Re: st: Multiple endogenous regressors

[William Buchanan <william@williambuchanan.net>]

Hi Elizabeth,

Also, if you're unfamiliar with IVE I would highly recommend taking at look at Angrist and Pishcke (2009) Mostly Harmless Econometrics: An Empiricist's Guide. Princeton, NJ: Princeton University Press.

The authors provide a fairly thorough discussion of the instrumental variable estimator and provide some discussion on the topic of multiple endogenous regressors.  Additionally, the package - ivreg2 -written by Baum, Schaffer, and Stillman has a help file with a wealth of information and references that would probably help.

- Billy
On Oct 20, 2011, at 4:41 PM, Yuval Arbel wrote:

> Elizabeth,
> 
> I'm also new to the statalist, but fortunately, I taught econometrics
> courses. Here are my answers to your questions
> 
> On Thu, Oct 20, 2011 at 10:38 PM, Lim, Elizabeth <nxl091000@utdallas.edu> wrote:
>> 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?
>> 
> 
> Yuval: I would strongly recommend not to deal with such a complex
> system of 5 endogenous variables. The problem is you should have
> enough exogenous variables outside the equations you would like to
> identify. i'm doubtful whether you can find so many exogenous
> variables, which are really exogenous. In fact, this problem of
> complexity has motivated econometricians to develop the VAR model,
> where the independent variables are different lags of the dependent
> variables.
> For a beginer I recommend "Ramu Ramanathan: Introductory Econometrics
> with Applications"
> 
> 
>> (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?
>> 
> 
> Yuval: this is a very serious problem, which is known as "unidentified
> equations" - in which case you get biased and inconsistent estimates.
> For further details I suggest to look at the unidentified supply and
> demand equations presented in Ramu Ramanathan. But anyway you have to
> be sure that your model is correctly specified
> 
> 
>> (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?
>> 
> 
> Yuval: First of all the problem would be to convince logically that
> the variables are really exogenous. Recall that at the end of the day
> the researcher is the one who is responsible for phrasing the
> econometric model and justify it. Secondly, I would recommend instead
> the Yu-Hausman test available in STATA (the command in STATA is
> "hausman"). The idea of the test is to compare the OLS estimates to
> the 2SLS estimates. The Hausman test measures the magnitude of the
> bias generated by improperly using the OLS instead of the 2SLS method
> 
>> (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?
>> 
> 
> Yuval: See my answer below. I don't see any reason to run an
> overidentification test.
> 
>> References related to any of these four questions would be greatly appreciated.  Thanks in advance for your advice and suggestions.
> 
> Yuval: for a begginer I would recommend the following textbooks in econometrics:
> 
> Ramu Ramanathan: Introductory Econometrics with Application - see the
> chapter that deals with simultaneous equation models
> 
> Jan Kmenta: Elements of Econometrics - I suggest to read the chapter
> that deals with the error-in-variable model. In this chapter you can
> find an explanation to the Hausman test.
> 
> If you are somewhat familiar with matrix algebra, you can also look at
> Greene textbook - find the hausman test and take a look at the
> explanations there
>> 
>> Regards,
>> Elizabeth
>> 
>> *
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>> 
> 
> 
> 
> -- 
> Dr. Yuval Arbel
> School of Business
> Carmel Academic Center
> 4 Shaar Palmer Street, Haifa, Israel
> e-mail: yuval.arbel@gmail.com
> 
> *
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