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RE: st: RE: overidentification test after treatreg


From   "Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>
To   <statalist@hsphsun2.harvard.edu>
Subject   RE: st: RE: overidentification test after treatreg
Date   Fri, 22 Oct 2010 18:37:15 +0100

Xiang,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Xiang Ao
> Sent: 22 October 2010 18:06
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: overidentification test after treatreg
> 
> Thank you, Mark, for the prompt reply.  I guess my question 
> is still why this would tell you the robustness of 
> instruments?

It tells you only what any overidentification test tells you, namely,
are the identifying restrictions supported by the data?

> The reason we can do a LR test is because of 
> the nonlinearity of the selection process (probit).

True.  The probit selection equation means there's only one way to
specify a just-identified model.

> Think of 
> a 2sls setting, we cannot do something like that since there 
> has to be excluded instrument(s), otherwise it's 
> unidentified.

Not so.  The standard Hansen-Sargan overid test is the same thing as a
GMM distance test between an overidentified model and a just-identified
model.  We're doing the same thing, transplanted to
treatreg/probit/LR-land.

> In treatreg, you can have no excluded 
> instruments simply because it's nonlinear.  The only 
> identification is through the normality assumption.  If your 
> rationale holds, we should be able to do this LR test for any 
> nonlinear model with endogenous regressors, as an 
> overidentification test.

True!  But I'd be interested to know if others agree.

> Also, do you have any idea what went wrong with my gmm codes?

Sorry, I had only a quick look but couldn't work it out.

--Mark

> 
> Thanks,
> 
> Xiang
> 
> On 10/22/2010 11:19 AM, Schaffer, Mark E wrote:
> 
> > Xiang,
> >
> >    
> >> -----Original Message-----
> >> From: owner-statalist@hsphsun2.harvard.edu
> >> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Xiang Ao
> >> Sent: 22 October 2010 15:10
> >> To: statalist@hsphsun2.harvard.edu
> >> Subject: st: overidentification test after treatreg
> >>
> >> Dear Statalisters,
> >>
> >> I have a question on how to do a Sargan's test after treatreg.  I 
> >> found Mark Schaffer's comments on this question from 2006:
> >> http://www.stata.com/statalist/archive/2006-08/msg00804.html
> >>
> >> In the reply, Mark suggested using a LR test between a full model 
> >> with all instruments in the second stage and a regular treatreg.
> >> My question
> >> is: this only tests the hypothesis that all excluded instruments 
> >> jointly being zero, how would that tell us the robustness of 
> >> instruments, as Sargan's test would do in an ivreg setting?
> >>
> >> Mark kindly replied to my email to him and suggested posting to 
> >> statalist to get more inputs.
> >>
> >> I am thinking of using gmm to frame the treatreg problem, then 
> >> Jansen's J would be a byproduct.  However, my code with 
> gmm does not 
> >> generate consistent estimates with treatreg, which I am 
> sure is due 
> >> to my lack of knowledge on this.  I post my code here; any 
> suggestion 
> >> is greatly appreciated.
> >>
> >>
> >> sysuse auto, clear
> >> global xb "{b1}*gear_ratio + {b2}*length + {b3}*headroom + {b0}"
> >> global phi "normalden($xb)"
> >> global Phi "normal($xb)"
> >> global lambda "foreign*$phi/$Phi - (1-foreign)*$phi/(1-$Phi)"
> >> global xb2 "{c1}*gear_ratio + {c2}*length + {c3}*headroom + {c0} + 
> >> {c5}*foreign"
> >> gmm (eq1: $lambda) (eq2: turn-$xb2), instruments(eq1:
> >> gear_ratio length
> >> headroom mpg)  instruments(eq2: gear_ratio length headroom 
>  foreign ) 
> >> winitial(unadjusted, independent) wmatrix(unadjusted)
> >>
> >> This is to try to estimate the same model as:
> >>
> >> treatreg turn gear_ratio length headroom, treat(foreign=gear_ratio 
> >> length headroom mpg)
> >>      
> > Here was my rationale for how to do an overid test using an LR 
> > statistic.  As I wrote it in that Statalist post from 2006 that you 
> > cite, I think I got it wrong.  Here's my next attempt:
> >
> > Consider a slightly simplified version of your treatreg model:
> >
> > treatreg turn, treat(foreign=mpg)
> >
> > There are two overidentifying restrictions.  First, mpg 
> appears in the 
> > treatment equation (foreign) but not in the outcome equation (turn).
> > Second, normality is also an identifying restriction, much 
> in the same 
> > way as normality can be used in a Heckman selection model as an 
> > identifying restriction.
> >
> > Now consider your treatreg model, but with mpg as a 
> regressor in the 
> > outcome equation:
> >
> > treatreg turn mpg, treat(foreign=mpg)
> >
> > This second version is just-identified, with normality as the sole 
> > identifying restriction.
> >
> > So, the following should be an LR test of the overidentifying 
> > restrctions in your original model:
> >
> > treatreg turn, treat(foreign=mpg)
> > est store troverid
> > treatreg turn mpg, treat(foreign=mpg)
> > est store trjustid
> > lrtest troverid trjustid, df(1)
> >
> > I should also note that this is a system test.  The overidentified 
> > system is (pardon the terrible shorthand notation):
> >
> > turn = a + b*foreign + c*mpg
> > foreign = d + e*mpg
> >
> > The just-identified system is
> >
> > turn = a + b*foreign
> > foreign = d + e*mpg
> >
> > And your overid test is an LR test of c=0.
> >
> > I *think* this is right, but perhaps you or others on the 
> list could 
> > comment.
> >
> > Cheers,
> > Mark
> >
> >    
> >> But they don't match.
> >>
> >> Thank you for your time,
> >>
> >> Xiang
> >>
> >>
> >> *
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> >>
> >>      
> >
> >    
> 
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