st: Re: st: RE: how to test with two suspect endogenous variables？

 From gjhxmu@sina.com To statalist Subject st: Re: st: RE: how to test with two suspect endogenous variables？ Date Tue, 04 Aug 2009 16:02:55 +0800

```Dear Mark and others,

I posted the same topic two months ago. However, I still do not unstandand how to deal with it.

I restate my doubt here, hoping someone can help me.

My equation is

y=al+a2x1+a3x2+a4z+e

where z is exogenous definitely.However, I suspect whether x1 or x2  or both are endogenous.

there are two instrument variables, z1 and z2 are instruments.

Firstly, I can test the first  null hypothesis Ho1: x1 is exog AND x2 is exog.
I typed the following in the stata and found the DWH test results rejected the first Ho. So at least one of x1 and x2 is endogenous.

ivreg2 z (x1 x2=z1 z2),endog(x1 x2)

Second, I want to check which variable (or both of them) is(are) endogenous.
Is the following typing right?

ivreg2 z (x1 x2=z1 z2),endog(x1)
ivreg2 z (x1 x2=z1 z2),endog(x2)

Thank you very much for anyhelp!

Best wishes,

Rose.

----- Original Message -----
From: Schaffer, Mark E <M.E.Schaffer@hw.ac.uk>
To: <statalist@hsphsun2.harvard.edu>
Subject: st: RE: how to test with two suspect endogenous variables？
Date: 2009-5-24 22:13:17

Rose,

A few points to make here:

- First, you are working with a single equation ("limited information estimation"), not a system of equations. In this context, you can't really say "z1 is the IV for x1" and "z2 is the IV for x2". The IV estimator uses both (if you did the estimation by hand using 2SLS, you'd take your linear projections in the first stage using BOTH z1 and z2). There are some good past Statalist posts on this by Kit Baum that you might want to look up.

- Second, you probably don't want to us classical Durbin-Wu-Hausman. If you use a GMM distance test ("difference-in-Sargan", "C-test"), you can get robustness to heteroskedasticity, serial correlation, whatever. DWH will be a special case. -ivreg2- has this facility with the -endog- and -orthog- options.

- Third, it sounds like the natural null hypothesis for you is Ho: x1 is exog AND x2 is exog. You'd reject this if either x1 or x2 is endog. You can test this in -ivreg2- by estimating your equation with x1 and x2 as exogenous, an empty endogenous variable list, z1 and z2 as exogenous instruments, and x1 and x2 in the -orthog()- option variable list. This compares the specification with x1/x2 as exogenous vs. the specification with them as endogenous. Alternatively, you can estimate the equation with x1/x2 as endogenous and instrumented with z1/z2, and test whether you can treat them as exogenous by putting them in the -endog()- option varlist.

- Fourth, you need to believe that your IVs meet the requirements of orthogonality and relevance. Orthogonality won't be testable in this case because the eqn is exactly identified, but you can and should test their relevance (Cragg-Donald, Anderson, Kleibergen-Paap, et al.) in the specification with x1/x2 as exogenous.

The -ivreg2- options and the theory behind them are discussed in the Baum-Schaffer-Stillman 2003 and 2007 Stata Journal articles.

Hope this helps.

Best wishes,
Mark

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of
> gjhxmu@sina.com
> Sent: 23 May 2009 18:42
> To: statalist
> Subject: st: how to test with two suspect endogenous variables？
>
> Dear all,
> I encountered a problem with endogeniety.Concretely, I have a
> equation below:
> y=al+a2x1+a3x2+a4z+e
> where z is exogenous definitely.However, I suspect whether x1
> and x2 are endogenous.
> and there are two instrument variables, z1 for x1 and z2 for x2.
>
> In wooldridge book, there is an introduction about how to
> test whether one variable is endogenous.i.e,hausman test.
> First get the residual and then add the residual to the
> equation.If the p value of residual is significant, the
> suspect variable is endogenous.
>
> However, how to test with two suspect endogenous variables?
>
> Hope replies sincerely. Thank you in advance.
>
> Rose
>
> *
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> * http://www.stata.com/support/statalist/faq
> * http://www.ats.ucla.edu/stat/stata/
>

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