st: overidentification test after treatreg

[Xiang Ao <xao@hbs.edu>]

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)

But they don't match.

Thank you for your time,

Xiang


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