressor of interest (leaving the others out).  For example, suppose
z is valid for x1, and x2 through x5 are just x1 plus noise.  It is
hard to imagine a real-world case where Daniel's concern would not be
justified, however.

Answers for Elizabeth's Q 1-4:
1. Mainly weak instruments; see e.g.
http://stata.com/meeting/5nasug/wiv.pdf
http://stata.com/meeting/dcconf09/dc09_nichols.pdf
http://www.stata-journal.com/sjpdf.html?articlenum=st0136
http://www.stata-journal.com/sjpdf.html?articlenum=st0030_3
2. Mainly invalid instruments; see Daniel's concern below and make
sure you understand all tests of assumptions.
3. No.  See Stock and Yogo work referenced in
http://stata.com/meeting/5nasug/wiv.pdf
and related material in http://fmwww.bc.edu/repec/bocode/i/ivreg2.html
(search for Yogo).
4. Yes, the J stat still works.

On Thu, Oct 20, 2011 at 8:15 PM, Millimet, Daniel <millimet@mail.smu.edu> wrote:
<snip>
instead of estimating
>
> ivreg2 y (x1-x5 = z1-z5)
>
> Suppose I only have a 1 instrument, z, and instead propose to estimate:
>
> ivreg2 y (x1 = z)
> ...
> ivreg2 y (x5 = z)
>
> In this case, each model looks exactly identified, so one can get estimates (of something!).  The problem here is that if the true model includes x1-x5, each model is mis-specified and includes the other 4 endogenous x's in the error term.  If z is correlated with each x1-x5, then z will be correlated with the error in each of the 5 IV regression models.  So, z cannot be a valid instrument for any of the 5 individual structural models.  So, each of the 5 separate TSLS models will give you biased and inconsistent estimates of the include endogenous regressor.
>
<snip>
 ----------
Elizabeth's numbered questions:
I am running the two-stage least squares (2SLS) test for 5 endogenous
regressors. Here are my questions:-

(1) 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) 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?

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