RE: re:Re: st: Multiple endogenous regressors

["Millimet, Daniel" <millimet@mail.smu.edu>]

I have not been following the entire thread, but in terms of the 2 questions below, if you omit x2-x5 from the model entirely, these end up as part of the error term IF they belong in the equation for y.  This depends on the application at hand and whether you can convince readers that z2-z5 do not end up in the error term.  If they do end up in the error term (plus whatever else ends up in the error term), then you need at least one valid instrument for x1.  To be valid, the instrument must be (conditionally) correlated with x1 and independent of the error term.  If x2-x5 are part of the error and the instrument is correlated with x2-x5, then the instrument is not valid.  There are two solutions here of which I am aware.  First, find a better instrument.  Second, see the recent paper by Nevo and Rosen, forthcoming in Review of Eco and Statistics, that addresses imperfect instruments

See http://www.mitpressjournals.org/doi/abs/10.1162/REST_a_00171?prevSearch=allfield%253A%2528nevo%2529&searchHistoryKey=
  
Plus, the recent NBER working paper by several authors

http://www.nber.org/papers/w17519

Best,
Daniel

****************************************************
Daniel L. Millimet
Research Fellow, IZA
Professor, Department of Economics
Box 0496
SMU
Dallas, TX 75275-0496
phone: 214.768.3269
fax: 214.768.1821
web: http://faculty.smu.edu/millimet
****************************************************


-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Lim, Elizabeth
Sent: Monday, October 24, 2011 3:24 PM
To: statalist@hsphsun2.harvard.edu
Subject: RE: re:Re: st: Multiple endogenous regressors

Hi Austin,

Thank you so much for the references which I will read in more detail. I also greatly appreciate your helpful answers to all my 4 questions. In addition, I think you've offered a very interesting insight which helped me see the problem of multiple endogenous regressors in a different light, and gave me an idea of how I might potentially circumvent the problem of finding sufficient instruments for so many endogenous variables, i.e., 5 endogenous variables!! :-( - sad but true.  But I cannot be sure whether this idea will work or not since I'm not an expert in econometrics/statistics/economics/finance.  I'm hoping that the gurus on Statalist might be able to offer some insight/help. I've read the helpful references provided by Cam, Bill B, Kit, etc, and while the readings gave me a better appreciation of IVE, I haven't really found the answers needed to resolve the actual problem.

First, let me offer a more precise explanation of the issue. From economics theory and prior financial economics literature, suppose I manage to find several instruments for CEO stock option grants, an endogenous variable (which incidentally is also a control variable or covariate). Let's say I also have 4 other endogenous variables related to CEO stock options (e.g., CEO unexercisable or exercisable stock options relative to reference point A, and CEO unexercisable or exercisable stock options relative to reference point B). These 4 endogenous variables are predictors.  I do *not* have theory or prior literature to guide me in my selection of instruments for these 4 endogenous regressors, although I guess one could argue that the instruments for CEO stock option grants might also work for these 4 endogenous variables since all 5 endogenous regressors are essentially about CEO stock options.  

So here are my questions:

(1) Given the potential 'weak instrument' problem associated with running all 5 endogenous variables in a single model, and the potential 'invalid instrument' problem (including Daniel's concern) with running each endogenous variable separately in differently models, do you think it might make sense econometrically to just focus on one endogenous variable, i.e., CEO stock options grants (albeit it being a control variable)?  In other words, taking your suggestion below into consideration, would it work if I leave out the other 4 endogenous variables x2-x5 (even though these are the predictors), and just control for the endogeneity of CEOs stock option grants (x1) because "x2 through x5 [might] just be x1 plus noise" as you mentioned below?  Would this "shorter" 2SLS model approximate the "real" model?

(2) If (1) doesn't work, what other alternatives do I have (bearing in mind the extreme difficulty in finding a large number of strong valid instruments for 5 endogenous variables)?

Thank you in advance for any thoughts and suggestions.

Regards,
Elizabeth

-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols
Sent: Monday, October 24, 2011 12:49 PM
To: statalist@hsphsun2.harvard.edu
Subject: Re: re:Re: st: Multiple endogenous regressors

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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