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Re: st: Multiple endogenous regressors

From   Yuval Arbel <>
Subject   Re: st: Multiple endogenous regressors
Date   Fri, 21 Oct 2011 01:41:54 +0200


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 <> 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
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

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