Re: st: treatreg vs ivreg revisited

[Andrea Menclova <andrea.menclova@canterbury.ac.nz>]

Thank you very much; this helps a lot.

Andrea



-----Original Message-----
From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Austin Nichols
Sent: Friday, 17 May 2013 5:42 a.m.
To: statalist@hsphsun2.harvard.edu
Subject: Re: st: treatreg vs ivreg revisited

Andrea Menclova <andrea.menclova@canterbury.ac.nz>:
You should have excluded instruments, so you rely less on the probit functional form assumption--in the extreme, you can drop the probit functional form assumption and just use IV, which is what I obliquely recommended. IV will give you the required diagnostics, particularly if you use -ivreg2- from SSC.

Note that -treatreg- with endogenous x is very like -ivreg- with endogenous x in that you can get the -ivreg- coefficient by regressing on endogenous x and the residual of a linear regression of x on instruments Z, while you can get the -treatreg- coefficient by regressing on endogenous x and the (generalized) residual of a probit regression of x on instruments Z. Note also that -treatreg- with endogenous x is just like -heckman- except that in -heckman- x=1 for all cases in the regression.

After running IV, there is a natural order to specification tests.
First check identification (you want to reject the null that the equation is under-identified) and weak instruments (you want to reject substantial bias and size distortions). Then check an overID test (you want to fail to reject the null that the instruments are uncorrelated with the residual), which needs more excluded instruments than you have included endogenous variables. Then check to see if you are getting essentially the same answer with IV you were getting with OLS (with a test of exogeneity, something of a misnomer, and compare overlap of the confidence intervals), and check for unmodeled nonlinearities with -ivreset- (SSC). See the help file for -ivreg2-
(SSC) for more discussion.

On Wed, May 15, 2013 at 9:40 PM, Andrea Menclova <andrea.menclova@canterbury.ac.nz> wrote:
> Many thanks for your helpful response.  However, I am still confused 
> on a couple of points and I am hoping you would be kind enough to answer them.
>
> 1. When you say I should " never rely on the inverse Mills ratio for 
> addressing endogeneity/selection", are you saying I should always 
> estimate an IVmodel in addition to the treatment effects model, and 
> not rely solely on the inverse Mills ratio approach?
>
> 2. Is a treatment effects/"treatreg" approach valid even if the
> instrument(s) are "weak?"  Are there any tests for the validity of 
> instruments in the context of a treatment effects/"treatreg" model?

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