RE: st: RE: overidentification test after treatreg

["Schaffer, Mark E" <M.E.Schaffer@hw.ac.uk>]

Xiang,

> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu 
> [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Xiang Ao
> Sent: 22 October 2010 19:10
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: RE: overidentification test after treatreg
> 
> Hi Mark,
> 
> Thanks for the explanation.  One other question I have on your example
> 
> "turn = a + b*foreign + c*mpg
> foreign = d + e*mpg
> 
> The just-identified system is
> 
> turn = a + b*foreign
> foreign = d + e*mpg"
> 
> is that here we have only one excluded instrument (mpg). My 
> understanding of overidentification test is that you'll have 
> to have multiple excluded instruments to do it. But I might be wrong.

In linear models, the only kind of identifying restrictions are
exclusion restrictions, in which case you are right.  But with treatreg,
the assumption of normality is also an identifying restriction.  One
exclusion restriction + normality means the model is overidentified, so
an overid test is possible.

> Regarding to my gmm code, I thought about it: it could be 
> that the two moment conditions I specified:
> E(lambda*z)=0 (for probit)
> E(residual*x)=0 (for second stage OLS)
> They do not specify the relationship between two equations.  
> In MLE, the two equations are related by rho (correlation 
> between two errors).  That might be problematic.

Still haven't had a chance to look at it properly.  But let us know if
you solve it.

--Mark

> Xiang
> 
> 
> On 10/22/2010 01:37 PM, 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 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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> >>      
> >
> >    
> 
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