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Re: st: IV with oprobit / mprobit?


From   "Stas Kolenikov" <skolenik@gmail.com>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: IV with oprobit / mprobit?
Date   Wed, 15 Mar 2006 14:24:48 -0600

I am used to think about estimation procedures in terms of estimating
equations. The estimating equations for -ivprobit- are

(*) sum_i the score from probit in i-th observation times an
instrument in i-th observation = 0

which is plug-in / empirical analogue estimator of the familiar
population identity

(**) E[ epsilon * Z ] = 0.

where epsilon is the unobserved residual in the index function
formulation of the probit. You square those estimating equations, add
them up, and get a GMM objective function. You minimize it and get
your estimates. Basically the estimator implied by (*) uses
information whether epsilon is greater or smaller than zero, and that
is some sort of a monotone relation; I am not sure how this
generalizes to ordered probit where you don't have that monotonicty,
but have multiple pieces of information instead.

As with all extremum/M-estimators, the variance generally has the
sandwich form that you are seeking. Not that it corrects for
heteroskedasticity or anything, it is just the only appropriate
estimator, although probably you can implement it in a number of
different ways that would be asymptotically equivalent.

I'd say you need to think in terms of estimating equations rather than
replicating what linear regression does with prediction of the fitted
values (which is a nice by-product of the linear model assumptions,
but that's all to it, it is not generalizable to non-linear models).
If you can figure out an anlaogue of (*) for oprobit, then you can try
to code it. You can probably tweak -ml- to do both minimization of the
sums of squares and sandwich matrix estimation for you.

Of course if you can show me that your procedure gives reasonable
estimating equations that are at least asymptotically unbiased, then I
will be OK with the point estimates. If additionally you show that
your correction is equivalent to the sandwich estimator, then I will
go and kill myself as I don't understand anything in generalized
linear models and instrumental variable estimation :))

On 3/15/06, Tobias Hofmann <hofmannt@gmail.com> wrote:
> Dear Bart, dear all,
>
> Please read this e-mail even if you are not interested in my response to
> Bart's question as you might be in the position to answer my follow-up
> question. ;-]
>
> There seems to be no ado-file like IVoprobit or IVmprobit. However, you
> should be able to do something like that "by hand". I'm certainly not expert
> on this field, but here is an example of how such a "self made" code could
> look like:
>
> clear
> sysuse auto
> xtile y2 = mpg, nq(3)
> quietly tab y2, gen(y2_)
> rename price y1
> rename trunk z
> rename weight x
> * First-stage ordered probit:
> oprobit y2 z x
> predict p1 p2 p3, p
> * Second-stage OLS:
> regress y1 p2 p3 x
> * Correction of standard errors:
> drop p2 p3
> rename y2_2 p2
> rename y2_3 p3
> predict residuals, resid
> replace residuals = residuals^2
> quietly sum residuals
> scalar realmse = r(mean)*r(N)/e(df_r)
> matrix bmatrix = e(b)
> matrix Vmatrix = e(V)
> matrix Vmatrix = e(V) * realmse / e(rmse)^2
> ereturn post bmatrix Vmatrix, noclear
> ereturn display
> clear
>
> Now, here is/are my follow-up question(s):
>
> a) What would the above code have to look like if I wanted Stata to return
> ROBUST corrected standard errors, i.e. if I wanted to use the
> Huber/White/sandwich estimator of variance?
>
> b) What would it have to look like to use clustering, let's say, using the
> variable "foreign" to specify to which group each observation belongs?
>
> Thank's for helping me out!
>
> Best regards,
> Tobias
>
>
>
> On 3/13/06, Bart Vanneste <bartvanneste@yahoo.com> wrote:
>
> Dear,
>
> Is it possible to use an instrumental variable approach with ordered or
> multinomial probit (or logit for that matter)? ivprobit / ivlogit seem to
> deal only with binary dependent variables.
>
> In recent months several other posts have asked the same question, but to my
> knowledge a satisfactory solution has not been given.
>
> Your response is greatly appreciated.
>
> Best,
> Bart
>
> *
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>


--
Stas Kolenikov
http://stas.kolenikov.name

*
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