Re: st: treatreg vs ivreg revisited

[Austin Nichols <austinnichols@gmail.com>]

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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