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st: overidentification test after treatreg


From   Xiang Ao <xao@hbs.edu>
To   statalist@hsphsun2.harvard.edu
Subject   st: overidentification test after treatreg
Date   Fri, 22 Oct 2010 10:09:54 -0400

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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